diff --git "a/dev_math_science_timestamp.json" "b/dev_math_science_timestamp.json" new file mode 100644--- /dev/null +++ "b/dev_math_science_timestamp.json" @@ -0,0 +1,13932 @@ +[ + { + "Q": "\nAt 4:30,Of what physical quantity or what measure does the Boyle's Law P.V=K gives or indicates us?Like momentum gives us a measure of the force to be applied on a body in motion to oppose its motion.", + "A": "Look at the units: Pressure = force / area = N/m^2 Volume = m^3 P*V = N/m^2 * m^3 = N*m N*m is the unit of force*displacement. What is force*displacement?", + "video_name": "x34OTtDE5q8" + }, + { + "Q": "At 19:05, what is the pinkish stuff on the white blood cell (first picture)? Thanks.\n", + "A": "It is a phagocyte (a kind of white blood cells) which helps kill bacteria.", + "video_name": "0h5Jd7sgQWY" + }, + { + "Q": "at 11:11 sal says the RNA goes to DNA. How does that happen? Also, how does DNA go to RNA in the first place?\n", + "A": "These are things you learn more about in Biology class. But basically, DNA and RNA are the instructions of the cell. DNA can be copied inside a cell and create more RNA or DNA molecules. RNA can go to DNA in a reverse method - in Sal s video he mentions reverse transcriptase.", + "video_name": "0h5Jd7sgQWY" + }, + { + "Q": "\nIn about 12:09 how can they change our genetic makeup", + "A": "it can affect a lot of things..like for example the way are mouth is shaped our body or eye color...ect i hope this helped a little x)", + "video_name": "0h5Jd7sgQWY" + }, + { + "Q": "\nWhat's the red thing at 19:20?", + "A": "I believe that is part of the infection of the HIV infection. It might be a rupture or infection of the white blood cell from the HIV infection.", + "video_name": "0h5Jd7sgQWY" + }, + { + "Q": "In 13:10 what is a provirus?\n", + "A": "The genetic material of a virus as incorporated into, and able to replicate with, the genome of a host cell.", + "video_name": "0h5Jd7sgQWY" + }, + { + "Q": "\nat 18:38, he says something about a nuclear membrane? Please explain", + "A": "Nuclear membrane is the membrane that envelops the DNA and nucleolus. In lysogenic cycle, the viral DNA becomes a part of the host s genome.", + "video_name": "0h5Jd7sgQWY" + }, + { + "Q": "That example with the plane at about 9:15 in the video- I don't exactly get it. I've been on a plane multiple times, and I always know if it's moving or not. Am I missing something here?\n", + "A": "Once you are at cruising altitude, how do you know the plane is moving and the world is not? Maybe the world is moving and you are standing still.", + "video_name": "CQYELiTtUs8" + }, + { + "Q": "\nat 6:04 after the 3rd resonance structure, why isn't the proton next to NO2 shift over to the positively charged C to make the 4th resonance structure and give positive charge on the Carbon that NO2 is attached to?", + "A": "You can move only electrons to form resonance strictures. If you move the H, you are creating a tautomeric isomer.", + "video_name": "rC165FcI4Yg" + }, + { + "Q": "\nAt 10:06, I'm confused as to how creating an ova is different through meiosis then creating sperm. How does the cell know if it is creating an ova or a sperm, and wouldn't only one type of sex cell be made inside each gender? Why would the cell create smaller non-functional ova cells that are not useful? What exactly is the difference between the process of making an ova and a sperm? I am very confused about almost the whole last two minutes of the video. Any help appreciated!", + "A": "Meiosis is basically the same for males and females, both males and females undergo the process but males make sperm and females make eggs (ova). There is effectively just a second cell division without replicating the DNA so that the germ cells end up with one copy of each chromosome instead of two (as happens in mitosis). The egg cell divides dispropotionately so that the one big cell has enough resources to support itself once it is fertilized, plus you don t need a lot of eggs.", + "video_name": "TX7-Kdn6lJQ" + }, + { + "Q": "At 7:17, why are the X chromosomes shown to have crossed over if they can't cross over?\n", + "A": "Hank explains that since the chromosomes are the same, they can cross over. The XY pair can t cross over because they are different chromosomes.", + "video_name": "TX7-Kdn6lJQ" + }, + { + "Q": "\nat 4:39 when Sal tells us the magnetic field direction is it always like that? is the magnetic field given which hasn't been drawn in the videos ?", + "A": "the magnetic field doesn t have to be to the left, it depends on where the source of it is, he s just arbitrarily chosen it to come from the left for this example.. is that what you meant?", + "video_name": "XMkUDyl1ZRo" + }, + { + "Q": "At 7:50 when he's talking about fluid being pushed in the cochlea, does he just mean that there's a pressure wave in the fluid filling the cochlea? Or is liquid actually sloshing back and forth in it?\n", + "A": "There really is fluid in there! It s called endolymph (in the middle part [scala media] where the hair cells project) and perilymph (in the scalae vestibuli and tympani).", + "video_name": "6GB_kcdVMQo" + }, + { + "Q": "At 9:20, when we are try to figure out the direction of the induced current are we referring to the conventional current or the actual electron flow? This becomes a point of confusion in a number of my homework problems for my AP class, do physicists generally stick to conventional current for all problems having to do with inducing a current?\n", + "A": "Current always refers to conventional current unless it says electron current.", + "video_name": "9q-T8o1HUcw" + }, + { + "Q": "Hmm im not sure if the explanation at 9:20 is sound. Would there be a magnetic flux outside of the circle also, then the circuit could not \"countertact (lenz)\" in any way. If the B Field created on the inside counteracts it will strengthen in on the outside ?\n", + "A": "We are only talking about the flux THROUGH the coil. The field lines (flux) are passing only inside the coil in this case. This is just a theoretical problem. You can t really do this irl", + "video_name": "9q-T8o1HUcw" + }, + { + "Q": "at 11:05 can a system ever truly have zero internal energy. Wouldn't the system itself contain energy? This sounds like a black hole situation. Is it possible for the balloon to have an absence of molecules and atoms...no internal energy at all? Or is this just hypothetical to make the equation simpler?\n", + "A": "At 11:05 this was referring to no change in energy, not no energy.", + "video_name": "aOSlXuDO4UU" + }, + { + "Q": "\nAt 6:43 Sal said that change in interal energy=Q+W is the definition for internal energy can you give me a more precise definition for it?", + "A": "Internal energy is all the energy contained in an object, including both kinetic energy and potential energy.", + "video_name": "aOSlXuDO4UU" + }, + { + "Q": "\nAt 2:14 Sal says that the egg cell is also a gamete. Isn't he wrong because a gamete is haploid while the egg cell, as a result of the fertilization, is diploid ? He confirms what I say at 4:45.", + "A": "The egg is not diploid. The egg and the sperm cell are gametes and haploid. The zygote is the result of the fertilization of the egg cell by the sperm cell. The zygote is diploid.", + "video_name": "dNp7vErqlaA" + }, + { + "Q": "At 4:40, is it ever possible for an ovum to carry a Y chromosome?\n", + "A": "Adding on to what Mubashra Igbal said, because the female has two X chromosomes, it is only possible to get an X from the female. The X chromosome is required for life so even if they could give a Y and if the male gave a Y, the baby would not survive.", + "video_name": "dNp7vErqlaA" + }, + { + "Q": "At 7:06 The drawing shows that we have 46 chromosomes, but do we los 23 of those chromosomes when sperm connects with the ovum\n", + "A": "Normal cells have 46 chromosomes or 23 pairs of chromosomes. Normal cell devision, mitosis, produces 2 cells with 46 chromosomes but during the creation of sex cells, meiosis, cells with 23 chromosomes are produced so that when the two sex cells come together they produce a cell with 46 chromosomes.", + "video_name": "dNp7vErqlaA" + }, + { + "Q": "\nAt 2:10, Sal talks about how if you had a mono-North pole on top of a mono-South pole, the mono-North pole would go around and get under the mono-South pole. He does this to describe magnetic fields, but what I don't get is why the mono-North pole doesn't just go strait down-strait to the mono-South pole. I don't understand why the field goes around rather than strait down. Somebody please explain.", + "A": "magnetic field lines actually pass through the object, they do not stop at the poles. some field lines are actually passing straight down.", + "video_name": "NnlAI4ZiUrQ" + }, + { + "Q": "\nIs the formula he used, the same as the formula for the Lorentz power? At 8:10 he defined the formula, and indicated the unit for B as Tesla. In my book, the formula for the Lorentz power is given as:\nF=B*I*L.\nF= Lorentz power\nB= magnetic induction\nI= electric current\nL= length of the magnetic field\n\nIt's a bit confusing which formula I should use. Can somebody explain it please?", + "A": "I think you mean Lorentz force, not power. This is a specific application of the Lorentz force.", + "video_name": "NnlAI4ZiUrQ" + }, + { + "Q": "\nAt 7:30, the generic acid, A, was used to deprotonate the H from the nitrogen group. Could we have used H2O to deprotonate, because that way it would become H3O+ in the end?", + "A": "Yes, the generic base A: could have been a water molecule.", + "video_name": "Gl7bQNm92fE" + }, + { + "Q": "At 3:35, How can we go around the sphere if its a 2 dimensional object? We can only go back and forth.\n", + "A": "The surface of the Earth is pretty much two dimensional... how do you travel on it?", + "video_name": "eUF59jCFcyQ" + }, + { + "Q": "\nHow is a sphere a 2D object? There's not much more to say other than it was at 3:21 in the video, so there's my question.", + "A": "A sphere is a 3D object but you can imagine its surface as a curved 2 dimensional space.", + "video_name": "eUF59jCFcyQ" + }, + { + "Q": "\nat 3:10 you are drawing a sphere while explaining about two dimensional space. please explain me this concept.", + "A": "The surface of the sphere has only two dimensions to it. You can think of those dimensions as latitude/longitude or right ascension/declination.", + "video_name": "eUF59jCFcyQ" + }, + { + "Q": "\nAround 6:22 Sal mentions a \"toroid would fit the bill\" Could someone explain this shape to me. I dd look up the definition by the way. I'm looking for something a bit more intuitive.", + "A": "A toroid is kind of like a donut shape. Its basically just a cylinder bend so thats its two ends connect.", + "video_name": "eUF59jCFcyQ" + }, + { + "Q": "At 6:30 sal talks about a torroid. Meaning, please ?!?!?\n", + "A": "A torroid is something that has the properties of a torus. A torus is something shaped like a donut.", + "video_name": "eUF59jCFcyQ" + }, + { + "Q": "\nAt 6:22 Sal mentiones a \"toroid\" (not sure of the spelling). What is a toroid, what does it look like?", + "A": "A toroid is a donut shape.", + "video_name": "eUF59jCFcyQ" + }, + { + "Q": "At 00:41 Sal said that evertything is packed in together? i dont understand whats that everything? And where this everything came from?\n", + "A": "We don t know where it came from. We just know that everything in the universe now was once much, much closer together before it was flung apart by the big bang.", + "video_name": "eUF59jCFcyQ" + }, + { + "Q": "\n@2:31 sal says finite area, what does that mean?", + "A": "No infinite or has a definable distance.", + "video_name": "eUF59jCFcyQ" + }, + { + "Q": "\nAt 5:15 when he is dividing by .3639, is he dividing by the molar mass of Hg?", + "A": "No, he is dividing by the number of moles of Hg.", + "video_name": "NM0WycKCCDU" + }, + { + "Q": "6:50 how is there more chlorine than mercury if there is .73% and 200 moles of Hg and only .27% and 36 moles of Cl?\n", + "A": "Because if you do 73/200.5(Mercury s Atomic Mass), you get .3640897756 as the amount of moles of Mercury. If you do 25/35.453, you get .7051589428 as the amount of moles of Chlorine. So, .7051589428 is greater than .3640897756. therefore, there are more moles of Chlorine than there are moles of Mercury. Is that clear?", + "video_name": "NM0WycKCCDU" + }, + { + "Q": "\nAt 5:42, it is said that the ratio of Chlorine to Mercury is 2:1, because 0.762/0.364 = ~2. and therefor stating that for each Mercury, we have 2 Chlorine.\nBut what about the ratio of Mercury to Chorine? Wouldn't that be 0.364/0.762= ~0.5, stating that for each Chlorine, we have 0.5 Mercury?", + "A": "You cannot have half of an atom.", + "video_name": "NM0WycKCCDU" + }, + { + "Q": "\nAt 1:28 something was said about shining a wavelength of light is specifically sensitive to the solute. my question is why is the spectrophotemeter set at certain wavelengths, why cant it just be set at any wavelength of our choice?", + "A": "That is because chemicals only absorb very specific wavelengths of light. This is why we can use a spectrophotometer to measure the concentration of a specific chemical. If the wavelength of the light is wrong, then the light won t be absorbed.", + "video_name": "qbCZbP6_j48" + }, + { + "Q": "at 1:18 why is #1 a lower concentration?\n", + "A": "For example s sake", + "video_name": "qbCZbP6_j48" + }, + { + "Q": "\nAt 2:24, if the same amount of light shine through the same beaker, why does the concentration of each beaker differ and why does one have a higher concentration from another? Somebody please explain.", + "A": "The concentration is not dependent on the amount of light shining through. It would be similar to having to glasses of water that have different amounts of food coloring in them. The concentrations differ for example s sake. He is simply showing how transmittance differs in varying conditions.", + "video_name": "qbCZbP6_j48" + }, + { + "Q": "\nAt 1:30, what do you mean by \"sigma\"?", + "A": "sigma usually stands for sum", + "video_name": "24vtg9Ehr0Q" + }, + { + "Q": "I don't get something at 10:00. It doesn't intuitively make sense to me that on one side the force is lesser and on the other its more, shouldn't force be conserved? I know if I look at the mathematical equations, it makes sense there, but how could the force be larger on one side, even though its being applied on the same amount of volume, and just a different surface area? Shouldn't it be smaller since its on a larger surface area?\n", + "A": "In this system, and for that matter all systems, it s the work that is conserved. work being force x distance means that the larger piston will travel a shorter distance than the smaller piston with a greater amount of force. It took me several times reviewing this video to understand the conclusion that he was coming to. he probably should have put that in the end of the video but we are all only human.", + "video_name": "lWDtFHDVqqk" + }, + { + "Q": "At 4:31 , he said about external pressure is distributed through out the fluid, That means if we jump into the ocean, then we give external pressure for throughout the ocean.?\n", + "A": "An EXTREMELY minuscule amount, but yes.", + "video_name": "lWDtFHDVqqk" + }, + { + "Q": "Why does Sal divide at 00:45\n", + "A": "because the force is being applied over an area A, in this case A1 which is just pressure right? When we compress something, we apply a pressure.", + "video_name": "lWDtFHDVqqk" + }, + { + "Q": "\nAt 6:02, how can two different orbitals have same sub shell.\nHow can 1st shell have s-sub shell and 2nd shell also have s-sub shell?", + "A": "The are not the same subshell, they are the same TYPE of subshell. So, 1s is the s-subshell belonging to the first shell. 2s is the s-subshell belonging to the second shell.", + "video_name": "KrXE_SzRoqw" + }, + { + "Q": "\nat 8:50, from the three values of ml: -1 0 1, how can we know that the orientation of the 3 types p orbital should be on the three axis but not somewhere else like in between the axis? And one more thing is that the spin quantum number indicates the way electrons spin around themselves, so why can't we use -1 and 1 or any different number instead of -1/2 and 1/2?", + "A": "It s complicated! The answer comes from a combination of quantum mechanics and the theory of special relativity.", + "video_name": "KrXE_SzRoqw" + }, + { + "Q": "4:22 How does it hold the hot water, wouldn't it melt? Or is it not plastic? Also on 6:03 wouldn't the water come out?\n", + "A": "Some plastics can handle tempatures well about the boiling poit of water.", + "video_name": "XQTIKNXDAao" + }, + { + "Q": "\nat 6:09,he said \"The heat to get in\" why do we need heat to get in?", + "A": "I think that was just a slip up as he fixed it with allowing air to get in its so that as it heats up inside it doesn t pressurize the air and and blow up.", + "video_name": "XQTIKNXDAao" + }, + { + "Q": "At 3:05, you say Gibbs Free Energy is only when there's constant pressure and TEMPERATURE. Gibbs Free Energy formula has temperature as a constant so how does that work?\n", + "A": "It means that the Gibb s Free Energy value can change if temperature changes. That kinda makes sense, since a reaction that may not be spontaneous with low inputs of energy may become spontaneous if there is a greater input of energy into the system.", + "video_name": "J2L-X2sUigs" + }, + { + "Q": "\nFrom 7:45 on, a intermolecular Fischer esterification that forms lactone is shown. Is it possible that at the same time of forming lactone, an OH part of one molecule attack the COOH part of another molecule, and form a ester with two 5-carbon chain (and no ring) in it?", + "A": "yes, you can also get the two 5 carbon chain product and you could essentially form a polymer from it because the OH portion of one can keep attacking the COOH on the other end of the molecule. Then theres also the possibility of a ring forming at any point in that process as well.", + "video_name": "ynBuPEmcjp4" + }, + { + "Q": "\non the 4:40 timestamp he talks about coronary artery disease but my question about the arteries is that since it caries deoxygenated blood to the lungs it would make it blue from the deoxygenated blood but why does it all just look red in the real life photo", + "A": "Deoxygenated blood isn t actually blue, it is dark red. Blue is used on diagrams to make them easier to read.", + "video_name": "vYnreB1duro" + }, + { + "Q": "Is it just my imagination, or are the absolute configurations of the alcohol and bromoalkane incorrect at 5:48? I thought the alcohol (with OH on a wedge and thus H on a dash) would be S and the bromoalkane (with Br on a dash and thus H on a wedge) would be R. :)\n", + "A": "The video is correct, perhaps take a second look at it? O is #1 priority, the right carbon is #2 and the left carbon is #3. Going from 1->2->3 is clockwise so it s R.", + "video_name": "KPh60w6McPI" + }, + { + "Q": "At 7:43, Sal integrated the entire equation. The right hand side of equation is zero. The integration of zero must be a constant as derivative of a constant is zero. But, instead after integrating the equation was written still equal to zero.\nCan anyone explain? It will be very helpful. Thanks.\n", + "A": "I did not watch the video but probably the answer is that Sal was doing a definite integral rather than an indefinite integral. When you do a definite integral, you are integrating the same function and calculating its value at two different points, and then subtract the starting point from the ending point. When you do that subtraction, the constant cancels out, so you can just say it is zero.", + "video_name": "ixRtSV3CXPA" + }, + { + "Q": "\nMin 3:40 How does he know that delta U and delta T have a linear relationship with teach other? Of course they are related, but the nature of this relationship could be non-linear...", + "A": "No it can t because U is internal energy and T is average energy of the molecules. If the average energy increases then U has to increase proportionally.", + "video_name": "ixRtSV3CXPA" + }, + { + "Q": "\nReferring to 7:04, how do you know that all of the base will react with the acid but not vice-versa?", + "A": "I would assume that this is because we have much less base than acid. In other words, the base is our limiting reagent. There are 0.005 mol of -OH and 0.0100 mol of H3O+. All of the available H3O+ cannot react with the added -OH because there is much more (double actually) of it than there is of -OH available to react to form water. Hopefully this makes sense.", + "video_name": "JoGQYSTlOKo" + }, + { + "Q": "\nSal mentioned the f-block at 2:14 . Why don't universities ask questions about the f-block on the chemistry exams?", + "A": "Sal is awesome", + "video_name": "qkLzAXUP_K0" + }, + { + "Q": "why is Andromeda then moving towards us?\nAlso was sal trying to explain relativity at 4:18\n", + "A": "Andromeda is moving toward us because it is drawn in by the mutual gravitational attraction between the mass in the Milky Way and the mass in Andromeda.", + "video_name": "1V9wVmO0Tfg" + }, + { + "Q": "Why have the points all moved away from each other during 0:41\n", + "A": "Here s a good experiment. Draw a couple dots on a deflated balloon. When you blow it up, all the dots move away from each other, like Sal explained in 4:26.", + "video_name": "1V9wVmO0Tfg" + }, + { + "Q": "At around 4:30 Sal demonstrates the universe be a sphere with small dots in it. Will the dots ever stop moving away from each other? Will the sphere ever stop growing?\n", + "A": "We currently think the growth will not ever stop.", + "video_name": "1V9wVmO0Tfg" + }, + { + "Q": "2:07. Why does the lone pair of the oxygen attack the carbon?\n", + "A": "Because it is more nucleophilic than the carbon. This is covered earlier in the organic chemistry lectures.", + "video_name": "bFj3HpdC4Uk" + }, + { + "Q": "\nLa and Ac belongs to d block, 3:05 as unlike Lanthanides and Actinides they possess no electron in f orbital.", + "A": "These two of the four elements whose position in the periodic table is disputed. You will see periodic tables with the disputed elements in either the d or f block. In the official periodic table maintained by IUPAC, La, Ac, Lu, and Lr all appear in the f block. But this is far from a settled matter amongst chemists.", + "video_name": "L-0FkEPPdXE" + }, + { + "Q": "At 4:10, Sal says that Xenon is the last noble gas with a lower atomic number than Neodymium. Why doesn't he just use Barium (56) instead.??\n\nThx in advance!!\nClarissa\n", + "A": "Barium is not a noble gas so can be changed at any time. In order to start electron configuration with an element you have to start with a element that cannot be changed, so we always start with a noble gas.", + "video_name": "L-0FkEPPdXE" + }, + { + "Q": "0:47, How did you know it was a first order reaction?\n", + "A": "He is saying, IF we know that the reaction is first order, this is how to do the math.", + "video_name": "Bt0mz4mGddk" + }, + { + "Q": "\nAt 3:17, Sal states that the cell takes in nutrients from the environment in order to grow. What sort of nutrients does the cell take in? And doesn't this intake of nutrients affect the concentration of cytosol which in turn may affect the organelles?", + "A": "The nutrition are what you eat. Everything you eat is broken down and divided up into carbohydrates, portein, fats, etc. which get sent off to the different parts of the body including the protein, which is sent to the cells. The proteins do affect the concentration of the cytosol, which does affect the organelles, but it will not affect it negatively. If you have any more questions or need more detail, comment below...", + "video_name": "VXLSTd_dlKg" + }, + { + "Q": "\nI don't get what the G1 and G2 phases are. This is mentioned in 3:40.", + "A": "Interphase: G1 phase -First phase cell enters if it\u00e2\u0080\u0099s going to divide / Normal cell functions, cell growth, and protein synthesis / Organelles replicate / May take anywhere from 8-12 hrs to months Interphase: G2 Phase -Protein synthesis / Preparation for division / Lasts 2-5 hours", + "video_name": "VXLSTd_dlKg" + }, + { + "Q": "\nAt 4:08, are you saying that over time, carbon will become nitrogen?", + "A": "Carbon-14 will decay into Nitrogen-14 over time.", + "video_name": "gqrh8wbPXVE" + }, + { + "Q": "\nBy 2:02 can we say that Deuterium and Tritium are radioactive? What about elements like Boron and Chlorine? Are they also radioactive as they do not follow this rule?", + "A": "Deuterium isn t radioactive, tritium is. What about boron and chlorine exactly? They both have two stable isotopes so I m not sure what you are getting at. If you mean because their N/Z isn t exactly equal to 1, that s a general rule only. There are exceptions to almost every rule in chemistry.", + "video_name": "gqrh8wbPXVE" + }, + { + "Q": "From 5:35 to 6:50, it seems more reasonable to me that water molecule should attach to secondary carbocation instead of tertiary carbocation because I think since secondary carbocation is more positive than the tertiary one, secondary carbocation would be more strongly attracted to a lone pair of electrons on the water molecule. Why is it not the case in the video?\n", + "A": "Yes, both C1 and C2 have \u00ce\u00b4\u00e2\u0081\u00ba character, but C1 has more of the + charge. The cyclic bromonium ion is a resonance hybrid of two contributors: one with the + on C1, and the other with the + on C2. The second one is the minor contributor, so its C-Br bond is closer to an ordinary covalent bond. The major contributor is closer to having a tertiary carbocation at C1, so that is where the water attacks.", + "video_name": "FaOOx6IZxV8" + }, + { + "Q": "Please refer instants 00:34 & 02:25 seconds of video Fluids (Part 5)\nIn the example you delt with, assume there is water in the jar, upto height h in the jar without any objects. Now we know, the pressure is going to vary as per formula (density times the (g * h)).\nPlease educate me on how the pressure at each and every point of the jar is going to get effected, if a cube denser than the water is suspended (and immersed) in the water using a thread. Is the profile of pressure with respect to the\n", + "A": "the density (or weight/mass) of the cube will not matter beyond causing it to sink because it will be off set by the tension in the string suspending it. putting it in the jar will be no different than augmenting the shape of the jar", + "video_name": "vzID7ds600c" + }, + { + "Q": "\n@2:03, why did Jay say that he \"has to\" make chlorine point up (axial)? Could't he make it point equatorial?", + "A": "He randomly chose that first carbon to be #1, and the up one on that carbon happened to be axial. He could have chosen the next carbon along instead and then it would have been equatorial, but then the problem is this mechanism wouldn t work.", + "video_name": "uCW6154hPkc" + }, + { + "Q": "\nAt 2:09, does anyone know more about Robert Hooke's microscope structure?", + "A": "When Hooke viewed a thin cutting of cork using his self designed microscope, he discovered empty spaces contained by walls, and termed them cells. They looked like honeycombs. In latin, cell means tiny rooms. Thus, as Robert Hooke thought the compartments looked like small rooms. Thus, he called them cells.", + "video_name": "1aJBToJrlvA" + }, + { + "Q": "at 3:28 Hank says microtubules are called (9+2) structure. Can anyone tell me that why are they called so?\n", + "A": "They are called the 9+2 structure because as he says at 3:24 there are made of 9 microtubules forming a ring around 2 microtubules.", + "video_name": "1aJBToJrlvA" + }, + { + "Q": "\nat 4:20 , aren't centrosomes also called centrioles", + "A": "Centrosomes are made up of a pair of centrioles", + "video_name": "1aJBToJrlvA" + }, + { + "Q": "At 4:23, what are centrosomes, are they centrioles?\n", + "A": "An organelle near the nucleus of a cell that contains the centrioles (in animal cells) and from which the spindle fibers develop in cell division.", + "video_name": "1aJBToJrlvA" + }, + { + "Q": "\nAt 13:14 how do you get 2p6? I thought each orbital only had 2 electrons, so how does this one have 6?", + "A": "each orbital can hold two electrons. in the p orbital shell, it has three orbitals, each holding two electrons, therefore holding a maximum of six", + "video_name": "FmQoSenbtnU" + }, + { + "Q": "7:05 (carbon) I'm confused about the P orbitals.. so in carbon the 1s2 and 2s2 are filled and then he goes to the P orbitals and why is it 2p2? I thought it filled only one of the first P orbital and then did one in the second so why isn't it 1p1 and 2p1 instead of 2p2?\n", + "A": "The base number measures the energy level, or the row # of the periodic table. The p block starts on level 2, so there is no 1p. Carbon is also the 2nd element in the p block of that row, so the exponent is 2.", + "video_name": "FmQoSenbtnU" + }, + { + "Q": "\nAt 6:10, he refers to the \"z\" direction as up and down, and the \"y\" direction as forward and backward, but isn't that reversed? I thought, that \"x\" was left-right, \"y\" up-down, and \"z\" forward-backward (representing 3 dimensions). Are these interchangeable, now? I'm only asking because it has been 18 years since I last took a math course.", + "A": "They are just labels for axes. Up and down depends on how you are oriented when you are looking at something.", + "video_name": "FmQoSenbtnU" + }, + { + "Q": "\nAt 1:30,would those be snapshots of different atoms or the same one?", + "A": "it s the same atom. It is just the electron, that is represented in different snapshots. When you overlay the different snapshots it becomes apparent, that the electron is more likely to be near the nucleus.", + "video_name": "FmQoSenbtnU" + }, + { + "Q": "I don't understand why the P orbital has Pz, Px and Py? 6:26\n", + "A": "Because there s 3 p orbitals in a shell (that s why a total p subshell can hold 6 electrons). There s one p orbital aligned on each 3-dimensional axis.", + "video_name": "FmQoSenbtnU" + }, + { + "Q": "At 13:26 how does he get the configuration for Silicon? Can someone please summarize this whole video. I'm confused\n", + "A": "That s a good explanation, but you explained how to get to Sulfur, not Silicon. So 3p2, rather than 3p4, because Silicon has 14 electrons.", + "video_name": "FmQoSenbtnU" + }, + { + "Q": "At 13:37, why does one write out the whole electron configuration, rather than just the last \"shell\"? In other words, wouldn't it be enough to write 3p^2 for silicon, since all the lower energy shells are always filled up?\n", + "A": "When you get to heavier elements you ll find what you say about the lower energy orbitals always being full isn t always true.", + "video_name": "FmQoSenbtnU" + }, + { + "Q": "\nat around 12:08. How does he know 3 electrons go in the p orbital. Is it because that is what is left over after filling the s orbitals?", + "A": "Yes, when determining the electron configuration, you count up from the bottom (1s) orbital and add electrons one at a time until all are used up for that atom or ion. The electrons are first put in singly, then double up with an opposite spin. You cannot move up to the next higher level until the lower orbitals are filled. When the level or sub-shells has more than one orbital (as there are 3 p orbitals), then each is filled up with a single electron first before they are doubled up.", + "video_name": "FmQoSenbtnU" + }, + { + "Q": "at 5:19, do the electrons fill the orbital from lowest energy orbital to highest energy orbital?\n", + "A": "Yes, nature always wants to minimize energy.", + "video_name": "FmQoSenbtnU" + }, + { + "Q": "He stated at 12:10 that the electron configuration for Nitrogen is 1s^2 2s^2 2p^3. However, how can 2p have 3 electrons when each subshell can only have 2 electrons?\n", + "A": "It is orbitals that can only have 2 electrons, not subshells. The p subshell contains 3 orbitals, so it can hold at most 6 electrons. The d subshell contains 5 orbitals, so it can hold at most 10 electrons. The f subshell contains 7 orbitals, so it can hold at most 14 electrons. And, of course, the s subshell has only 1 orbital so it can only hold 2 electrons.", + "video_name": "FmQoSenbtnU" + }, + { + "Q": "\nat 1:27 he talks about the s, why are the orbitals called s,p,f,etc?", + "A": "Those letters represent terms that are now outdated and no longer used. The terms were sharp, principal, diffuse, and one I can t remember.", + "video_name": "FmQoSenbtnU" + }, + { + "Q": "Hi\u00ef\u00bc\u008cI am confused about P orbital. I can understand s orbital and it seems like it follows orders of electrons numbers in each circle. (it seems like follow 2,8,8,18,18,32,32..). However, in the video 7:56, it suddenly jumps to P orbitals without explanations. What does P orbitals refer to\n", + "A": "The orbitals each have a given amount of electrons, s can have 2, and then it must move up to p. The p orbital can have up to 6 electrons, and when you run out, you must move on to the d orbital, which can have 10 electrons. Lastly, you have the f orbital, and that orbital can have up to 14 electrons.", + "video_name": "FmQoSenbtnU" + }, + { + "Q": "\nAt 14:00, could someone explain why all the electron configurations look so strange?", + "A": "They are based on complex math equations that calculate the likelihood of an electron being within the configurations with 90% accuracy.", + "video_name": "FmQoSenbtnU" + }, + { + "Q": "At 5:13 Sal mentions that the water molecules on the skin surface are linked by hydrogen bonds. Would the cooling effect of a liquid be different if there was no hydrogen bond? I would assume that evaporation of other liquids without hydrogen bonds would take away less energy (=heat), because not having to break up a hydrogen bond would need less energy? Am I correct?\n", + "A": "Yes, hydrogen bonds take energy to form, and actually take a larger amount of heat to disrupt a hydrogen bond putting hydrogen bonds. So in theory other liquids with the same evaporating temperatures would take less energy.", + "video_name": "_eEONOJHnEs" + }, + { + "Q": "\nAt the beginning of the video (around 0:38) he said that life is carbon based. What is that supposed to mean?", + "A": "What Sal means at 0:38 is that all known lifeforms contain the element carbon. Of course, there are other elements that are found in a majority of life-forms as well. But Carbon is the most prominent. Scientists have yet to find a living organism that does not contain carbon in it s Chemical Make-Up. Therefore, as far as we can tell, all life is carbon-based.", + "video_name": "JgYlogdtJDo" + }, + { + "Q": "At 13:10 isn't the height 6m?\n", + "A": "No, if you think about it, if that ball has a radius of 2m. So when the ball is touching the ground, it s center of mass will actually still be 2m from the ground. It s true that the center of mass is initially 6m from the ground, but when the ball falls and touches the ground the center of mass is again still 2m from the ground. That means the height will be 4m. If you work the problem where the height is 6m, the ball would have to fall halfway through the floor for the center of mass to be at 0 height.", + "video_name": "5eX5WnPDnvs" + }, + { + "Q": "\nAt 1:48, why isn't the concentration of Cl- taken into consideration? Although it's an extremely weak base, I thought it would still make some difference in the pH.", + "A": "HCl is a strong acid, so that means Cl- has to be an extremely weak base as you stated. Essentially the reverse reaction of Cl- + H+ -> HCl does not happen, so no need to account for it.", + "video_name": "lsHq5aqz4uQ" + }, + { + "Q": "\nThis may seem trivial, but at 3:40, why is the hydroxide ion written with the charge on the left-hand side, instead of the right? I've seen it that way consistently in these chemistry videos, but never anywhere else.", + "A": "It is preferable to put the charge on the atom that has the charge, so we should write \u00e2\u0081\u00bbOH or HO\u00e2\u0081\u00bb. However, many people still write the formula as OH\u00e2\u0081\u00bb. It s OK, as long as you remember that the O atom has the charge.", + "video_name": "lsHq5aqz4uQ" + }, + { + "Q": "\nAt 1:00 how do you know if the Ka value is 5.6 x10^10 ?", + "A": "So in this problem, it is just given to you. Even though it doesn t appear to be written as part of the original question, during exams you would be given a Kb value or a Ka value to work with. Also, ammonia s Kb value is 1.8 x 10^-5 (memorized from constant use). We know that (Ka x Kb = Kw) so all we have to do is take 1.0 x 10^-14 / 1.8 x 10^-5 (Kw / Kb) which gives us 5.6 x 10^-10 (Ka). Hope that helped!", + "video_name": "lsHq5aqz4uQ" + }, + { + "Q": "at 0:01 the picture are real or not\n", + "A": "Yes, those pictures are real", + "video_name": "N6IAzlugWw0" + }, + { + "Q": "at about 9:00, you show the chlorine in AlCl4 giving its' electron to the hydrogen, then the hydrogen giving it's electron back to the benzene ring so it can form a double bond and become aromatic again. You don't mention what happens to that chlorine atom and hydrogen after? do they then form HCl? thank you!\n", + "A": "I just watched the next video, Friedel Crafts Acylation Addendum, that answers my question!", + "video_name": "vFfriC55fFw" + }, + { + "Q": "At 4:40, what is the general formula for an exponential decay and wat does each letter in the formula represent?\n", + "A": "The formula for an exponential decay is (1-r)^t. T is time, r is the rate or percent,", + "video_name": "Hqzakjo_dYg" + }, + { + "Q": "\n6:26 What is \"e\" for? why the alphabet becomes 2.71?", + "A": "Sal has done a few videos on where e comes from. Look for the Introduction to compound interest and e video in the Precalculus playlist.", + "video_name": "Hqzakjo_dYg" + }, + { + "Q": "6:26 What is \"e\" for? why the alphabet becomes 2.71?\n", + "A": "e is an important mathematical constant that is roughly equal to 2.71.", + "video_name": "Hqzakjo_dYg" + }, + { + "Q": "At 1:11 Sal says light travels fastest in a vacuum, I thought the speed of light was constant.\n", + "A": "light slows down more in more densely packed things since the photon crashes into more particle in a time period. however, the speed of light in a vacuum is constant.", + "video_name": "y55tzg_jW9I" + }, + { + "Q": "At 8:19, what does axial and equatorial mean?\n", + "A": "It refers to which way the groups of a cycloalkane are pointing in the chair conformation. Axial = up or down Equatorial = sideways", + "video_name": "FGq9-R6Yw18" + }, + { + "Q": "\nat 3:08 Sal says that \"w\" (omega) is the angular velocity but souldn't it be the angular frequency", + "A": "Omega is in rad/s. I do believe that angular frequency would be in rev/s. They are essentially the same thing just their units are different.", + "video_name": "xoUppFlif04" + }, + { + "Q": "\nAround 5:30 the Hank talks about the centrosomes moving away from the nucleas and leaving behind a trail of microtubles. But the animation shows the tubules growing from the centrosomes towards the chromosomes. I am confused on how the microtubles form. Anyone got a good tubular breakdown for meh?", + "A": "To my understanding, the centrosomes are building the mitotic spindle/microtubules in the prophase, whilst they are moving.", + "video_name": "X1bmedVziGw" + }, + { + "Q": "At 4:47 , is Hank saying that a double chromosome is still considered one chromosome? His use of the plural is a bit confusing.\n", + "A": "A chromosome that has reproduced and is still attached at the centromere is still considered one chromosome.", + "video_name": "X1bmedVziGw" + }, + { + "Q": "At 8:23, why use the volume of room rather than the volume of the container? Shouldn't the ideal gas law produced in the video be designated exclusively to the container of the water since the water is exclusively within the two liters, rather than the 42500 liters of room?\n", + "A": "The 2.00 L is the volume of the liquid water in the open container. When the water evaporates, the water vapour expands to fill the whole room, so that\u00e2\u0080\u0099s the volume you use.", + "video_name": "-QpkmwIoMaY" + }, + { + "Q": "\nAt 1:23, WHAT keeps water in its liquid state ?", + "A": "The attractive forces among water molecules keep water in its liquid state.", + "video_name": "-QpkmwIoMaY" + }, + { + "Q": "\nAt 10:50, the video notes that the two chair forms of cyclohexane are in equilibrium. So, does a single molecule spontaneously flip back and forth between the two forms? Or, must a single molecule, say, collide with another molecule for the flip to occur?", + "A": "When cyclohexane is synthesized, it is in the two forms, but remember that equilibrium s can lean towards one side. The chair formation is a little bit more stable so the atoms rearrange (this is kind of your question, not much is known about how they do this, but it would help to understand hybridization) to be different than the boat conformation. Also some of the chair configuration can go back into the boat configuration.", + "video_name": "YUEkOBvJSNg" + }, + { + "Q": "Around 4:00, where is the boundary between non-polar and polar?\n", + "A": "The boundary is approximately a difference of 1.7 between elements, but there are exceptions.", + "video_name": "126N4hox9YA" + }, + { + "Q": "\n09:55, it is said that if the electronegativity is greater than 1.7, the compound is usually considered ionic. In the previous video (\"Electronegativity\"), it is said that the compound is considered ionic if the electronegativity is greater than 2.0.\nWhich one is more reliabe? How can I tell in an exam if a compound is ionic or covalent or nonpolar?", + "A": "Different books use different cutoffs, though 1.7 is the most common, as Ryan mentioned. Ask you teacher which cutoff they want you to use for an exam.", + "video_name": "126N4hox9YA" + }, + { + "Q": "\nAt about 4:30, in discussing microstates, Sal says that we can know the position and the momentum. I thought that, because of the uncertainty principle, we can never know both the position and the momentum of any given particle. Is he just simplifying things so that we understand the difference between microstates and macrostates, or am I missing something?\nThanks.", + "A": "According to the Heisenberg Uncertainty Principle, you cant know both the location and momentum of a particle so you are correct. I believe it is a simplification.", + "video_name": "5EU-y1VF7g4" + }, + { + "Q": "At 3:47, don't chloroplasts have a double membrane instead of just 1?\n", + "A": "Yes , the chloroplast technically has 2 membranes ; the outer and the inner one", + "video_name": "GR2GA7chA_c" + }, + { + "Q": "At 3:00, Sal said that the chloroplasts reflect green light, so does that mean that if \"green\" photons were to hit the chloroplast, photosynthesis wouldn't occur?\n", + "A": "Well, green photons can t be absorbed because they are the wrong wavelength. The energy comes from photons that are absorbed. So the green photons can t provide energy for photosynthesis, and if you shone only green light on the chloroplast it would have no energy to photosynthesize. So, you are correct.", + "video_name": "GR2GA7chA_c" + }, + { + "Q": "At 12:00, When H+ goes through the ATP synthase, it \"puts\" ADP and Pi to form ATP?\n", + "A": "Well, assume the synthase is a wind turbine. Wind turbines generate electricity, but they cannot do so without any wind. Now, pretend that the flow of protons (H+) is that wind. Once the wind flows, the turbine is able to spin and generate ATP.", + "video_name": "GR2GA7chA_c" + }, + { + "Q": "At 5:30, he mentions that organelles were independent organisms that at some point evolved together (a process called \"endosymbiosis\"). This is true of mitochondria and chloroplasts, but I believe it is inaccurate to say of all organelles, correct?\n", + "A": "this is possible because they both have DNA", + "video_name": "GR2GA7chA_c" + }, + { + "Q": "Did he mean hydrogen ions instead of hydrogen \"protons\"? (11:07)\n", + "A": "A hydrogen ion (H+) is a proton. So, the terms are used interchangeably.", + "video_name": "GR2GA7chA_c" + }, + { + "Q": "At 1:00 I don't why there is NH3. Is it solvent?\n", + "A": "NH3 is the solvent. If you are talking about -NH2, that is from NaNH2 and is a very strong base.", + "video_name": "HbDWBeRJboE" + }, + { + "Q": "\nAt about 4:20, you mention that we cannot decipher the design of the rim of a wheel of a moving car because the parvo pathway has poor temporal resolution. I agree that this is true. However, then why can we not use the Magno Pathway to determine the design of the rim of the wheel since it has better temporal resolution?", + "A": "Because the magno pathway is not good at detecting fine detail, like the the rims of the wheels. (I think this is the right answer).", + "video_name": "0ugcw7wOZBg" + }, + { + "Q": "At 8:10, you say that the force of gravity (Fg) that acts on A is equal to the force that the table acts on A (Ft; normal force) because of Newton's second law of motion. Is it also correct to say that these two forces are equal because of Newton's first law of motion?\n", + "A": "If the object is not accelerating, we know that the net force must be zero. The first law is sort of just a special case of the second law.", + "video_name": "VfpKzwrhmqQ" + }, + { + "Q": "\nAt 0:25, David says opposite and writes a negative. Is there such a thing as a negative force?", + "A": "Yes, it s a force that is in the opposite direction of whatever direction you decided is positive.", + "video_name": "VfpKzwrhmqQ" + }, + { + "Q": "\nOn 3:54, why does Sal say that helium's configuration is 1s2, when helium is in the p block?", + "A": "Helium is not part of the p block. It appears on the far right of the periodic table because it is a Nobel gas, so has similar reactivity to the other elements on the far right of the periodic table. However, helium has no electrons in p orbitals so does not count as part of the p block.", + "video_name": "NYtPw0WiUCo" + }, + { + "Q": "\nIn 5:19, Sal said Carbon has 2 + 2 valence electrons. Meaning the electrons from the s2 shell and the p2 shell. Is the s2 shell not filled? Why not use only the p2, which is the outermost shell? Help please.", + "A": "2s and 2p are both subshells of shell number 2. So you have to consider both the s and p.", + "video_name": "NYtPw0WiUCo" + }, + { + "Q": "Apologies if this has already been answered, but at 9:20 Sal tells us that from the n=4 S subshell, the element \"backfills\" electrons into the n=3 D subshell. Why does it do this, rather than going directly to 4d^6? Is this a special case, or does it happen for all elements in the D subshell and/or beyond? Thanks!\n", + "A": "This happens for all elements in the d block and beyond. In the fourth level and beyond, the energy levels get all mixed up. For example, in cerium (Ce, element 58), the outermost electron configuration is 6s\u00c2\u00b2 4f\u00c2\u00b9 5d\u00c2\u00b9 6s2 4f1 5d1", + "video_name": "NYtPw0WiUCo" + }, + { + "Q": "\n\"They would say, \"Okay,\" \"these are the two Valence electrons\" \"for all of these transition metals.\" Well that doesn't hold up for all of them because you even have special cases like copper and chromium that only go four S one and then start filling three D depending on the circumstances.\" Could someone explain to me how can copper and chromium only go 4s^1 not 4s^2 (they have 2 groups in s subshells in their period)? 10:15", + "A": "You would expect Cu to be 4s\u00c2\u00b23d\u00e2\u0081\u00b4. But a half-filled d subshell is more stable than one with only 4 d electrons. It takes a little energy to promote a 4s electron to the 3d level, but you get back more than this by getting a 4s3d\u00e2\u0081\u00b5 configuration. In the same way, a filled d subshell is more stable than one with only 9 d electrons. It takes a little energy to promote a 4s electron to the 3d level, but you get back more than this by getting a 4s3d\u00c2\u00b9\u00e2\u0081\u00b0 configuration.", + "video_name": "NYtPw0WiUCo" + }, + { + "Q": "at 10:16, why does the d group belong to the number 3 not four. Since it is in the fourth group why is it written at 3d6\n", + "A": "Well, when you get to the D sub-level you have to take into account that the 4s orbital is filled BEFORE the 3d! The 5s orbital fills before the 4d, so, it even though the 5s seems like it would be farther out than the 4d, the 4d has more energy, so to speak.", + "video_name": "NYtPw0WiUCo" + }, + { + "Q": "At 6:50, Sal talks of Methane having a logical structure of CH^4, with 8 valence electrons. How then, is methane so reactive and explosive? Hydrogen is flammable, yet saying that Methane is flammable only because it has Hydrogen atoms would be like saying water is flammable because it is H^2O.\n", + "A": "A full octet of electrons doesn t mean it will completely unreactive to anything. It s not simply hydrogen atoms that are flammable, methane can be turned into more stable products (CO2 and H2O) when it is burned.", + "video_name": "NYtPw0WiUCo" + }, + { + "Q": "\nAt 5:14, he says \"that has not been completed yet\" what does he mean by that? Doesn't the 2s^2 mean that it's 2nd s orbital has been full so it has to move onto the p orbital? A little confused on Valence electrons still.", + "A": "The 2s orbital is full, but those electrons are still part of the outermost shell. The 2s and the three 2p orbitals make up the second shell.", + "video_name": "NYtPw0WiUCo" + }, + { + "Q": "At 7:15, Sal mentions covalent bonds between hydrogen and carbon. What are covalent bonds?\n", + "A": "As opposed to ionic bonds, which donate and receive electrons to get charged, get full shells and stick together, covalent bonds share electrons to stick together and get full shells. Covalent bonds happen between elements with a smaller electronegativity difference than the amount required for an ionic bond, so generally nonmetals.", + "video_name": "NYtPw0WiUCo" + }, + { + "Q": "at 5:38, i don't really understand why 2s\u00c2\u00b22p\u00c2\u00b3......also, for school purpose, should i memories the whole table like Sal did and how to make it easier...someone help me\n", + "A": "just see and by heart the name of elements minimum till 30 and some important like gold or zinc fe etc.. and to explain the first question its not possible in this box i would suggest you to go through all the previous topics of periodic table or read a source like your text and then go through this. it will explain everything as Mr khan always does:)", + "video_name": "NYtPw0WiUCo" + }, + { + "Q": "\nAt 9:32 Sal asks : \"what are the highest energy electrons ?\" and then at 9:36 he asks \"what are the furthest out ?\".\n\nHow do we determine which one are the furthest out and the one which have highest energy ? Is it a specificity of blocks ?", + "A": "You can t determine it unless you have prior knowledge of it. But Sal is not correct here, because the 4s electrons are both the furtherest out and the highest energy for the transition metals.", + "video_name": "NYtPw0WiUCo" + }, + { + "Q": "In 5:43, Why is it written as [He]2s2, 2p2 instead of 1s2, 2s2, 2p2? And why does Carbon only have four valence?\n", + "A": "Because Helium s electronic configuration is 1s2, which is a complete electron shell, so 1s2 is replaced with [He] instead. For example, potassium(K) s electronic configuration is 1s2, 2s2, 2p6, 3s2, 3p6, 4s1. Since the last complete electron shell is 1s2, 2s2, 2p6, 3s2, 3p6, which is Argon, it could be substituted into K s electronic configuration. Thus, it could be written as [Ar] 4s1. Carbon has four valency electrons and needs to gain or lose FOUR more electrons to obtain a complete electron shell.", + "video_name": "NYtPw0WiUCo" + }, + { + "Q": "Why does Sal, at 7:39 state that any element in Carbon's group will have four valence electrons?\n", + "A": "Because of the group it is in. All group 1 elements have one valence electron, group 2 elements have two, skip groups 3-12 for now (they are the exceptions to the rule), group 13 has three, group 14 has four (carbon being part of this group), and so on.", + "video_name": "NYtPw0WiUCo" + }, + { + "Q": "\n8:22 so? H2Te or Li20 could both be similar to H20? or even Li2Te? or did I just give a completely different molecule", + "A": "Yeah H2Te and Li2O are similar to H2O and also to Li2Te. Slightly tricky since Hydrogen is NOT an alkali metal(group I metal) It s position is analogous.That s why Hydrogen s box is green. So, Hydrogen won t have the properties of Lithium. But Oxygen and Tellurium on the other hand are both Chalcogens and exhibit similar properties.So, H2Te is similar to H2O Li2O is similar to Li2Te", + "video_name": "NYtPw0WiUCo" + }, + { + "Q": "At 1:56 How did we know that Carbon has sp3 hybridized orbitals and that it forms a tetrahedral shape?\n", + "A": "Because each carbon has four other atoms directly attached to it. You have already learned that this requires sp3 hybridization and the sp3 bond angles are 109.5\u00c2\u00b0.", + "video_name": "IkmM4CPnqF0" + }, + { + "Q": "\nAround 2:50 Sal started talking about prokaryotes. I know about how organisms and species have evolved over time but how is this possible for single celled organisms to evolve exactly? Did these organisms gather in massses and shift into the next cellular organism? Or did they latch on to soil thus creating plants?", + "A": "This isn t known at all, but we do know that they evolved somehow. It s kind of like the apes evolving into humans, it s just natural I guess.", + "video_name": "nYFuxTXDj90" + }, + { + "Q": "\nAt 9:08 Sal said that all life was happening in the ocean and the ocean was still iron rich. Doesn't too much iron kill you?", + "A": "It wouldn t be enough to kill them, in fact it might help (hemoglobin?).", + "video_name": "nYFuxTXDj90" + }, + { + "Q": "9:00 on the video there is suddenly an ocean. What happened? Where did it come from?\n", + "A": "actually, when a meteriote formed, it had some ice on it. that ice melted and started the water cycle. this happened over thousands of years", + "video_name": "nYFuxTXDj90" + }, + { + "Q": "\ni have another question.My teacher mentioned that nuclues in unicellular organisms help in reproduction.ie-the organism breaks itself into 2 and so,there is a new organism.The video mentioned that there were so many in number(i am talking about the procaryotes).So did many procaryotes come into being in a flash because it cant reproduce?The time could be approximately 3:00", + "A": "Nothing comes into being in a flash.", + "video_name": "nYFuxTXDj90" + }, + { + "Q": "At 8:10, he mentions stromatalites, something about sediment and bacteria. What are they exactly?\n", + "A": "Stromatolites are layered mounds, columns, and sedimentary rocks. They were formed upon layer by layer of cyanobacteria, a single celled organism that lives in many different habitats. I hope that helped you.", + "video_name": "nYFuxTXDj90" + }, + { + "Q": "at the end of the video< im kind of confused on how sal got the ratio 1:2. can you explain?\n", + "A": "We discovered, in this video, that the bottle of molecular substance we were dealing with had 1.02 moles of Sulfur, 2.04 moles of Hydrogen, and 4.08 moles of Oxygen. The goal of the Empirical Formula is to represent the elements in simplest form. To simplify, we can divide each element by the least common factor (in this case, 1.02 happens to be the lcf) and we come up with 1, 2 and 4. We cannot reduce these any more.", + "video_name": "sXOIIEZh6qg" + }, + { + "Q": "My question is: In the case of Fe2O3 that are in the ratio of 70% iron and 30% oxygen.\nThe atomic weight of iron is 56 and I get 70/56 = 1.25 moles.\nThe atomic weight of oxygen is 16 and I get 30/16 = 1.87 moles.\nHow do I know that their ratio is 2:3?\nI know that 1.25 / 1.87 = 0.666666667, so I have to find which numbers divided among themselves make 0.666666667 and discover that is 2/3.\nThere is no way to know immediately without having to do a lot of divisions? Thank you.\n", + "A": "Another way to write 0.6 repeating is 6/9 or 2/3. If you think of the fraction as the ratio of the number of Iron Atoms (numerator) to the number of Oxygen Atoms (denominator) then you get Fe2O3 pretty quickly. Conversely, if you were to multiply the numerator and denominator by 1000 you get 1250/1875 (you rounded 30/16 to 1.87, but it is 1.875). when you reduce that you get 2/3. As the numerator represented Fe, you have 2 atoms of that and the denominator represented O, you had 3 atoms of that", + "video_name": "sXOIIEZh6qg" + }, + { + "Q": "\nAt 0:07 why is hydrogen at 2.04 %", + "A": "That is just the way the problem is set up.", + "video_name": "sXOIIEZh6qg" + }, + { + "Q": "\nAt 3:30, doesn't P1=V2 and P2=V1", + "A": "No. Because its not P1/Vi=0 and P2/V2=0. If that was the case then you would have been correct. But as the temperature, no. of moles and constant does not change, both P1*V1 and P2*V2 are equal to nRT. Hope this helps :)", + "video_name": "GwoX_BemwHs" + }, + { + "Q": "\nAt 2:30, how can V1 and V2 be equal to each other when their volume is clearly decreasing?", + "A": "The volume in each IS different V1=9L and V2=3Liters. When setting up the equation both are equal to nRT since he states these are constants. The next step he makes them equal to each other divides which eliminates 3 and the L leaving 9 atm.", + "video_name": "GwoX_BemwHs" + }, + { + "Q": "At 3:30 in the video the answer is revealed to be 9 atm. When you divide the 3 over, why isn't the 9 divided as well, because should ((3atm x 9L)/(3L))= 3atm?\n", + "A": "Sorry, but no. If you divide a sum by a number, then you divide each member of the sum. But if the numbers are all multiplied, you only divide one time.", + "video_name": "GwoX_BemwHs" + }, + { + "Q": "\nSo, before Sal changed the pressure in the initial problem at 6:10, the proportion was set up as (1atm x 2m^3)/300K = (2atm x 1m^3)/T. If the proportion was solved as such, wouldn't a temperature of 300K have been achieved even though the pressure of the second container was increased and the volume of the second container was decreased?", + "A": "I think I understand the algebra behind the problem, I was just a little confused conceptually. If the pressure of a container is increased and the volume is decreased, wouldn t the result be a smaller, more pressurized space? And would this scenario not lead to a higher temperature?", + "video_name": "GwoX_BemwHs" + }, + { + "Q": "At 6:45 sal says that 2 over 300 = 5 over t2. I get that, but then he says that 1500=2t2. how did he get 1500 and how did he get 2t2?wouldn't it be t2?\n", + "A": "If you have 2/300=5/t2, you cross multiply on both sides. So basically, first you multiply both sides by t2, which results in 2t2/300=5. Then you multiply both sides by 300, resulting in 2t2=5x300 which is 2t2=1500.", + "video_name": "GwoX_BemwHs" + }, + { + "Q": "at 4:41 What is quantum mechanics ?\n", + "A": "Quantum mechanics is basically what chemists and physicists use to describes how subatomic particles behave. You ll learn more about it as you learn more about chemistry :)", + "video_name": "Rd4a1X3B61w" + }, + { + "Q": "at 2:30 the carbon is more electronegative than hydrogen has been said and it atract the shared pair of electrons\nbut why cant oxygen atom do this inspite o is more electronegative than c and h.\n", + "A": "Oxygen is more electronegative than carbon and hydrogen. It does attract the bonding electrons significantly more than those two.", + "video_name": "rhuYuerbhIE" + }, + { + "Q": "\nAt 3:58 Sal says a \"slightly negative pH\" i think what he means is a pH slightly below 7, but can you actually have a negative pH?", + "A": "Yes, you can. You can easily have a 10 mol/L solution of a strong acid, so [H+] = 10 mol/L. pH = -log[H+] = -log10 = -1. When acids are very acidic, though, we must use measures of acidity other than pH. You have not yet learned about these, though.", + "video_name": "BBIGR0RAMtY" + }, + { + "Q": "at 2:16 what does he mean by PH\n", + "A": "I am struggling with my online Chemistry class and was wondering if someone could help me understand the group numbers. For example what are the group numbers for X and Y?", + "video_name": "BBIGR0RAMtY" + }, + { + "Q": "1:21 Sal says that Sulphur's mass number is 32, but on the periodic table it says that the mass number is 32.07. Why?\n", + "A": "We calculate the mass number of one specific sulphur atom, which has 16 neutrons. So, it s mass number is exactly 32. In this big wide world, there exist other isotopes of sulphur too, having different mass numbers. The average mass of all sulphur atoms is 32.07, as calculated by scientists.", + "video_name": "koAFBScR41A" + }, + { + "Q": "\nAt 0:58, Sal mentions that every isotope of Sulfur will have 16 protons.\nAre there exceptions to this rule? Can an isotope have a number of protons different from its' Atomic Number?", + "A": "No, because then it would not be an isotope of sulfur. Every sulfur atom in the universe has 16 protons. If it had say 15 protons then it would be phosphorus instead.", + "video_name": "koAFBScR41A" + }, + { + "Q": "\nAt 0:56, Sal used the word reproduce. What does that mean? I forgot.", + "A": "Reproduction is the process by which a living organism is able to create their own offsprings.", + "video_name": "dQCsA2cCdvA" + }, + { + "Q": "\nAt 5:41pmvideo Biology overview why is biology so important to us humans.", + "A": "It s important because we need to know how life around us works. How the living matters that surround us came to be. It s good to have a basic knowledge down about living matter.", + "video_name": "dQCsA2cCdvA" + }, + { + "Q": "At about 3:00, bacteria is between life and non-life, what would you call non-life?\n", + "A": "Viruses are non-living.", + "video_name": "dQCsA2cCdvA" + }, + { + "Q": "at 6:00\nthe alcohol used is connected to a tertiary carbon. Why does an Sn2 reaction occur and not an Sn1 ?\n\nThank you\n", + "A": "The alcohol used is not connected to a tertiary carbon, it is connected to a secondary carbon. Tertiary carbons are required to be bonded to three other carbon atoms (do not confuse these with the number of bonds they make with atoms that aren t carbon). In the video, the alpha carbon is connected to two other carbons and one oxygen atom. This makes it a secondary carbon. Therefore, SN2 can occur.", + "video_name": "j-rBgs_p-bg" + }, + { + "Q": "How are you going to know which six month period to choose in order to have an isosceles triangle?At 1:49 he mentions finding the maximum parallax angle that the star makes during the year.Doesn't that require daily observation for a year?\n", + "A": "isn t it just the 2 different 6 month periods? aren t there only 2?", + "video_name": "6FP-hLuAlr4" + }, + { + "Q": "\nAt 4:55, you mention prothrombin becoming thrombin, but this isn't mentioned again as you go through the cascade. Is prothrombin one of the Roman Numerals in the cascade or how does it fit in?", + "A": "Yes, it is one of the numerals in the cascade. Prothrombin is Clotting Factor II, and Thrombin is IIa (activated factor 2). For whatever reason, most people use prothrombin/thrombin rather than calling it Factor 2 / Factor 2a.", + "video_name": "FNVvQ788wzk" + }, + { + "Q": "if this sn2 mechanism only works in 1* or 2* alcohols, why is he starting with tert butanol? at 0:00?\n", + "A": "It s not impossible for SN2 to happen to tertiary alcohols, it s just slow. There is a strong nucleophile and we have formed a good leaving group so it is possible.", + "video_name": "LccmkSz-Y-w" + }, + { + "Q": "Why does the formation of an alkyl chloride (at 3:00) require a base , while the formation of an alkyl bromide (at 8:00) doesn't?\n", + "A": "Pyridine is required in chlorination of alcohols by SOCl2 to nuetralise the HCl produced during the reaction. By the way, preparation of alkyl chloride by SOCl2 can also take place in abscence of pyridine via sNi mechanism{look up in wikipedia}.", + "video_name": "LccmkSz-Y-w" + }, + { + "Q": "From 6:33 to 6:46, Sal talks about how light takes 8 minutes to hit the earth from the sun. At 6:42 he says that if the sun were to disappear, it would take 8 minutes for the people on Earth to know that light disappeared. Say the sun did disappear. What would happen in terms of gravity? Would we feel the absence of its gravitational effects right away? If not, why? And if so, wouldn't that mean the effects were faster than the speed of light?\n", + "A": "gravity travels at the speed of light", + "video_name": "GZx3U0dbASg" + }, + { + "Q": "6:35 Sal says if the sun disappeared it would take 8 minutes for us to notice it. Would the sun's gravitational effects travel as quickly were it to somehow disappear? Does gravity propagate as quickly as light?\n", + "A": "Yes the effect of gravity propagates through space at the speed of light.", + "video_name": "GZx3U0dbASg" + }, + { + "Q": "3:13 109 times the circumfrence. Is that 109 times bigger/wider/taller (Pretty much is the sun 109 x, y, z or all of the above then the earth)\n", + "A": "Probably bigger.", + "video_name": "GZx3U0dbASg" + }, + { + "Q": "At 1:42, how did we find the circumference of the Earth?\n", + "A": "I think I read somewhere in the physics textbook that you can approximate the radius of Earth by using two point of surface to the center of earth and use basic phytagoras to solve it. And yeah, after finding the radius you can easily find the circumference since Earth is nearly round. So, it s possible to find it with math, especially with geometry.", + "video_name": "GZx3U0dbASg" + }, + { + "Q": "\nabout 10:20, route 19.6h m^2/s^2 = route velocity(f)^2\nbut it turns out velocity(f) = - route 19.6h m/s. Where - < negative sign come from?", + "A": "he explains it a about 8:55. It s because you took a square root (which has positive and negative solutions) and you want the one that goes in the downward direction, which you ve defined as negative", + "video_name": "2ZgBJxT9pbU" + }, + { + "Q": "\nAt 9:45 Sal says that we need to take the negaitve square root of 19.6*h m/s. I don\u00c2\u00b4t quite understand why he does this. Is it because our convention was that downward vectors have to have a negative algebraic sign? Thank you for your answers!", + "A": "You can define direction however you want. If you make up positive, then down is negative, and you just have to stay consistent throughout the problem. So if he defined up as positive earlier in the problem, then down has to be negative.", + "video_name": "2ZgBJxT9pbU" + }, + { + "Q": "Is the formula shown at 9:00 applicable for every free falling projectile dropped with zero initial velocity? Vf=(-)sqrt(19.6h)\n", + "A": "Yes. As long as the air resistance is neglected and your g = 9.8m/s^2, you can use the kinematic equations for uniform motion. Here for calculating final velocity: v^2 - u^2 = 2*g*h if u = 0 and downward direction is taken as positive, then v = sqrt(2*9.8*h). Note that the final velocity doesn t depend on the mass and dimensions of the body. As long as your projectile can be approximated as a point mass particle, you are good to go.", + "video_name": "2ZgBJxT9pbU" + }, + { + "Q": "at 0:29 sal says cellular membrane is semi permeable. But actually it is selectively permeable. *why does he say so?*\n", + "A": "Both semi permeable and selectively permeable refer to the same thing that the cellular membrane only allows certain substances (molecules or ions) to pass through it. Usually, the solvent molecules can pass through however certain solute molecules can not. That s why both terms can be used.", + "video_name": "afWnU10ZNfg" + }, + { + "Q": "\nAt 4:49, how do you know which ones are Adenine?", + "A": "He assigned random bases as Adenine (not accurate in the sense that those were actually Adenine) then assigned Thymine to complement Adenine.", + "video_name": "AmOO4j0E408" + }, + { + "Q": "at 6:59 what if your characteristics are nothing like you parents and does this mean we all come from two people and if so why are we all so different?\n", + "A": "Characteristics don t always have to be like your parents, sometimes you find that people have eyes like their grandmother or their uncle s nose. Remember that mutations do occur, and the process of crossing over contributes to genetic variety. These characteristics are recessive. The idea that we all come 2 people is biblical and not necessarily scientific.", + "video_name": "AmOO4j0E408" + }, + { + "Q": "12:00 Why are Adenine pairing with Thymine and Guanine with Cytosine ??\n", + "A": "It is a direct result of the molecular structure of the bases, A/T only have 2 side groups which can form hydrogen bonds whereas C/G have 3.", + "video_name": "AmOO4j0E408" + }, + { + "Q": "at 9:50 you said that the carbon dioxide will diffuse across and into the plasma, and that some of the carbon dioxide can make its way across the membrane into the red blood cell itself where it will be converted into carbonic acid, so does only some of the carbon dioxide get converted into carbonic acid and the rest remain in the plasma? because i thought that all the carbon dioxide gets converted into carbonic acid?\n", + "A": "thank you, but does it travel in the blood as carbonic acid or as carbon dioxide?", + "video_name": "LWtXthfG9_M" + }, + { + "Q": "(2:35) Sal says that cooperative binding is when \"one binding makes other bindings more likely.\" What causes binding to stop in the first place?\n", + "A": "So when one oxygen binds (perhaps in the lungs), that encourages additional oxygen to bind (up to 3 more) as hemoglobin can carry 4 O2 molecules. When the red blood cell carrying hemoglobin gets to other tissues outside the lung, the increased carbon dioxide diffuses into the red blood cell and through carbonic anhydrase and the production of H+, induces hemoglobin to let go of the oxygen - where the binding stops. The oxygen then diffuses out of the RBC to the tissues.", + "video_name": "LWtXthfG9_M" + }, + { + "Q": "At 11:40 the carbon that takes the 1st H ends up having 5 bonds towards the end. How would that be correct? The last H that he adds in there shouldn't be there. It was a double bond that \"broke\" and an H is added, or did I misunderstand?\n", + "A": "I can t see where any carbon has 5 bonds? Are you sure you counted correctly? Is it the front of back one that originally had the double bond? Note that there looks to be one very long bond from the front carbon to a hydrogen, but that s actually a bond between the front and back carbons, and then a bond between the back carbon and the hydrogen.", + "video_name": "fSk1Crn3R2E" + }, + { + "Q": "\nDoes adsorb mean anything (0:34) or is it just a different pronunciation of absorb?", + "A": "They are different words. Adsorb means to hold molecules of a gas as a thin film on the outside surface of a solid. Absorb means to suck up or soak up. For example, a sponge absorbs water.", + "video_name": "fSk1Crn3R2E" + }, + { + "Q": "I'm confused.... at 6:30 where jay says that Carbon has been reduced as it gained an electron from Hydrogen, I thought C-H interactions were non-polar so they share electrons as oppose to carbon gaining one.... :(\n", + "A": "In reality it does not mean that C-H is non-polar. Because of the small difference in electronegativities, the C\u00e2\u0088\u0092H bond is generally regarded as being non-polar. But theres still a difference in electronegativities. But it doesnt really matter in this case because concerning the oxidation state you simply look at the atom which is more electronegative, which gain more electron.", + "video_name": "fSk1Crn3R2E" + }, + { + "Q": "At 2:10, Sal says that speed is the magnitude of velocity but speed may not always be the magnitude of velocity (as in the case of average speed and average velocity). I'm still a little confused by what Sal meant here\n", + "A": "THe magnitude of velocity is a speed It may or may not be the speed you are looking for in a particular problem", + "video_name": "D1NubiWCpQg" + }, + { + "Q": "\nAt 1:56, Sal said that if he'd written the word velocity rather than speed then the second statement would be true, but if we consider an unbalanced force on a body, so maybe the force will \"only\" change it's direction or the other way around, so i didn't understood that how can we say the unbalanced force will Always impact it's \"velocity\" (speed+direction) when it maybe changing it's direction \"only\" and not the speed or vise versa.\nI hope my question is clear.", + "A": "If the force changes the direction of motion, then it changed the velocity, even if the speed is the same.", + "video_name": "D1NubiWCpQg" + }, + { + "Q": "@7:14 i m bit confuse here like centripetal force balances centrifugal force so here will the ice scater have balanced force............\nnd the speed example was really good\nwant to learn through such examples from daily life\n", + "A": "The forces are not balanced, if they were the skater would have uniform motion and not be accelerating in a circle. Centripetal force is a real force which accelerates an object to travel in a circle. Centrifugal force is fictitious force which is felt from being in a reference frame which is rotating. The perceived centrifugal force is equal and opposite to the centripetal force.", + "video_name": "D1NubiWCpQg" + }, + { + "Q": "at 1:30, sal says the is a minuscule amount of gravity in space, what causes gravity in space? is their any forces apart from the small about of gravity in space?\n", + "A": "If you look at the equation for the gravitational acceleration A = G * M/r^2 you can see that A goes to 0 at an infinite distance so even deep space in not infinity far from any mass so there still be a small amount of gravity out there.", + "video_name": "D1NubiWCpQg" + }, + { + "Q": "At 6:46 in the video, Mr. Kahn mentions 'deceleration' but my science book tells me there is no such thing as \"deceleration.\" It says that there is acceleration in the direction of velocity or in the opposite direction of velocity, but in physics, it is always called acceleration. Which is accurate?\n", + "A": "It s better to talk about negative acceleration but of course people do use the term deceleration and scientists do need to be able to talk to regular people. It s certainly not right to say there s no such thing as deceleration, because everyone knows there is. But that doesn t make the term or concept something we want to use when we are trying to do physics.", + "video_name": "D1NubiWCpQg" + }, + { + "Q": "\nAt 1:01, If the net force on a body is zero, would it have any velocity or would it be a stationary object?", + "A": "it can either be in motion or can also be in rest. force is not required to keep the object which is already in constant velocity in motion thats why they say a object in constant velocity to have a net force of 0", + "video_name": "D1NubiWCpQg" + }, + { + "Q": "At 10:45 Sal said that a hot spot could have created the Mid-Atlantic Ridge as well as the African Rift Valley. The Mid-Atlantic Ridge is much bigger than the African rift valley, so how could the same type of hot spot have created them both?\n", + "A": "A hot spot cannot create a ridge, they create volcanic island chains, Hawaii and its islands are prime examples. The Mid-Atlantic Ridge was created by diverging tectonic plates, the magma which streamed up from the mantel solidified in the ocean and created the ridge.", + "video_name": "FK1s1-OJ5BE" + }, + { + "Q": "\nAround 7:40, Sal says the time taken for the momentum to change is 2x/v, bt isn't the actual time taken that tiny instant it JUST strikes the wall and reverses its velocity?", + "A": "| _.->_| Starting |<-. __| Back at the same point, but not with the same velocity. | _.->_| Back at the same point with the same velocity. The distance traveled therefore must be twice the length. This distance over the velocity component in this direction will be the time required for the average pressure equation.", + "video_name": "qSFY7GKhSRs" + }, + { + "Q": "\nAround 6:31, why is the change in momentum a positive number? if P2 = -mv due to the velocity being in the opposite direction, then should change in momentum not be = P2 - P1, which is -2mv ?? Thanks for helping me out of my misery:-(", + "A": "I have this exact same question, and no one seems to have answered it yet. The only explanation I can come up with is that the negative is just an indication of the direction, and when looking at the force that results from this pressure, a positive value should be used.", + "video_name": "qSFY7GKhSRs" + }, + { + "Q": "isnt it sn=3+2=5 in ~5:40?\n", + "A": "No. Before the electrons move, there are 3 \u00cf\u0083 bonds and 1 lone pair, so SN = 3 + 1 = 4", + "video_name": "kQCS1AhAnMI" + }, + { + "Q": "\n@0:45 is the structure on the left trigonal pyramidal because of the lone pair? is it still a resonance structure with the right given the different pyramidal/planar structures of Nitrogen?", + "A": "If it is not conjugated, the N atom with a lone pair is trigonal pyramidal. If the N atom is conjugated, it is sp\u00c2\u00b2 hybridized and therefore trigonal planar.", + "video_name": "kQCS1AhAnMI" + }, + { + "Q": "\nHow can p orbital from N (4:44) create pi bond if it already has 2 electrons? Confused...", + "A": "What makes you think that would stop it from being able to form a pi bond..? Something to keep in mind in aromatic molecules is that they technically are not double bonds at all, every atom in the ring is sharing the 6 pi electrons because that makes it aromatic, and being aromatic is VERY favourable energetically.", + "video_name": "kQCS1AhAnMI" + }, + { + "Q": "12:25 a willing mother could be one going for an abortion? i mean....instead of killing the embryo,doctors could extract it and utilise the stem cells?? just saying....: )\n", + "A": "Actually no, embryonic stem cells are derived from the surplus embryos not used or not suitable for use from in-vitro fertilization. While a religious person might still consider this immoral, it is not technically the same thing as an abortion.", + "video_name": "-yCIMk1x0Pk" + }, + { + "Q": "at 00:27 seconds, you say that only one sperm can get into the egg. If so, how would a couple get twins?\n", + "A": "Sumangal is right concerning monozygotic or identical twins. In the case of fraternal (dizygotic) twins, the mother produces 2 egg cells that are then fertilized by 2 separate sperm. Each develops in its own amniotic sac with its own placenta (identical twins share a placenta but usually have separate sacs depending on when they divided) and is no more or less identical than any other pair of siblings born at different times.", + "video_name": "-yCIMk1x0Pk" + }, + { + "Q": "\nStarting at 6:34, why did he not use pythagorean theorem to describe V?", + "A": "Good question. The reason he said it this way is because he was referring to vectors and not the magnitude (length) of the vectors. If you want the magnitude, then you are correct in saying that you would need the Pythagorean theorem.", + "video_name": "2QjdcVTgTTA" + }, + { + "Q": "\nso are we sapouse to add up all the small areas to get the total work amount? 7:14\nthanks again", + "A": "Yep, on 7:14 you do.", + "video_name": "M5uOIy-JTmo" + }, + { + "Q": "\nAt 0:59, aren't 3 sulfur atoms called sulfate instead of sulfide?", + "A": "No, the sulfate ion has the formula SO4^2-", + "video_name": "vVTwzjvWySs" + }, + { + "Q": "On the last example at 5:00, what is the difference between 5.60x10^4 and 5.6x10^4\nthat trailing 0 seems pretty important and I don't understand why.\n", + "A": "I understand it simply as how detailed you want your number to be. 5.6 could actually be 5.61 or 5.64, depends on how many decimals you want, and that means that 5.60 is more accurate.", + "video_name": "eMl2z3ezlrQ" + }, + { + "Q": "\nWhat does trans specify at 5:20", + "A": "Trans is a type of isomerism. All it specifies is that it is a type of isomer. Just so you know - Isomers have the same molecular formulae but different structural formulae. Hope that helps.", + "video_name": "z8h7QgevqjM" + }, + { + "Q": "At 4:37, Why did we put the hydrogen molecules opposite to each other? Why not in the same direction?\n", + "A": "NO. This is an equilibrium reaction. Therefore, the most stable molecules will form. Trans is much better then cis....steric repulsion (eclipsed atoms).", + "video_name": "z8h7QgevqjM" + }, + { + "Q": "\nAt 6:28 Sal writes ||a|| = 5. What does '|| ||' mean?", + "A": "It means the magnitude, or length, of the vector. This is the hypotenuse length formed by the vector components.", + "video_name": "xp6ibuI8UuQ" + }, + { + "Q": "At 3:40, Sal mentions that the formula for vectors was a + b = c\nwhere 'a' and 'b' are the horizontal and vertical vectors. But when you add up vector 'a' (3) and 'b' (4) in this problem the don't equal 'c' (5).\n", + "A": "and ply if it forms a right triangle else you use the formula (a^2+b^2+2ab cos{theta})^1/2 which will be equal to the sum of given two vectors", + "video_name": "xp6ibuI8UuQ" + }, + { + "Q": "\nat 3:00 cant we draw vector A from the tail of vector of vector B\nwill there be any difference", + "A": "No. There will not be any difference. If you find the resultant vector with any head-tail arrangement, you ll still get the same resultant vector.", + "video_name": "xp6ibuI8UuQ" + }, + { + "Q": "Starting after 6:00 with the new problem, why were the numbers used so specific?\n", + "A": "Well, for an example, if you take out your calculator and take the sin of a random number, it ll most likely be a non-terminating number and will look like something just vomited random numbers out. I think he used such a specific angle on purpose to get his answer close to 3 in this problem. A nice, whole number is better than something like 3.58912385423168.", + "video_name": "xp6ibuI8UuQ" + }, + { + "Q": "\nAt 5:25, Can the same fusion process that causes Hydrogen to turn into Deuterium and then Helium continue past Helium and make all the elements given enough gravity?", + "A": "Yes, the next few videos explain it pretty well.", + "video_name": "i-NNWI8Ccas" + }, + { + "Q": "\nIn 1:14 you have said that the atoms condense. But condensation happens only when temperature reduces. But you have said temperature increases. Aren't they contradicting?", + "A": "Not condensation as the moisture that appears on cool objects. Condensing as in the atoms fill a smaller volume, getting denser. This builds up pressure, which builds temperature.", + "video_name": "i-NNWI8Ccas" + }, + { + "Q": "At around 5:37, what is a nucleon? Sorry if I missed it in another video...\n", + "A": "A nucleon is a particle that exists in the center of an atom, like a proton or neutron.", + "video_name": "i-NNWI8Ccas" + }, + { + "Q": "At 3:52, Sal says that one of the protons degrades into a neutron - how does that happen?\n", + "A": "The instability essentially forces one of the constituent up quarks to decay into a down quark, resulting in a proton becoming a neutron.", + "video_name": "i-NNWI8Ccas" + }, + { + "Q": "At 5:56, why it wouldn't form tritium from deuterium?\n", + "A": "It can if a free neutron fuses with deuterium. But free neutrons aren t readily available at the early stages of stellar fusion, and tritium is unstable and will decay to Helium-3.", + "video_name": "i-NNWI8Ccas" + }, + { + "Q": "@ 0:18 sal is talking about gravity...well, what type of gravity is present in the stars...?\nand how these hydrogen atoms are attracted to each other due to gravity...?\n", + "A": "There is only one type of gravity Hydrogen atoms are attracted to each other because they have mass All mass attracts other mass. That s what gravity is.", + "video_name": "i-NNWI8Ccas" + }, + { + "Q": "\nAt 2:20, why don't the positivily charged nucleuses want to go any where near each other?", + "A": "The positively charged nuclei don t want to go anywhere near each other because both of them a positively charged, and just like a magnet, positives don t attract each other.", + "video_name": "i-NNWI8Ccas" + }, + { + "Q": "\nat 3:40 sal says when the fusion occurs, the atoms that fuse weigh a little bit less. One of the atoms turns into a neutron. Where does that extra weight go? Is it turned into energy or another substance? If it's energy it needs to have weight and that's not possible.", + "A": "Well, that doesn t exactly happen, You must have got confused between Beta decay and fusion, where the proton emits a positron and turns into a neutron. But that isn t exactly the case over here. The fusion occurs when two hydrogen atoms fuse together, and no weight is lost either.", + "video_name": "i-NNWI8Ccas" + }, + { + "Q": "\nat 0:45 why does cloud get dense", + "A": "because of the forces of attraction acting over forces of repulsion in between the two nucleus and this works because the size is massive.", + "video_name": "i-NNWI8Ccas" + }, + { + "Q": "\nAt 0:03, it is said that we consider that two things have the same charge. What if they are not of the same charge? Will like charges not repel each other in that case? And opposite charges attract each other?", + "A": "Like charges always repel. Opposites always attract.", + "video_name": "2GQTfpDE9DQ" + }, + { + "Q": "At 11:13, why does the final answer have two significant figures when the measurements only have 1 significant figure? I thought that, when multiplying or dividing significant figures, the result can only have as much significant figures as the measurement with the least amount of significant figures (which in this case is 1).\n", + "A": "sal often makes mistakes with sig figs", + "video_name": "2GQTfpDE9DQ" + }, + { + "Q": "In 11:04s why the [10^-4*10^-1] do not have to take off the minus sign? Isn't it a absolute value?\n", + "A": "There is a modulus sign there so -tive ans will not be considered\u00f0\u009f\u0098\u008a", + "video_name": "2GQTfpDE9DQ" + }, + { + "Q": "\nAt 8:28: The Coulomb's Law equation is used to calculate the electrostatic force (in Newtons) between two charges. But is there an independent way to measure this force (and thus verify that Coulomb's equation is correct)?", + "A": "You could think about lot of ways of measuring this, you could set the two charges (known charge) at a known distance and use a spring to keep them in place, you could extrapolate the force through the hook law, by knowing the constant or the spring. Or,for not depending on hooke law you could put your guessed Force(given by the Coulomb\u00c2\u00b4s equation) in the way of weight, and see if a spring , identical to the ones in the beginning , elongated the same, if it does the formula is correct.", + "video_name": "2GQTfpDE9DQ" + }, + { + "Q": "is there any mistakes on this video?\nI guess after meiosis I, you duplicate one diploid cell to two diploid cell; so that for meiosis II, each of two diploid cell will be \"simplified\" to four haploid cell? (4:14)\n", + "A": "Yes, two division events occur. You start with a replication of DNA, then divide the cells so you have 2 diploid cells, then you divide each of those cells to get 4 haploid cells.", + "video_name": "IQJ4DBkCnco" + }, + { + "Q": "\nAt 4:22, it's noted that the cells at the end of meiosis II become gametes. Why can't the cells produced at the end of meiosis I become gametes, if they're also haploid cells? And if meiosis isn't a cycle, how can so many gametes be produced--are there just a ton of diploid cells undergoing meiosis?", + "A": "Prior to a cell division of a diploid cell, chromosomes are duplicated and condensed. In meiosis I homologous chromosomes swap chunks of genes with each other (called crossing over), then they are randomly assorted into two cells. Meioses II is responsible for separating the sister chromatids of a chromosome (of the two cells formed in meiosis I) yielding two more cells that are also haploid, for a total of four haploid cells.", + "video_name": "IQJ4DBkCnco" + }, + { + "Q": "\naround 2:40, sal says that each of the two cells after the first division has 23 chromosomes. I thought that during S1 the parent cell duplicates its chromosomes to 46 pairs, 92 total, while still being 2n, and then the homologous pairs split and the two cells then each has 46 chromosomes 2n. Then after meiosis 2 each of the four daughter cells has 23 chromosomes. Is this correct?", + "A": "The chromosomes are still considered 1 because they are connected. The sister chromatids are just split apart.", + "video_name": "IQJ4DBkCnco" + }, + { + "Q": "at 0:02 sal sayes arbitrary amino acids. what does that mean?\n", + "A": "Any of a class of organic compounds that contains at least one amino group, \u00e2\u0080\u0093NH 2, and one carboxyl group, \u00e2\u0080\u0093COOH: the alpha-amino acids, RCH(NH 2)COOH, are the building blocks from which proteins are constructed. Your welcome!", + "video_name": "nv2kfBFkv4s" + }, + { + "Q": "\nAt about 13:35 when he says it's intuitive for Heat to be represented as Q, because heat does not start with Q, was he being sarcastic, or am I missing some reason as to why Q is heat?", + "A": "Sal is being sarcastic about Q being an intuitive representation of heat, since Q is completely unrelated to the word heat. However, he is serious about the use of Q to represent heat, as an accepted method.", + "video_name": "Xb05CaG7TsQ" + }, + { + "Q": "At 2:50 why does he round the mass of the elements? Isn't it more accurate to keep it unrounded?\n", + "A": "He does that to make the examples easier to follow. In real calculations you cannot do that. It is standard practice to use 4 significant digits for your atomic masses, unless your problem requires using more.", + "video_name": "jFv6k2OV7IU" + }, + { + "Q": "\n2:15 , 4:40 , 8:42 ! Why is the Charge on each of the individual Capacitors in series is SAME as the charge on the Equivalent Capacitor ?\nFull video is on this Idea!!\nBut, Why ?", + "A": "Picture each conductor with one end at a capacitor plate, and the other end at another plate. Since this conductor needs to be with total charge 0, then if the plate at the right has charge +Q, the other must have charge -Q. Thus, the charge of each pair of plates is the same.", + "video_name": "-MaD9Ycy3a4" + }, + { + "Q": "\nAt 6:32, why is the charge stored on each of the individual capacitors equal to the charge stored on the equivalent capacitor? Why aren't the charges divided between the four- like each one has 192/4 C of charge?", + "A": "NO, remember that the Capacitance unit is F, not C, So basically you messed up, you should NOT sum like this, they have the same amount of Charge NOT Capacitance. So you add (1/48F) + (1/16F) + (1/96F) + (1/32F) = 0.125F, Then taking the reciprocal you get 8F which is the equivalent of CAPACITANCE. When you try to find the Voltage you do this ( 192/48 ) + ( 192/16 ) + ( 192/96 ) + ( 192/32 ) = 24v which is the same voltage of the battery. I Hope that helped!", + "video_name": "-MaD9Ycy3a4" + }, + { + "Q": "\nAt 6:19 why does Sal not put 3d10 instead of 4s2 and then 3d8? Does it make a difference which way you do it?", + "A": "Yes, it makes a difference. 3d\u00c2\u00b9\u00e2\u0081\u00b0 means 10 electrons in the 3d orbitals. 4s\u00c2\u00b2 3d\u00e2\u0081\u00b8 means two electrons in a 4s orbital and 8 electrons in the 3d orbitals. Since the 4s orbital is lower in energy than the 3d orbitals, the 4s orbital gets filled up first. 3d\u00c2\u00b9\u00e2\u0081\u00b0 would represent an excited state of the atom.", + "video_name": "YURReI6OJsg" + }, + { + "Q": "what does he mean by \"go back to fill the previous shell, so subtract 1\" at 2:27\n", + "A": "when the shells are filled, there are certain spots, where are still no electrons, the d and f blocks fill up those spots(because thats closer to the nucleus).", + "video_name": "YURReI6OJsg" + }, + { + "Q": "For the element Zr, discussion starting around 7:50, energy level 5s (5s2) is filled before level 4d (4d2). Will the electrons \"peel\" in the opposite order that they're \"put on\"? or will 5s electrons \"peel\" before 4d electrons? for this element, which would be considered the valence electrons? Thanks.\n", + "A": "The electrons fill in that order, but when they are used in bonding ( peeling? ), the electrons with the highest quantum number (period 5 before period 4 electrons) are used first. So the 5s2 will be used before the 4d electrons.", + "video_name": "YURReI6OJsg" + }, + { + "Q": "at 2:07 why do we fill 4s orbital 1st than 3d ?\nand if we do so why do we consider 4s as the valence shell and not 3d??\n", + "A": "We put them in that order because that is the order they actually fill up in. The 4s is very much valence. A partially filled 3d is counted as valence electrons by some scientists but not by others. The reason for the disagreement has to do with the way that d electrons get involved in chemical reactions -- it is not as straightforward as what happens with the outermost s and p orbitals.", + "video_name": "YURReI6OJsg" + }, + { + "Q": "How did Sal at 2:00 know the third shell was not full? Why does the formula 2(n)^2 determine the shells max capacity?\n", + "A": "Sal was using the relative energy levels of the different orbitals to explain the order in which they are filled. The empty 4s orbital is of slightly lower energy than the empty 3d orbitals so is filled first. The formula you quote works simply because of the algebraic relationship between n and the magnetic quantum number.", + "video_name": "YURReI6OJsg" + }, + { + "Q": "\nAt 8:01 Sal says you have to minus 1 from the period for d. Why is this?", + "A": "It s just how it goes. The 3d orbitals happen to be about the same energy as the 4s orbital. Similar story for the 4d and 5s etc.", + "video_name": "YURReI6OJsg" + }, + { + "Q": "At 2:30, Sal says that in the d-block, the period is subtracted by 1. Why is this the case and how was it calculated?\n", + "A": "Because the 4s2 orbital electrons are in a higher energy state than the 3d8 orbital electrons, so they are further from the nucleus. So instead of 4d8, it s 3d8 (-1, as in lower energy). The 4s2 orbital only fills with electrons before the 3d8 orbital", + "video_name": "YURReI6OJsg" + }, + { + "Q": "\nIs there any difference between \"3-phosphoglycerate\" (3:17), and Glycerate 3-phosphate (which is what I have in my textbook)?", + "A": "no they are theoretically the same thing with just a slightly different structure (isomerization)", + "video_name": "DnNqe8o0ehc" + }, + { + "Q": "At 4:41\nhow can three different orientation of the same sub shell exist at the same time?\nIn other words how can the sub shell be aligned at the x-axis, the y-axis and z-axis at the same time.\n", + "A": "Because there are exactly three p orbitals per shell (except the first)", + "video_name": "qLU0X154wlE" + }, + { + "Q": "\n@ 1:07 Sal says that when silk is rubbed with glass for long, one of the objects might discharge on touching another object ? What does that mean ?", + "A": "That means that the charges are transferred to the earth through that object.", + "video_name": "IDQYakHRAG8" + }, + { + "Q": "\nAt 6:35... when the hair losing electrons , does that affect on the structure of the hair because the atoms of the hair lost electrons ?", + "A": "great question! My answer is this. I dont think it would; with these reasons a) the electrons come from surface of the hair not from inside. So it is less likely to effect structure. b) although the effect is strong , the actual number of electrons exchanged is relatively small. c) your hair is possibly being charged up many times a day as objects (including the wind) rub against it and no harm seems to come of it. ok??", + "video_name": "IDQYakHRAG8" + }, + { + "Q": "\nAt 2:57 why did Sal said like charges are going to repel (It is just a convention). Why can't they attract each other.", + "A": "They just don t. It s like asking why does gravity pull mass together instead of repel them. That s just not how it works. Like charges repel, and unlike charges attract. Why they do that, we don t know.", + "video_name": "IDQYakHRAG8" + }, + { + "Q": "How does top part of the hair have positive charge and bottom part have negative charge and doesn't the hair build up tension at 6:51?\n", + "A": "By rubbing the balloon electrons move from your hair to the balloon. The top of the hair becomes positively charged because they are attracted to the negative charge of the balloon. The negative ions still in the hair are repelled from the negative charge of the balloon. Yes, it will a little bit!", + "video_name": "IDQYakHRAG8" + }, + { + "Q": "At 6:38, why we got different masses for different points? Aren't they the same? because they are all on the same ball.\n", + "A": "Great question. If you sliced up the baseball into lots of little chunks, then, if you were careful, you might be able to make every chunk have the same mass. But dividing a sphere into many, many little pieces that all have the same volume (and thus mass if the density is constant) is very difficult. So it would probably be the case that each small mass element would have a different mass.", + "video_name": "o7_zmuBweHI" + }, + { + "Q": "dose that dash preforms away must be three lines? or it can be random dashes?\nat 2:40\n", + "A": "It doesn t have to be three lines, just dash it :-)", + "video_name": "ZAgQH2azx3w" + }, + { + "Q": "at around 3:30 he calls carbon-12 an isotope, but i thought that isotopes were defined as atoms that have more neutrons than protons in their nucleus. carbon-12 has 6 protons and 6 neutrons in the nucleus, why is it an isotope?\n", + "A": "All atoms are isotopes. Isotope simply refers to the specific number of nucleons for a given atom. It doesn t matter if the number of neutrons is more, less or equal to the number of protons, or if there are no neutrons, the atom is still a specific isotope.", + "video_name": "NG-rrorZcM8" + }, + { + "Q": "\nAt 3:29 in this video Sal says that an Atomic Mass Unit is a very, very small fraction of a gram; but in an earlier video he said that an Atomic Mass Unit was a very, very small fraction of a kilogram. So what exactly is an Atomic Mass Unit a very small fraction of?", + "A": "A gram is a small fraction of a kilogram (1/1000) So both of those statements you mentioned are true, aren t they?", + "video_name": "NG-rrorZcM8" + }, + { + "Q": "At 3:35 Sal references carbon-12 as being an isotope. Why is carbon-12 considered an isotope? The number of protons matches the number of neutrons in the nucleus.\n", + "A": "Every atom is an isotope. It has nothing at all to do with the number of protons matching the number of neutrons. There is nothing special at all about having equal protons and neutrons. There are quite a few elements whose most common isotopes happen to have that, but if you look at the periodic table you will see that as the elements get heavier you tend to have more neutrons than protons.", + "video_name": "NG-rrorZcM8" + }, + { + "Q": "I thought atomic weight is determined using the relative abundances of only stable isotopes of elements. At 7:16, Mr. Khan says that the weighted average of C-12 and C-14 is used to obtain the atomic weight of carbon. Is this a mistake? The only stable isotopes of C are C-12 and C-13. C-14 is radioactive.\n", + "A": "Atomic weight is determined using the relative abundance of the element as it occurs in nature. Highly unstable isotopes will only be found in very small amounts in nature, because they will have decayed. C-14 has a half-life over 5000 years and it is constantly produced in the atmosphere, so a small amount of the natural carbon is C14", + "video_name": "NG-rrorZcM8" + }, + { + "Q": "\nat 6:28 you explained that carbon 12 has 6/ neutrons and protons each. so doesnt it make a balanced atom but you are saying its an isotope??", + "A": "All atoms are isotopes. There is no such concept of a balanced atom as far as protons and neutrons are concerned. There are stable isotopes, but stability can apply to multiple isotopes, and the ratio of protons to neutrons varies as the atomic size increases.", + "video_name": "NG-rrorZcM8" + }, + { + "Q": "At 0:55, he says it's confusing when you go to Europe, where they use the metric system to give you their weight. Why is it different if you were say in the USA where they use pounds? Are pounds a form of mass or weight??\n", + "A": "I suppose it s because Sal is based in the USA so therefore he sees weight from the US pound perspective.", + "video_name": "NG-rrorZcM8" + }, + { + "Q": "\nat 2:58 , can the (CH3)2CHOH also be (CH3)2 CH2O?", + "A": "The -O- is connected to the -C-. One -H- is connected to the -C- , while the other -H- is connected to the -O-. In short : No.", + "video_name": "XEPdMvZqCHQ" + }, + { + "Q": "At 5:28, Jay says that the lone pairs for Oxygen can form a pi bond between Oxygen and Carbon. Why can't they form pi electrons inside the Benzene ring?\n", + "A": "If the electrons in the C=O pi bond (from the oxygen lone pair) were pushed into the ring, that would leave oxygen with a +2 charge and an incomplete octet. This would be very unstable so does not happen.", + "video_name": "i9rfWOAEplk" + }, + { + "Q": "At 2:40, would not natural selection cause organisms that were attracted to useless traits to drop out of the gene pool? Organisms attracted to useful traits would survive and sexual selection would no longer be a factor as being attracted to useful traits would actually make the organism fitter, thereby making it natural, and not sexual, selection.\n", + "A": "No. Other ones with okay mutations wouldn t drop, so the gene pool gets rid of REALLY useless organisms.", + "video_name": "tzqZsPjHFVQ" + }, + { + "Q": "\nIs the cyclical form of ribose a furanose ? And where does the Oxygen attached to Carbon 2 goes ? I guess the Hydrogen attached to Carbon 2 in deoxyribose form is not the same from the O-H. 08:56. So, where does the Hydrogen comes from? Thanks.", + "A": "I think it is because the phosphate groups are negative and hydrogen is a positive ion, so it attracts it.", + "video_name": "L677-Fl0joY" + }, + { + "Q": "At around 0:26 in the video, why does Sal do \"deoxy\" and \"ribo\" in two different colors? Isn't deoxyribose one word and one type of sugar?\n", + "A": "he is separating the roots of the word. deoxy means lack of oxygen and ribo, I think means with sugar, and you know acid. So, therefore, it is a lack of acid, with sugar and acid.", + "video_name": "L677-Fl0joY" + }, + { + "Q": "\nAt 11:34, can we classify Adenine and Guanine as Purines and Cytosine and Thymine as Pyrimidines", + "A": "Yes, that s how they are classified.", + "video_name": "L677-Fl0joY" + }, + { + "Q": "at 0:50 he dose not go deeply into what reactants are\n", + "A": "Reactants are the things that react together in a reaction. They are on the left side of a chemical equation.", + "video_name": "TStjgUmL1RQ" + }, + { + "Q": "At 6:35 what are the reactants and products in reversible reaction?\n", + "A": "Typically, you name the ones on the left the reactants and the ones on the right the products, although they are technically both reactants and products. See also which chemicals you start with, and these will be your reactants. Alternatively, those being reduced in concentration to suit the equilibrium are the reactants.", + "video_name": "TStjgUmL1RQ" + }, + { + "Q": "\nat 3:30 Sal said energy is provided but from where does it come from?", + "A": "Humans e.g. a spark of fire (Heat) can overcome the activation energy to kickstart the reaction and allow it to occur spontaneously from that point forward", + "video_name": "TStjgUmL1RQ" + }, + { + "Q": "At 2:37 he calls the water molecules, but later calls them compounds. What is the difference between a molecule and a compound, and why is he able to call water both names?\n", + "A": "A molecule made of more than one element is a compound. Water is a compound of hydrogen and oxygen.", + "video_name": "TStjgUmL1RQ" + }, + { + "Q": "\nAround 8:30, he mentions that carbolic acid is good for your body. But how does it help our bodies?", + "A": "For digestion", + "video_name": "TStjgUmL1RQ" + }, + { + "Q": "what happens if at 8:15, you didn't have the valves? what would happen to you blood\n", + "A": "If you didn t have the valves, your blood might flow backwards. Your blood might not get the oxygen it needs from the respiratory system. Also, the muscles in your body might not receive the oxygen it needs to expand and contract if the oxygenated blood is flowing backwards and away from the muscle tissue that needs oxygen to move. This will also cause the pressure in the circulatory system to be unstable. Hank talks about this at 8:16.", + "video_name": "L1qpKn2hNF0" + }, + { + "Q": "\nwhat does the sub exponent thing do? (at 1:24)", + "A": "The subscripts on a and b allow you to have lots of different coefficients without using up all the letters of the alphabet. All the cosine terms have coefficients named a_sub_something and all the sine terms use b_sub_something. This way of naming is handy for talking about the terms in order: the 0th term, the 1st term, etc.", + "video_name": "UKHBWzoOKsY" + }, + { + "Q": "\nat 7:55 the second molecule is determined to be di-substituted. How come the methyl group on the second carbon is not counted in to be tri-substituted?", + "A": "It is the number of carbon atoms directly attached to the double-bonded carbons that determines the degree of substitution. C-1 has no C atoms attached to it. C-2 has two C atoms attached to it ( a methyl and an ethyl group). Total attached atoms = 0 + 2 = 2. So the alkene is disubstituted.", + "video_name": "MDh_5n0OO2M" + }, + { + "Q": "\nIn the equation shown at 1:52, why is H2O formed and not H3O+? How would I know which to write as a product?", + "A": "Acid + base -> salt + water This is something you should memorise", + "video_name": "aj34f2Bg9Vw" + }, + { + "Q": "At 0:32 he said lesser and great apes. What is the difference between lesser and greater apes?\n", + "A": "The great apes are chimpanzees, gorillas, humans, and orangutans. The lesser apes are gibbons.", + "video_name": "oFGkYA_diDA" + }, + { + "Q": "\nAt 4:00sec why did you take the force(10n) as kg.m/s2", + "A": "That s what a Newton is. It is 1 kg*m/s^2. It s the force you need to apply to 1 kg to get it to accelerate at 1 m/s^2.", + "video_name": "ou9YMWlJgkE" + }, + { + "Q": "AT 3:23 HOW CAN WE WRITE F=M^2*A^1/2\n", + "A": "We can t, that was just an example of a more complicated equation that, in another universe, could have been the relationship between mass, force, and acceleration. He mentioned it just to point out how simple the real equation, F=ma, was.", + "video_name": "ou9YMWlJgkE" + }, + { + "Q": "\nAt 1:58 what does netforce mean?", + "A": "net force means total force. remember that forces can cancel each other out as well if opposing forces act upon an object. for example, if your bank account is overdrawn by $100 and you deposit $100, your net amount will be $0 (-100+100=0), forces behave in the same way depending on their magnitude (size) and direction (which direction they act on an object).", + "video_name": "ou9YMWlJgkE" + }, + { + "Q": "\nIn many Khan academy videos, Sal does what I belive is called a dimensional analasis (5:10 in this video), and while I understand how this works, I cannot find anything on this site about where to use them, and the rules for doing so. Help?", + "A": "The rules of it are just the rules of algebra. You should use it pretty much all the time when you are doing physics problems. It provides a good check on your answers. If the units don t come out right, you did something wrong.", + "video_name": "ou9YMWlJgkE" + }, + { + "Q": "At 4:00 why are seconds squared?\nAnd what does Seconds^2 mean? Other then Second * Seconds.\n", + "A": "F = ma. Force is mass times acceleration. Acceleration is change in velocity over time. Velocity is distance over time. So acceleration is change in distance over time over time, or distance over time squared.", + "video_name": "ou9YMWlJgkE" + }, + { + "Q": "At 1:15, the second law of motion is stated. How is this equation derived?\n", + "A": "It s not derived, it s an empirical observation.", + "video_name": "ou9YMWlJgkE" + }, + { + "Q": "\nat 14:12 , to get the value of T2 cant we just assume that mg=T1+T2 i.e. 30N=60N+T2?\nThat would be T2=-30N..... would that be wrong?", + "A": "Yes that would be wrong because you have to separate forces and tensions acting on the x-axis from those acting on the y-axis. That has to be done because forces and tensions acting on the x-axis have no effect on those acting on the y-axis (at least as long as they act on the same point of the object). T2 is horizontal so it acts on the x-axis, mg is vertical so it acts on the y-axis and T1 actually acts on both the x-axis and the y-axis which is why David had to break it into its components.", + "video_name": "aHlOp5nYs28" + }, + { + "Q": "\nAt 11:31 mvr = Iw. What is the Iw stand for?", + "A": "moment of Inertia*angular velocity", + "video_name": "viLpmZtQYzE" + }, + { + "Q": "At 10:10, David says that there is no external torque exerted on the system. But, isn't the mass exerting torque on the system by hitting the moment arm?\n", + "A": "The system includes the mass, so the mass is not external to the system, although it is external to the rod. This is why the angular momentum of the rod can change without violating conservation of momentum, but the combined angular momentum of rod plus mass cannot.", + "video_name": "viLpmZtQYzE" + }, + { + "Q": "\nAt around 09:00 , the second step of the Sn1 reaction, I was just wondering if instead of a new metanol, an Iodide could come and take the proton away? Isn't that even more electronegative than the metanol? And if so, which of the two happens more often? Thank you", + "A": "Yes, an iodide ion could certainly remove the proton. but you must remember that the solvent is methanol, so there are many more methanol molecules than iodide ions present in the solution. Also, the cation is probably solvated by a shell of methanol molecules. The probability of the H being attacked by a methanol molecule is therefore much greater than the probability of being attacked by an iodide ion.", + "video_name": "MtwvLru62Qw" + }, + { + "Q": "\nAt 13:20 Sal showns that the change in entropy after the cycle is (2Q_f)/T. The left side of the equation is a subtraction, not an addition like in the last video. In the last video, he showed that the change in entropy is equal to Q_1/T_1 + Q_2/T_2. What's going on here? These are clearly not the same. This doesn't make any sense.", + "A": "In this video Sal talks about irreversible system. That s where (2Q_f)/T comes from: it s a heat generated by friction. About the signs of Q: in the previous video Sal puts a plus sign in front of the Q, but actual value of Q is negative (he actually mentioned that we ll see its actually negative somewhere in the video). In this video Sal assumes the value of Q to be positive (as he mentions at about 10:20, so he puts a negative in front.", + "video_name": "PFcGiMLwjeY" + }, + { + "Q": "\nAt 1:29, it's said that heat is released (Q2), and right after he says that the change is adiabatic, and no heat is being transferred to and from the system. Isn't that contradictory?", + "A": "He was pointing to the horizontal paths when talking about heat transfer, but was pointing to the vertical paths when talking about the adiabatic paths.", + "video_name": "PFcGiMLwjeY" + }, + { + "Q": "at 6:27, how 2sp2 and why not 2sp3?\n", + "A": "sp3 is in the case of a single bond sp2 is in the case of the double bond sp is in the case of a triple bond", + "video_name": "lJX8DxoPRfk" + }, + { + "Q": "From 11:20 to 12:06, why do pi bonds pull the nuclei of the two carbons in ethylene closer together? Wouldn't the electrons be repelling each other?\n", + "A": "pi bonds occurs when there is a parallel bond between two p orbitals.We know that an orbital is nothing but a probability cloud representing possible positions of electrons.Now, because in the pi bonds the two p orbitals overlap, this would mean that in that particular region there is a higher possibility of finding an electron.More electrons (-ve charge) would attract the nuclei of the two atoms more strongly, thus bringing them closer.This is also the reason of why these molecules are smaller. Hope this helped...!", + "video_name": "lJX8DxoPRfk" + }, + { + "Q": "At 6:57, how do you find the probability, and if you use probability would the answer be accurate?\n", + "A": "You don t! You measure the concentrations experimentally. Sal s use of probabilities here was just a way of trying to get you to intuitively understand why the expression for the equilibrium constant looks the way it does.", + "video_name": "ONBJo7dXJm8" + }, + { + "Q": "\nIf at around 11:20, Sal divided by [Y]^c [Z]^d, wouldn't that change the answer? But then again a constant divided by a constant is another constant. So couldnt the equilibrium constant be the reciprocal of what it actually is?", + "A": "If he had divided by [Y]^c[Z]^d instead, he d end up with the reciprocal, yes. This, however, gives the equilibrium constant for the reverse direction of the reaction, i.e, the products reacting to form the reactants. As a general rule, the equlibrium constant for the reverse reaction is equal to the reciprocal of the equlibrium constant of the forward reaction.", + "video_name": "ONBJo7dXJm8" + }, + { + "Q": "\nAt 9:00, what does the Keq stand for?", + "A": "The Equilibrium Constant K", + "video_name": "ONBJo7dXJm8" + }, + { + "Q": "@ 5:00 sal says that the concentration is a rough approximation of the probability. But what if Concentration is greater than one? we know that probability is always less than or equal to one. Then how can concentration be an approximation for probability in that case?\n", + "A": "If you think of concentration as the number of molecules of the substance of interest divided by the number of all other molecules in the mixture then concentration will have the same limits as probability, that is, between 0 and 1.", + "video_name": "ONBJo7dXJm8" + }, + { + "Q": "\nat 4:40,sal says when sun is just setting,why not observe it as sun is just rising; like in the previous case?", + "A": "If you looked at the star as the sun was rising exactly 6 months later, while on the other side of the sun, you would be facing the wrong direction. At 5:21, Sal says that at sunset 6 months later straight up is the same direction .", + "video_name": "ETzUpoqZIHY" + }, + { + "Q": "\nAt 3:46, the switching on and off is called pulse-width modulation, right?", + "A": "That is correct.", + "video_name": "a16uKH2K7gM" + }, + { + "Q": "@7:30 ish, if it was a high frequency, why would we hear? I thought we couldn't hear high frequencies and only certain animals could or is that just a myth?\n", + "A": "He is saying that the high frequency affects other electronic devices, such as radios, it would have the same effect as when you are getting a phone call or message when you are near the radio.", + "video_name": "a16uKH2K7gM" + }, + { + "Q": "At 1:13 how does a radio uses electricity and how much ?\n", + "A": "it uses 5watt-hours, or after 200 days of such use", + "video_name": "a16uKH2K7gM" + }, + { + "Q": "\nAt 0:24, the hydrogen atom is represented by the Bohr model but isn't the Bohr model incorrect because electrons are actually not orbiting the nucleus in a circle and actually can behave as a wave as well? Then why is this model used?", + "A": "Because the Bohr model will help you explain basic things in Chemistry. You could use a quantum mechanical model of an atom or even think of electrons as cloud charges instead of having a particle-wave duality --- but why would you if a simpler model can suffice? Models are (almost) always wrong, not just in Chemistry either, and that s OK because they are supposed to help you understand and a Bohr model will do this.", + "video_name": "AznXSVx2xX0" + }, + { + "Q": "5:25 what is brass?\n", + "A": "Brass is basically an alloy of copper and zinc. If you do not know what an alloy is, it is just a metal formed by mixing two or more other metals to give it a special property. Steel for example is an alloy as well and its purpose is as you might know, is to make it super hard! Hope this was informative", + "video_name": "qLMsZKx_a8s" + }, + { + "Q": "at 9:08, when you say force, are you talking about the net force?\n", + "A": "yes, as a body is constantly acted upon by a number of forces at any instant, it is rather easier to calculate net fore than the individual forces", + "video_name": "Mz2nDXElcoM" + }, + { + "Q": "what is happening at 4:50?\n", + "A": "At 4:50 Sal was finishing talking about the supposed formation of the Earth, and started talking about the supposed extinction of the dinosaurs.", + "video_name": "DRtLXagrMHw" + }, + { + "Q": "\n2:10 How can we know at what time humans had evolved to the point that they were \"modern humans\" who appeared and thought in similar ways to the way we did today? How can we really project an estimate for something like that? Evolutions is really a gradual process, and people say that we are still evolving now.", + "A": "Highly sophisticated, beautiful paintings of animals found in caves in Europe have been dated back 40,000 years. That says to me that modern humans have been around for at least 40,000 years.", + "video_name": "DRtLXagrMHw" + }, + { + "Q": "\nAt 6:40,how is velocity 19.6m/s if time is zero ?", + "A": "You can start the stopwatch whenever you want, right?", + "video_name": "T0zpF_j7Mvo" + }, + { + "Q": "At 14:06 in the video, Sal says the velocity is decreasing at a constant pace. Isn't it really decreasing gradually, and then increasing gradually in the opposite direction?\n", + "A": "isnt that the same thing? Think about the acceleration. What is its value throughout?", + "video_name": "T0zpF_j7Mvo" + }, + { + "Q": "Around near 2:40,if both the vectors point toward the centre of circle i,e gravity,what will be the force on the Wooden floor then?\n", + "A": "Newton s Third law says that if the Wooden floor is exerting a force on the ball then the floor is exerting the same amount of force on the ball.", + "video_name": "Xpgsg-fY4DY" + }, + { + "Q": "\nat 11:44 when Hank is describing the electron configuration chain I got lost what exactly is happening and where is the ATP being produced?", + "A": "ATP is produced in the mitochondria inside the cell.", + "video_name": "CIyAs0bxeoI" + }, + { + "Q": "\nat 3:57 Hank is saying that usually 29-30 molecules of ATP produced for 1 glucose, but if it was a best scenario it would be 38 ATPs, so where do the rest ATPs are going, why there is not always 38?", + "A": "People are still studying this topic.", + "video_name": "CIyAs0bxeoI" + }, + { + "Q": "\nHow do you know when to do a hydride shift? Couldn't you of just moved the Cl where the positive charge is in the second hexane? 6:28", + "A": "You want the most stable carbocation - meaning you want that positive charge to be on a carbon connected to as many other carbons as possible, or to be resonance stabilized. That hydride shift happens to move the positive charge onto the most stable carbocation (from the secondary to the tertiary carbon).... Tertiary > Secondary > Primary being the order of preference there.", + "video_name": "iEKA0jUstPs" + }, + { + "Q": "At 12:00 carbon at 1 is categorized as tertiary because it is connected to 3 other carbons (implies connection to ring (connection beyond zigzag) is not taken into account. However, later at 12:42 carbon 1 is said to be connected to 3 other carbons and hence tertiary while according to earlier logic the connection to the ring should not be counted and so carbon #1 is not tertiary it is secondary. What am I missing?\n", + "A": "That carbon 1 at 12:00 is quaternary, but he seems to be talking about where the prefixes might come from not the actual classification of those carbons.", + "video_name": "joQd0qVnX4M" + }, + { + "Q": "\nAt 1:05, why is the longest carbon chain consisting of only 2 carbons? Why cant it be 3 carbons?", + "A": "You number the continuously-attached carbons of the side-chain from the carbon that is attached to the main chain. If you start at C-1, you can go out only one carbon with your pencil. To get to the third carbon without removing your pencil, you would have to re-trace your steps back to C-1, and that is not permitted.", + "video_name": "joQd0qVnX4M" + }, + { + "Q": "At 12:48, isn't that carbon bonded to 4 carbons\n", + "A": "no it bonded to 3 carbons and the extra one available bond is attached to hydrogen , and this is why its called Primary", + "video_name": "joQd0qVnX4M" + }, + { + "Q": "\nAt about 8:45 in the video i just wanted to verify that FADH is being created and not FADH2. Is the 2 supposed to be out in front of the FADH?", + "A": "It s easy to get these confused, because two things are created: NADH and FADH2. The 2 should appear as a subscript (as in, there are 2 hydrogens). In addition, plants don t use NAD+/NADH, they use NADP+/NADPH. Just remember, at the end of the day, these molecules are very similar in their function, as they all contribute to the electron transport chain (next video).", + "video_name": "juM2ROSLWfw" + }, + { + "Q": "At 8:32 , Sal says that FAD is oxidised to FADH2 when before he mentioned that the NAD+ molecules are reduced to NADH2. This seems contradictory to me since they both involve the gain of hydrogen, therefore wouldn't that mean that both the NAD+ and FAD are reduced? If so then how do my notes say that the CAC includes oxidations which generate high-energy electrons that will be used to power the synthesis of ATP ?\n", + "A": "Oh I think I get it now,,, they are produced by reduction making them high electron carriers and they are then oxidized in the ETC for synthesis of ATP. Thanks :)", + "video_name": "juM2ROSLWfw" + }, + { + "Q": "\nat 08:37 sal says FADis oxideised......but FAD is gaining proton...so as per the rule(OIL RIG) reduction is gaining proton so FAD will be reduced not oxidised.", + "A": "Oxidation and reduction involve the lose or gain or electrons, not protons. What Sal is saying is that in the Krebs cycle, FAD is first reduced and gains electrons becoming FADH2, which it later looses (is oxidized) for the electron transport chain.", + "video_name": "juM2ROSLWfw" + }, + { + "Q": "\nAt 5:00 you say the force to move the particle towards the charge needs to be equal and opposite to the force being pushed out...but shouldnt it be greater? Shouldnt the force needed to move the particle towards the charge be greater since equal and opposite forces would just cancel each other out?", + "A": "Equal and opposite force pairs do not cancel out because they don t act on the same object. The moon is attracted to earth with the same force that the earth attracts the moon. If you draw those forces, you will see that only one of them is acting on the moon, and one of them is acting on the earth, so there s no canceling going on. This is a common hurdle people face in understanding Newton s 3rd law.", + "video_name": "CqsYCIjSm9A" + }, + { + "Q": "I have a question regarding the integral setup at 6:44. Mr. Khan said that the lower limit should be x=10 and upper limit x=5. However, would we still need the negative sign (attached to the force equation) since the integral takes care of direction? Or does the sign stuff actually matter (I'm not sure if work is considered a vector or scalar quantity)? Thank you and great video!\n", + "A": "Yes,we would still require the negative sign as it specifies that we are moving in the opposite direction of the force..and integral has negative sign because we are going from 10 to 5.", + "video_name": "CqsYCIjSm9A" + }, + { + "Q": "At around 7:17 wasn't Sal meant to write 1/-k*q1*q2* the integral? This doubt arised due to Sal getting rid of the -k*q1*q2 by diving the integral by the term.\n", + "A": "Here -k*q1*q2 is just a constant. Because of the linearity of the integration the integral of c*f is equal to c times the integral of f, where f is some function and c is a constant.", + "video_name": "CqsYCIjSm9A" + }, + { + "Q": "At the minute 2:34 I cannot understand why the middle C of the propyl group is a secondary carbon: ok, it's a secondary carbon if I don't consider its bond with the main chain (DECANE)... So I don't have to consider the bond with the main chain? Always?\n", + "A": "Is it a secondary carbon because it is the second-to-last carbon in the group?", + "video_name": "O9RPGJcAfJk" + }, + { + "Q": "\nAt 4:15, Mr. Sal Khan mentioned the systematic name 1-methylethyl. Would it be wrong to name this compound in alphabetical order( i.e.. 1-ethylmethyl)?", + "A": "Yes, it would be wrong. The longest chain in the group is 2 carbons long, so the base name is ethyl. There is a methyl group on C1, so the name of the group is 1-methylethyl.", + "video_name": "O9RPGJcAfJk" + }, + { + "Q": "In the \"work example problems\" video, they say that in lifting an object at constant velocity, the net work is 0, since the change in kinetic energy is 0 (we give energy into the system to push it up, and the gravity does negative work...in total, no work is done). They don't even consider PEgravitational.\n\nBut here, they say work is the same as change in energy, so lifting an object changes its gravitational potential energy and thus wok is done (2:35).\n\nWas the first video wrong?\nThanks\n", + "A": "The NET work includes the work you do to lift AND the work done by gravity, which is opposite of the work you do. So the KE doesn t change. But you did work against gravity so you added PE to the system.", + "video_name": "sZG-zHkGR4U" + }, + { + "Q": "where do you get the yellow thing that you used at 5:00?\n", + "A": "those are alligator clips, they are wires with little alligator like clips on them.", + "video_name": "Kq0Er6JBMmc" + }, + { + "Q": "At 10:19 why does he say \"Then it goes to the heart, rubs up against some alveoli \"?\n", + "A": "Well, rubbing up against some alveoli means that the oxygen diffuses from any alveolus (singular for alveoli) to enter in the blood stream as oxygenated blood.", + "video_name": "QhiVnFvshZg" + }, + { + "Q": "At 3:56 he say blue one is an artery but at 7:15 Bro Sal says that blue one is a vein??\nEm confused! :/\n", + "A": "Remember, blue simply represents deoxygenated blood. So, the pulmonary artery carries deoxygenated blood from the heart to the lungs. The vena cava veins carry deoxygenated blood from the rest of the body back to the heart.", + "video_name": "QhiVnFvshZg" + }, + { + "Q": "\nI thought the veins carried oxygenated blood, 9:08 says the vein carried deoxygenated blood ?? I'm confused", + "A": "Arteries take blood away from the heart. Most arteries carry oxygenated blood away from the heart to other parts of the body. The veins take blood back to the heart. Veins carry oxygenated blood is carried in veins. The pulmonary artery takes blood away from the right ventricle to the lungs where it is oxygenated. The pulmonary vein takes oxygenated blood from the lungs to the left atrium - back to the heart.", + "video_name": "QhiVnFvshZg" + }, + { + "Q": "\nhow long dos it take to get your blood circulating 0:20 minutes", + "A": "round about 1 sec actually time taken for one breath", + "video_name": "QhiVnFvshZg" + }, + { + "Q": "at \"0:42\" I could not hear it with my volume at full, what did he say?\n", + "A": "He didn t really say anything important. He said I don t know and came up with (1/2)m^2 for the second area.", + "video_name": "xlJYYM5TWoA" + }, + { + "Q": "At around 5:15, why are the 3 branches drawn off of the monocyte cell branch? Could it have been drawn just coming from the myeloid (Is it just to save space)?\n", + "A": "There is a reason to it :) The Common Myeloid Progenitor cell (the first red one) grows into 4 different cells; RBC, Mast cell, Megakaryocyte and MYELOBLAST. Myeloblast then later grows into; Neutrophils, Eosinphils, Basophils, and monocyte. He kinda skipped this step because it makes it a little bit more complicated.", + "video_name": "ddifthdMNVc" + }, + { + "Q": "\nAt approximately 6:00, what was Sal implying by the term, \"superimposed\" when he was referring to enantiomers?", + "A": "To superimpose means to put on top of eachother, so putting the image of one on top of the other and only seeing one since they re the same (or not since they re different.", + "video_name": "z8M4EciPpYI" + }, + { + "Q": "Perhaps I missed it in the video, but at 3:13 Sal is talking about the Helium absorbing light energy. Is this light coming from the Cepheid itself, or does he mean light from an outside source?\n", + "A": "I think he meant from the inside of the cepheid.", + "video_name": "X_3QAB3o4Vw" + }, + { + "Q": "\nAt approximately 3:17 he states the peak at 1100cm^-1 corresponds to a C-O single bond. However, in prior videos he described the area below 1500 as the \"fingerprint\" area, and the area above 1500 as the diagnostics area. Can you explain the significance of this?", + "A": "Some peaks are so strong and so characteristic that you can identify them even they are in the fingerprint region.", + "video_name": "ALLSsIDhFdU" + }, + { + "Q": "\n10:31 Why is keto form more stable than enol form ?", + "A": "Good Question! Enols are less stable because the C=C (double bond) is weakened by the electronegativity of oxygen.", + "video_name": "NdRl1C6Jr5o" + }, + { + "Q": "Would the reaction still be complete if we didn't \"open up the structure\"? (Meaning leave it at the epoxide Jay drew at 4:16)\n", + "A": "Yes, if you simply want the epoxide, the reaction would be complete.", + "video_name": "KfTosrMs5W0" + }, + { + "Q": "1:30 How come the electrons between the O and H move twards the alkene's C? What triggers it? Thank you.\n", + "A": "i think C is more electronegative than H so that due to inductive effect electrons move towards C rather than H", + "video_name": "KfTosrMs5W0" + }, + { + "Q": "\nAt 7:46, why does Jay say that there is only 1 pi bond? Are pi bonds made up of more than 2 valence electrons?", + "A": "There s only one pi bond. It contains two electrons - one electron comes from the p-orbital on the left carbon and the other from the p-orbital on the right carbon.", + "video_name": "ROzkyTgscGg" + }, + { + "Q": "@12:17 there's a bubble that pops up which says 'trigonal planar', as if in correction of what Jay says in the video. (He calls it planar). However, I think that what he says, planar, is correct, and not the box: the empty p orbital exists on BOTH sides of the molecule, and so the sp2 orbitals don't bend out of shape\n", + "A": "No the word trigonal planar is correct as it lies in plane and it is not a 3D structure!", + "video_name": "ROzkyTgscGg" + }, + { + "Q": "at 2:00 aren't there 4 bonds on every carbon? so why don't we get sp3\n", + "A": "To determine the hybridization, look at the # of sigma bonds + # of lone pairs, rather than the total number of bonds. Here, each carbon does have 4 bonds, but only 3 sigma bonds, so it is sp2.", + "video_name": "ROzkyTgscGg" + }, + { + "Q": "At 8:21 shouldn't it be A with a circle on the top? Not on the side? Or are both forms of the angstrom acceptable?\n", + "A": "Yes. The symbol for angstrom is \u00c3\u0085. In cursive writing, we don t always get the little circle directly on top of the A. Of course, it would be preferable to use the SI units of picometres (pm) instead of angstroms.", + "video_name": "ROzkyTgscGg" + }, + { + "Q": "At 11:45, jay tells us that boron acts a lewis acid because it has no electrons in its unhybridised porbital and hence can gain two electrons.\nbut the sp2 hybrid orbital have only 3 electrons and hence will they be able to gain 3 MORE electrons?\n", + "A": "Each sp\u00c2\u00b2 orbital has one electron, and they each gain another electron when they form bonds to the fluorine atoms. That makes six electrons in the valence shell of boron. Boron needs two more electrons to complete its octet.", + "video_name": "ROzkyTgscGg" + }, + { + "Q": "\nAt 2:37, why has he written 36?", + "A": "This is a known error in the video. A box pops up and tells you it should be 81 and the final answer is sqrt(97)", + "video_name": "gluN2wxqES0" + }, + { + "Q": "When you squared that negative number in 2:37, does it become non negative?\n", + "A": "Yep. Squares of negative numbers are positive(non negative) since we are multiplying a negative with a negative which gives a positive result.", + "video_name": "gluN2wxqES0" + }, + { + "Q": "\nWhen you squared that negative number in 2:37, does it become non negative?", + "A": "yes...for example squaring is the same thing as multiplying by the same number ..so here -4 X -4=16 ..the negatives cancel out", + "video_name": "gluN2wxqES0" + }, + { + "Q": "8:26 would even a metal chain stretch?\n", + "A": "sure, it would stretch a bit. You might not be able to notice it.", + "video_name": "QKXeZFwFPS0" + }, + { + "Q": "\nAcceleration of 3Kg box is downwards so it shotld be negative but you wrote it as positive in the equation above at 10:06", + "A": "Typically the acceleration of the 3kg block would be considered to be negative, because downwards and to the left are typically considered to be the negative direction and upwards and to the right are typically considered to be positive directions. However in this case he just used different signs instead of following the normal convention. He chose downwards and leftwards to be positive and upwards and rightwards to be negative.", + "video_name": "QKXeZFwFPS0" + }, + { + "Q": "why cant the outer shell electrons repel the inner shell electrons towards the nucleus? (5:57) the inner shell atoms could easily get sucked into the nucleus with the pushing( (repelling) force from the outer shell and the pulling force from positive charge of the nucleus, Right?\n", + "A": "The thing about atoms is they have this property where they only can occupy certain states, so electrons can only jump between orbits if they are empty and energy levels. There is no orbit in the nucleus and thus they can t be there. I d suggest looking at the lesson in chemistry about the electronic structure of atoms.", + "video_name": "rKoIcgBM4Vg" + }, + { + "Q": "at 9:07, wouldn't it be that the neutral atom is smaller than the cation? If not, how come?\n", + "A": "Cations are positively charged because they lost an electron, so they have fewer electrons than protons and therefore the pull toward to nucleus is stronger per electron. The cation is therefore smaller than the neutral atom.", + "video_name": "rKoIcgBM4Vg" + }, + { + "Q": "at 4:40 he says insulator is charged, how can an insulator get charged , i wont get an electric shock from it if i touch it\n", + "A": "Yes you can get an electric shock from an non-conducting material. It is commonly known that if you walk on a carpet with socks on, and then tough a doorknob you feel a shock. Basically you are being shocked by the charge accumulated by your socks travelling through the point of contact. This is called electrostatic discharge or ESD. On a grander scale, lightning is also an example of ESD caused by charge build up.", + "video_name": "ZgDIX2GOaxQ" + }, + { + "Q": "\nIn the example at 10:0, what would happen if the can wasnt connected through a wire to a metal but they were just touching. Would a transfer of electrons still occur?", + "A": "yes but there would be virtually no resistance", + "video_name": "ZgDIX2GOaxQ" + }, + { + "Q": "\nat 6:30 he says most plastics are insulator, can you give me an example of a plastic which is not an insulator?", + "A": "exposure of few plastics in ionic beam shows conductance like metals, and some are made semi conductors.", + "video_name": "ZgDIX2GOaxQ" + }, + { + "Q": "\nAt 8:26, why did you add the area of the triangle and the rectangle together? Wouldn't the displacement only be the area of the triangle because the base of the triangle is where the initial velocity is?", + "A": "The initial velocity causes displacement, too, doesn t it? If the velocity didn t change, wouldn t there still be displacement?", + "video_name": "MAS6mBRZZXA" + }, + { + "Q": "at 8:05, it says that the area of the triangle is 1/2 x 4 x 8. in the other videos it says that the area of the triangle is one half times base times height. why?\n", + "A": "that s exactly the SAME 1/2x 4 x 8 = HALF= 1/2 BASE= 4 HIEGHT= 8", + "video_name": "MAS6mBRZZXA" + }, + { + "Q": "@4:27 why did Sal cancel the \u00e2\u0080\u009cseconds\u00e2\u0080\u009d and the \u00e2\u0080\u009cseconds squared\u00e2\u0080\u009d to make it just \u00e2\u0080\u009cseconds\u00e2\u0080\u009d? I thought we were multiplying. Wouldn\u00e2\u0080\u0099t it be \u00e2\u0080\u009cseconds cubed\u00e2\u0080\u009d? PLEASE HELP!\n", + "A": "If you have a number, let s say X^2 and you have that X^2 divided by X, you end up with just having X as the answer because X^2 is the same as X*X, So, if you divide X*X by X, you cancel out one X in the numerator, and the X in the denominator. Hope that helps!", + "video_name": "MAS6mBRZZXA" + }, + { + "Q": "\nat 8:15 with the answer equaling 77664439914.3 my calculator gets 7.77*10^-52 is there a fix around this?", + "A": "With an answer of that magnitude different, you must have typed something into your calculator wrong. If you type the following into Google it gets pretty close to Jay s answer (not exact because he hasn t rounded the first number) 3.53E-20 * 2 / 9.11E-31", + "video_name": "vuGpUFjLaYE" + }, + { + "Q": "(about 0:30): If shining a light of the right frequency and wavelength on a substance can knock electrons loose, therefore creating ions, wouldn't that change the properties of the substance? Is the requirement for light to free electron a minimum amount of energy, or is it a range? Does it have anything to do with why things bleach in the sun, or why, in some museums, there is no flash-photography allowed?\n", + "A": "When an electron is knocked loose, the remaining material is positively charged, which means you can t knock too many electrons loose because it will get harder and harder for them to move away. The positively charged object will attract electrons from the surroundings to neutralize itself. So the photoelectric effect is not going to make any significant change to the material. It has nothing to do with bleaching, which is a process of chemical breakdown due to the incoming energy from the sun.", + "video_name": "vuGpUFjLaYE" + }, + { + "Q": "\nAt 9:30, Why do non bonding electrons take up more space than bonding electrons?", + "A": "Bonding electrons have to spend most of their tine between two nuclei. Nonbonding electrons are attracted to a nucleus only from one side, so they are free to wander further away.", + "video_name": "0na0xtIHkXA" + }, + { + "Q": "\nAt 9:25 are these resonant structures? Is the second structure possible as later at 11:58 it is said that VSEPR theory predicts first one more?", + "A": "They aren t resonance structures, they re two possible ways to arrange the electron pairs. The molecule will do whichever is more stable.", + "video_name": "0na0xtIHkXA" + }, + { + "Q": "\nAt 5:49, Sal explains just out of the blue how we reduced 2NAD+'s into 2NADH's when we went from the 2 pyruvates to Acetil-CoA, but nowhere in the previous minutes he explains how that came to happen. Any help? :(", + "A": "Glucose has 12 hydrogens. Pyruvate has 3 hydrogens (X2=6 for two molecules). 4H from the glucose molecule go to produce the 2 NADH in the first step (2H are needed to produce one NADH). The remaining 2H are used with 2H from two coenzymeA molecules (H-S-CoA) to produce 2 NADH when pyruvate is converted to acetyl CoA.", + "video_name": "9zoS5WGsmpc" + }, + { + "Q": "At 3:05 Sal says that the most compact state of water is liquid. Why?\n", + "A": "Because when water turns into a solid, it forms crystals, and those crystals take up a little more volume than when the water molecules are allowed to mix freely without forming crystals.", + "video_name": "zjIVJh4JLNo" + }, + { + "Q": "\n~4:00 he says the CL is smaller than the Na. Why is it a smaller molecule? Doesn't it have more electrons?", + "A": "as we go across the periodic table nuclear charge as well as no. of electrons increase BUT increase in nuclear charge dominates over increase in no. of electrons so overall atomic radius decreases and this is the case with Cl and Na.", + "video_name": "zjIVJh4JLNo" + }, + { + "Q": "\nAt 3:21, Sal said that some molecules will be hitting the wall and would have a change in momentum. Does the net energy of the molecules change with the change in momentum?", + "A": "Of course energy changes if momentum changes.", + "video_name": "tQcB9BLUoVI" + }, + { + "Q": "At 7:21 he says \"they have the same kinetic energy.\" But in order to \"squeeze\" the box, at least one wall must move inward, and while moving it will hit some of the particles and make them move faster. So wouldn't the kinetic energy increase (both the energy of some individual particles and the average energy)? Maybe this is negligible (especially if we squeeze the box very slowly)?\n", + "A": "We don t squeeze the box it s more like transferring the particles from a larger box to a smaller box keeping the kinetic energy same.", + "video_name": "tQcB9BLUoVI" + }, + { + "Q": "at 8:51 they have written cos60 equals 3^1/2/2but actually cos60 equals 1/2\n", + "A": "Yup he took the value wrong.", + "video_name": "KDHuWxy53uM" + }, + { + "Q": "At 6:38, why is that proton acidic?\n", + "A": "The carbon atom is sp hybridized (50% s character). Since s electrons are held more tightly to the carbon nucleus, they are further from the hydrogen nucleus. The H atom is not tightly held, so it is more easily removed. The proton is acidic.", + "video_name": "_-I3HdmyYfE" + }, + { + "Q": "8:37 Howcome theres not actual recorded history we learn about, on humans from 200,000 years ago?\n", + "A": "We have not found any records that go that far back. The earliest writing we have discovered is from around 3200 BCE (about 5,200 years ago).", + "video_name": "MS7x2hDEhrw" + }, + { + "Q": "\nAt 3:39, Sal says there is only one Snowball Earth. However, the chart says there are two.", + "A": "He probably only mentioned one.", + "video_name": "MS7x2hDEhrw" + }, + { + "Q": "\nAt 2:00, when Sal explains, why is there in the velocity formula, an \"s\" instead of a \"d\" can the letter \"s\" stand for space to be covered? in other words moving from one point to another?", + "A": "the letters don t matter. You can define any variable to be anything you want. Focus on the concepts.", + "video_name": "oRKxmXwLvUU" + }, + { + "Q": "Isn't there any other way to convert it? 7:26 Maths seems to be easier here in Brazil...\n", + "A": "The conversion method is certified by the system international units so if we use it it would be better and can be applied on almost every sum used in maths and physics. by the way no math is difficult or easy in any country provided the way u think lol,", + "video_name": "oRKxmXwLvUU" + }, + { + "Q": "\nAt 11:16 in the video , sal calculates 5000/3600 which is somewhere 1.38888888888889. so my question is how did that 1.888888888889 become 1.39 ?", + "A": "when we estimate 1.38888888 ,we round it off to 1.39 because it is better to write it shorter.if in case you had to multiply it with another number,it would be difficult .For example, 1.38888888888888.....*19 will be never ending ,so we do it.And by the way its 1.3888 not 1.88888", + "video_name": "oRKxmXwLvUU" + }, + { + "Q": "at 2:20 he says you use d for calculus, but don't you put an arrow on top for displacement? Do you use an arrow for the dirrivative operation too?\n", + "A": "Haha no, it just means that our alphabet ran out of letters, and it is generally a bad idea to use one letter for 2 purposes.", + "video_name": "oRKxmXwLvUU" + }, + { + "Q": "\nAt 7:23 Sal says km is going to cancel out with the denominators but the numerator is meters.\nCould someone pls. help", + "A": "What Sal meant was at the denominator, the unit was also km. in direct variation, you cancel out the units to change a value of a particular unit into a different value with a different unit. In other words, Sal was saying that in 5 km X 1000 m/ 1 km, the kilometers will cancel out, and you will be left with just the meters. He then multiplied it and came out with 5000 meters.", + "video_name": "oRKxmXwLvUU" + }, + { + "Q": "Can you simplify velocity? At about 7:20, Sal stated 5 km per hour is the velocity. Usually, in physics, do you simplify final answers or leave it in their original measurements, the question asked with?\n", + "A": "we should probably simplify them because we usually count them per 1 hour.", + "video_name": "oRKxmXwLvUU" + }, + { + "Q": "Can someone please explAin the h2o part which sal talks about from 3:00. Thanks\n", + "A": "What he s saying is that in each H-O bond two electrons are being shared. However, oxygen, being more electronegative than hydrogen, grabs more than its fair share of the electron density in the bond. (You can think of it as a tug-of-war between oxygen and hydrogen, with oxygen winning by dragging more electron density its way.) This means that the bonds are polarised, with oxygen having a partial negative charge and each of the hydrogens a partial positive charge.", + "video_name": "Rr7LhdSKMxY" + }, + { + "Q": "9:05 Is nuclear envelope and nuclear membrane the same thing?\n", + "A": "Yes, they are just different terms. You could call my shirt clothing or a textile envelope, although most people say the first I prefer the latter.", + "video_name": "mMCcBsSAlF4" + }, + { + "Q": "\nAt 7:04, how exactly do the glycolipids help the cell to be recognized or tagged? Do they form specific patterns across the cell membrane? Do they have specific components that signal different things?", + "A": "One example is that immune cells have receptors that can attach to them. So a cell with a type of glycolipid that isn t normally present in your body (the glycolipid is then an antigen) will attach to the immune cell, and so be identified as an invader.", + "video_name": "cP8iQu57dQo" + }, + { + "Q": "\nAt 4:49, he states the concentration of the Hydronium ions is 5.0 x 10^-14\nWhere did he get that figure from? Thanks", + "A": "Well, (1.0 * 10^-14) / (0.2) is the equal to 5.0 * 10^-14. All he did was divide both sides by 0.2 in order to isolate for the variable x . Hope this helps!", + "video_name": "gsu4gjrFApA" + }, + { + "Q": "At 1:30, he says that the concentration of HNO3 andH3O are the same. Would the NO3- also have that same concentration of .03M? Why or why not?\n", + "A": "It would, we just don t care about it", + "video_name": "gsu4gjrFApA" + }, + { + "Q": "At 11:40, why do we not square the concentration of OH? From previous lessons, I remember we have to raise the concentration to the power of the molar ratio. So shouldn't it be 1.0*10^-14/(0.012)^2 for OH? Thanks\n", + "A": "That rule is only for finding the equilibrium constant. But here, when we are finding the pH, we are supposed to multiply it by 2 as we need to know the number of moles.", + "video_name": "gsu4gjrFApA" + }, + { + "Q": "At 3:35 in the video, I attached my 2 hydrogens to the nitrogen at different places. I put one hydrogen on the top and one on the bottom. Is that incorrect? Would my way of drawing it be acceptable?\n", + "A": "Your way is equally correct to Sal s way. These dot structures show connectivity, but not shape, so it doesn t matter where you drawn in your H s attached to the nitrogen.", + "video_name": "BIZNBfBuu1w" + }, + { + "Q": "How will I know which part will I put the hydrogen? For example @4:54. How did you know that the hydrogen is to be put at the right side of oxygen?\n", + "A": "It doesn t matter exactly where as long as it s bonded to the oxygen. It would be just as valid to put it on the top or bottom of the oxygen instead of right.", + "video_name": "BIZNBfBuu1w" + }, + { + "Q": "\nI don't understand the part after 1:34 . The part about carbon with 8 electrons and hydrogen with 2", + "A": "Hydrogen can only have two electrons total but Carbon can have 8 valence electrons total.", + "video_name": "BIZNBfBuu1w" + }, + { + "Q": "At 5:49, Sal forgot to right hemoglobin!\n", + "A": "Everyone makes mistakes. :)", + "video_name": "xKJ3txXIuQk" + }, + { + "Q": "\nAt 10:23, David talks about how voltage is the difference in Electric Potential. So is the analogy Volts:Electrical Potential::Impulse:Momentum correct in the sense that one is the measurement of the difference of the other?", + "A": "eh, sort of, but that s not a very useful way to think of it. Impulse is a transfer of momentum. Volts are units that we use to measure electrical potential difference. Voltage is the electrical engineers terms for what physicists call electric potential difference . You can subtract any two quantitites you want from one another. That doesn t mean that any time you choose two pairs of quantities to subtract that there s some interesting comparison to make between the differences.", + "video_name": "ks1B1_umFk8" + }, + { + "Q": "\nWhat differentiates the blue star 3:55 lifecycle from the red giant or main sequence stars? What makes them burn hotter and faster?", + "A": "Its all about mass. A massive star will be hotter and burn brighter. Every star was once main sequence. It does not matter how massive, as long as it is stably burning hydrogen, it is main sequence. Once a star runs out of hydrogen or leaves the main sequence, it becomes a red giant or supergiant.", + "video_name": "w3IKEa_GOYs" + }, + { + "Q": "At 2:40 Sal mentions a supernova that may have blown away a portion of the Eagle Nebula, and that we wont be able to see the effects of it for another 1000 years. Why only 1000 years and not 7,000? Do we know that said supernova occured 6,000 years ago?\n", + "A": "Yes, from what we can see right now, which is the Eagle Nebula 7,000 years ago, a burst of energy from a nearby supernova is heading towards the Eagle Nebula. At such a rate, it has destroyed the Eagle Nebula 6,000 years ago.", + "video_name": "w3IKEa_GOYs" + }, + { + "Q": "\n2:40 \"There was another supernova that happened that could have blown away some of this dust\".\nHow do you know it happened if you can't see it yet?", + "A": "Supernovae happen all the time, its very likely one has happened.", + "video_name": "w3IKEa_GOYs" + }, + { + "Q": "\nAt 5:46, Isn't (10^6) ^2 (ten to the sixth power squared) supposed to be 36?", + "A": "Nope. (10^6)^2 is 10^12. Remeber, (a^m)^n = a^mn", + "video_name": "391txUI76gM" + }, + { + "Q": "Dear Sal,\nat 3:09 of the video above, you said that you found out the Earth's mass on Wikipedia. My teachers always say not to trust wikipedia because it is based off of other people's information/opinions. After watching the whole video (which by the way was really helpful) I found out that the Earth's mass is 5.972 multiplied by 10 to the 24th with the unit as kilograms. On your video, did you just round up the decimal? I just want to make sure so I don't get it wrong on my test next week.\nSincerely,\nAva F.\n", + "A": "Teachers should stop telling students not to trust wikipedia. It is quite reliable for scientific information.", + "video_name": "391txUI76gM" + }, + { + "Q": "\nAt 0:52, Rishi draws a rectangular human cell. I thought that human cells are rounder and plant cells are the rectangular ones. Am I wrong?", + "A": "Human cells have no specific shapes. It is just for diagramming.", + "video_name": "MNKXq7c3eQU" + }, + { + "Q": "\nAt 1:28 why did Sal say that Force/Mass=Acceleration?", + "A": "Because it does. F = m*a. Solve for a.", + "video_name": "wlB0x9W-qBU" + }, + { + "Q": "\nWhere did the formula at 2:32 come from?", + "A": "its the formula to calculate gravity between 2 objects. m1 = mass object 1 (kg) m2 = mass object 2 (kg) r = distance between objects (m) G = 0.0000000000667 Your result is in m/s^2", + "video_name": "wlB0x9W-qBU" + }, + { + "Q": "\nAt 2:23, Sal said over the square of the distance between the two things but wrote : (r^2) but isn't the sign for distance d?", + "A": "Either is acceptable. It s just a different letter that represents the same thing.", + "video_name": "wlB0x9W-qBU" + }, + { + "Q": "I'm just curious, in the equation at 3:17 is m2 referring to the mass of the projectile?\n", + "A": "Indeed it is. Since m1 is the mass of the Earth, m2 must be the mass of the other body interacting with the Earth i.e the mass of the projectile.", + "video_name": "wlB0x9W-qBU" + }, + { + "Q": "\n4:00 so the force of gravity is accelerating the object downwards (makes sense) then if you were to be nosediving the force of gravity is pushing against you, or in other words upwards, causing \"g\" forces. Why is this? Or if I'm wrong can someone explain g forces, like in the previous video when the pilot of the fighter jet was pushed back by gravity?", + "A": "Gravity does not push against you, it pulls you down. When a pilot feels g forces, that s not really because of gravity, it s because of acceleration of his plane. It s called g force because it FEELS like he is getting heavier, but that s not because of gravity, it s because the seat of the plane is pushing on his backside.", + "video_name": "wlB0x9W-qBU" + }, + { + "Q": "Why did Sal use average velocity as opposed to just velocity in the equation: displacement = average velocity multiplied by change in time in 4:54?\n", + "A": "Because the velocity is not constant through out the process. Acceleration is constant. If you plot a graph of Velocity vs. Time, you ll see more clearly why using avg. Velocity is pretty much the same as finding the area below the curve.", + "video_name": "wlB0x9W-qBU" + }, + { + "Q": "\nAt 3:00, Sal says, \"The little g, is really all of the business over here........\". Is it because m2's mass is really too small compared to the Earth's mass, we say: g = [ G X (Earth's mass) ]/r\u00c2\u00b2?\nI'm getting confused of to why we exclude the 'm2' in the equation?\n\nThanks,\nRamana", + "A": "We don t exclude it. We have F = GMm/r^2. We don t want to write all of that every time. GM/r^2 doesn t change as long as you stay on the surface of the earth. So we give it a new name, g, and we re-write that equation as F = mg. The little m is still there.", + "video_name": "wlB0x9W-qBU" + }, + { + "Q": "\n9:00 what is a delta t", + "A": "delta means change in . Delta t means change in t.", + "video_name": "wlB0x9W-qBU" + }, + { + "Q": "\nAt 3:15, what distance should one no longer assume that the radius (the earth in this case) is constant (say, assuming 2 or 3 significant digits)?", + "A": "g = GM/r^2 If you plug in a few numbers for r, you can decide for yourself when g varies enough from 9.8 so that you have to worry about changing r Note that even on the surface of earth, g varies in the second decimal place, due primarily to density variations but also due to changes in altitude", + "video_name": "wlB0x9W-qBU" + }, + { + "Q": "\nAt 9:15 shouldn't the systematic name be 1,3-bis(2-methylpropyl)cyclopentane ?", + "A": "but in that case the longest chain will be of 2 carbon atoms. whereas it is of 3 carbon atoms.", + "video_name": "6BR0Q5e74bs" + }, + { + "Q": "Wouldn't the structure at minute 5:20 be named 4,4,7,10-tetramethyldodecane? With this numbering we get a total of 25 vs. 27 with the 3,6,9,9-tetramethyldodecane.\n", + "A": "There is no rule that says we sum the numbers together, the rule is we are looking for the lowest number at the first point of difference. How you determine this is by making a list of the numbers and compare them one at a time until we find a point of difference: yours: 4,4,7,10 the video s: 3,6,9,9 As 3 is lower than 4, the numbering in the video is correct.", + "video_name": "6BR0Q5e74bs" + }, + { + "Q": "At 5:56 Sal says that you won't see meniscus in plastic because it doesn't have the same polarity as the glass. Does this mean there is no capillary action in a plastic straw?\n", + "A": "There is capillary action in plastic straw. Ever seen a cold drink with a straw? When you insert the straw into the drink..the liquid rises over a height. But capillary action in glass is more than that observed in plastic straws. All plastics have different abilities for adhesion.", + "video_name": "eQXGpturk3A" + }, + { + "Q": "\nAt 5:56 Sal says that you won't see meniscus in plastic because it doesn't have the same polarity as the glass. Is this true for every kind of plastic?", + "A": "Not all plastics are exactly the same but they all have the same type of carbon-polymer-structure. As far as meniscus is concerned, none of them will cause a meniscus.", + "video_name": "eQXGpturk3A" + }, + { + "Q": "Am I missing something? At 2:27 Sal says that each Silicon is paired with two Oxygen but the video shows four Oxygens for every Silicon (though two of the Oxygen are shared in a covalent bond).\n", + "A": "No, well Sal did not draw the complete picture here, Silicon dioxide is the complete molecule here and what you see above is a silicon dioxide lattice which is just many silicon dioxide forming bonds with each other. You saw silicon bonded to 4 oxygen bonds but actually that silicon is bonded to 2 of them and the other 2 oxygen is bonded to some other silicon atom.", + "video_name": "eQXGpturk3A" + }, + { + "Q": "At 9:30 and onward, it is stated that the accelerations for each of the block would have a magnitude of 1.84 m/s^2. But doesn't that contradict from the previous video, which stated that the accelerations would have a magnitude of 3.68 m/s^2? Could someone please explain why this is? Thanks! :)\n", + "A": "No contradiction. In the previous examples, friction was ignored. In the last example, where the 1.84 m/s^2 was calculated, friction was taken into consideration. And this makes sense - if we have friction, then there s an opposing force to a moving object.", + "video_name": "UrfLAlk2b_8" + }, + { + "Q": "At around 6:30, when he starts solving the problem, is he assuming the penny immediately just falls down or something? Because the penny will move in some parabolic motion and have its own change in distance, which would then be added to the height of the hill.\n", + "A": "First of all, Sal does not assume that the penny falls down immediately, because he said that it has an initial velocity of positive 30 m/s, which means that it has an upward direction. Second, Sal assumed that the object was thrown straight upward and not at an angle, and therefore, it would not have a parabolic path.", + "video_name": "emdHj6WodLw" + }, + { + "Q": "\nAt 0:28 Sal said that the sun orbits around the Milky Way Galaxy. So does the sun also move and orbit just like the planets do?", + "A": "Yep! Our whole solar system orbits around the center of the Milky Way Galaxy, just like how our planets orbit the Sun. Though at a much higher velocity of 828,000 km/hr", + "video_name": "FEF6PxWOvsk" + }, + { + "Q": "At 5:05, why is scandium's electron configuration the same as argon's?\n", + "A": "It isn t, but each electron configuration builds on from the last. We use the noble gas from the previous row in square brackets to represent all of its electron configuration which saves us time and space. Argon has the electron configuration: 1s2 2s2 2p6 3s2 3p6 Scandium has the electron configuration: 1s2 2s2 2p6 3s2 3p6 3d1 4s2 When we use the shorthand scandium s electron configuration can be written as: [Ar] 3d1 4s2 [Ar] just means all of argon s electron configuration from earlier", + "video_name": "UXOcWAfBdZg" + }, + { + "Q": "\n3:05 what is a valence electron?", + "A": "A valence electron is electrons in the outermost shell of the atom. They determine properties of the atom and bonding behavior. The Octet Rule states that the outermost energy shell has 8 electrons.", + "video_name": "UXOcWAfBdZg" + }, + { + "Q": "\nat 6:42, carbon is described to have same configuration to helium, but then he says that carbon has 4 valence electrons or valency 4. how can it be similar to helium? is there a difference between configuration and valence electrons? I just couldn't understand..", + "A": "He didn t mean carbon has EXACTLY the same electron configuration as helium, but what he is showing is a shorthand way of writing out electron configurations. You take the noble gas from the previous row and put its symbol inside square brackets, this represents the electron configuration for that noble gas, eg [He] means the same thing as 1s^2, [Ne] means the same thing as 1s^2 2s^2 2p^6. This is for our convenience later on when full electron configurations get VERY long.", + "video_name": "UXOcWAfBdZg" + }, + { + "Q": "\nAt 08:30, are there lots of different types of bacteria or just one?", + "A": "There are billions of species, some are harmful to us, some are beneficial.", + "video_name": "TDoGrbpJJ14" + }, + { + "Q": "At 1:45 sal says that if we put bacteria in milk it becomes yogurt. But then if you eat the yogurt wont the bacteria get in your body and make you sick.How is that a good thing.\n", + "A": "There are predominately two bacteria used in making yogurt. One is non-probotic so it does not survive the stomach. The other, which is probotic, in non pathogenic, but aids in fermentation (common in the intestines). It is important to remember that not all bacteria make you sick, and to make it more complicated different sub-specie of a bacteria CAN make you sick, while a different subspecie of the same bacteria is ESSENTIAL to stay alive, such as E. Coli.", + "video_name": "TDoGrbpJJ14" + }, + { + "Q": "\nAt the start off the video, and at 2:06, why does Sal use the word \"rate\"? Is't distance divided by time just \"speed\" ?", + "A": "Rate is used here as shorthand for rate of change. An object s speed is the rate of change of its position over time, so he could have used speed here. Using rate helps make it clear that the same mathematical tools can be used for non-speed rates of change (e.g. water filling a tank, population growth, and so on).", + "video_name": "6FTiHeius1c" + }, + { + "Q": "At 1:55, what is a mole of a molecule?\n", + "A": "The first one is easy, and I hope this explains it for you. A mole consists of an Avogadro s Number of atoms, molecules, or whatever. That number is 6.02 x 10\u00c2\u00b2\u00c2\u00b3 So if you have 6.02 x 10\u00c2\u00b2\u00c2\u00b3 molecules of water, then you have EXACTLY one mole of it.", + "video_name": "LJmFbcaxDPE" + }, + { + "Q": "\nat 4:29 Sal says when you increase the OH, you decrease the pOH and it increases the pH? I'm a bit confused by this, can someone please explain? Thanks", + "A": "The same way that you you increase the concentration of H+ the pH goes down, the pOH would also go down. Don t forget that pOH=-log10([OH-]). Looking at [OH-]=.01 and .001 respectively, the pOH is 2 and 3.", + "video_name": "LJmFbcaxDPE" + }, + { + "Q": "\nat 0:54 Sal says that this oxygen could grab a hydrogen from the water essentially creating OH. What is OH?", + "A": "OH is a hydroxyl radical. But when A\u00e2\u0081\u00bb grabs a proton from the water it forms OH\u00e2\u0081\u00bb, which is hydroxide ion.", + "video_name": "LJmFbcaxDPE" + }, + { + "Q": "@13:15 how does -log ([HA]/[A-]) turn into log ([HA/A-])^-1 ?\n", + "A": "That is an application of a basic identity of logarithms. log (a/b) = log(a) - log (b) = -log (b) + log(a) = - [log(b) - log (a)] = - log (b/a) Thus, log (a/b) = - log(b/a)", + "video_name": "LJmFbcaxDPE" + }, + { + "Q": "\nAt 3:53 Sal says that the electric field has a 3 n/c electric field. However, doesn't the electric field depend on the distance between the two particles? Isn't the equation K*Q/D^2?", + "A": "It does except in this example Sal gave where it is a constant electric field. If it were not constant, you would use the equation you have defined provided the charge on the plate is defined (Q). Then you would solve in same manner by multiplying E times the test charge to get Force then multiply force times distance", + "video_name": "zqGvUbvVQXg" + }, + { + "Q": "\nAt 8:18 Sal said voltage is regardless of how small or big the charge is\nbut to find the potential we divide the work done by the charge\nso isn't the potential dependent upon the size of charge?", + "A": "The potential is not dependent on the size of charge, but the potential energy is. The potential is a property of the field. It s similar to gravity. g does not depend on the mass of an object on the surface of the earth. But the gravitational potential energy does depend on the mass (mgh)", + "video_name": "zqGvUbvVQXg" + }, + { + "Q": "\n5:29\nIs that to say the electric potential energy of electrons is dependent on its position? In an electric circuit, how do we change the electric energy per charge? When electrons pass through a load in a circuit, such as a lamp, how is electrical energy lost (converted to light energy)? How does it affect current and amperes?", + "A": "Potential energy ALWAYS relates to position. That s what PE is. The battery provides chemical energy to separate charges and give them PE. The PE is converted to KE when the circuit is complete and the charges flow as current. When they pass through the load, they bump into the atoms of the load and transfer some of their KE to the load.", + "video_name": "zqGvUbvVQXg" + }, + { + "Q": "\nAt 5:12, Sal mentioned other species in the Homo genus, Neanderthals. What are Neanderthals?", + "A": "Neanderthals were an extinct species of human, or possibly a subspecies. They are very closely related to modern humans, differing in DNA by only about 0.1%. Neanderthals were larger and heavier than modern humans. They went extinct sometime between 30,000 to 45,000 years ago, possibly due to inability to adapt to the changing climate of the era, or they simply interbred with humans.", + "video_name": "oHvLlS_Sc54" + }, + { + "Q": "Why are sharks fish and dolphins and whales mammals? (brought up at 10:02)\n", + "A": "This is due to very notable differences between the two. Sharks have cartilaginous bones, gills, and a swim bladder, all of which are associated with fish. Whales and Dolphins have dense bones, lungs, and are warm blooded, things associated with mammals. Ocean mammals also have vestigial hip bones even though they lack legs and they are incapable of drinking salt water. Like many desert mammals, ocean mammals get their water from the food that they eat.", + "video_name": "oHvLlS_Sc54" + }, + { + "Q": "At 1:16 , The force with which we pull will be stored as potential energy and it will be converted to kinetic energy once we leave the object.... But Sal said that the kinetic energy is converted into potential energy.. If I'm wrong, please someone correct me..\n", + "A": "The energy bounces back and forth between KE and PE.", + "video_name": "Nk2q-_jkJVs" + }, + { + "Q": "\nAt 1:09, shouldn't the carbonyl O be protonated first because H2O is a relatively weak nucleophile?", + "A": "Not necessarily, assuming you don t have other stronger electrophiles in your reaction vessel. H2O is actually a pretty decent nucleophile (which is why for most SN2 reactions where it is NOT the intended substituent, we take great care to remove it from our system).", + "video_name": "632MAqIB14E" + }, + { + "Q": "at 6:40, you talk about how adding Cl groups causes it to be more reactive by withdrawing electronegativity, why is it then that Ketones are more stable than Aldehydes as stated in the reactivity video? Wouldn't the extra R group also withdraw electronegativity and cause it to be more reactive?\n", + "A": "R groups mean they re carbon substituents and assuming they have C-H bonds they re electron donating through hyperconjugation. Obviously if you replaced all the C-H bonds with something highly electron withdrawing like C-Cl bonds you will make a very reactive ketone.", + "video_name": "632MAqIB14E" + }, + { + "Q": "\nAt 0:26, Sal is naming the alkene. He notes the methyl group at Carbon-2, but not Carbon-1 or Carbon-5-- so I'm a bit confused. We don't have to name those?\nAs in: wouldn't it be 1,2,5-methylpent-2-ene?\n\nThanks for any help!", + "A": "They re not methyl groups, they are part of the main chain. They ve already been accounted for by calling it pentene.", + "video_name": "O_yeKo6-qIg" + }, + { + "Q": "\nAt 7:40, if two oxygen electrons are shared, then why isn't a double bond formed??", + "A": "2 electrons is a single bond 4 electrons is a double bond", + "video_name": "O_yeKo6-qIg" + }, + { + "Q": "\nAt 3:22, shouldn't it be -ke^2/r instead of ke^2/r?", + "A": "the thing is, the final result of this calculation doesn t result in a vector, so we really don t need the energy, we only need the magnitude. In the second case however, it is a vector, so sign is required for vector algebra", + "video_name": "7Zin8hG9Nhw" + }, + { + "Q": "Whoa, hold on\u00e2\u0080\u0094that value of 0.15 at 10:40 is not a probability! Sal picked the box size arbitrarily. If he had picked a box that were ten times greater in volume, then the \"probability\" would be 1.5; that is, there would be a 150% \"chance\" of there being a hydrogen molecule in that box. That's obviously not right. Instead, it represents the expected, or average, number of hydrogen molecules per box of that volume. To go from an average value to a probability is quite hand-wavy indeed.\n", + "A": "The volume of that box is 1 Liter; because SI units.", + "video_name": "psLX080RQR8" + }, + { + "Q": "at 7:15, what did sal mean by scaling factor?\n", + "A": "He scales the units so they are all the same. It is basically converting a unit to another. For example 0.01 l is equal to 1 ml, so the scaling here would be 1 ml * 10^-3 = 0.01 l", + "video_name": "psLX080RQR8" + }, + { + "Q": "\nAt 8:13 Jay says that the Bohr model is incorrect. Is this because the Uncertainty Principle showed that the position of the electron would be at a distance greater than 2 times the radius. Whereas the Bohr model had the position of the electron at r1?", + "A": "The Bohr model could not be correct because it only worked for H and even for H it did not properly explain all the observations about the emission spectrum of H. That s why physicists continued to search for a better model, and through the work of DeBroglie, Schrodinger, Heisenberg, Born and others, the modern model was developed.", + "video_name": "PZIoFD_Z73M" + }, + { + "Q": "\nAt 3:46, what does he mean by the electron being in the ground state?", + "A": "Ground state means the lowest energy state", + "video_name": "PZIoFD_Z73M" + }, + { + "Q": "at 7:02 jay took away 2 pi electrons, one from each corresponding carbon atom. how is it possible to take 2 pi electrons from different carbon atoms. i do know about breaking a pi bond where one carbon attains a positive charge where other attains a negative charge for showing resonance. i am finding it hard to believe that two corresponding carbon atoms attains a + charge. pls do explain why.\n", + "A": "You need a reagent that really wants those electrons, like SbF\u00e2\u0082\u0085 in SO\u00e2\u0082\u0082Cl\u00e2\u0082\u0082", + "video_name": "I6wzan4hNc4" + }, + { + "Q": "''5:38\"\n\nno ones dug that far?\ncool!\nhow deep is the earths core?\ndoes anyone at khan academy know?\n", + "A": "did u guy ever see ice age continental drift. if so do u remember when scrat the little weird animal that loves acorns. well he went to the earths core and he didnt burn up and die.", + "video_name": "KL0i1RSnpfI" + }, + { + "Q": "At 5:36, why did he move the hydrogen to the other side of the periodic table?\n", + "A": "He showed that the hydrogen could belong to the alkali metals (because it could lose one electron like them and have a complete outer shell) OR it could gain one electron and still have a full outer shell (like the halogens which are group 7 elements). Remember the first electron shell only holds 2 electrons, then each shell after that holds 8.", + "video_name": "CCsNJFsYSGs" + }, + { + "Q": "\nAt 14:03, how did the answer become -6.37 m/s^2? I substituted the same values in the exact same kinematics equation and I got -62.83 m/s^2. Did I possibly enter something wrong with my calculator (it was in radians mode).", + "A": "I know the answer to your question! Ok, so when you put them into the calculator, ALWAYS PUT PARENTHESIS FOR PI! It is so important! If you just divide -(40rad/s)^2 by 80pi (2*40pi), then you will get -62.8319... If you divide -(40rad/s)^2 by (80pi), you will get the right answer -6.3662...", + "video_name": "TBlDBaUGqNc" + }, + { + "Q": "\nAfter the third resonant structure at 6:58,what happens??", + "A": "The third resonance structure can become the second resonance structure and then the first resonance structure, so on and so forth. The blue pi bond is more than one carbon away from the positive charge so it can t move to the carbocation to form a fourth resonance structure.", + "video_name": "fpq0eICjuSI" + }, + { + "Q": "\n2:28 Why are Ischemic Strokes are more common then Hemorrhagic strokes?", + "A": "It is simply more common for blood clots to form and plaques to break off and cause ischemic strokes. The rupture of a vessel is just less likely.", + "video_name": "xbyfeEW56Nc" + }, + { + "Q": "7:17- Are the valves in the veins tethered to the walls; or do they not need to be because of the low pressure?\n", + "A": "The valves are attached to the walls, as in the are not free moving. But there are not any other attachments like there are in the heart i.e. the chordae tendineae stoping the valves from flipping back.", + "video_name": "iqRTd1NY-pU" + }, + { + "Q": "At 1:32 it says that the very small arteries are called arterioles. When does an artery turn into an arteriole, and likewise for veins and venules? Does it depend on the size or the structure of the blood vessel or something else?\n", + "A": "Size does define the classification of artery versus arterioles. When there is two or less medial layers of smooth muscle. This is typically less than 0.1 mm diameters. Structurally, arteries contain more elastic tissue and the arterioles contain more smooth muscle. Functionally, arterioles contribute more to restriction of blood flow and consequently control total peripheral resistance. There is also some gas exchange in arterioles.", + "video_name": "iqRTd1NY-pU" + }, + { + "Q": "At 9:04, where does the joules sign go?\n", + "A": "Sal forgot to write it in, but it should still be there!", + "video_name": "lsXcKgjg8Hs" + }, + { + "Q": "\nAt 1:32, what is spin (in terms of chemistry) ?", + "A": "If you want to think of it like a ball rotating clockwise or anticlockwise that is more than likely going to be fine for this level of understanding. The major thing it means for chemistry is that each orbital can only have at most 2 electrons, each with opposite spins (ie one spin up and one spin down per orbital)", + "video_name": "u1eGSL6J6Fo" + }, + { + "Q": "At 12:08 he says that the Carbon has 1s and 3sp3 orbital, so my question is that ; that each of those 3 sp3 orbitals would contains a single electron ? Am i right?\n", + "A": "Instead of having one s and three p orbitals, the carbon atom has four sp\u00c2\u00b3 orbitals. Each of those four sp\u00c2\u00b3 orbitals contains a single electron.", + "video_name": "u1eGSL6J6Fo" + }, + { + "Q": "At 5:57 when you is not dissolved, do you mean it is not dissolved in water or in gas.\n", + "A": "In this particular reaction, all the other components are gases, so it means that the C is not a gas. In other words, the carbon is not dissolved in the gaseous phase.", + "video_name": "TsXlTWgyItw" + }, + { + "Q": "At 7:12 Sal mentioned about buoyancy effect. What do you mean by that ?\n", + "A": "buoyancy is upthrust acting on a body", + "video_name": "R5CRZONOHCU" + }, + { + "Q": "\n8:50 I did not understand the equation. It sounds logical that if we have parallel flow the resistance is lower, but how do we get to the equation?", + "A": "We have less resistance when there is less flow. When we double the amount of identical paths, we halve the amount of flow through each individual path. By doubling the amount of paths, we halve the resistance. Opening more doors makes it easier to exit the theater. Even if only one person gets out through the new door, everyone else experiences less competition for all the other doors.", + "video_name": "E-q9JpkGc-8" + }, + { + "Q": "\nAt 2:53 why we only use centripetal acceleration on the left side of the equation? Shouldn't it be centripetal acceleration plus acceleration due to gravity? When the ball is in the air isn't it always accelerating downwards due to Earth's gravity?", + "A": "I believe, it is because the direction chosen in the free body/force diagram is towards the centre of the circular path. The effect of gravity is included in the weight or gravity force( m x g ).", + "video_name": "2lcaBPLLoLo" + }, + { + "Q": "\nin 1:42 the example, does that actually work?", + "A": "Try it! Put a pot of water on a stove and only heat one side. See what happens!", + "video_name": "f8GK2oEN-uI" + }, + { + "Q": "\nYou know, that is something I wondered. At 4:54, Sal says \"degrees Kelvin\", even though it's supposed to be just plain \"Kelvin\". I know that. I'm cool with that. But why is that? Why are the other temperature readings in degrees but Kelvin is not?", + "A": "Because the other scales don t actually measure a physical quantity, just relative warmth. 0 degrees F is not zero somethings . Same for Celsius. But zero kelvin represents zero thermal energy, and 100 K is twice as hot as 50 K.", + "video_name": "erjMiErRgSQ" + }, + { + "Q": "At 3:24 Sal says the lowest possible temperature in C is -273.15 Degrees C, and I was wondering, what would happen if we could quickly freeze a person to -273.15 Degrees C? Then if we could return their temperature back to a normal temperature, would they be ok?\nI know it sounds kind of odd, but I was considering forensic science, and just wondering....\nThanks!- MP\n", + "A": "Technically speaking, you cannot actually reach absolute zero, because the would be a state of no thermal energy at all. But we can get very close to it. No, the person would die.", + "video_name": "erjMiErRgSQ" + }, + { + "Q": "At 6:12 I understand why you would pick a certain R value, but how are they derived? On my chemistry worksheet they aren't given or anything.\n", + "A": "R is nothing more than the Boltzmann constant multiplied by Avogadro s constant with a few unit conversion factors thrown in to adjust for whatever units you are using.", + "video_name": "erjMiErRgSQ" + }, + { + "Q": "At 6:11, where did Sal come up with the numbers for R?\n", + "A": "R is the universal or ideal gas constant in PV = nRT. These problems are called ideal gas equations because it is assumed that the gas behaves in an ideal manner, which would allow us to use the constant that Sal shows. It is a constant that makes the equation work... you ll either have a table or have to memorize this number, unfortunately.", + "video_name": "erjMiErRgSQ" + }, + { + "Q": "At 1:37, how big is one atm?\n", + "A": "One atm is the amount of air pressure that is normally on you if you are near sea level.", + "video_name": "erjMiErRgSQ" + }, + { + "Q": "\nThis might be a silly question but at 7:42, how come the (.082 L . atm/mole . K) becomes 1/mole??\n\nCheers", + "A": "Just look at the units. If you ve used consistent units then RT/PV has the units of 1/mol because the pressure and volume units have cancelled out. Or, a more useful way of looking at it is : PV = nRT divide by RT PV/RT = n Thus, PV/RT has units of mol, with all the other units cancelling out.", + "video_name": "erjMiErRgSQ" + }, + { + "Q": "at 4:04 why does it say peed in orange?\n", + "A": "I think it reads PE = 0. That is, the potential energy is equal to zero.", + "video_name": "kw_4Loo1HR4" + }, + { + "Q": "\nAt 4:04, Sal said you could solve this problem using kinematic formulas but how could you? Don't you only know distance and acceleration?", + "A": "s = 1/2*a*t^2", + "video_name": "kw_4Loo1HR4" + }, + { + "Q": "At 2:15 how does the object have no energy?I thought that everything always has energy\n", + "A": "everything has some combination of potential energy, kinetic energy, and internal energy...the internal energy of the block (related to the material at the atomic level) doesn t change during this example so it got left out of the explanation...but, yes, everything does always have some energy in the real world", + "video_name": "kw_4Loo1HR4" + }, + { + "Q": "\nAt 9:00- 9:30 Sal talks about how the velocity can be determined, but wouldn't that be affected by the shape of the slope? Which we haven't taken into account? An upslope at that particular height would cause a different velocity than a downslope surely?\nPlease clarify", + "A": "Your argument is totally correct ,but according to the question we have to only find the velocity of the body on the surface and not on the iceberg.", + "video_name": "kw_4Loo1HR4" + }, + { + "Q": "At 6:15 , all the potential energy gets converted to K.E.\nLet us say it fell straight down. At the last instant all the P.E. would be converted into K.E.\nBut then it hits the ground and will come to a rest. Then its height = 0 and so is its velocity. So both P.E. and K.E. are zero, then where did that energy go?\n", + "A": "That energy went into impacting the ground - making noise, deforming it, heating it.", + "video_name": "kw_4Loo1HR4" + }, + { + "Q": "\nAt 6:10 when the object is sliding , some of the energy will be converted to heat energy due to fiction right?? So, all the energy will not be converted to kinetic energy right?", + "A": "That s correct", + "video_name": "kw_4Loo1HR4" + }, + { + "Q": "\nIn example at 9:00 we evaluate velocity knowing PE, height and mass. But what about a slope? If you would drown the slope differently, let's say an infinite straight line at height 5 m. , then an object would have stopped after some amount of time due to friction or air resistance. Does Sal assumes that there are no other forces but gravity?", + "A": "yes, he s ignoring air resistance and friction so that you can focus on the concepts of PE and KE.", + "video_name": "kw_4Loo1HR4" + }, + { + "Q": "\nAround 9:05 Sal says that glycolysis is aerobic but , my understanding is that a cell without enough oxygen will go through fermentation instead of glycolysis. So, how is glycolysis still anaerobic?", + "A": "fermentation happens instead of the TCA cycle and oxidative phosphorylation and thus after glycolysis. Glycolysis does not require oxygen, and as such it is considered anaerobic; however, unlike fermentation it still occurs in the presence of oxygen.", + "video_name": "2f7YwCtHcgk" + }, + { + "Q": "At 13:05, it is said that each NADH produces 3 ATPs in the electron transport chain. So, glycolysis and Kreb's cycle give us 10 NADHs, which amounts to 10 \u00c3\u0097 3 = 30 ATPs in the electron transport chain. However, the electron transport chain produces 34 ATPs as said. May anyone please tell me from where the other 4 ATPs come from (All mechanisms proceed ideally, of course)? Thank you for any help.\n", + "A": "The Krebs cycle also produces 2 FADH2, which produce 1.5-2 ATP each during the electron transport chain = ~4 more ATP", + "video_name": "2f7YwCtHcgk" + }, + { + "Q": "\nAt 13:11, Sal says that FAD is being reduced to FADH during these processes. Isn't the reduced form of FAD actually FADH2?", + "A": "You are correct. I think if you go to that spot in the video, a small box should come up with the correction on the bottom right corner.", + "video_name": "2f7YwCtHcgk" + }, + { + "Q": "at 7:35 it needs 2 ATPs for cellular respiration?\n", + "A": "2ATP is needed to start cellular repiration (in glycollosis). In short, the 2ATP breaks into 2ADP and the remaining phosphate bonds to the gluclose molecule (and the other remianing phophate later in the cycle). This gives the energy required for glycollosis to occur and produce energy which results in a gain in at (38 in the full cycle for one glucose)", + "video_name": "2f7YwCtHcgk" + }, + { + "Q": "I don't understand what Sal means by \"on a net basis\" at 7:37. Someone please explain this concept to me...\n", + "A": "He summarized the glycolyse reaction - in some stage of this reaction you need to use 2ATPs [-2] and in some you produce 4ATPs [+4]. And, summing up, you generate ( produce ) 2 ATPs [-2 +4 = +2].", + "video_name": "2f7YwCtHcgk" + }, + { + "Q": "\nAt 7:34, what does it mean by net ATP?", + "A": "Some ATP are used in the production of ATP. Net is the produced - the used", + "video_name": "2f7YwCtHcgk" + }, + { + "Q": "\nIn my textbook, it is said that in cellular respiration, energy is produced in the form of ATP. But, in this video, around 3:19, Sal said that energy is used to produce ATP. Which one is correct ? I am confused. :(", + "A": "ATP is the energy currency in the cell and can be thought of as chemical form of energy. One way to think about is to think about it like a rechargeable battery. ATP can be used, giving up its stored energy in the phosphate bond and then recharged with the addition of energy to reform the phosphate bond.", + "video_name": "2f7YwCtHcgk" + }, + { + "Q": "At 8:54, he said that the structure on right is not going to contribute to the hybrid as much, what does he mean by that? If the structure is supposed to be a hybrid of both, does that mean the resonance structure is closer to the structure on the left?\n", + "A": "It means the true structure of the molecule is closer to the left one than the right. The bond lengths in acetone are consistent with a C-O double bond which gives a bit of weight to what he s saying.", + "video_name": "UHZHkZ6_H5o" + }, + { + "Q": "at 9:40 , why is the resonance structure on the right a minor contributor compared to the one on the left when the right one has both negative and positive charges assigned corresponding to the electro negativity of the atoms in the compound?\n", + "A": "Because in the right structure those full formal charges have been introduced where the left structure has none Less formal charges are generally better structures", + "video_name": "UHZHkZ6_H5o" + }, + { + "Q": "\nAt 4:00 min when sal names the 7,7, dibromo oct - 5 - yn - 4 -ol isn't there a chiral center on the number 4 carbon?", + "A": "You re right, there is a chiral center on C4. Since it s drawn flat (no wedges or dashes) there is no way to tell whether it s R or S and we d just assume that there is a racemic mixture (which you could indicate explicitely with +/- or R/S in a more complete name). If, for example, the OH was shown on a wedge or a dash, then we would indicate whether it was R or S in the name.", + "video_name": "nQ7QSV4JRSs" + }, + { + "Q": "at 5:20, is the informal name phenol?\n", + "A": "its not a benzene either way because he doesnt identify the conjugated double bonds. so it is only cyclic but not aromatic", + "video_name": "nQ7QSV4JRSs" + }, + { + "Q": "at 4:22 why is it not OCT-3-yn-5-ol since the double bond ought to take precedence over the -OH group? thanks!\n", + "A": "The double bond does not take precedence over the alcohol. Carboxylic acids > esters > amides > ketones > aldehydes > alcohols > amines > alkenes > alkynes > R = OR = X = Ph (those of equal precedence go in alphabetical order.", + "video_name": "nQ7QSV4JRSs" + }, + { + "Q": "At 8:55, I don't understand clearly why i1 equals (V1-V2)/R1.\n", + "A": "V1 and V2 are node voltages . That means they are measured with respect to the reference node (ground). This is suggested by the two orange arrows that start at the ground node and curve up to each node. Resistor R1 is connected between node 1 and node 2. The element voltage that appears across R1 is the difference of the two node voltages, V1-V2. Using Ohm s Law you compute the current through R1 as i = Voltage across resistor / R i = (V1 - V2) / R", + "video_name": "2lY757QaaKs" + }, + { + "Q": "at 5:09, can plasma be considered to be the fourth state of matter?\n", + "A": "Yes, it is the fourth state of matter.", + "video_name": "WenwtcuqOj8" + }, + { + "Q": "7:46: Sal mentions NH3 then at 8:09 Sal mentions HF and water is H2O. Is there a certain way to label a compound? Because the H appears in different spots in the examples provided.\n", + "A": "In general it is convention to have carbon first then hydrogen then followed by other compounds (C6H12O6). However, there is also a convention that in binary acidic compounds the hydrogen is at the beginning (HCl, HF, HBr etc.), and at the end of organic acids (R-COOH). Long story short there are several different formula conventions and naming conventions and they use separate rules, so you wind up with some variations in writing classic formulas.", + "video_name": "WenwtcuqOj8" + }, + { + "Q": "at 0:58, I don't understand what a plasma is\n", + "A": "Plasma is when an atom is vibrating so fast that the electrons are shaken off. This can be accomplished with high heat, low pressure, or an electromagnetic field.", + "video_name": "WenwtcuqOj8" + }, + { + "Q": "at 4:45 hank mentions that the hagfish doesn't have a vertebrae yet it is a vertebrate. how?\n", + "A": "He actually doesn t classify it as a vertebrate, just a chordate. Chordates are known to have spinal chords be their main attraction. But to be classified you also need a skull, a post-anus tail at one point in one s life cycle, the ability to make mucus, and other minor details. The hagfish, while not containing most of these has at least a skull and a post-anus tail so it can be grouped into this section because there nowhere better to put it.", + "video_name": "c7Yy9v8dH8s" + }, + { + "Q": "\nhow can I find the plane of symmetry in the meso compound in 9:30....it is impossible to find it?!", + "A": "Carbons on each end, and a OH group attached on both. Try to imagine drawing a line of symmetry DIAGONALLY.", + "video_name": "zNAL1R-hZr0" + }, + { + "Q": "In the last section of the video with the astronaut glove won't the reaction force of the heavy box push you even further away from the space arm contraption? slightly puzzled , Thankyou in advance\n(Sorry the timing is 1:09 and onwards)\n", + "A": "no. newton s third law says that every action has an equal and opposite reaction. So, pushing the box away from the space arm results in a force applied in the opposite direction, which is towards the space arm.", + "video_name": "By-ggTfeuJU" + }, + { + "Q": "At 7:16, when the astronaut is pushing an object away from their body, will the force increase if the astronaut increases the amount of time it takes to throw the object? (i.e. will the object have a greater equal and opposite force if the astronaut takes a long time to throw the object than if it was thrown quickly)\n", + "A": "No, the force is determined by how hard the astronaut pushes, not how long. The total momentum for the astronaut is a combination of how hard he pushes and how long", + "video_name": "By-ggTfeuJU" + }, + { + "Q": "At, 7:40, will the astronaut have to let go of the object to accelerate in the opposite direction or not?\n", + "A": "Of course she has to let go.", + "video_name": "By-ggTfeuJU" + }, + { + "Q": "3:15 - 4:30. Would it not mean if you took your foot away (presuming that your foot is not part of you), the sand would accelerate upwards. In the same way as: two persons pushing against each other and one of them moves out of the way. It's obvious that the person that didn't move out the way would fly forwards, unbalanced. Is this not the same thing as what Newton is saying. I'm not disregarding Newton's Law, I just don't understand it.\n", + "A": "The sand pushes up on you foot and your foot pushes down on the sand. If you foot does not push on the sand, the sand does not push on your foot. For the sand to accelerate upwards, something would have to be pushing upward on the sand. The sand cannot push on itself.", + "video_name": "By-ggTfeuJU" + }, + { + "Q": "\nat 4:09 , Sal said that the molecules of the rock would align themselves to the poles , but how do people track molecular alignment?", + "A": "In this instance, the alignment is evident because the rock has become magnetized.", + "video_name": "6EdsBabSZ4g" + }, + { + "Q": "\ni have studied in my text books that index finger should point towards the magnetic field.so i am a bit confused cz in this video at approx 6:40 and 10:00 ,sal has said that index finger should be pointing in the direction of the current....", + "A": "There are many different versions of these rules. Some use the right hand, some use the left, some define fingers one way, some do it another. They all lead to the same answer. Use whatever one works for you, and stick with that.", + "video_name": "l3hw0twZSCc" + }, + { + "Q": "\nAt 8:40, you talked about voltage drop. So, does the voltage differ from resistor to resistor? what does voltage drop mean?", + "A": "The voltage drop refers to the difference in electric potential at opposite ends of the resistor. If the resistor is carrying current there must be a potential difference, otherwise why are the charges moving. The PD is given by V = IR, where I is the current through the resistor.", + "video_name": "7vHh1sfZ5KE" + }, + { + "Q": "\nAt around 10:50 in the video sal goes from 20= current * 10 ohms to current = 2 AMPERES. How did he get to amperes from ohms?", + "A": "Voltage = Current x Resistance in terms of units: (volts)=(amperes) x (ohms) (ohms)=(volts) / (amperes) with a little rearranging, you get: (amperes)=(volts) / (ohms)", + "video_name": "7vHh1sfZ5KE" + }, + { + "Q": "At 13:00, why did you choose this as the longest chain? they're all the same.. can we choose any of the three lines as our main group? And the rest is methyl ? or is there a specific rule to follow?\nThank you so much.\n", + "A": "Right. They are all the same length. You can choose any one of them. Whichever one you choose, it will be an ethyl group with two methyl groups on C-1 (1,1-dimethylethyl).", + "video_name": "TJUm860AjNw" + }, + { + "Q": "\nAt 12:42, why is it necessary to say \"dimethyl\" instead of simply \"methyl\" if it's already indicated by the \"1,1\" that there are two methyls branching out?", + "A": "It works the other way. You count the methyl groups first, then you tell where each of them is. The name says, You have two methyl groups, and they are each on carbon-1 .", + "video_name": "TJUm860AjNw" + }, + { + "Q": "I am not sure but at 11:50 wont the compound name be (2,2-dimethylpropyl)cyclopentane ?\n", + "A": "In the older systematic name you use the point of connection to the parent chain as carbon #1. So from that carbon the longest chain is 2 carbons long which is why it is ethyl. There s also two other carbons coming off that first carbon so that is why it is 1,1-dimethyl. All together that is (1,1-dimethylethyl)", + "video_name": "TJUm860AjNw" + }, + { + "Q": "\nIs there any reason that Isobutylcyclopentane can't be written as i-butylcyclopentane?\nOr is it just one of those, \"we don't do this because they tell us not to,\" kind of science situations? (8:48 in video)", + "A": "No. There s no reason. isobutylcyclopentane, i-butylcyclopentane, and 3-methylpropylcyclopentane are all IUPAC names. You can write any of these.", + "video_name": "TJUm860AjNw" + }, + { + "Q": "\nIN 4:30 WHAT DOES 'sec' actually means?", + "A": "It means that the bond coming from the rest is attached to 2 carbons.", + "video_name": "TJUm860AjNw" + }, + { + "Q": "at 4:22, why do you call it secbutyl cyclopentane instead of 2-butyl-cyclopentane ?\n", + "A": "It is called sec-butyl cyclopentane because the sec shows how many carbons are attached to the carbon in the butyl chain that attaches to the cyclopentane, in this case, 2 carbons (on either side of the attached carbon). If it were 2-butyl cyclopentane, it would mean that you had a butane substituent in the second position of the cyclopentane..", + "video_name": "TJUm860AjNw" + }, + { + "Q": "At 13:05 near the end of the video, when describing the molecule. Is it not important to label the molecule in alphabetical order? For example. the end result is (1,1 dimethylethyl)cyclopentane. Would it not be more correct to have it as (ethyl - 1,1 -dimethyl)cyclopentane? as E is before M in the alphabet.\n", + "A": "(1,1-dimethylethyl) does not need to go alphabetically. Ethyl is the parent chain of this group, the 2 methyl groups are coming off of that ethyl, so the name needs to show that. It would be similar to naming 4-ethyldecane as decane-4-ethyl because d comes before e.", + "video_name": "TJUm860AjNw" + }, + { + "Q": "I had learned that while naming, the functional groups should be added in alphabetic order, . In 13:01, you named t-butyl cyclopentane as (1,1-dimethyl ethyl) cyclopentane. shouldn't it be (ethyl 1,1, dimethyl)cyclopentane because 'e' comes before 'm'?\nThanks!\n", + "A": "Hu hu. they re right", + "video_name": "TJUm860AjNw" + }, + { + "Q": "\nAt 9:55 where did he get the square root of 3/2 from?", + "A": "The cosine of 30 degrees is equal to the square root of three over two.", + "video_name": "_UrfHFEBIpU" + }, + { + "Q": "\nAt 16:00, Sal talks about all the different variations, 2 to the 46th. how does this work in twins? My cousins are identical but one has slightly curlier hair than the other, how can this work if they have exactly the same DNA, there both very different from each other in personality too. I know there monozigotic, but I don't know what that means.", + "A": "Even identical twins are not completely identical. There were slight differences in the womb, there continue to be differences when they are babies. Genes can be expressed more or expressed less depending on what other genes do and depending on environmental factors.", + "video_name": "DuArVnT1i-E" + }, + { + "Q": "\nAt 18:26 why did Professor Sal think that Sexual Reproduction is variation of population?", + "A": "Sexual reproduction is a huge contributor to genetic variation in a population. Because each parent only donates half of their genome, each indivudual offspring is guaranteed to have a unique genome of its own (Except in the case of identical twins). Mutation also contributes to variation in an important but less immediately noticeable way.", + "video_name": "DuArVnT1i-E" + }, + { + "Q": "\n14:01. Why is it 2 to the power 23 of possible combinations?", + "A": "Statistics: you have 23 [blanks] to be filled in a new chromosome. In each [blank] you can have genetic material from one or the other type (2 options). Therefore, the total combination is 2^23.", + "video_name": "DuArVnT1i-E" + }, + { + "Q": "At 12:22, it mentions different versions of allele genes. How many are there?\n", + "A": "We don t know. A gene can have any number of different alleles. Some alleles may have no phenotype at all, others may have a very significant phenotype.", + "video_name": "DuArVnT1i-E" + }, + { + "Q": "How can an organism be both a male and a female? @4:29\n", + "A": "Many organisms in nature are hermaphordites, possessing both male and female reproductive organs. The worm C. elegans is a common example of a hermaphrodite.", + "video_name": "DuArVnT1i-E" + }, + { + "Q": "\nsal u just told(15:07)that we get the chromosome from our parents and that means our parent too follow this then this will mean that the chromosome that the first human ever had are shill carried.am i right?", + "A": "Unless the first human didn t have children.", + "video_name": "DuArVnT1i-E" + }, + { + "Q": "2:35\ncan we modify DNA accroding to our wish.\ncan we design the codons on our own.\n", + "A": "Yes, technically in I think it was late 2007 a group a microbiologists created a new species of bacteria that was blue. The blue bit was just so that they could see them easier if it worked, but it s true. However the technology, like CarlBiologist said, is in its infancy and when they created the bacteria it was impossible for them to create anything much more complex then that. Medium-complexity bacteria was their limit, just because of how much trouble it is to assemble long strands of DNA.", + "video_name": "DuArVnT1i-E" + }, + { + "Q": "\nAround 14:10, Sal says he has 2^23 forms of contributing to his \"son or daughter\" . Wouldn't it be 2^22 since one chromosome indicates the sex?", + "A": "No, he will contribute a chromosome that will help decide what gender the child could be.", + "video_name": "DuArVnT1i-E" + }, + { + "Q": "At 2:45 what does delta T mean?\n", + "A": "Say we heat something from 20 Celsius to 50 Celsius, the delta T would be 50 - 20 = 30, i.e. 30 is the change in temperature. Now say we cool something from 60 Celsius to 10 Celsius, the change in temp is 60 - 10 = 50 celsius. It doesnt matter if we heat or cool something, we still have to use energy to change the state of the substance; the only difference is when we heat something, it takes in energy, when it cools it releases energy, but the calculation is the same. I hope u understand", + "video_name": "H7nrVDV8ahc" + }, + { + "Q": "At 1:00 where do the 2 hydrogen cations come from as showed on the products side of glycolysis?\n", + "A": "The H+ comes from NADH", + "video_name": "ArmlWtDnuys" + }, + { + "Q": "Around 9:00 Hank says \"Haeckel influenced from Darwin and Darwin disagreed with him\".\n\nWhat does that mean? Is it a mistake?\n", + "A": "It is not a mistake, it just means that Haeckel was inspired by Darwin, but Darwin didnt agree with where Haeckel was taking his (Darwins) ideas.", + "video_name": "cstic6WHr2E" + }, + { + "Q": "\n09:09 PE=m*g*h right? why he did not multiply it to the gravity?", + "A": "The weight of 10 N is already the result of Fg = m * g.", + "video_name": "vSsK7Rfa3yA" + }, + { + "Q": "\nAround 9:22, Sal mentioned that PE is 10kg times height. What about gravity? I thought PE equals Mxgxheight?? Please help. Thanks.", + "A": "I think you misheard. He didn t say 10kg he said 10N. N would already include any relevant gravitational force.", + "video_name": "vSsK7Rfa3yA" + }, + { + "Q": "At min 9:00 you say that the heater is switched off by the bimetallic strip if it gets too hot. That means that the fan switches off too, right? Because as you said, the heater works as a resistor to the fan motor....\nThis implies that the dryer stops from working if it gets hot, which obviously cant be true!\nI am loving this video btw :D\n", + "A": "If the circuit is broken then both the heater and the motor would stop functioning, however metal takes time to cool down. I do not know the schematic of the circuit", + "video_name": "Vq7EOmvU1eQ" + }, + { + "Q": "\nAt 5:20, why does the lone pair repel the other bonds more strongly? Didn't it act just like a regular bond in the previous videos?", + "A": "When you are drawing dot structures, you are not dealing directly with geometries. When you start talking about bond angles, the difference between the repulsion from two electrons belonging to a single atom (lone pair) vs the repulsion from two electrons being shared by two atoms (sigma bond) becomes important.", + "video_name": "BM-My1AheLw" + }, + { + "Q": "at around 4:50 minutes sal said the volume of 1 pound lead is more than volume of 1 pound lead .shouldn't it be the reverse of it?\n", + "A": "he says that the volume of one pound of feathers will be a lot more than the volume of 1 pound of lead because feathers have a smaller density than lead", + "video_name": "5EWjlpc0S00" + }, + { + "Q": "at 7:13 howcome ligers arnt species\n", + "A": "Organisms are considered part of a species if they can breed amongst themselves. Since ligers are sterile and unable to produce offspring, then that s your explanation.", + "video_name": "Tmt4zrDK3dA" + }, + { + "Q": "At,08:23,why is the upper limit zero ,as we are putting r^infinity which will be zero so what happened to the h^2?\n", + "A": "As r gets larger, theta gets larger. As theta gets larger, the vertical force component gets shorter. At point infinity, theta becomes a right angle and the force is effectively flat (0 vertical).", + "video_name": "TxwE4_dXo8s" + }, + { + "Q": "6:14\nHe integrates u^(-3/2) to -2u^(-1/2). Shouldn't it instead be (-2^(-1/2))/3 ? (since you have to divide by -3/2)\n", + "A": "Try taking the derivative of your answer and see if you get the original equation", + "video_name": "TxwE4_dXo8s" + }, + { + "Q": "At 5:12, David says 'from 3 to 5'. Wouldn't that be -5?\n", + "A": "Yes, that s correct. Since the turtle never makes it to +5m, you can assume that whenever he says five in this video, he means -5m.", + "video_name": "GtoamALPOP0" + }, + { + "Q": "\nWhy at 4:04 does the .0100 turn into acetate?", + "A": "As you use up the reactants, you are making products. So, as CH3COOH and OH are being used up( hence the (-) sign), CH3COO is being made ( hence the (+) sign).", + "video_name": "WbDL7xN-Pn0" + }, + { + "Q": "at 00:27, whats velosity\n", + "A": "first of all it is velocity not velosity velocity is the rate of change of the position of an object ,equivalent to a specification of its speed and direction of motion or Or it is speed in a specific direction", + "video_name": "zAx61CO5mDw" + }, + { + "Q": "\nIs angular velocity a pseudo scalar quantity or a pseudo vector quantity? He mentions it as a (pseudo) scalar at 3:47 but as a pseudo vector at 2:57. Which one is correct?", + "A": "Angular velocity is a vector. Sal mentions at 2:57 that angular velocity is a vector quantity and at the 3:47 he says it is often treated as a scaler not that it is a scaler.", + "video_name": "zAx61CO5mDw" + }, + { + "Q": "\nAt 2:04 you were talking about net force. I do not know what the net force is. So please tell me.", + "A": "Net force is a resultant force or the vector sum of all the forces onto the body.", + "video_name": "1E3Z_R5AHdg" + }, + { + "Q": "At 1:56,what is the normal force?\n", + "A": "The normal force is the force from the surface perpendicular to the object. In this case, it is the force of the chair pushing up on the person.", + "video_name": "1E3Z_R5AHdg" + }, + { + "Q": "At 1:05 , if the air resistance isn't assumed negligible,is vertical velocity going to slow down,too?\n\n(sorry if grammar mistakes... not very good at English...)\n", + "A": "yes. Both vertical and horizontal velocities will be affected by air resistance", + "video_name": "sTp4cI9VyCU" + }, + { + "Q": "@3:40 What don't we use velocity as a vector quantity?\n", + "A": "Sal does. It is showing the direction ( displacement ). At least this is my understanding. You can try to ask Sal.", + "video_name": "vZOk8NnjILg" + }, + { + "Q": "at 3:00 sal starts drawing change in velocity vectors. they are essentially the difference of the 2 velocity vectors, right?!\n", + "A": "Essentially, yes. The 2nd velocity vector minus the 1st velocity vector.", + "video_name": "vZOk8NnjILg" + }, + { + "Q": "\n@3:04 when the tail of the two vectors are joined together, shouldn't the resultant vector be the diagnol (parallelogram law of addition) ?", + "A": "Sal is calculating change in velocity, not overall velocity. If it was overall velocity, then yes, you would draw the head of one of the arrows adjoining the tail of the other, and calculate the diagonal.", + "video_name": "vZOk8NnjILg" + }, + { + "Q": "\nat 5:00 why did you preform SN1 even though the nucleophile carries a negative charge and it is supposed to be a strong nucleophile so it must go SN2 ??", + "A": "The answer is: steric hindrance. There isn\u00e2\u0080\u0099t enough room for the nucleophile to attack the back side of the carbon bearing the leaving group.", + "video_name": "sDZDgctzbkI" + }, + { + "Q": "\nAt 1:40, where is the blood pressure taken?", + "A": "on the upper arm where the brachial artery is. this is because the artery is close to the skin here and it is more convenient than taking it from the neck or the leg", + "video_name": "J97G6BeYW0I" + }, + { + "Q": "\nAt 02:06, why blood pressure is measured on brachial artery", + "A": "It s easy to get to, in most people it s a very reliable measurement, and most people don t mind having the cuff around their arm during the measurement process.", + "video_name": "J97G6BeYW0I" + }, + { + "Q": "At 8:24, why is there a layer of non-fusing helium? isn't all helium supposed to fuse and form carbon and oxygen? Help!\n", + "A": "That layer isn t at a temperature/pressure where it can fuse.", + "video_name": "EdYyuUUY-nc" + }, + { + "Q": "\nAt 3:15 is are sun a \"main sequence\" star?", + "A": "Yes, for now. In 5 billion years, it will run out of hydrogen and move away from the main sequence line and into the red giant phase.", + "video_name": "EdYyuUUY-nc" + }, + { + "Q": "At 1:41, it is mentioned that the sun today is 'brighter and hotter' as it is fusing faster than it was when it was born 4.5 to 4.6 billion years ago. Is this an antithesis for global warming?\n", + "A": "No, the Sun warming process is much slower than global warming appears to be. The Sun will get 1% brighter in the next 100 million years.", + "video_name": "EdYyuUUY-nc" + }, + { + "Q": "At 11:58 Sal says it would take a long time for a white dwarf to turn into a black dwarf, but do we have any estimation for the time it would take? And how long does it take for a planetary nebula to disappear?\n", + "A": "If we define a black dwarf as a white dwarf cooled to 5 K, then it would take 10\u00c2\u00b9\u00e2\u0081\u00b5 years to form (which is considerable larger than the current age of the universe). Planetary nebulae, however, are very short-lived. They only last for tens of thousands of years on average.", + "video_name": "EdYyuUUY-nc" + }, + { + "Q": "\nAt 8:38 why did Sal say 'you have helium that is not fusing'- whatever helium is there outside the core is continuously fusing due to the pressure right?", + "A": "No, that s what he just explained to you. The helium outside the core may not be fusing because the pressure may not be high enough.", + "video_name": "EdYyuUUY-nc" + }, + { + "Q": "What part(s) of a star are luminous? Does the outside gas layer of a star produce light? (Such as at 11:11).\n", + "A": "The core of the star produces light from fusion. The rest the gas just puts pressure on the core and scatter the light emitted by fusion.", + "video_name": "EdYyuUUY-nc" + }, + { + "Q": "at 2:30 why does the pulse turns upside down after reflection?\n", + "A": "on reflection, there is a change in phase. (If the medium is fixed... if it is free to move, then there is no phase change)", + "video_name": "gT0IqL1dyyk" + }, + { + "Q": "\nat 1:47 does anyone know what galaxies the circled ones are?", + "A": "I don t think anyone would bother to name all the billions of galaxys that Hubble can see. If they had names, they would be numbers.", + "video_name": "Wl4re38deh0" + }, + { + "Q": "\nAt 0:36, she says that there is a dynamic equilibrium. I thought we were discussing chemical equilibrium. How do chemical and dynamic equilibriums relate?", + "A": "They are the same thing - the chemical equilibrium is dynamic, as per Le Chatelier s Principle.", + "video_name": "5gujU2QcGcY" + }, + { + "Q": "At 5:36 there is a mention of when you add calcium carbonate (solid), you don't interrupt equilibrium. However thinking about that makes me wonder... For example, you add a scoop of calcium carbonate, which has a certain volume into this 'fixed' volume, isn't it so that it will change the pressure and/or volume slightly? And by doing so change the equilibrium a bit? Hope I'm clear. Thanks\n", + "A": "That s a great question Sander Sloof! The assumption made in the video, which I unfortunately failed to state, is that changing the amount of solid did not change the total volume of the container significantly. I apologize for any confusion! Your thinking is entirely correct-if enough solid was added to change the volume of the container, that would also change gas pressures and perturb the reaction from equilibrium. Thanks for commenting!", + "video_name": "5gujU2QcGcY" + }, + { + "Q": "\nat 0:22 my beloved Mr.Khan said if there is g the situation will be little bit different but from equation T = 2pi sqrt(m/k) , must not g have any effect on this case?", + "A": "Good observation :-). He said that because the figure that he made wouldn t be as simple as it is if we were dealing with gravity. There would be the weight of the object acting downwards (which would affect its position) and a whole lot other things. But eventually the formula would turn out to be the same.(T=2pi sqrt(m/k)). So I think he said that so that we don t get confused by the diagram. That s it. :-)", + "video_name": "oqBHBO8cqLI" + }, + { + "Q": "\nat 9:28, Sal used the formular Qr=2*pi*r*dr*sigma (i'm sorry i can't write the sigma symbol on my laptop) to calculate the area of the ring but i don't quite get it. Can anyone show me how to understand it? Thank you very much.", + "A": "2*pi*r shows the circumference of the ring which the width can be ignored. cut the ring into infinite tiny rectangles, each rectangle has a width of dr. so the total area can be expressed as 2*pi*r*dr sigma. Hope this would help.", + "video_name": "prLfVucoxpw" + }, + { + "Q": "at 9:52 sal mentioned test charge what does that mean?\n", + "A": "A test charge is a small charge that we imagine placing somewhere in a field to help us think about the direction and magnitude of the field at that point.", + "video_name": "prLfVucoxpw" + }, + { + "Q": "\nAt 8:50, \"Acyl\" groups are introduced. But what is the difference between an acyl group and a carbonyl group? Don't they have the same structures?", + "A": "Great question, very tricky to answer too! A carbonyl has the structure of C=O only. An acyl has the structure of R-C=O, where R is any hydrocarbon. A carbonyl is present in a acyl group. Example: (CH3)2-C=O is has an acyl group, which is CH3-C=O. It also has a carbonyl group, C=O.", + "video_name": "OpyTJbzA7Fk" + }, + { + "Q": "\nat 7:48 why would Oxygen have a positive charge?", + "A": "2 electrons in the S orbital (-2), and 1 lone pair of electrons (-2), and 3 covalent bonds (3 x-1), give a total electron charge of -7 and oxygen has 8 protons so it ends up with a net positive charge.", + "video_name": "OpyTJbzA7Fk" + }, + { + "Q": "I noticed how you said, at 3:10, \"The period does not change this way.\" This statement was referring to the horizontal period I presume. Is there a vertical period I am unaware of?\n", + "A": "The period is the time for one oscillation. There s no horizontal or vertical to it.", + "video_name": "6M_bjRzyUn0" + }, + { + "Q": "At 1:58 why is it that although there are two sets of genetic code, the sister chromatids are still considered as only 1 chromosome?\n", + "A": "The sister chromatids are still attached to each other by a centromere. Only when separated are they considered 2 chromosomes. You usually visualize a chromosome as X-shaped, do you not? That is a chromosome that has undergone DNA replication therefore it has two sets of genetic code.", + "video_name": "TKGcfbyFXsw" + }, + { + "Q": "\nat 8:36 what is happening here how the two events are experienced at different times\nin A and B frame of reference", + "A": "Time is relative.", + "video_name": "2BVGig1LXLs" + }, + { + "Q": "\nOK, at 2:20, why did you divide acceleration by 2?", + "A": "mm. alight thnx", + "video_name": "P7LKEkcNibo" + }, + { + "Q": "I don't understand Sal's \"Oil Rig\" reference at 8:57, it is something to do with NADPH's function in cellular respiration?\n", + "A": "It refers to Redox reactions! Its a little acronym to remember the difference between oxidation and reduction. O-oxidation i-is l-lose and R-reductuion i-is g-gain. I was taught Leo the lion says Ger. Which is the same principle! (Loss electrons= oxidation (LEO) and Gain electrons=reduction (GER))", + "video_name": "-rsYk4eCKnA" + }, + { + "Q": "At 10:35, Sal says that the dark reactions are called the Calvin Cycle, aren't light reactions called the Calvin cycle and dark reactions, the Hill reactions?\n", + "A": "The Light Reactions are called the Light Reactions and the Calvin Cycle is sometimes called the dark reactions, but it is more accurate to describe the Calvin Cycle as the light independent reactions because the Calvin Cycle occurs whether the sun is shining or not.", + "video_name": "-rsYk4eCKnA" + }, + { + "Q": "at 9:20, the molecule has 3 carbons instead of 4, right? because the double bond is between two carbon molecules\n", + "A": "Yes that molecule only has three carbons", + "video_name": "8x8tA4YPhJw" + }, + { + "Q": "\nat 8:22, why doesnt the n\n-14 also have a half life", + "A": "Some atoms are stable, others aren t. C-14 is not, so it decays, but N is stable, so it doesn t decay.", + "video_name": "9REPnibO4IQ" + }, + { + "Q": "At about 7:25, why didn't he just add T2 to the zero in the blue equation so he would get sqrt(3)T1 = T2 and plug that into any T2s as opposed to him multiplying the second equation from the bottom by the sqrt(3) and making it more complicated? I got the same answer for both. Is there a mathematical reason he didn't do that?\n", + "A": "That s just the strategy that he used to solve this calculus , your strategy is correct too.I think he did this way because it makes more easy to solve the system of equations by elimination.", + "video_name": "zwDJ1wVr7Is" + }, + { + "Q": "\n7:25 \u00c2\u00bfand according with that graph how many electrons will lose the element with tahat energy 1 or all the shell?", + "A": "That graph is for the first ionisation energy only, so the energy required for an atom to lose one electron only.", + "video_name": "5CBs36jtZxY" + }, + { + "Q": "At 2:26, how do you know what to dram for the ion size?\n", + "A": "These are just schematics (pictures not intended to realistically depict something or indicate actual values)!", + "video_name": "HBi8xjMchZc" + }, + { + "Q": "\nSal says that fog is an example of a colloid. And he says at 5:38 that fog is water molecules(H2O) that are inside air. Isn't H2O's molecular mass much less than 2nm. I think it has to be because Cs is 0.26 nm. If the H2O molecule is less than 2nm, shouldn't it also be a solution ?", + "A": "Eventhough, the size of H2O particles is less than 2nm, fog is a colloid as it exhibits tyndall effect(scattering of light), a distinguishing traits among colloids.", + "video_name": "3ROWXs3jtQU" + }, + { + "Q": "\nAt around 4:45 Sal draws a cup with liquid in it and says \"this could be air, whatever...\" . Funny cause AIR isn't liquid.", + "A": "Gases are quite able to make solutions.", + "video_name": "3ROWXs3jtQU" + }, + { + "Q": "at 7:20 what does aq stand for?\n", + "A": "aq is the state description for an aqueous solution.", + "video_name": "3ROWXs3jtQU" + }, + { + "Q": "\nAt 2:38 you talked about the amplitude, but if I have a higher amplitude does it make the frequency low or high?", + "A": "Amplitude is independent of frequency.", + "video_name": "tJW_a6JeXD8" + }, + { + "Q": "\nat 6:48 in the video i still don't get the 10 cycles over second what does that equal", + "A": "A cycle is the same as a period. That is, one full wave from peak to peak. The number of cycles per second is the frequency of the wave. So 10 cycles per second means there are 10 full waves every second, and this means the frequency is 10 Hz (Hertz is a unit which just means cycles per second ). It also means that the period is T = .1 s. The frequency and the period are always reciprocals of each other.", + "video_name": "tJW_a6JeXD8" + }, + { + "Q": "\nAt 8:54, Doesn't the wave length get reduced or shortened as time progresses?", + "A": "actually the amplitude of the wave decreases which slowly brings it to end the wavelength remains constant.", + "video_name": "tJW_a6JeXD8" + }, + { + "Q": "at 1:04 you said that waves don't really need a medium to travel in. Can you give an example of a type of wave that doesn't need a medium(other than light)\n", + "A": "Any other electromagnetic wave. Microwaves, for example. Mechanic waves always require a medium.", + "video_name": "tJW_a6JeXD8" + }, + { + "Q": "Is Sal saying 'Lamda' at 12:55 or is he saying 'Landa'?\n", + "A": "Lambda (the Greek letter that looks like an upside down Y ).", + "video_name": "tJW_a6JeXD8" + }, + { + "Q": "At 10:15 when Sal says that he could write it as a Vector, What does he mean? What is a vector?\n", + "A": "A vector is a value that also has a direction. Since velocity has a direction, Sal is saying he could write down not only the value of the velocity (the magnitude ), but also the direction. Doing math with vectors is little more complicated and the subject of later material. Sal didn t bother to do that in this video.", + "video_name": "tJW_a6JeXD8" + }, + { + "Q": "why does nitrogen not 'like to react' with other chemicals? 8:25\n", + "A": "In its gaseous form (N2) it is triple bonded which is quite strong and thus doesn t want to react.", + "video_name": "lzWUG4H5QBo" + }, + { + "Q": "at 4:18 what is ATP?\n", + "A": "Adenosine Tri-Phosphate (ATP) is a small molecule that cells use as a coenzyme. It s one of the most basic signal transporting molecules in living things. It does many biochemical processes: From activating membrane transporters to regulating transcription.", + "video_name": "lzWUG4H5QBo" + }, + { + "Q": "\nAt 3:53, can someone clarify what temperature has to go with the energy in the molecule?", + "A": "Temperature IS kinetic energy of molecules.", + "video_name": "WScwPIPqZa0" + }, + { + "Q": "\nWhen the equation P=nRT is formed at 4:56 I tried to find the units for R. I got it as m(superscript) -3 i.e. volume. So if the equation is correct then why do we need the equation PV=nRT?", + "A": "R is a constant for accuracy. R s units should be atm*L/moles*K. That allows all the units to cancel. The reason why you need Volume in the equation is because volume also affects pressure.", + "video_name": "WScwPIPqZa0" + }, + { + "Q": "\nAt 2:20, can you please explain how is temperature related to average energy?\nCan you also tell me which video explains pressure,density,volume for a substance are explained ?", + "A": "It comes from the video on the Kinetic Molecular Theory of gases. The result at the end of the video is that KE(avg) = \u00c2\u00bdkT. So KE(avg) \u00e2\u0088\u009d T and T \u00e2\u0088\u009d KE(avg). I m don t think there is a video explaining how P, V, and \u00cf\u0081 are related for substances in general, but the video on Boyle s Law explains the relationship between P and V for an ideal gas.", + "video_name": "WScwPIPqZa0" + }, + { + "Q": "1:45 does that mean that helium particles \"whiz around\" faster then air particles?\n", + "A": "yes. its for the same reason when you inhale helium gas and try to speak your voice seems to be at a very high pitch", + "video_name": "WScwPIPqZa0" + }, + { + "Q": "At 3:42, the example compares two balloons, one with many particles and one with only one particle. The particles are the gas particles, how can we have only 1 gas particle in a balloon?\n", + "A": "The example is a simplification of the real world. Each particle in the example represents many billions of trillions of particles in a real balloon.", + "video_name": "WScwPIPqZa0" + }, + { + "Q": "at 6:50 or any other equations why are there constant?\nlike PV=nRT <- what is that \"R\"?\nand they don't explain what's it for.\nare those things so complicated that we can't understand ?\n", + "A": "The R is just a conversion factor that takes account of the types of units you chose to use for P, V, and T. Nature does not arrange herself to match Pascals, cubic meters, and Kelvin, so we have to adjust to her.", + "video_name": "WScwPIPqZa0" + }, + { + "Q": "\nAt 4:39, he changes one of the hydrogens to an R group for the H3O+. Why was this necessary? I understood that that could stay H3O+.", + "A": "I believe the reaction will be taking place with alcohol as the solvent (not in water), so there really wouldn t be any H3O+ ...", + "video_name": "rL0lDESwwv8" + }, + { + "Q": "\nAt 9:12, we learn that the oxygen was reduced by the carbon. Wasn't it also reduced by the hydrogen, as 2 out of the 4 oxygens gained their negative reduction because of the addition of 2 positive hydrogens each?", + "A": "The hydrogens don t change oxidation states through the reaction though so they didn t take part in the reduction/oxidation part of this reaction", + "video_name": "OE0MMIyMTNU" + }, + { + "Q": "Hello! I'm a beginner in chemistry and at 8:20 I lost it. Why does the oxygen gain 8 electrons and not 2? It's oxidation number is 2- Can someone explain? What happens to the other 6 gained electrons?\n", + "A": "There s four oxygen atoms because of the coefficients. Four of them each gaining 2 electrons = 8", + "video_name": "OE0MMIyMTNU" + }, + { + "Q": "\nAt around 8:00, is hydrogen also reducing oxygen by giving oxygen electrons?", + "A": "No. Hydrogen doesn t change its oxidation state in this reaction. Thus, it cant oxidise or reduce anything. Hope this helps :)", + "video_name": "OE0MMIyMTNU" + }, + { + "Q": "at 2:28, does it matter if the equation isn't balanced?\n", + "A": "In most cases yes! If you have an unbalanced redox equation involving charged ions, then if the equation is not balanced, the oxidation numbers will be wrong and therefore your half equations will be wrong. In the case of the video, balancing would not matter, but it s safest to balance first and then work out oxidation numbers. Hope that helps! :)", + "video_name": "OE0MMIyMTNU" + }, + { + "Q": "\nAt 9:15 , why don't both the oxygen's make double bonds with sulfur? I know this breaks the octet rule, but sulfur is in the 3rd period, so isn't it more important to have no formal charge than obey the octet rule?", + "A": "It is because Oxygen is more electronegative, and therefore will consume more of the electrons. Sulfur, being less electronegative, cannot have more electrons around it than the more electronegative oxygen", + "video_name": "3RDytvJYehY" + }, + { + "Q": "Isn't boron trifluoride tetrahedral, not trigonal planar as the video states at 4:25?\n", + "A": "No, BF\u00e2\u0082\u0083 is trigonal planar.", + "video_name": "3RDytvJYehY" + }, + { + "Q": "At 10:15, why wouldn't the 2 non-bonded electrons be in different electron clouds, or different orbitals? It seems that Hund's rule would cause the 2 electrons to join different oribitals.\n", + "A": "Which orbital do you suppose the second one would go in to? Something to keep in mind: VSEPR theory predicts a bond angle of 120 degrees for SO2, and that s very close to what we actually observe (119 degrees)", + "video_name": "3RDytvJYehY" + }, + { + "Q": "At 2:50 he said that the completed-octet version of the dot structure and the dot structure with minimized charge are acceptable representations of the molecule. But which ones do molecules generally \"pick\" in nature?\n", + "A": "The actual structure is a hybrid of all possible structures, but the ones with minimized charge separation are closest to the actual structure.", + "video_name": "3RDytvJYehY" + }, + { + "Q": "\nAt 2:00, Khan resembles a ray to a marching band, however, I don't see how one part of a single ray would leave the water before its other part. Also, if (in any way), a piece of a ray does leave he water first, why doesn't the speed differentiation cause the photon (ray= photon?) to start spinning instead of bending??", + "A": "A ray is just a way to draw light. The light is really a wave, right? Not an arrow. To understand refraction, you really have to use the wave behavior of light, not think of it as a photon.", + "video_name": "jxptCXHLxKQ" + }, + { + "Q": "\nat 1:02, why is refractive index useful and what is it used to measure", + "A": "Refractive index is used to measure how much the speed of light travels faster in a medium than that of air. For example, refractive index of diamond is 2.41. So, in air, the light travels 2.41 times faster than in diamond. I hope this helped!", + "video_name": "jxptCXHLxKQ" + }, + { + "Q": "4:08 I think this is hept-2,4-diene.\n", + "A": "ya it is", + "video_name": "KWv5PaoHwPA" + }, + { + "Q": "\nAt 3:30 why is the answer hepta-2,4-diene and not hept-2,4-diene. Where does the letter a come from? Does the letter a indicate something or is it just spelling?", + "A": "It s just how you name molecules with multiple double bonds. Also makes it flow a bit better off the tongue.", + "video_name": "KWv5PaoHwPA" + }, + { + "Q": "at \"4:17\", why did the first C of the chain named H3C and why not CH3?\n", + "A": "It was written as H3C to highlight that it is the carbon of the methyl group (CH3) that bonds the the neighboring carbon in the chain, not a hydrogen. The methyl group can be written as either H3C or CH3, it does not matter; it s just clearer if written as H3C in this case. H3C is usually used at the ends of molecules.", + "video_name": "KWv5PaoHwPA" + }, + { + "Q": "Brother Sal, I don't understand this> At 4:35 u said that \"double bond will take presidence....\". What does it mean?\n", + "A": "well answered =]", + "video_name": "KWv5PaoHwPA" + }, + { + "Q": "at 6:22, if you are trying to find the largest carbon chain, shouldn't it be 8 if you start counting from the carbon on the far left methyl group? Is it different if its a cycle?\n", + "A": "If there is a ring structure that has more carbons than any chains connected to the ring, then use the number of carbons in the ring as the longest chain. In this case, 6 carbons = hex , and since it is in a ring use the prefix cyclo- . The methyl group then becomes a substituent.", + "video_name": "KWv5PaoHwPA" + }, + { + "Q": "\nAt 2:47 Sal says 'if we are stationary relative to the ether right now'. How can earth be stationary relative to the ether at a point in its orbit, if the earth is always moving at 30 km/s.", + "A": "Exactly! That s Sal s point.", + "video_name": "88hs5LcCoX4" + }, + { + "Q": "\n1:30 why Na+ cant react with water ?", + "A": "Na+ is a cation, having a positive charge. Needing a negative charge from water, it could potentially react with either H+ or OH-. H+ doesn t work since it has a positive charge. OH- does not work because the supposedly formed substance would be NaOH, a strong base. Strong bases are not formed since they dissociate to near completion.", + "video_name": "HwkEQfsJenk" + }, + { + "Q": "\nAt 1:18 , how is pH related to the formation of salts?", + "A": "Salt of strong acid + strong base \u00e2\u0086\u0092 pH = 7. Salt of strong acid + weak base \u00e2\u0086\u0092 pH < 7. Salt of weak acid + strong base \u00e2\u0086\u0092 pH > 7. Salt of weak acid + weak base \u00e2\u0086\u0092 pH depends on which is stronger acid or base.", + "video_name": "HwkEQfsJenk" + }, + { + "Q": "at 1:25 what is an oxidation state?\n", + "A": "An oxidation state is a tool to write the electronic charge(s) of a molecule without resorting to partial charges (e.g. 1/2-).", + "video_name": "M7PnxSQedkM" + }, + { + "Q": "\nAt 2:27 what is the reducing agent?", + "A": "a substance that tends to bring about reduction by being oxidized and losing electrons.", + "video_name": "M7PnxSQedkM" + }, + { + "Q": "3:36 so if the 2 was positive it would not be neutral ?\n", + "A": "Right it would be positive, and vice versa. But in both of these compounds the positive and negative charges cancel each other out.", + "video_name": "M7PnxSQedkM" + }, + { + "Q": "At 1:19,why does magnesium loose two electrons?\n", + "A": "It loses two electrons because it strives as any element to become stable, which is to say to have either 8 or 2 electrons on its outer shell. So to become stable, it only needs to lose the 2 electrons on its outer shell for the shell under the initial shell to become the outer shell.", + "video_name": "M7PnxSQedkM" + }, + { + "Q": "9:21 Why aren't children vaccinated against meningococcus earlier than the age o two?\n\nEdit: I found an answer to this question in an Infectious diseases textbook. Apparently the immune system of children less then two years old is not mature enough to respond to a polysacharide antigen of N. meningitidis, thus vaccination before the age of two would be futile.\n", + "A": "I disagree with Amelia on one point. Babies are given a Heb B vaccine at birth. I d assume that there would be just as much of a stigma regarding that. Also, babies are now given a whole slew of vaccines at age 2 months old. If it were safe and effective in neonates, it would be on the schedule starting at 2 months.", + "video_name": "CnXuSCaCNBo" + }, + { + "Q": "I've noted that Jay writes ionic compounds like this: Na+-OH (7:32)\nIs this the standard way of writing it? I'm used to seeing Na+OH-, with the sign after the anion... (both of course in superscript).\n", + "A": "see the things are same........but specifically in the hydroxide anion , due to the more electronegative character of the oxygen atom the bonded pair of electrons in the molecule rest near the oxygen atom.....hence jay has made the negative charge over the oxygen atom...", + "video_name": "My5SpT9E37c" + }, + { + "Q": "\nat 10:06 what does he mean when he says increases the strength of the nucleophile?", + "A": "In a polar protic solvent, the nucleophile is solvated by the solvent molecules. The nucleophile has to push these solvating molecules out of the way in order to attack the \u00ce\u00b1 carbon. A polar aprotic solvent preferentially solvates the metal cation. That means that the nucleophile is relatively unsolvated or \u00e2\u0080\u009cbare\u00e2\u0080\u009d. It can then much more easily attack the \u00ce\u00b1 carbon. This makes it a stronger nucleophile.", + "video_name": "My5SpT9E37c" + }, + { + "Q": "At 4:43 it shows water molecules moving through protein channels. I am aware that the cell membrane does not allow watersoluble/hydrophillic/lipidphobic substances to pass straight through but I thought small molecules such as oxygen gas, carbon dioxide and water were able to pass through easily because of their size, without needing to move through channel proteins. Is this incorrect? Thanks\n", + "A": "Channel proteins allow passive transport of the small molecules like oxygen gas and water, meaning these molecules can flow through from the higher concentration to the lower one without using energy. This is what the video means by easily passing through the membrane, since no ATP is required. The water and oxygen cannot pass through anywhere they want, otherwise the membrane would be so full of holes that it would be useless! Hope this helps!", + "video_name": "TyZODv-UqvU" + }, + { + "Q": "Sorry I'm confused because at 4:00 it was mentioned, I thought Hypotonic was when water would rush in and explode while hypertonic was when it would shrivel up.\n", + "A": "That is correct - however, this terminology is very tricky. See the example below: You have a situation with less water in cell, more in envirnoment The cell is hypertonic to the solution, and the solution is hypotonic to the cell. The cell is in a hypotonic solution.", + "video_name": "TyZODv-UqvU" + }, + { + "Q": "\nat 8:34 Sal said that if we cut a magnet into half then two more magnets will appear. But notice that the left side (from the viewer's point of view) of the 1st magnet is north pole but the left side of the second magnet is south. But why?", + "A": "because a magnet is made of a bunch of smaller magnets that stick together, north to south and south to north", + "video_name": "8Y4JSp5U82I" + }, + { + "Q": "In 6:39, what is the nearest star? I just want to know.\n", + "A": "Proxima Centauri", + "video_name": "5FEjrStgcF8" + }, + { + "Q": "I'm not sure where I heard this (probably early elementary school), but I remember learning that the red spot on Jupiter is 3x as big as Earth. If that's true, I feel like Jupiter can't be 10x as big as Earth, like Sal says at 4:12, because the red spot isn't 30 percent of the planet. Am I crazy in remembering that the red spot is the size of 3 Earths?\n", + "A": "Jupiter s circumference is 11 times that of Earths. But that gives it a surface area more than 100x larger. The red spot is about 2 or 3 earth diameters wide.", + "video_name": "5FEjrStgcF8" + }, + { + "Q": "at 0:15 Sal says that we can't comprehend thing that are small compared to the size of the universe, is he referring to the galaxies?\n", + "A": "An example would be galaxies, other examples also include black holes, superclusters, clusters, et.c", + "video_name": "5FEjrStgcF8" + }, + { + "Q": "At 6:56 Sal said that the nearest star is 200,000 times the distance from the earth to the sun; but isn't the sun considered a star?\n", + "A": "Yes. Obviously he meant the nearest star other than the sun, right?", + "video_name": "5FEjrStgcF8" + }, + { + "Q": "5:37 What does AU stand for?\n", + "A": "It stands for Astronomical Unit, which is the average distance between the Earth and the Sun, about 93 million miles, or 1.5*10^11 meters.", + "video_name": "5FEjrStgcF8" + }, + { + "Q": "\nAt around 7:45, the second equation of CO2 plus HbO2 does not seem to be a balanced equation. Where does an extra H+ on the right hand side of the equation come from? According to the reactants, shouldn't it be CO2+HbO2 = HbCOO- + O2 ??", + "A": "Hemoglobin is a protein so it s formed of amino acids , carboxylic acid having amide group -NH2, so in this equation CO2 binds to the terminal amide group forming amide linkage and -NH2 loses H+ _-NH2 + CO2 ------> _-NHCOO- + H+", + "video_name": "QP8ImP6NCk8" + }, + { + "Q": "At 8:01, we see an equation where CO2 bonds with Hb and creates H+. Where does the hydrogen come from? Has it already created carbonic acid by reacting with H2O?\n", + "A": "Yes you re right CO2 already has reacted with water and then formed carbonic acid, from which the hydrogen dissociates..", + "video_name": "QP8ImP6NCk8" + }, + { + "Q": "\nAt 1:10, is diffusion kind of like osmosis?", + "A": "Yes, osmosis is specifically for water, while diffusion is for other solutes :)", + "video_name": "QP8ImP6NCk8" + }, + { + "Q": "At 0:29 when Sal mentions that c3 mixes with RuBis what does that mean.\n", + "A": "C3 means the number of c in an triose phosphate molecule and in the calvin cycle the after some ofthe triose phosphate is sent to make stuff like glucose and lipids, the remaining triose phosphate does not mix but is converted to Rubp with the help of ATP.", + "video_name": "xp6Zj24h8uA" + }, + { + "Q": "\n7:00 Wouldn't getting the dam out of the way release the rest of the toxic copper sediments?", + "A": "They would use bioremediation to remove toxic elements from the water before getting rid of the dam.", + "video_name": "3BBqL_F9fxQ" + }, + { + "Q": "At 1:06, It is great to learn about the restoration of the river system in Montana. Is there other examples (positive or negative) of Restoration Elology? Is there a way to restore Chernobyl nuclear site, since we know exactly what went wrong?\n", + "A": "Well, one example is the Chesepeake Bay Watershed. The watershed was very polluted at one time but now, laws, regulations, and ordinary efforts from people are making it better! This applies to most polluted places in the US because of the EPA. Oh, and about Chernobyl, we have to wait until the radiation goes away", + "video_name": "3BBqL_F9fxQ" + }, + { + "Q": "At 2:11, Sal says that \"almost nothing\" is completely smooth on an atomic level. Is there any known substance that is completely smooth?\n", + "A": "A substance that is completely smooth will be frictionless. As far as our knowledge is concerned, there is no substance that is completely frictionless. Thus, till date, we do not know of any substance that is completely smooth, that is, frictionless. This is because the atoms of all substances interact and nudge each other when they are close to each other. Hope this helps :)", + "video_name": "J9BWNiOSGlc" + }, + { + "Q": "At 7:24, wouldn't the liquid just stay inside because the hole is the only way for air to get in?\n", + "A": "not only that, but a vacuum would have negative pressure wouldn t it? unless outside is a vacuum too. the liquid would just turn into a vapor and fill the container.", + "video_name": "QX2YLR09Q78" + }, + { + "Q": "\nAt 2:00, the carbon gaining the negative charge is sp3 hybridized right? The only reason the compound is still aromatic is that the negative charge(lone pair) is delocalised even when that carbon does not have a p orbital. Am I correct? If not, please correct me. Thanks :)", + "A": "No it s sp2, it doesn t rehybridise itself. When you have a lone pair next to a pi system, that lone pair will be in a p orbital because there is a large energy benefit to the aromatic system.", + "video_name": "wvVdgGTrh-o" + }, + { + "Q": "at 2:42 although the nitrogen in pyrrole is sp2 hybridised once the lone pair of electrons participate in resonance does the positive charge on nitrogen not mean anything when said that it is sp2 hybridised.\n", + "A": "the fact that nitrogen has a positive formal charge in some of the resonance structures is simply a consequence of the way formal charge is calculated. it has no bearing on the hybridization of nitrogen. Geometry specifies hybridization.", + "video_name": "wvVdgGTrh-o" + }, + { + "Q": "At 2:57, Sal uses the resistance formula to combine the 4 parallel resistors. But doesn't the current just go through the path of smallest resistance? If that is the case, then wouldn't all the current go through 3 ohms resistor and then the 1 ohm resistor? Combining these, since they are in series, gives us a 4 ohm resistor. Then by V=IR, we have 5 amps.\n", + "A": "No, current goes through any path it can go through. There is no such law as current goes through the path of smallest resistance . If you put 5 volts across a 1 ohm resistor, 5 amps will go through the resistor. The same 5 volts across a 10 ohm resistor will give you 0.5 amps through that resistor. Since parallel resistors have the same potential difference across them, if you put the 1 ohm and the 10 ohm both connected to the 5 volt source, that source is going to send out 1.5 amps.", + "video_name": "3NcIK0s3IwU" + }, + { + "Q": "At 4:20 when there are 4 H is it impossible there would be a lone pair or lone single e- making FC -1 or 0 respectively? Is steric hindrance at play?\n", + "A": "Yes it is not possible. Nitrogen can only have up to 8 valence electrons around it and in this case there are 4 bonds which is 8 electrons. It can fit no more.", + "video_name": "5-MM39VCwc0" + }, + { + "Q": "\n0:05 Sal mentioned that \"parsec\" is science fiction...is this true?", + "A": "It is often used in science fiction shows like Star Trek and Star Wars (Han Solo misuses it in episode IV). But a parsec is a real unit that astronomers use.", + "video_name": "6zV3JEjLoyE" + }, + { + "Q": "\nat 8:52 its been said that DMSO i.e a polar aprotic solvent increases the nucleophilicity of the ethoxide aninon therefore increasing SN2.... but i dont understand how DMSO increases the nucleophilic strengh of ethoxide anion?? plz help", + "A": "I don t think he said it s favoring substitution over elimination in the way that you re thinking, which is that the SN2 products are the major products. I think he s just trying to say that in order to increase the % of SN2 products, you can change the solvent to make it happen.", + "video_name": "vFSZ5PU0dIY" + }, + { + "Q": "\nAt 2:10, why was the E1 mechanism excluded ?", + "A": "The strong base favors E2. I think this is because carbocations are energetically unfavorable. So, if you can do E2 or E1, then E2 will win and in the presence of a strong base you can do E2 ...", + "video_name": "vFSZ5PU0dIY" + }, + { + "Q": "at 7:08 as T=>Ta ,then how T can be HOTTER if T=Ta\n", + "A": "Sal should have written T > Ta. In that case, T will always be hotter than Ta.", + "video_name": "IICR-w1jYcA" + }, + { + "Q": "\nA quick, slightly off topic question. At \"11:45\" Sal says g = 9.8 m/s^2, and that the acceleration is 33m/s^2. Why exactly do we square the seconds? Couldn't we do a few more steps and express it as m/s? That would seem to be easier for people to process.", + "A": "The m/s^2 just means meters per second every second...so if gravity is 9.8 meters per second every second.", + "video_name": "VYgSXBjEA8I" + }, + { + "Q": "At 3:57, Sal starts to take displacement for the solution. Why did he not use any other formula except for the displacement or distance?\n", + "A": "Because the problem asks for ddisplacement/", + "video_name": "VYgSXBjEA8I" + }, + { + "Q": "\nAt 7:34, where is 72 coming from?", + "A": "He took 260 km/h and changed the units to m/s seconds, which means: 260 km/h, 1km =1000m, 1h = 3600 seconds. Hence: (260 * 1000 m) / 36000 s = 72 m/s.", + "video_name": "VYgSXBjEA8I" + }, + { + "Q": "\nAt 14:00 Sal says that after 2 seconds, the plane would go 66 meters. Shouldn't it be 99 meters because of acceleration?", + "A": "aceleration is at the rate of 33m/s^2 .so, after 2 seconds its speed will be 33m/s x 2 = 66m/s", + "video_name": "VYgSXBjEA8I" + }, + { + "Q": "\nAt 9:34, the amino acid is being called a \"Zwitter ion.\" Sal explains that \"zwitter\" means \"hybrid\" in German. Why can't it be called \"polar?\"", + "A": "It cannot be explained as polar because polar substance is that which has a partial negative charge inside the molecule. While this has a charge which can be explained as a full charge. Polar substances are not either anion or cation.", + "video_name": "Pk4d9lY48GI" + }, + { + "Q": "\nhi, at \"4:00\" when mr khan was naming the compound, i was wondering if he made a mistake by saying 2,3-dimethyl instead of saying 2,3-trimethyl coz there are three CH3's.....or maybe someone correct me and explain it to me please? =) thank you x", + "A": "There are 3 CH3s but only two of them are groups, one of them is part of the main chain", + "video_name": "peQsBg9P4ms" + }, + { + "Q": "@6:10 so even if the carbon next to the chiral center has a F plus 2 CH3 groups attached to it, we still consider the C attached to the Br as the higher one? Thanks\n", + "A": "oh, I see. Now what if there were more CH3 groups attached to the other C ? And thanks on your answer!", + "video_name": "peQsBg9P4ms" + }, + { + "Q": "at 9:15 why does the # 1 group stay in place and the rest of the groups rotate?\n", + "A": "Group 1 stays in the same place because the rest of the groups need to rotate in order to put the hydrogen behind all other atoms. You need to think about the molecule in three dimension. The hydrogen in this situation is pointing towards you and therefore in order to put it away from you, you would need to keep group 1 in the same spot and rotate the rest of the groups in order to make hydrogen face away from you.", + "video_name": "peQsBg9P4ms" + }, + { + "Q": "\nAt 3:10 What is mole ratio?", + "A": "A mole ratio is a ratio between the amount of mols of each substance. In this case, it s the ratio of the amount of mols of Fe2O3, which is 1, and the amount of mols of Al, which is 2. So, the mole ratio is 1:2", + "video_name": "SjQG3rKSZUQ" + }, + { + "Q": "i didnt get the part at 8:20 that why do you multiply to get the mass of aluminum required.\ncan u pls help me?\n", + "A": "You multiply avogadro s number by the number of grams in aluminium to get the number of amus in aluminum. I recommend watching the video The mole and Avogadro s number on khan academy. Hope this helps! Excellent question. If you require further clarification, please don t hesitate to comment on my answer.", + "video_name": "SjQG3rKSZUQ" + }, + { + "Q": "at 7:12 how does Sal get how many moles of Al are there\n", + "A": "he just multiplyed the Fe2O3 s mole(0.53) by 2. so you get 1.06. in the chemical equation. we have 2 Al for every Fe2O3. it s that easy", + "video_name": "SjQG3rKSZUQ" + }, + { + "Q": "I have a question that says \"How many liters of oxygen are required to form 6.0 L of water\" and it gives me this balanced equation: 2H2+1O2-->2H20\nWhat I don't understand is what I'm supposed to to with the 6 L and the 2 mol of H20 to get to O. Do I divide the 6 by two so I have a 1:1 ratio or what?\n", + "A": "You shouldn t divide the 6, because the equation isn t dealing with liters, it s dealing with moles. 2 moles of H(2) and 1 mole of O(2) form 2 moles of H(2)O. 6 L is 6000 grams, so your next step is to find how many moles are in 6000 grams of water. THEN, you find the number of moles of oxygen you need using the 1:2 ratio, and then find the number of grams(then liters) of oxygen that you need, which should be your response.", + "video_name": "SjQG3rKSZUQ" + }, + { + "Q": "\nAt 4:34, does it make more sense to use the average mass number?", + "A": "Yes ideally he should not be rounding these. He should have used the number on the periodic table and round to the appropriate significant figures at the end of the calculation.", + "video_name": "SjQG3rKSZUQ" + }, + { + "Q": "At 6:00, what is the relationship between moles and grams?\n", + "A": "For atoms 1 mole equals the relative atomic mass with units of grams (g). e.g. 1 mole of oxygen atoms has a mass of 16 g. For molecules, 1 mole equals the relative formula mass with units of grams (g). e.g. 1 mole of water (H2O) has a mass of (2(1) + 16) = 18 g.", + "video_name": "SjQG3rKSZUQ" + }, + { + "Q": "\nat 8:04, in the balanced equation, the coefficient is 2 for Al. So why wouldnt you multiply it's atomic mass by two, since 2 Al atoms are necessary?", + "A": "When balancing, you are initially not looking for mass ratios, but atom ratios. For instance magnesium oxide is MgO, or a 1 to 1 ratio between Mg and O. So the balanced chemical equation would be: 2 Mg + 1 O2 --> 2 MgO Next you could use the masses to find out what mass of Mg would react with what mass of O2 and thus give the product mass formed IF both reactants get used up completely.", + "video_name": "SjQG3rKSZUQ" + }, + { + "Q": "At 6:05, you said that there was Fe3O3 but before that you said it was Fe2O3, so wouldn't the final answer be different\n", + "A": "He meant Fe203. If you have the pop ups enabled, a pop up shows up saying Sal wrote Fe303 but meant 1 mole of Fe203", + "video_name": "SjQG3rKSZUQ" + }, + { + "Q": "\nAt 8:40 Sal said that the Black hole at the center of our galaxy is 4 million times the mass of our sun. How is this possible aren't black holes an object of infinite density", + "A": "The mass is in an infinitesimally small volume which would make any finite amount of mass have an infinite density.", + "video_name": "DxkkAHnqlpY" + }, + { + "Q": "\nAt 6:15, Sal mentioned quantum fluctuations. What does that mean?", + "A": "It is the temporary change in the amount of energy in a point in space.", + "video_name": "DxkkAHnqlpY" + }, + { + "Q": "Wait, at 0:42, he talks about the event horizon saying that if anything gets past it, it cannot go back, but wouldn't gravity be like a constant, no just one line that separates things?\n", + "A": "The farther away you move from an object, the weaker its gravity gets. This is why the astronauts in orbit don t feel Earth s gravity and can float about. Well the event horizon is the distance where the gravity becomes strong enough to draw in light.", + "video_name": "DxkkAHnqlpY" + }, + { + "Q": "At 5:06, when Sal says that the math starts to break down, what does he mean? Is it that different laws of physics apply inside a black hole as opposed to outside of it? How is that possible?\n", + "A": "The math starts to break down means that you are starting to try to do things like divide by zero, which you generally can t do.", + "video_name": "DxkkAHnqlpY" + }, + { + "Q": "At 1:12 Sal said there are Stellar Blackholes and at 4:18 he said there are Primorial (super massive) Blackholes. Is there any other type of Blackhole?\n", + "A": "There could be, but those are the only two types we have discovered.", + "video_name": "DxkkAHnqlpY" + }, + { + "Q": "at 8:18 he says the center of the universe (unintentionally, and then fixes it) but it got me thinking .Is there a center of the universe?\n", + "A": "There is no center of the universe, so far as we can tell. There is a center of portion of the universe that we can observe, which we call the observable universe. By definition, we are at the center of that, because we can observe the same distance in every direction.", + "video_name": "DxkkAHnqlpY" + }, + { + "Q": "\nat 7:31, he said that there were might be black holes between stellar mass black holes and supermassive black holes. are there?", + "A": "Yes but not very many", + "video_name": "DxkkAHnqlpY" + }, + { + "Q": "\nAt 8:14 the stars could be orbitting something besides a black hole that scientists haven't discovered yet, right?", + "A": "We aren t just orbiting the black hole (its much to far away to affect us greatly), we are orbiting every other thing in our galaxy that is closer to the center. We orbit the common center of mass for our galaxy. Our galaxy began just orbiting that one black hole but as it got bigger, it needed the gravity of every other thing in it to keep it together.", + "video_name": "DxkkAHnqlpY" + }, + { + "Q": "4:31... Why would the two groups attached to a carbon be named in order of how big each of the R-groups are, and not alphabetically?\n\nI would have thought that butyl should come before propyl, not the other way round. (and I do realize that this is a common name, not the IUPAC name)\n", + "A": "Even in common names, the rule is to list the groups alphabetically. The name methyl ethyl ketone is traditional and was assigned long before anyone thought of a system for common names. That name is still used by many people. But the systematic common name puts the names of the groups in alphabetical order.", + "video_name": "wD15pD5pCt4" + }, + { + "Q": "\nFrom 6:05 to 6:30, Jay mentioned that exactly 10.2 eV is needed to promote the level 1 electron to energy level 2. Does that mean that if x eV of energy is given to the level 1 electron, such that 10.2 < x < 12.9, the electron will not be promoted to level 2?", + "A": "Yes, photons whose energies don t match the possible jumps are not absorbed.", + "video_name": "nJ-PtF14EFw" + }, + { + "Q": "At 1:11, what hormone is being referred to? Also, at 3:43, what neurotransmitter is she talking about?\n", + "A": "Ghrelin is the hormone that signals hunger. Orexin/hypocretin is missing in narcolepsy patients (in most cases).", + "video_name": "VBcEz8bVbL0" + }, + { + "Q": "\nWhy Momentum of Ball A and B in y direction at initial position is zero ? 3:07", + "A": "okay thanks i got it :)", + "video_name": "CFygKiTB-4A" + }, + { + "Q": "\nAt around 4:52, Sal calculated that the X-component is the square root of 3. I thought since the velocity was 3, you would just move the vector and the x-component would be 3. Could someone explain please?", + "A": "Actually v=3 is the initial velocity of the ball before the collision.After collision it reduces to \u00e2\u0088\u009a3.Just think of a collision between two carrom pieces or two snooker balls if you still don t understand this. Hope it helps", + "video_name": "CFygKiTB-4A" + }, + { + "Q": "At 7:41 you write the name of the second molecule and you say\n\"which alphabet comes after b ,whcih is h (for heptyl)\"\nbut must it not be which chain comes is nearer to the first C Atom?\n", + "A": "No, when naming molecules, the order in which you name the chains is alphabetically. To indicate where each branch goes, you use numbers to put in front of the name of the branch", + "video_name": "Se-ekDNhCDk" + }, + { + "Q": "\nAt around 0:48, Sal says to always choose the chain that has the most alkyl groups on it. Why?", + "A": "It s a rule made to make naming strict and universal.", + "video_name": "Se-ekDNhCDk" + }, + { + "Q": "did you mean displacement near 3:35 or are you talking about distance?\n", + "A": "Silver Night, That s a good question considering how displacement and distance can be easily mixed up despite having subtle differences. In his example, he is referring to displacement considering he uses it in an equation involving velocity instead of speed, and denoting it has a directional component.", + "video_name": "Y5cSGxdDHz4" + }, + { + "Q": "At 0:52, (specifically at the definition you gave) could you also say \"Work is the amount of Kinetic Energy that is required for an object to get from its resting position to its current position\"?\n", + "A": "No. Kinetic energy is energy associated with motion, not position. You could replace KE in your sentence with PE, and add that at the current position the object is also at rest, and then it would be right.", + "video_name": "3mier94pbnU" + }, + { + "Q": "At 2:05, Is it ok if we make the same approximations or should we work things out accurately?\n", + "A": "It depends on how the answer is expected. if the answer is expected in whole nos. then you can do approximations to make your given values into whole nos. if answer is needed upto 2 or 3 decimal places then you can t make approximations.", + "video_name": "3mier94pbnU" + }, + { + "Q": "Hi Sal, in the example \"5:30\", how could the distance between two points in the universe be 30 million light years if the whole universe has only been expanding for 300K light years? Could the universe be expanding faster than the speed of light?\n", + "A": "Actually, there s nothing preventing the universe from expanding faster than the speed of light.", + "video_name": "6nVysrZQnOQ" + }, + { + "Q": "At 2:26, arc length can also be found using a degree.\nso why do we use radians if we can find arc length by using\n(Theta/360)*2pi*r? I mean why do we have to use radians?\n", + "A": "radians have no units. This makes them much more convenient than degrees.", + "video_name": "dVYYh8C80zo" + }, + { + "Q": "at 7:13, Sal says \"...solar systems...\", then something says Sal meant \"planetary systems\". way is that? way aren't they called solar systems?\n", + "A": "Sol is the old name for our sun specifically. so our planetary system is called The Solar system. Other planetary systems would be named after the star they orbit, like the Wolf system.", + "video_name": "rcLnMe1ELPA" + }, + { + "Q": "\nat the picture in 12:23 what is that shiny bright light in the lower left corner", + "A": "It is a planet. Difficult to say which one without knowing when this picture was taken. Although my guess would most likely be Jupiter.", + "video_name": "rcLnMe1ELPA" + }, + { + "Q": "At 1:27 he says that the Voyager space craft was the fastest thing that has been made by man and sent out in space. I thaght it was the New Horizens space craft on the way to Pluto that was the fastest. Wich is the faster one?\n", + "A": "While New Horizons may have started off faster, Voyager 1 is the fastest as it got more of a speed boost from its gravitational assists from Jupiter and Saturn.", + "video_name": "rcLnMe1ELPA" + }, + { + "Q": "At 8:54 in the video, Sal mentioned the word supermassive black holes.What is a supermassive black hole and what is it's purpose?\n", + "A": "Supermassive black holes are giant black holes that are in the center of galaxies (well most of them). The Milky Way has one called Sagittarius A*", + "video_name": "rcLnMe1ELPA" + }, + { + "Q": "\nAt 12:14, Khan shows a picture of the Milky Way galaxy. In the bottom (and a little to the left) there is an IMMENSLEY COLOSSAL star or billions of stars that make a huge, bright and perfect star-shaped figure or formation. Please explain all about this form so I will understand.\n-Thanks, Easton", + "A": "But it is an artist hypothesized sketch?", + "video_name": "rcLnMe1ELPA" + }, + { + "Q": "At 9:40, he talks about how we see things in space as they were. How do they come up with these numbers? If we see something 5 billion light years away, how do we know if it's not 3, or 7 billion light years away?\n", + "A": "Astronomers have several techniques for measuring distance. These include stellar parallax, spectroscopic parallax, the use of Cepheid variable stars as standard candles , and measurement of the spectral red shift of distant galaxies. Sal has videos about parallax and Cepheid variables. He also has vids about the redshift, although I am not sure he explains how it can be used to estimate distance.", + "video_name": "rcLnMe1ELPA" + }, + { + "Q": "This may sound like a stupid question, but if you look in the middle of the galaxy at around 5:30 you see that there is a very bright yellow spot that is immensely long. What is it?\n", + "A": "That is a very large cluster of densely packed yellow stars. There are probably several clusters like that in the center of the galaxy.", + "video_name": "rcLnMe1ELPA" + }, + { + "Q": "@ 6:55, during the discussion of London dispersion forces, it is assumed that the molecules produce opposite, and therefore attractive, momentary charges. Why wouldn't the molecules produce just as many same, and therefore repulsive, momentary charges, thus canceling any net effect?\n", + "A": "That is very possible!", + "video_name": "pBZ-RiT5nEE" + }, + { + "Q": "\nAt 7:38 is there an omitted hydrogen on the first carbon? I understand that hydrogens aren't always drawn but is the hydrogen that was added bonded to that firs carbon?", + "A": "At about 5:33 you ll see pi bond picked up the H and it was added to the far left carbon, which formed a secondary carbocation on the carbon next to it. The secondary carbocation is more stable than if the H was added to the second carbon from the left which would result in a primary carbocation.", + "video_name": "dJhxphep_gY" + }, + { + "Q": "\nAt 8:30 so there is no cis or trans in this molecule? And why do?", + "A": "Because one side has a methyl group and the other side does not. Both carbons of the double bond would have to have the same substituents in order for there to be cis/trans isomerism.", + "video_name": "dJhxphep_gY" + }, + { + "Q": "At 3:42, Sal gets the average speed. How does he do that? What is the 12pi?\n", + "A": "12pi is the circumference of the circle. The formula for circumference is C = 2(pi)(r), and the radius of the loop is 6 meters, so the circumference of the loop is 12pi meters. He finds the speed of the car by doing distance divided by time. The time for the loop is 2 and 14/30 seconds.", + "video_name": "zcnnZz2pCSg" + }, + { + "Q": "\nat 2:05, aren't there other pieces of evidence besides fossils, such as mountain ranges?", + "A": "I think there is.", + "video_name": "axB6uhEx628" + }, + { + "Q": "at 6:07 it is easy to understand how the unpaired electrons repel the hydrogens attached to nitrogen so that a trigonal pyramidal shape is achieved. But what forces drive the formation of a tetrahedral shape for methane? Why doesn't it assume a flat plane? Wouldn't that create the greatest distance among the hydrogens?\n", + "A": "If it assumed a flat plane, then the angles between the Hs would be 360\u00c2\u00b0/4 = 90\u00c2\u00b0. A tetrahedral shape allows the angles between the Hs to be 109.5\u00c2\u00b0, greater than the 90\u00c2\u00b0 that a flat plane would allow.", + "video_name": "ka8Yt4bTODs" + }, + { + "Q": "At 3:50, how is it that 109.5 separates all the clouds better on a single plane compared to 90?\n", + "A": "But it isn t on a single plane, it s in 3D space. 109.5 degrees just happens to be the maximum angle when you have 4 equal groups. If you need proof then Jay did do a mathy video that proves this on here, might be easier just accept it for what it is.", + "video_name": "ka8Yt4bTODs" + }, + { + "Q": "\n5:30 how do you apply bond breaking energy? just heat?", + "A": "Heat is certainly an option because it is a form of energy, in fact, any form of energy will work as long as there is enough quantity of energy to break the bond. In fact, some experiments are so spontaneous that yelling at the reactants (sound energy) will start the reaction", + "video_name": "Ce4BGV1DVVg" + }, + { + "Q": "\nAt 0:45, how can a reaction have a zero order while the molecularity can never be zero? Because the powers raised over the concentration in an elementary reaction while using rate law is equal to the stoichiometric coefficients of reactants and these coefficients can also never be zero.", + "A": "I think you are gravely mistaken the powers are not the stoichiometric coefficients, they are the order of reaction with respect to the given atom or molecule, and order as we discussed is experimental and molecularity is very different from order they are two different things..i hope you got your error...", + "video_name": "49LcF9Zf9TI" + }, + { + "Q": "At 6:46 in the diagram of the 1.0 M NaCl solution what are the two blue and 1 green circles representing? and the red ones?\n", + "A": "The red and white molecule (which forms Mickey Mouse s head) would be H2O, water. The blue and green molecule is NaCl, salt. As he says, And here they visualise Sodium Chloride at the surface. while pointing to the green/blue molecule.", + "video_name": "z9LxdqYntlU" + }, + { + "Q": "@3:12, did he mean \"lower the freezing point\"?\n", + "A": "I believe he meant lower the melting point.", + "video_name": "z9LxdqYntlU" + }, + { + "Q": "(1:50) since the dark reactions are independent, why do they require ATP, NADPH, AND CO2, but not the protons, can anyone help me better understand?\n", + "A": "ATP and NADPH in non-cyclic photophosphorylation are created in the light reactions using the photons. This byproducts from the Light dependent reactions are used in the Calvin cycle. So, ATP and NADPH are created in light reactions because this are needed in the calvin cycle to produce glucose or any other carbohydrate which can be used by the plants later. Hope this helps.", + "video_name": "slm6D2VEXYs" + }, + { + "Q": "9:30 How do we get glucose (C6H12O6) from 2 G3Ps which is 3 carbon with phosphate? Don't we need Hydrogen as well as more Oxygen?\n", + "A": "It s because there are materials from the Light Dependent Reactions (Photosynthesis) that go into making glucose", + "video_name": "slm6D2VEXYs" + }, + { + "Q": "\nCan someone refresh my memory here? At 2:10, Sal says the Oxygen wants to give away an electron. I thought Oxygen's goal was to take electrons in order to complete it's valence shell.", + "A": "Remember that all molecules want a neutral charge. The oxygen atom here has a negative charge. When he says it wants to give away an electron he really means that the oxygen really wants to share its electron with a proton, forming a covalent bond, which in turn will keep its octet, and make the molecule neutral (no charge).", + "video_name": "J0gXdEAaSiA" + }, + { + "Q": "At around 7:15, Sal says that the speed is independent of the inertial frame of reference. But if Sal and Sally are traveling at different speeds, how can they observe the speed of light as being the same? Isn't Sally closer to the speed of light, so she has greater relative velocity compared to it?\n", + "A": "What you are saying makes common sense but that is not how velocities that are a significant fraction of the speed of light work. Any observer that is not accelerating will always measure light in a vacuum traveling at the same speed.", + "video_name": "OIwp8m3S30c" + }, + { + "Q": "At 3:00, why does the carbonyl reform? I thought oxygen can hold the negative charge?\n", + "A": "Yes, it can, but a C=O double bond with no charge is more stable than a C-O\u00e2\u0081\u00bb single bond with a charge.", + "video_name": "rNJPNlgmhbk" + }, + { + "Q": "\nat 10:28 ,isn't h2 and Pd going to reduce the aldehyde ester AND the benzene ring also.", + "A": "no, reducing the benzene would need H2 over a Rhodium/Carbon catalyst. H2 over Palladium catalyst is selective to alkenes and alkynes than aldehydes and ketones if it s in the same molecule.", + "video_name": "rNJPNlgmhbk" + }, + { + "Q": "Near 8:01, Jay said that NaBH4,reduces the aldehyde to alcohol.\n\nIt's correct. I have no objections in that. But, my teacher taught us that NaBH4 also reduces the alpha-beta-conjugated double bonds. So,by my teacher's side, the product should be a cyclic ring with two double bonds and no double bond in the right side... Was my teacher correct or is Jay correct?\n", + "A": "No, NaBH4 is a mild reducing agent and will only react with more reactive carbonyls like ketones and aldehydes. Alkenes require more reactive metal catalysts like Pd or Pt. There are special cases where the nucleophilicity of the alkene can be adjusted to react with NaBH4, but these are not addressed in an undergraduate class.", + "video_name": "rNJPNlgmhbk" + }, + { + "Q": "at 1:18 Sal circles one set of arrows on the Nazca plate and just a little to the right and above there is another set of arrows. These arrows are pointing in a directions almost perpendicular to the set Sal circled. How can a plate be moving in two directions at once? Or is this map from wikipedia inaccurate?\n", + "A": "plates move in different directions, so in one part a plate will slide under another and in another part of the same plate might be seperating away from another or they can spread or converge at the same time", + "video_name": "f2BWsPVN7c4" + }, + { + "Q": "\nHey :)\nAt 13:38 , I dont really understand how can NH3 give NH4 and hydroxide ions?\nand isnt it NOT reversible reaction? :O\n\n-Sahil, Mumbai", + "A": "Put in the first term of reation water and you can understand better. Amonia is a weak base and water, in this case, is a weak acid. There is a Ka in this case.", + "video_name": "3Gm4nAAc3zc" + }, + { + "Q": "At 1:40, Sal says that is a conjugate-base. How do we know that is not a conjugate-acid?\n", + "A": "Watch the conjugate acids and bases video. Because HA is an acid in the first place, A- has to be the conjugate base.", + "video_name": "3Gm4nAAc3zc" + }, + { + "Q": "\nAt 4:13, why do we know that Si has 4 bonds to F atoms?", + "A": "Si has 4 valence electrons so it needs to form 4 bonds to complete its octet.", + "video_name": "p7Fsb21B2Xg" + }, + { + "Q": "\n5:05 You mention the term terminal atoms. What is that ?", + "A": "The word Terminal Means End so a terminal atom is just the outermost atom of the molecule.", + "video_name": "p7Fsb21B2Xg" + }, + { + "Q": "\nWhat is \"lumen\" mentioned at 7:08 ?", + "A": "Lumen is the inside space of a tubular structure, such as an artery or intestine. Source: Wikipedia", + "video_name": "6UqtgH_Zy1Y" + }, + { + "Q": "\nAt 2:51, wouldn't the magnetic field be flowing out of the page instead of into on the right side of wire 2? Sal has it going into the page, but with my right thumb down my fingers go out at that position?", + "A": "The field he has drawn there is the field from wire 1, that is, the field that produces a magnetic force on wire 2. There will also be a (larger) contribution to the total magnetic field at that point from wire 2 pointing into the page, but since the field from wire 2 is symmetric around wire 2, it will produce no net force on wire 2.", + "video_name": "4tctB1wZNiI" + }, + { + "Q": "\nAt 1:18, why is the magnetic field of the right wire going into the page? When I use the right hand rule, I flip my thumb upside down which makes my fingers go clockwise, as opposed to counter-clockwise like the left wire.", + "A": "Yup, that s wrong :).", + "video_name": "4tctB1wZNiI" + }, + { + "Q": "Why did you multiply by area 4:18?\n", + "A": "He multiplied for 1 teorically, [1 = a/a = b/b =A/A] so you can multiply and divide by the area whenever you want, he did that so that it lets him take [F/A = P]", + "video_name": "uqyLOuAzbvo" + }, + { + "Q": "\nAt 6:33 when Sal is substituting for the potential and kinetic energies for the energy equation he substitutes with mass times gravity times height and mass times velocity squared divided by 2 respectively. In subsequent videos he uses rho instead of mass. I was wondering which version is correct.", + "A": "rho is density or mass per unit volume in this case", + "video_name": "uqyLOuAzbvo" + }, + { + "Q": "At \"3:38\" SAL says that Vi*t= D in the formula work=fd. what does distance have to do with time?\n", + "A": "distance is the amount something travels in a given time. So, if distance is unknown, you would need time to solve for it- requiring either solving mathematically or measuring. If it needs to be solved mathematically you would need the time to figure out how far something traveled in a certain amount of time. Additionally, Force= mass * acceleration- where again time could be important to know as acceleration is the change in velocity over a given time.", + "video_name": "uqyLOuAzbvo" + }, + { + "Q": "\nAt 1:50, why is there 1% of carbon dioxide in the alveoli? I thought we breathe all the carbon dioxide out.", + "A": "because we are not perfect human beings and 1% will remain", + "video_name": "fLKOBQ6cZHA" + }, + { + "Q": "\nat 14:12, how can red blood cells have NO nucleus or DNA. How do blood tests work if they don't?", + "A": "When they blood type they are looking for the presence of cell surface antigens. A antigens, B antigens, both of them together (AB), or no antigens at all (O type).", + "video_name": "fLKOBQ6cZHA" + }, + { + "Q": "\nAt 3:02 you said that Artery's go away from the heart but don't they come from the heart?", + "A": "Going away from the heart and coming from the heart are the same thing. Going away from the heart and coming to the heart are opposites. Arteries carry blood away from the heart This can also be said as blood comes from the heart through arteries.", + "video_name": "fLKOBQ6cZHA" + }, + { + "Q": "\nAt 9:08, Sal says that the N2 does diffuse in the blood, so what do we do with it? And can we make amino acids out of nitrogen?", + "A": "simply no. Nitrogen is removed as a waste product. Nitrogen is either expelled out of our body when we breathe, or removed from our waste products.", + "video_name": "fLKOBQ6cZHA" + }, + { + "Q": "\nAt 12:35, Sal stated that from the outside of the body, veins appear a blue-green color. I looked more closely and saw that little purple colored vessels. Is this a capalary or an artery and if a capalary then what is contained in side of it?", + "A": "No, the technical term for them is veins. Veins are the vessels that carry blood towards the lungs so this blood is not oxygenated which makes it blue. When oxygen binds to the iron in the blood, the iron rusts so the blood is red. When the iron is not bonded to oxygen, then it is gray and the other colors in the cell are more prominent making it blue.", + "video_name": "fLKOBQ6cZHA" + }, + { + "Q": "\nAt 15:16 you said \"They get rid of their nucleus.\" Does the dent in the center have anything to do with that, or is that just a structure created by evolution?", + "A": "The dent increases surface area allowing for more oxygen to be absorbed, yes, you could say it s evolution that imposed its structural development.", + "video_name": "fLKOBQ6cZHA" + }, + { + "Q": "At around 3:00, when he's talking about arteries, he said earlier in the video that it was capillaries. Are arteries and capillaries the same thing?\n", + "A": "arteries are blood vessels that take blood aay from the heart and lungs. Capillaries are tiny, very tiny blood vessels that help with diffusion etc.", + "video_name": "fLKOBQ6cZHA" + }, + { + "Q": "\nat 1:40 he says there is less than 1 percent of Carbon dioxide in the atmosphere but their are trillions of humans breathing it every second how is that possible?", + "A": "Photosynthetic organisms (plants, bacteria etc.) take CO2 and transform it to O2 in the process of photosynthesis. That s why there is more O2 than CO2 in the atmosphere. Interestingly, before photosynthetic organisms appeared there was less O2 in the atmosphere. About 300 million years ago, the amount of Oxygen peaked at about 30%. Also, (as of 2012.) there are about 7 billion humans on Earth not trillions.", + "video_name": "fLKOBQ6cZHA" + }, + { + "Q": "\nAt 2:06 sal says pulmonary capillaries.\nwhat are pulmonary capillaries?", + "A": "Pulmonary capillaries surround the alveoli and are where gas exchange takes place between the pulmonary arteries and pulmonary veins.", + "video_name": "fLKOBQ6cZHA" + }, + { + "Q": "\nAt 3:56, why is this membrane so thin, and why is it there at all?", + "A": "The membrane is thin because you need to get O2 and CO2 across it. The thicker a membrane is, the harder it would be for small molecules like this to diffuse through. And it is there in the first place to keep everything else in the right place. Without a membrane there, your blood would pour into the alveoli and you would cough it up. Not very good for oxygen delivery to your tissues! :)", + "video_name": "fLKOBQ6cZHA" + }, + { + "Q": "5:16 to 5:30 does that mean time/2 * acceleration of gravity = initial velocity. I want to now if in this equation does it have to be acceleration of gravity or can it be just acceration.\n", + "A": "I think it can just be acceleration.", + "video_name": "IYS4Bd9F3LA" + }, + { + "Q": "Why at around 7:10 Sal divides by 2?\n", + "A": "He finding the average velocity. To get the average of 2 number you add them and devide by 2. Since one of the numbers is 0 you end up dividing the other by two. For example the average of 1 and 3 is (1 + 3)/2 = 4/2 = 2 but the average of 0 and 2 is (0 + 2)/2 = 2/2 = 1", + "video_name": "IYS4Bd9F3LA" + }, + { + "Q": "\n@8:00 Sal is talking about dividing by 2 then multiplying by 2.5, why cant you multiply by 1.5 instead of complicating it? I did the math and it doesn't add up the same. Why is that?", + "A": "I am not sure how you got the factor of 1.5. Sal is talking about taking the average of the initial velocity which is 24.5 m/s and the final velocity in the upward trajectory of the ball, which is 0 m/s. In constant acceleration motion, to find the average velocity, you just take the average of final and initial velocities: (u+v)/2. Displacement \u00ce\u0094S = average velocity * \u00ce\u0094t. = {(u+v)/2} * \u00ce\u0094t", + "video_name": "IYS4Bd9F3LA" + }, + { + "Q": "At 3:24, Sal showed that -9.8 was the velocity. I am confused about how he got that number. Was it from the previous video? Because i remember seeing it there.\n", + "A": "-9.8 is the acceleration not the velocity maybe if you ask again i can clarify more", + "video_name": "IYS4Bd9F3LA" + }, + { + "Q": "\nHi! At 1:13, Sal says that the time it takes the object to go up is the same as the time it takes for the object to come down. I understand that we are not taking air resistance into account, but wouldn't gravity make the ball come down faster? The ball is working against gravity on it's way up and falling with gravity on the way down so it seems like the ball's decent would be faster than its ascent. Thanks for the help!", + "A": "The acceleration due to gravity is the same throughout the flight. Acceleration is rate of change in velocity. Won t it take exactly the same amount of time to go from 20 m/s to 0 as it will take to go from 0 to -20 m/s?", + "video_name": "IYS4Bd9F3LA" + }, + { + "Q": "how does he know (19:34) that there is more heat going in the systm than heat going out?\n", + "A": "Since work=heat, and from step C to A (that the system is receiving heat) the work is less than from step A to C. And this is because when the temperature of a system is at lower state you need less force to do work to the system.", + "video_name": "aAfBSJObd6Y" + }, + { + "Q": "At 4:30 you said you want the triple bond to have the lowest # of Carbon placement possible for its naming. But what if there is a double bond within the structure too, and they happen to tie for this \"lowest # of Carbon placement possible.\" Which bond would get priority for naming?\n", + "A": "To answer your question, alkenes have priority over alkynes. Thus the molecule C-C\u00e2\u0089\u00a1C-C=C-C would be named hex-2-en-4-yne by IUPAC.", + "video_name": "qZTeyhR1akA" + }, + { + "Q": "At 2:24 sal says halogens are group 7 elements but they are group 17\n", + "A": "In the new system halogens occupy group 17... Older system puts halogens into SevenA group. Also keep in mind that halogens have seven valence electrons. he may have been referring to that...", + "video_name": "__zy-oOLPug" + }, + { + "Q": "\nAt 0:44, Why do sal put O2 instead of just O?", + "A": "Because oxygen doesn t hang around as single atoms on the surface of earth, it comes as a diatomic gas with 2 oxygen atoms bonded together, so O2", + "video_name": "eQf_EAYGo-k" + }, + { + "Q": "\nAt 10:14, why is he converting moles to moles?", + "A": "You can also think about it this way grams A -> moles A -> moles B -> grams B", + "video_name": "eQf_EAYGo-k" + }, + { + "Q": "\nAt 12:00 why did Sal multiply 0.833 with 32? Where did the 32 come from?", + "A": "For every mol of O2 there are 32g O2, so you can multiply something by 32g O2/1mol O2. It s like multiplying by 1/1. He did that so that you can cancel out the mol O2 on top and bottom and solve for g of O2.", + "video_name": "eQf_EAYGo-k" + }, + { + "Q": "at 0:25 why does glucose react with oxygen?\n", + "A": "It s the equation for respiration and is how the body acquires energy.", + "video_name": "eQf_EAYGo-k" + }, + { + "Q": "\n@10:50, is it 0.833 of O2 or O? Does it make a difference?", + "A": "Its moles of O2. This makes a difference in calculating grams as there are 2 oxygen atoms per mole. Hope this helps :)", + "video_name": "eQf_EAYGo-k" + }, + { + "Q": "\nAt 10:11, so the coefficient symbolizes the amount of moles?", + "A": "Mostly, but not exact. The coefficients represent the ratios of the numbers of molecules of the chemicals involved in the reaction. As such, something like 2H\u00e2\u0082\u0082 (g) + O\u00e2\u0082\u0082(g) \u00e2\u0086\u0092 2H\u00e2\u0082\u0082O (g) The coefficients could mean 2 molecules of H\u00e2\u0082\u0082 and 1 molecule of O\u00e2\u0082\u0082 reacting. Or it could be 2 moles of H\u00e2\u0082\u0082 and 1 molecule of O\u00e2\u0082\u0082 reacting. Or it could be 0.0150 moles of H\u00e2\u0082\u0082 and 0.0075 moles of O\u00e2\u0082\u0082 reacting. So, it doesn t actually specify the quantity you have, it is just the ratio of the numbers of molecules,", + "video_name": "eQf_EAYGo-k" + }, + { + "Q": "\n4:35 oxygen is spelled incorrectly", + "A": "Yes, Sal has missed the y in the spelling of oxygen.", + "video_name": "eQf_EAYGo-k" + }, + { + "Q": "at 12:51, you used every one mole of glucose we produce 6 mole of carbon dioxide\" and found the moles of co2 first, does it make any difference if i take the moles of glucose and find out the number of h2o moles first, or i cant do that because there is no carbon in h2o so i have to find the moles of carbons first?\n", + "A": "He didn t even have to write the balanced equation. He knew that i mol glucose contains 6 mol f C, and 6 mol of C must produce 6 mol of CO\u00e2\u0082\u0082. You can start anywhere you want when balancing an equation, but usually the procedure that works best is to start with the most complicated formula (glucose); balance all atoms other than O and H (i.e., balance C); balance O; balance H last.", + "video_name": "eQf_EAYGo-k" + }, + { + "Q": "at 0:56, is there a way to check your stoichiometry problem to make sure its right?\n", + "A": "You can google the reaction after trying it out for yourself to see if you are right :) read the language in the question carefully to work out what is a reactant (left side) and what is a product (right side). Most gases like Oxygen and Hydrogen will exist as O2 and H2, not just a single atom O Fun fact! This reaction is known as respiration.", + "video_name": "eQf_EAYGo-k" + }, + { + "Q": "at 1:42 sal uses the term notional charge\nwhat does it mean?\n", + "A": "Physicists do not use the term notional charge. It is probably because Sal has a finance background and is bringing terminology from that world into play. In this case, he is using the term notional charge to imply a test charge.", + "video_name": "0YOGrTNgGhE" + }, + { + "Q": "\nat 8:22 , he said positive test charge . what is a test charge ?", + "A": "A test charge is a charge that we imagine is so small that it does not affect the field we are trying to test.", + "video_name": "0YOGrTNgGhE" + }, + { + "Q": "What is static electric force at 12:10?\n", + "A": "static electric force is the force acting between two charges Static charge is charge that is not moving (unlike current)", + "video_name": "0YOGrTNgGhE" + }, + { + "Q": "\nWhat is silican? As said in 3:23", + "A": "Silicon is an element. It has the symbol Si.", + "video_name": "T2DaaGuKOTo" + }, + { + "Q": "\nAt 8:35, he says that since water has positive and negatively charged sides, the molecules will stick together, hydrogen side to oxygen side, and I am wondering, does that explain the hexagonal patterns that are formed at a molecular level when water freezes?", + "A": "That is exactly why water freezes the way it does.", + "video_name": "T2DaaGuKOTo" + }, + { + "Q": "At 0:01 you started out with the static friction and the kinetic friction. What is the formula to be able to figure those amounts out? I need help for my physics class,.. Please help.\n", + "A": "He gives these equations at 1:24 and 2:01. The equation for static friction is: ||Fb|| / ||Fn|| = \u00ce\u00bcs Where ||Fb|| is the budging force, or the amount of force required to make an object start moving, ||Fn|| is the normal force, and \u00ce\u00bcs is the coefficient of static friction. The equation for kinetic friction is: ||Ff|| / ||Fn|| = \u00ce\u00bck Where ||Ff|| is the force of friction, ||Fn|| is the normal force, and \u00ce\u00bck is the coefficient of kinetic friction.", + "video_name": "ZA_D4O6l1lo" + }, + { + "Q": "1:22 I don't understand why he says that coefficient of static friction deals with the force to move the object (budging force). Is it not rather maximum friction force that can be applied BEFORE it moves. Meaning any more force and then it will move (becoming kinetic friction)?\n", + "A": "The coefficient of static friction tells you how much frictional force you get for a given normal force. Friction force = coeff of sf * normal force. Friction is a reactive force, which means that it only responds to applied forces. When you multiply the coefficient of static friction times the normal force, that tells you the maximum budging force that the friction will resist. Apply more force than that, and the object will start to move.", + "video_name": "ZA_D4O6l1lo" + }, + { + "Q": "\nAt 11:40 Sal says that he should have looked up the exact frequency of hemophilia in men. He estimates that is in roughly 1/7000. Does anyone know a more exact frequency?", + "A": "Hemophilia occurs in about one out of every 7,500 live male births. There are approximately 17,000 people in the United States who have hemophilia. Factor VIII deficiency accounts for about 80% (1 in every 5,000 male births) of the hemophilia population and Factor IX deficiency accounts for about 20% (1 in every 30,000 male births) of the hemophilia population", + "video_name": "-ROhfKyxgCo" + }, + { + "Q": "12:25 If haemophilia is recessive, why would a man who carries only one of the alleles for haemophilia (because he is XY, and so it can only ever be on one gene) have the condition present? If he has two chromosome (the X and Y) and only one can / does carry the allele for haemophilia, and then the condition is present, wouldn't that make it dominant?\n", + "A": "No, in order for an allele to be dominant, it has to show its phenotype even in the presence of another recessive allele of that gene. When only one gene is present an allele cannot be determined to be dominant or recessive. Haemophilia is recessive as in females (who are XX), there are indeed two copies of the gene and one haemophilia-causing allele is not enough for the disease to be present.", + "video_name": "-ROhfKyxgCo" + }, + { + "Q": "\nIn the video ,10:28 you said a man only one hemophelia cromosome to past it to the off spring. so does that mean that most cancer comes from men?", + "A": "Cancer is a mutation of genes, not genetically inherited from parents (unless the cancer was present in gametes).", + "video_name": "-ROhfKyxgCo" + }, + { + "Q": "is the X chromosome always longer compared to the Y?\njust curious... 07:43\n", + "A": "Yes it is a huge giant by comparison.", + "video_name": "-ROhfKyxgCo" + }, + { + "Q": "At around 5:48 what would the hybridization of the transition state be?\n", + "A": "The hybridization of the carbon atom in the transition state would be sp\u00c2\u00b2.", + "video_name": "3LiyCxCTrqo" + }, + { + "Q": "8:40 what represnt those arrows?\n", + "A": "The arrows represent the electrons. You can have up to two electrons in an orbital but, if there are two electrons, they must have opposite spin. (Spin is defined by the fourth quantum number that you will have seen in earlier videos.) Opposite spin is represented by drawing one arrow pointing up and the other arrow pointing down.", + "video_name": "649ZlWMp0LE" + }, + { + "Q": "1.At 5:24, Sal said isostatic process. What does it mean?\n2. Why did he use natural log instead of common log? Either way is fine?\nThanks!\n", + "A": "1. By isostatic, he means any one of the isobaric, isochoric, adiabatic, isothermal, etc (if any) processes. 2. Since integral of 1/x = ln x, he used natural log so that the answers match.", + "video_name": "WLKEVfLFau4" + }, + { + "Q": "\nat around 10:06 you say that the temperature doesnt change because everything is in isolation thus adiabatic. In previous videos, with the cilinder/pebbles, when everything was adiabatic, the temperature DID change. The only time the temperature didnt change back then was when there was a reservoir added (Isotherm).\n\nSo why is it different here? Just because the system doesnt have to do any work?", + "A": "I guess i found my answer at ~6:55, sorry", + "video_name": "WLKEVfLFau4" + }, + { + "Q": "@02:13,\nshouldn't it be x(x-1)(x-2)(x-3).....\nbecause a already ocupied 1 state so b has only x-1 states to go to?\n", + "A": "But the states are changing as the molecules have velocity. If they wouldn t have had a velocity then your proposition would have been correct", + "video_name": "WLKEVfLFau4" + }, + { + "Q": "\nThe 1,3-Diflurocyclopentane.....at 8:58; wouldnt it have an axis of symmetry straight down the center as if folding a sheet of paper hot dog style?", + "A": "Yes. Sal was just using the same axis of symmetry to compare it to the first example. You would, in fact, have an axis of symmetry if you chose to do it that way; however, it still would not be chiral, because if you started counting from either fluorine there would still be an unequal number of carbon/fluorine groups on each side.", + "video_name": "QQMZ1ljepWg" + }, + { + "Q": "\nhow can a structure have a chiral atom and be not chiral? does it matter? 9:33.", + "A": "Well a Meso compound would have a chiral atom but not actually be chiral, wouldn t it?", + "video_name": "QQMZ1ljepWg" + }, + { + "Q": "At around 5:30, the video is talking about chromate being CrO4^2-, but when it is dichromate it is Cr2O7^2-. Why are there 7 oxygen atoms? I thought there would be 8, as 4*2 is 8. Sorry for the notation.\n", + "A": "The di means that there are two chromium atoms in the ion, not that it consists of two chromate ions. The missing O atom ends up as water. For example: 2K\u00e2\u0082\u0082CrO\u00e2\u0082\u0084 + H\u00e2\u0082\u0082SO\u00e2\u0082\u0084 \u00e2\u0086\u0092 K\u00e2\u0082\u0082Cr\u00e2\u0082\u0082O\u00e2\u0082\u0087 + H\u00e2\u0082\u0082O + K\u00e2\u0082\u0082SO\u00e2\u0082\u0084", + "video_name": "DpnUrVXSLaQ" + }, + { + "Q": "At around 4:45, he did not explain where the second hydrogen atom came from to make hydrogen phosphate become dihydrogen phosphate. Can someone explain that to me?\n", + "A": "It doesn t really matter where it came from, he s just showing you how those phosphate molecules are related to one another. It probably came from water if you have to have an answer to understand.", + "video_name": "DpnUrVXSLaQ" + }, + { + "Q": "\nBasic question... Why at 3:45, the H is coming out, instead of stay in the sheet planar?", + "A": "We have to consider what the molecule looks like in three dimensions, in reality the molecules are not flat like the paper we draw them on. There really is no good way to prove this to yourself other than playing around with a molecular modelling kit. They are very handy for learning about stereoisomers. In the example in this video there is a methyl group going away from us, and we can only see 3 bonds to that specific carbon, so there is an implied hydrogen atom coming out of the page towards us.", + "video_name": "9IYTqlVk_ZI" + }, + { + "Q": "Starting around 7:30ish, Sal is using Hess's Law. Correct?\n", + "A": "Sorry, I think you aren t right Hess s law states that the overall enthalpy change in a reaction is the sum of all the reactions for the process and is independent to the route taken this might look like Hess law at the first glance...", + "video_name": "fYUwEAPejbY" + }, + { + "Q": "at \"8:52\", if the crab nebula is 65,00 light years away, couldn't a star or more than one star formed in the 65,00 years it took for that image to reach earth?\n", + "A": "It takes more than 6500 (that was the number in the video) years to form a star. It actually takes more than 65,000 years to form a star.", + "video_name": "qOwCpnQsDLM" + }, + { + "Q": "\nWhat does exothermic mean? At around 00:50", + "A": "Exothermic reactions are one of the two types of chemical reactions. An exothermic reaction releases energy, while endothermic reactions absorb energy.", + "video_name": "qOwCpnQsDLM" + }, + { + "Q": "\nAt 2:51 he talks about \"Beta negative decay\". What is it?", + "A": "It s the conversion of a neutron into a proton in the nucleus of an atom. When that happens, an electron is emitted. That electron is called a beta particle.", + "video_name": "qOwCpnQsDLM" + }, + { + "Q": "\nHey Sal, at 9:56 you mention that the current model for the formation of our solar system is that it was created by a supernova. That should have left behind a neutron star. Do we have a good candidate for the particular neutron star that is the remnant of the supernova that created our solar system?", + "A": "The objects in our galaxy orbit around the center at different speed. After 4.5 billion years, it could be anywhere. Currently, any neutron star could be from the supernova that stimulated the nebula collapse.", + "video_name": "qOwCpnQsDLM" + }, + { + "Q": "\n\"During the eclipse Sal talks about at 5:28, why is the moon the exact size of the sun, offering complete 1 for 1 coverage?\"", + "A": "Happy coincidence.", + "video_name": "qOwCpnQsDLM" + }, + { + "Q": "\nAt 7:45, is killing itself the process of apoptosis? or is it another mechanism specific to the immune system?", + "A": "Apoptosis is where a cell receives signals in order for it to kill itself. In the immune system, the cytotoxic T cells release granzymes and other chemicals that kill the cell. For example, spores may be punctured in the cell causing an increase in water intake and eventual lysing (bursting).", + "video_name": "YdBXHm3edL8" + }, + { + "Q": "at 8:00 why is the o positive , didn't it make a covalent bond ? so shouldn't it be partially positive ?\n", + "A": "For oxidation number purposes, the O lost one of its lone pair electrons when it bonded with the H, so it gained a full positive charge.", + "video_name": "U9dGHwsewNk" + }, + { + "Q": "\nAt 5:53 why will the O of ethanol donate its electron to the bonded H atom ?? Why not directly to the positively charged carbocation ? Well I think O can donate an electron to C (+) ......", + "A": "This is because of the steric hindrance of the ethanol. Due to its larger/bulkier size it is more apt to react with the hydrogen that is further away and less crowded by the overall molecule . This is ultimately why an E1 reaction occurred and why and S1 reaction didn t occur.", + "video_name": "U9dGHwsewNk" + }, + { + "Q": "6:20 - Would EtOH take the H if the C were not a cation? In other words, is if necessary for the carbocation to exist to enable EtOH to take the H? Does the presence of the carbocation enable EtOH to take the H by reducing the strength of the H-C bond by pulling electrons towards itself? Do the electrons in the H-C bond move towards the carbocation before the H is taken, or only afterwards?\n", + "A": "No. The EtOH would not take the H if the C were not a cation. The cation must be there to make the H atom acidic enough to be removed by the relatively weak base EtOH. The cation does this by pulling the electrons in the C-H bond towards itself. The electrons in the C-H bond have already moved towards the carbon before the EtOH attacks, But they move entirely to C atom after the EtOH has attacked.", + "video_name": "U9dGHwsewNk" + }, + { + "Q": "\nat \"7:40\" could you also write 350. feet (with a decimal at the end) to show that you meausred it to the nearest one? Or does nobody do that? Because I remember you doing that in the first significant figures video.", + "A": "You could also write 350. feet, although that has three significant didgits when the building was 350 feet with only two significant didgits, meaning that the measurement of the building may have been a guess or may have been exact. We just cannot tell without the decimal point, which is what the guy was trying to express.", + "video_name": "xHgPtFUbAeU" + }, + { + "Q": "\nat 7:23, 350 ft is 2 significant figures but when you multiply out 3.5 e^2, that would make it 350. which is 3 significant figures, not 2, right?", + "A": "No, the significant digits are still 2. You are not adding precision by multiplying. If you want to represent 3 significant digits, you will right 3.50*10^2", + "video_name": "xHgPtFUbAeU" + }, + { + "Q": "\n5:30 What would drive the reformation of the carbonyl?", + "A": "Delocalization of electrons leads to increased stability. Before 5:30, the negative charge is localized on the O atom. After 5:30. there is no charge and a lone pair on O is now delocalized in the \u00cf\u0080 orbital of the C=O bond.", + "video_name": "CafRuKs7EfE" + }, + { + "Q": "\n10:00 I'm not sure I understand why it's important to know what components of the vectors in the 2-d plane are perpendicular to the other... I mean as long as your 3rd vector is sticking in or out of the page it will be perpendicular to both a & b so how does finding their components help with this ?", + "A": "This will become important with torque, which will most likely be seen in the next video. If they don t cover it I would google it.", + "video_name": "o_puKe_lTKk" + }, + { + "Q": "Can you please explain that what does Sal means by distances are proportional? (at 5:35)\n", + "A": "It means that if you increase the distance to the edge, the distance the edge travels down also increases. When he says that the distance increases proportionally, he means that if the distance to the 7N force increases by 10%, the travel distance will also increase by 10%.", + "video_name": "DiBXxWBrV24" + }, + { + "Q": "So basically the Na-K pump exchanges Na+ for K+ ions? (1:50)\nWhy would the cell exchange one ion for the other?\nIf the answer is concentration gradients then another question.\nSuppose one side of the wall contains a higher concentration of both Na+ and K+ than the other side. In that case what will happen?\n", + "A": "Yes the answer is concentration gradient. If there is hihger conc at one side then a potential difference will be established that causes polarization of membrane that propagates. This happens in the case of impulse conduction by nerves.", + "video_name": "vh166DKxYiM" + }, + { + "Q": "At 4:00, aren't the three dot structures the same, just rotated? Why are they considered different?\n", + "A": "I wondered the same thing initially. I think that an important thing to consider is that the diagrams are only the-same-but-rotated if you don t care which oxygen atom is which. If you labeled the oxygen atoms, then it wouldn t be the same. So in real life, if you were somehow able to hold the molecule still and look at just one oxygen atom, the three structures would not be the same (it could have either a single or double bond to the nitrogen).", + "video_name": "bUCu7bPkZeI" + }, + { + "Q": "At 1:41 doesn't each O atom should have a negative charge and at 2:49 N atom should have a possitive charge?\n", + "A": "Yes to both of these", + "video_name": "bUCu7bPkZeI" + }, + { + "Q": "\nI don't quite understand when at 6:28, Sal says that two particles \"buzz past each other.\" Can two particles collide too quickly? I thought that as long as they had energy greater than that of the reaction's activation energy, they would react.", + "A": "Water and carbon dioxide can form carbonic acid . But in high temperature they can t form a lot because it will breakdown (They did not just buzz past each other , they did react ) (positive delta S & H, high T , negative delta G , not spontaneously reactions ). In low temperature they can form a lot of carbonic acid because it is stable. (positive delta S & H, low T , positive delta G). It will not spontaneously breaking down (not enough reaction s activation energy)", + "video_name": "CHHu-iTwHjg" + }, + { + "Q": "\nAt 3:03 mitosis goes in to a bunch of what?", + "A": "Into a bunch of me . In other words, the bunch of cells turns into a human s organs.", + "video_name": "PvoigrzODdE" + }, + { + "Q": "\nOk so just to clarify, can mutations happen in both the female and male cells? Sal only sued sperm cells in his example at 8:45 so I just wanted to make sure. Also when Sal is talking about how the somatic cells differentiate into all the different body parts at 2:31 aren't they called stem cells?", + "A": "the mutation occurs in both cells they somatic cells can be called as stem cells", + "video_name": "PvoigrzODdE" + }, + { + "Q": "\nIt talks about Theia colliding with Earth in 4:51 , how come the Earth is a perfect sphere? Did the collision do anything?", + "A": "The collision would have released so much energy that the surface of the Earth would have been turned into molten rock. Gravity acts on the molten rock, and the molten rock fills the crater and leaves a relatively smooth surface.", + "video_name": "VbNXh0GaLYo" + }, + { + "Q": "\nAt 8:18, Sal mentions we don't have any rocks or artifacts of any sort from the Hadean Eon. So what makes us sure we had a Hadeon Eon?", + "A": "Actually, in the last few decades of the 20th century, some rocks from this period were found in several countries. They were found in Greenland, Canada and west Australia. They were apparently altered due to volcanic dike. But, you see, there is proof that the Hadean Eon existed.", + "video_name": "VbNXh0GaLYo" + }, + { + "Q": "\nAt 9:50, during the late Hadean, Do these asteroid impacts contribute to the elemental makeup of our planet? I understand some metals are so heavy that they can only form in supernovae. But do these impacts provide enough energy to form new elements?", + "A": "Yes, it added compounds (like most of our water) and elements to the planet. But it DID NOT create new elements.. Elements are only created inside a sun or a supernova, An asteroid impact will never create a new element.", + "video_name": "VbNXh0GaLYo" + }, + { + "Q": "At 5:03 What was the evidence that was used to come up with the idea that collision occurred between Earth and Theia? How strong is the evidence?\n", + "A": "We have noticed that the Moon has a lot less heavy elements than the Earth and that the composition of the surface of the Moon is very similar to that of the Earth except that sometime in the past, it experienced extreme heat. This could mean a few things but it would seem to suggest that the Moon used to be part of the Earths mantle or crust and was launched into orbit by a powerful event.", + "video_name": "VbNXh0GaLYo" + }, + { + "Q": "at 06:43 so Thea formed into a ball fusing with earth, is that why earth is egg shaped?\n", + "A": "Earth is not egg shaped. It is very close to a sphere, with a small bulge near the equator. The bulge is the result of the rotation of the earth.", + "video_name": "VbNXh0GaLYo" + }, + { + "Q": "\n@3:47 Sal draws a double bond? what is this? is this just showing they are all attached together? If they weren't drawn would this be incorrect?", + "A": "It s complicated. Benzene doesn t really have alternating single and double bonds as depicted but there isn t a very good way to show its true structure. Another common way is the hexagon but with a circle in the middle.", + "video_name": "bmjg7lq4m4o" + }, + { + "Q": "At 6:29, Sal draws a water molecule. I've always seen water molecules drawn wit the hydrogen atoms at the same angle. what is that angle and why is it at that angle\n", + "A": "this is to do with bonding angles. as the water molecules have two lone pairs and two bonding pairs, the electrons are trying to get far away as possible which is 107.5 degrees which is why Sal had drawn them that way. hope this helps", + "video_name": "bmjg7lq4m4o" + }, + { + "Q": "At 3:45, Sal said that you have a double bond every other bond. Could someone explain why that is and what do double bonds mean?\n", + "A": "A double bond is just 2 bonds to the same atom, it s shown by 2 lines between the atoms instead of 1. With benzene it s a bit more complicated than this but it isn t worth worrying about yet.", + "video_name": "bmjg7lq4m4o" + }, + { + "Q": "\nAt 3:44 why we have a double bond in every other carbon atom", + "A": "That is a way of drawing the structure of benzene, which has what we call an aromatic ring. You will learn more about this when you start to study organic chemistry.", + "video_name": "bmjg7lq4m4o" + }, + { + "Q": "At 3:46, why are there three double bonds in the carbon hexagon ? What do they signify ?\n", + "A": "That is the structural formula for benzene. In a double bond, four electrons are shared between the carbon two atoms, compared with only two in a single bond. In fact, the structure of benzene is a little more complicated than shown and you will learn more about single and double bonds, and the benzene structure, in later videos. Benzene is not the best example that Sal could have chosen to explain the different types of formulae.", + "video_name": "bmjg7lq4m4o" + }, + { + "Q": "at 3:47, he says that every other bond is a double bond, but he doesn't explain why that is. How do we know when something has a double bond and in this case would be every other one?\n", + "A": "Yeah I think using this isn t the best example as this exact question seems to come up often. You know what a single covalent bond is right? 1 bond (2 shared electrons) between 2 atoms. Well a double bond is 2 covalent bonds (4 shared electrons) between atoms. You can t really know where to place those bonds simply from the formula once the number of carbon atoms gets this high, but if you continue with organic chemistry you are going to become very familiar with that benzene molecule.", + "video_name": "bmjg7lq4m4o" + }, + { + "Q": "\nAt 4:40 ; What is organic chemistry?", + "A": "It also involves the shape!", + "video_name": "bmjg7lq4m4o" + }, + { + "Q": "2:35, How much evidence have scientists found for this theory? If that theory turns out true, that would be amazing!\n", + "A": "First thing I will say is that a theory is never proven. We can t test all conceivable circumstances that could happen and with historical events like the incorporation of ancient ancestor of the mitochondria into a cell we were not there to observe it. As for the mitochondria having been a separate bacteria like entity it is very well supported by what we know about bacteria and the mitochondria.", + "video_name": "i1dAnpSFbyI" + }, + { + "Q": "\nIn 9:14, Sal mentions Glycolysis. What is that?", + "A": "Glycolysis is the process by which glucose or any other food substance is broken down for use in the creation of ATP", + "video_name": "i1dAnpSFbyI" + }, + { + "Q": "at around 1:55 he says that there are 29 protons and electrons. are the amount of electrons and protons equal in every atom?\n", + "A": "The electrons and protons are equal in every neutral atom. If an atom loses or gains an electron, we call them ions .", + "video_name": "ZRLXDiiUv8Q" + }, + { + "Q": "At 1:10 he talks about electrons in orbits; I thought electrons are believed to flow around the nucleus in \"shells\" (delineated by mathematical probability) as opposed to defined orbits...\n", + "A": "Hello Chaba, You are correct about the mathematical probability. However, for a first introduction it is preferable to use the simplified model that defines orderly fixed orbits. It is easier to explain and visualize. Regards, APD", + "video_name": "ZRLXDiiUv8Q" + }, + { + "Q": "at 3:30 Hank says that all organelles are suspended in cytoplasm, but isn't cytosol the correct term for the fluid inside of the cell?\n", + "A": "No cytoplasm is the correct term.", + "video_name": "d9GkH4vpK3w" + }, + { + "Q": "At 5:59, Hank says that animals who can digest cellulose and lignin have a certain type of bacteria in their stomachs that break down these complex molecules into glucose molecules. What exactly are these bacteria, and how are they able to do this?\n", + "A": "Fibrobacter succinogenes, Ruminococci, etc They have the enzyme cellulase that can break down cellulose to get the nutrients they need.", + "video_name": "d9GkH4vpK3w" + }, + { + "Q": "At 4:08 why are zeros that are in between other digits significant? Aren't those in-between zeros just placeholders?\n", + "A": "because there not at the very beginning they represent numbers in 705.001 the two zeros represent tenths and hundredths.", + "video_name": "eCJ76hz7jPM" + }, + { + "Q": "At 3:51 I don't get how 10.0 is 3 significant digits because I thought zeros after the decimal or \"leading zeros\" is consider non-signifcant\n", + "A": "The 1 is a significant digit because it is not a zero. The 3rd zero is a significant digit because it is after a decimal point AND after a significant digit (the 1). Also, the 2nd zero is significant because this zero is between two other significant digits.", + "video_name": "eCJ76hz7jPM" + }, + { + "Q": "\n0:50. He shows that there are only three significant digits in that number. How do you discern significant digits from insignificant digits?", + "A": "Significant digits are the numbers that actually give you the precision. The 0 s after the 7 tell you that the measurement is more precise, but the 0 s before are just basically placeholders. It is the first non-zero number then all the numbers, including zeros, after that which are significant figures.", + "video_name": "eCJ76hz7jPM" + }, + { + "Q": "\nAt 3:40, why was all three numbers in the number 10.0 significant figures when the number was rounded to the nearest tenth?", + "A": "When counting significant numbers, you count all the numbers, counting from the right of the first non-zero number. so as 1 is the first non-zero number and there are two zeros to the right of it you have 3 significant numbers. As opposed to the first example, which has 3 leading zeros and seven being the first non-zero number you would count 3 significant numbers in the number 0.00700", + "video_name": "eCJ76hz7jPM" + }, + { + "Q": "\n2:20--How is it that there can be any kind of \"wind\" in space? Wind is movement between atoms, right? In space there's nothing to move....", + "A": "Why thank you, Andrew M.", + "video_name": "jEeJkkMXt6c" + }, + { + "Q": "\nAt 7:27, he says voyager 1 has a speed about 17 km/s. So how can be New Horizons the fastest spacecraft with a speed of about 15 km/s?", + "A": "New Horizons has the fastest launch velocity of any spacecraft. However, Voyager 1 got several gravity assist boosts from the gas giant planets to its velocity, giving it a faster overall velocity.", + "video_name": "jEeJkkMXt6c" + }, + { + "Q": "\nat 1:25, it was stated high energy electrons were spewed out at 400km/s. isnt that faster than light? i thought nothing travels faster than light?", + "A": "That is a lot slower than light. Light speed in a vacuum is 299,792,458 m/s or 299,792.458 km/s. Empty space can expand faster than light, in the first few Planck times after the Big Bang, space was expanding at around 100-1000 light years per Planck time (light travels one Planck length per Planck Time, there are 5.85356655 \u00c3\u0097 10^50 planck lengths in a light year). However, space expanding faster than light does not violate Einstein s Special Relativity.", + "video_name": "jEeJkkMXt6c" + }, + { + "Q": "6:42 If Alpha Centauri is closest, what's that really close light ball diagonal from the sun.\n", + "A": "This is a 2D picture of a 3D mapping of stars. That star would simply be within the line of sight of the Sun, but closer or further from the viewer than the Sun.", + "video_name": "jEeJkkMXt6c" + }, + { + "Q": "\nAt 3:17, Sal says that light is able to pass through the half-silvered mirror. How can light pass through a mirror?", + "A": "Same way it passes through other things it passes through, like windows.", + "video_name": "3G_Q6AggQF8" + }, + { + "Q": "At 1:57, why is the information of carbon-13 being added to carbon-12's information?\n", + "A": "Because that s how the atomic weight of an element is calculated. (mass of isotope 1 x abundance of isotope 1) + (mass of isotope 2 x abundance of isotope 2) + ...", + "video_name": "EPvd-3712U8" + }, + { + "Q": "\nAt 9:00 and shortly after in the video, he refers to the snowball period in which the earth kind of iced over. My question is how did life survive this? Wouldn't that cold have negatively affected (rather, killed) both the prokaryotic and the eukaryotic organisms?", + "A": "could be but some could survive underground where it is always 64 degrees Fahrenheit so they would be able to survive the whole snowball timeline and when everything thaws out they can come on the surface again", + "video_name": "E1P79uFLCMc" + }, + { + "Q": "At 6:11, why is tension considered an internal force? What is the difference between internal and external forces?\n", + "A": "My teacher taught me to just draw a big circle around the whole system you re trying to deal with. Anything outside of that circle is external, and anything inside is internal. If you drew a circle around both of the boxes and the string attaching them, the tension force is inside of the circle and thus internal.", + "video_name": "_0nDUXO0k7o" + }, + { + "Q": "At 1:42 he says hat you shouldn't open a plug without a professional, why not? what might happen?\n", + "A": "I would say only worry about that if you plan to plug it back in. if certain parts are messed up inside the plug it can be a fire hazard, parts may explode, or it may ruin some of the wiring in your house. If you make sure it is unplugged and you won t be plugging it back in you wouldn t need a professional.", + "video_name": "gFFvaLzhYew" + }, + { + "Q": "\nHow would you name tert-butyl chloride in the UPAC system please? (7:41)", + "A": "First, find the longest carbon chain: 3 carbons, so it is a propane. Next, find the substituents: one methyl group at carbon 2 and one chloro group also at carbon 2. We name the substituents in alphabetical order, so the overall name is: 2-chloro-2-methylpropane.", + "video_name": "aaZ-isZs4ko" + }, + { + "Q": "The compound at 2:05 is a haloalkane so shouldn't it be named 3-Bromo-4,6-dimethylheptane? I was taught that the functional group is given first preference?\n", + "A": "You were taught wrong. A halogen substituent and an alkyl substituent have equal priority, so you number from the end that is closer to either one. IN A TIE, halogens take priority over alkyl groups. Hence, 2-bromo-4-methylhexane is correct, while 4-bromo-2-methylhexane is not.", + "video_name": "aaZ-isZs4ko" + }, + { + "Q": "At 7:22 I got lost at the finding the ration of H2C2O4 AND NaOH how did he get this result of 1;2\n", + "A": "H2C2O4 + 2NaOH ----> Na2C2O4+2H20 The chemical equation.", + "video_name": "XjFNmfLv9_Q" + }, + { + "Q": "\nat 2:09, why do they pump blood into the vein not the artery?", + "A": "It because the Artery is under very high pressure, and the vein has very low. Does this help?", + "video_name": "Nnqp_3HMlDU" + }, + { + "Q": "\non 4:23, shouldn't there also be a H2O at the left side of the equation?", + "A": "No, because the H20 (2 Hydrogens + 1 Oxygen) bonded with one more Hydrogen. Thus it s now H3O+ (positive balance since H is a proton). An equation features the same molecules but rearranged.", + "video_name": "Y4HzGldIAss" + }, + { + "Q": "\nAt 6:40 if the water splits the sodium hydroxide to OH- and Na +\nthen why the sodium ion dont react with the water? its an alkaline metal", + "A": "The polar nature of water causes water to form intermolecular (between molecule) bonds with the sodium, which is what causes it to split from hydroxide ion (OH-). The sodium ion doesn t react with water to form a new chemical substance because it is happy with eight outer shell electrons.", + "video_name": "Y4HzGldIAss" + }, + { + "Q": "how does sal say in 5:03 that hcl is a strong acid?\n", + "A": "Arrhenius acids are proton donors, they completely ionize to give H+ and conjugate base. HCl - H+ Cl- H2SO4 - 2H+ SO4-2 HNO3- H+ - NO3-1 The key word is completely, they do not form an equilibrium.", + "video_name": "Y4HzGldIAss" + }, + { + "Q": "at 2:41 Shouldn't the 2-propanol be named as 1-methyl-1-ethanol since it would give the hydroxyl group the lowest number ie. 1?\n", + "A": "No, you pick the longest chain that has the OH attached and then give the lowest possible number to the C bearing the OH group. The longest chain has three C atoms, and the OH group is on C-2.", + "video_name": "kFpLDQfEg1E" + }, + { + "Q": "At 4:52 as by the longest chain rule i think the name would be 6-chloro-6-methyl-4-octane-1-ethyl-ol or maybe 6-chloro-6-methyl-1-ethyl-ol-4-octane instead of what you said in the video : 5-chloro-5-methyl-3-propyl-2-heptanol ?? I am not sure if i am saying right or wrong but i have learned from previous videos that the chain should be longest.\n", + "A": "You took into consideration only the longest carbon chain rule and forgot about other rules. we can never have ethyl-ol it should be ethan- ol and according to you, that should be octan-1-ol. that s true that the chain should be longest but it also has been mentioned in the video that we have to provide the lowest locant rule to the -OH and other groups.", + "video_name": "kFpLDQfEg1E" + }, + { + "Q": "\nWhat greek character is Sal using at 7:30 when he's explaining the polarity of water and what does it mean? For instance, a theta usually means angle and delta means change.", + "A": "It is another form of the Greek letter delta and in this case means slightly or partially .", + "video_name": "Rw_pDVbnfQk" + }, + { + "Q": "Sal you mention at 7:53 that the Na+ is attracted to the o- of the water and Cl- is attracted towards the H+ side of water. My question is that why they get attracted to the o- and h+ poles of the water? Is this due to the more positive charge on the h+ than Na+ and cause Na have remaining 10 electrons in its outer shell? and the same case in Cl-.\n", + "A": "The Na+ is much more positive than the partial H+ in water, BUT many H2O molecules work together to seperate each Ion from the crystal lattice. So the attraction between 1 Na+ and 1 Cl- is stronger than 1 Cl- and one partial H+, many partial H+ polar molecules can pull the ions apart. This works the same for the Na+ and partial O- attraction as well.", + "video_name": "Rw_pDVbnfQk" + }, + { + "Q": "\nAt 1:37, what does covalent network mean?", + "A": "It means the atoms form a rigid network as Sal explains.", + "video_name": "Rw_pDVbnfQk" + }, + { + "Q": "At 2:15, what is the melting point of carbon?\n", + "A": "That depends on what allotrope of carbon it is and what the atmospheric pressure is. Graphite normally sublimes rather than boils. The temperature at which this happens depends on the pressure but it is usually above 3900 K. Diamond can be made to boil at very, very extreme pressures and temperatures. If you can get the pressure high enough, diamond will boil at over 5100 K, which is close to the temperature of the surface of the sun.", + "video_name": "Rw_pDVbnfQk" + }, + { + "Q": "Since the element would change if the amount of protons in an atom changed (7:31), then why is the subscript necessary? If all carbon atoms have 6 protons, why do we need to make a subscript that says it has 6 protons, if by definition carbon has 6 protons? Why doesn't just noting the element suffice?\n", + "A": "Yes it s redundant when you know the identity of the element. The only time you re likely to use atomic number as a subscript is in nuclear chemistry reactions.", + "video_name": "I-Or4bUAIfo" + }, + { + "Q": "\nAre there non-neutral atoms?At 6:21, Jay said,\"if it is a neutral atom.... It got me confused", + "A": "Of course. Atoms that aren t neutral are called ions. They are still atoms, they just do not have the same number of electrons and protons.", + "video_name": "I-Or4bUAIfo" + }, + { + "Q": "At 2:41 the third isotope is called tritium, I'm wondering if there are specialized names for each element's isotopes or if all elements use the same names. For carbon to have more/less neutrons are its isotopes also called deuterium and tritium?\n", + "A": "Only hydrogen isotopes had the privilege to be called with their own names. All other elements isotopes are simply called by the element s name and the atomic mass (for instance carbon fourteen, uranium twohundred and thirtyfive, and so on).", + "video_name": "I-Or4bUAIfo" + }, + { + "Q": "At 2:10, how do a neutrons have mass? Isn't neutrons part of an atom?\n", + "A": "Yes, neutrons have mass. An isolated neutron is about 1.008665 u. And neutrons are found in all atoms beyond Hydrogen-1.", + "video_name": "I-Or4bUAIfo" + }, + { + "Q": "At 1:17, why do the isotopes of hydrogen all have different names (protium, deuterium, tritium), and where do they come from?\n", + "A": "They have names for convenience. Pro means 1 Deu means 2 Tri means 3 See?", + "video_name": "I-Or4bUAIfo" + }, + { + "Q": "\nAt 3:20, does he mean that protium and deuterium, and tritium are specific words used only for NITROGEN atoms, or does he mean you can use these words on any element?\nThank you!", + "A": "They are specific terminology for Hydrogen only. Hydrogen with 1 proton and 0 neutrons= Protium, Hydrogen with 1 proton and 1 neutron = Deuterium, Hydrogen with 1 proton and 2 neutrons =tritium.", + "video_name": "I-Or4bUAIfo" + }, + { + "Q": "\nAt 8:57, he says the atomic mass is 235, but isn't the atomic mass 238.03?", + "A": "He says 235 is the mass number of this isotope The relative atomic mass or atomic weight of uranium is 238.03. These are not the same thing!", + "video_name": "I-Or4bUAIfo" + }, + { + "Q": "What is meant by superscript ? said at 3:27\n", + "A": "A superscript is just text set above the line and smaller than usual, like the 2 in x\u00c2\u00b2. Similarly, a subscript is like the 0 in x\u00e2\u0082\u0080. I used special characters to make this work, so you can copy the \u00c2\u00b2 if you want to use it elsewhere.", + "video_name": "I-Or4bUAIfo" + }, + { + "Q": "At 0:07, he talks about the Atomic Number (z), why do scientists use letters to symbolize numbers or elements? Just curious.\n", + "A": "i think its because it helps in writing chemical formula and equation ..its easier to use them symbolically coz there are so many elements and compounds formed from them(elements)", + "video_name": "I-Or4bUAIfo" + }, + { + "Q": "At 5:41 why can you not have more than three isotopes or can you and you just did not show it?\n", + "A": "There is no set number of isotopes per element. Each element has whatever number of naturally occurring isotopes it just happens to have. With hydrogen, there are three naturally occurring isotopes. There are a few more that have been made artificially, but they are so radioactive they only exist for a tiny fraction of a second. On the other hand, mercury has seven stable, naturally occurring isotopes and dozens of radioactive isotopes (mostly artificially made isotopes).", + "video_name": "I-Or4bUAIfo" + }, + { + "Q": "\nAt 8:15 we are shown another way to depict an isotope is by writing it like, carbon-14, for instance. Would it not be simplest to just use the atomic symbol and keep the mass number in the superscript since the atomic number in subscript will never change?", + "A": "You can use whatever method is most convenient. It is simpler to avoid superscripts in typing, but you can t avoid them when writing nuclear equations.", + "video_name": "I-Or4bUAIfo" + }, + { + "Q": "Just to make sure I did not misunderstood this: At 1:19, we have four covalent bond for ammonium but calculated that we need 9 valence electrons.\nIs the reason that there are only 8 electrons (covalent bonds) because we have a cation and therefore took one electron \"away\", as in 9-1?\nI know it is explained pretty clearly but I want to make sure that I understood the reasoning behind it.\n", + "A": "Yes that is it. It is a +1 cation so there is 1 less electron than protons, so there s 8 valence electrons.", + "video_name": "dNPs-cr_6Bk" + }, + { + "Q": "\nAt 9:49, he mentions significant figures. What are significant figures? My science teacher didn't exactly explain them properly. And she explained them differently.", + "A": "At 9:45, when he is trying to round the pKa to 2 significant figures, he actually rounds to 4 significant figures (10.57 has 4 significant figures). The pKa correctly rounded to 2 significant figures would be 11 (I rounded 10.5686362358 up to 11).", + "video_name": "DGMs81-Rp1o" + }, + { + "Q": "At 2:26, what does he mean that we multiply them?\n", + "A": "He means that we multiply the given values of Ka and Kb respectively. We do it in order to equate it to 1 x 10^-14 which is actually Kw..... Hope this helps.... : )", + "video_name": "DGMs81-Rp1o" + }, + { + "Q": "\nWhat did he mean by ''overcome the heat of fusion'' at 0:37? there's no fusion occurring there.", + "A": "by definition heat of fusion is: The energy required to change a gram of a substance from the solid to the liquid state without changing its temperature is commonly called it s heat of fusion . So this is the energy to break the bonds in the solid state to be able to flow in the liquid state. In this case fusion is not about two atoms fusing to form a heavier atom as in a physics way, but that the atoms are in a giant solid lattice that must be broken to change the state.", + "video_name": "hA5jddDYcyg" + }, + { + "Q": "\nAt 12:08, Is the atmosphere part of the closed container as well? Otherwise, I am not sure how the molecules that comprise the atmosphere are interacting with the gaseous water molecules.\nAlso, when we speak of partial pressure does that indicate that gaseous water molecules within the container experience different amount of pressure than the liquid water molecules?", + "A": "The closed container is assumed to contain air which will exert pressure on the surface of the liquid water. Both the molecules in the air and the molecules in the gaseous water are exerting pressure on the surface of the liquid water.", + "video_name": "hA5jddDYcyg" + }, + { + "Q": "at 7:50 ,does given temperature mean that the temperature has to be kept constant while this process goes on?\n", + "A": "Yes. The vapor pressure depends on the temperature of the liquid. As you raise the temperature, you raise the average kinetic energy of the molecules. More of these energetic molecules will be able to escape from the liquid, and the vapor pressure will increase. This means that you must always state the temperature at which you measured the vapor pressure. For example, the vapor pressure of water is 0.6 kPa at 0\u00c2\u00b0C, 2.3 kPa at 20\u00c2\u00b0C, 12.3 kPa at 50\u00c2\u00b0C, and 101.3 kPa at 100\u00c2\u00b0C.", + "video_name": "hA5jddDYcyg" + }, + { + "Q": "Can anyone define equilibrium for me to understand? Sal says it at 10:11.\n", + "A": "The word equilibrium in general means balance. The situation Sal is talking about in the video is balanced because in a certain amount of time the -same number- of particles will evaporate and leave the liquid to become gas as -the same number -condense and return to the liquid state. So the number of particles in each state does not change. It is in equilibrium.", + "video_name": "hA5jddDYcyg" + }, + { + "Q": "\nAt 4:47, we calculate the total moles of NH4 given off by the reaction assuming it starts with 0 moles of NH4. Although, wouldn't we start with more than 0 moles because the NH3 molecule would have been disassociating before we even added the HCl?", + "A": "You start with NH3 and you have 0.004mol of NH3. Afterward, it reacts with HCl to form NH4. Before the reaction, NH3 remains as NH3 and does not start dissociating.", + "video_name": "kWucfgOkCIQ" + }, + { + "Q": "At 8:23 when you start the last reaction mechanism, I know it is E1 elimination, but the first two were dehydration of alcohol, is there a specific name for this third reaction?\n", + "A": "Dehydrohalogenation - loss of a hydro(gen) and a halogen.", + "video_name": "l-g2xEV-z7o" + }, + { + "Q": "\nAt 4:00 the guy says that the water will take the the proton from hydrogen attached to the beta carbon...\n\nwhy would the water behave in such a way? we just said that oxygen is very electro negative and does not like to have a positive formal charge.\n\nso what's the deal?", + "A": "In solution there will be a ton of water and a small quantity of acid......since water is amphoteric (it is both an acid and a base) it can act as a Bronsted base....", + "video_name": "l-g2xEV-z7o" + }, + { + "Q": "At 1:06 I Noticed that elements 58-71 are missing? Was this intentional or a bad Periodic Table?\n", + "A": "At 2:10 it shows why.", + "video_name": "t_f8bB1kf6M" + }, + { + "Q": "\nAt 1:09 when you're numbering the groups with A's after them, why do you skip groups 3 through 12?", + "A": "Because some chemists decided a long time ago that that is how they are to be numbered. It is an old system and both the European and US ways to number groups used the same numbers and letters to refer to different groups. That is why it has been depreciated and have officially been replaced with 1-18. Still some people continue to use it today.", + "video_name": "t_f8bB1kf6M" + }, + { + "Q": "What are valence electrons? (Mentioned at 1:29.)\n", + "A": "With sal s vids about electron configurations", + "video_name": "t_f8bB1kf6M" + }, + { + "Q": "\nAt 00:12, the Speaker explains the definition of acceleration as \"the change in velocity over time\" and that got me to rethink about its meaning. Does his definition mean the velocity increases and decreases? Before, my thoughts were acceleration only meant the increase in velocity.", + "A": "Acceleration does not only mean increase in velocity, but also decrease.", + "video_name": "FOkQszg1-j8" + }, + { + "Q": "\nat 4:23 if acceleration is 20 miles per hour per second then how can we multiply seconds with hour ?", + "A": "You aren t multiplying seconds and hours. by saying 20 miles per hour per second you are saying that every second you are going to go 20 miles per hour faster. if you start at 0 miles per hour then 1 second later you would be going 20 miles per hour and the next second you would be going 40 miles per hour. so it is the change in speed over the amount of time it takes to change the speed.", + "video_name": "FOkQszg1-j8" + }, + { + "Q": "\nAt 0:20 Sal said that \"Acceleration is the change in velocity over time.\" but shouldn't the definition be 'The rate of the velocity INCREASING (over time' because if the velocity decreases it is DECELERATION.", + "A": "We define acceleration as increasing or decreasing. All we do is change the direction of the acceleration. For example, you are moving east at 10m/s but the acceleration is 5m/s^2 to the west. So you are still accelerating. Deceleration can be used at that point but the scientific and more correct term would be what I described above.", + "video_name": "FOkQszg1-j8" + }, + { + "Q": "At 5:20 Sal says he is going to use a logarithmic scale. What is that and how does it proportionally work?\n", + "A": "A logarithmic scale is a nonlinear scale used when there is a large range of quantities. Common uses include the earthquake strength, sound loudness, light intensity, and pH of solutions.", + "video_name": "BWs-ONRDDG4" + }, + { + "Q": "\nAt around 7:09 Sal says that the heat added to the system is equal to the work we did. but it is the system (the piston and pebbles) that do the work by expanding right?", + "A": "Work is the transfer of energy. There are two instances where energy is transferred. First from the thermal reservoir to the thermodynamic system (gas enclosed by cylinder walls and piston). This energy is then transferred from this volume of gas to the piston and pebbles. The piston and pebbles gain (kinetic) energy as their speed increases.", + "video_name": "M_5KYncYNyc" + }, + { + "Q": "At 3:00, would the kinetic energy in the same gas be transferred?\n", + "A": "Yes of course, just like there are some parts of a thing that are colder or hotter, I suppose that every molecule has a different escalar value of kinetic energy, but due to the collisions in a very small area they are approximately equal.", + "video_name": "PA-T6lMxCBI" + }, + { + "Q": "At 2:10, why is there a kelvin scale? where did it come from?\n", + "A": "The kelvin is a measure for temperature. It is an absolute scale for thermodynamics as it has 0 in the middle instead of at the beginning like the celcius scale ie. The scale of Celsius scale starts with 0 degrees but in the Kelvin scale, 0 is at the centre. To convert some temperature from Celsius to Kelvin, we add 273.15 from the temperature. For example, 45 degrees Celsius= 45 + 273.15 = 318.15 kelvin. Hope this helps :)", + "video_name": "tvO0358YUYM" + }, + { + "Q": "at 6:43 why didn't sal multiply it with \u00ce\u0094T?\n", + "A": "Because there was no change in temperature at that point (liquid turning into vapour). Heat of vaporisation is just mass times latent heat.", + "video_name": "tvO0358YUYM" + }, + { + "Q": "\nAt 3:25 Ronald says \"It's called rhodopsin because it's in a rod\" but I feel like that's not actually true. Wikipedia says it's derived from the greek word \"rhodos\" which sounds much more likely. And the Opsines in cones are called Iodopsines.", + "A": "True. But Ron s reasoning serves as at least a mnemonic to remember the protein name in rods. :)", + "video_name": "CqN-XIPhMpo" + }, + { + "Q": "At 8:24, it is said \"cells are hyperpolarized and turn off\". why is it OFF, not ON? hyperpolarization activates the cell and ON seems to be better to name the event.\n", + "A": "Hyperpolarization is inhibitory. It opposes the depolarization necessary to fire an action potential that allows glutamate to be released into the synapse. This glutamate is inhibitory in ON bipolar cells and excitatory in OFF bipolar cells. When the the rod is hyperpolarized, it is no longer able to release glutamate and it loses the inhibition of the ON bipolar cells, thus turning them on.", + "video_name": "CqN-XIPhMpo" + }, + { + "Q": "\nat 12:30,one carbon is oxidised but one carbon is reduced.This implies that there must have been a reducing as well as an oxidising agent simultaneously.How is that possible?", + "A": "To answer that, you really need to see the chemical reaction ( redox reaction) which created the change in oxidation states. Remember, individual atoms within a molecule are not oxidizing or reducing agents, but the entire molecule ITSELF is the agent.", + "video_name": "bJMUKNbAsTY" + }, + { + "Q": "\nIs there a difference between amplitude as described in :47 (which is on the displacement vs time graph) and the green arrows at 4:20 (on the displacement vs 'position x' graph)?", + "A": "No the amplitude is same", + "video_name": "-_xZZt99MzY" + }, + { + "Q": "\nI just realized something. At 7:30, Sal says that the length of the vial is 1 centimeter, while the problem says that it is 1.0 centimeter. When he gets to his final answer at 12:15, he reports the answer to three significant digits. Since the length of the vial only had 2 significant digits, shouldn't the answer be 0.010, instead of 0.0998? Thanks for the input.", + "A": "Yes, Sal should only keep 2 significant figures if the length of the vial is to two significant figures. You are correct in your understanding of this.", + "video_name": "VqAa_cmZ7OY" + }, + { + "Q": "At 1:15 he said 'spectrometer', we he soon corrected. I wonder, what is the difference between spectrometer and a spectrophotometer?\n", + "A": "A spectrometer is An apparatus used for recording and measuring spectra, esp. as a method of analysis. . However, a spectrophotometer is ;An apparatus for measuring the intensity of light in a part of the spectrum, esp. as transmitted or emitted by particular substances.;, Hope that helped!", + "video_name": "VqAa_cmZ7OY" + }, + { + "Q": "At 0:08, What is a Spectrophotometer?\n", + "A": "A spectrophotometer is a photometer that can measure intensity as a function of the light source wavelength. Important features of spectrophotometers are spectral bandwidth and linear range of absorption or reflectance measurement. Therefore it is an apparatus that uses light, that is a particular colour (wavelength), and measures the absorption/transmittance or reflected light strength/intensity.", + "video_name": "VqAa_cmZ7OY" + }, + { + "Q": "In 5:57, does 'visible universe' mean how much space we can see with really powerful telescopes or even more than that? If it is more than why is it 'visible'?\n", + "A": "It is that part of the universe which is within range so that light from there would have had time to reach us since the time of the big bang. Light that originated too far away has not had time to reach us, and objects at that distance are outside the visible (or observable ) universe, regardless of how good our telescopes are.", + "video_name": "JiE_kNk3ucI" + }, + { + "Q": "\nWhy do some people think that the universe is flat? At 5:55, the visible universe looks like a sphere. So how can it be flat?", + "A": "The flatness refers to the curvature of space itself, not the geometry of the boundary of the visible universe, which obviously would have to be spherical.", + "video_name": "JiE_kNk3ucI" + }, + { + "Q": "\n5:55 I thought that the universe was much \"darker\" compared to this picture. Or white is just used to mark superclusters and not actual visible electromagnetic radiation? If we could actually have a look at this universe from somewhere else (impossible, since what we see here is essentially a map of time, the periphery of the circle being the first radiation reaching the Earth that we could detect) I think we would not see much light...", + "A": "I believe that the white dots represent superclusters, and not electromagnetic radiation. I agree with your idea that if we were to look at the universe in a real time picture of the periphery of the circle we would see a much darker image, new born stars reduced to black dwarfs, etc.", + "video_name": "JiE_kNk3ucI" + }, + { + "Q": "\nCa. at 9:40 we see the Virgo Supercluster oriented as center. Is there an actual center to the visible universe and where is the Milky Way located in proximity to that center?", + "A": "The center of the visible universe is Earth. This is because it is from our reference point that we determine if something is visible.", + "video_name": "JiE_kNk3ucI" + }, + { + "Q": "12:57 Can you give examples of specific protein receptors on the postsynaptic membrane that the neurotransmitters would bind to? Are they all channel coupled receptors? Thanks:)\n", + "A": "Most of them are channel coupled receptors. One example would be a ligand-gated sodium channel ( ligand-gated because the presence of a ligand, such as a neurotransmitter, is what opens the gate, and sodium channel because it causes an influx of sodium into the post-synaptic neuron)", + "video_name": "Tbq-KZaXiL4" + }, + { + "Q": "\n13:50 What is the deciding factor in neurotransmitters being excitatory (Na channel) vs inhibitors (K channel). Does one neuron hold multiple types of neurotransmitters or are they specific?", + "A": "First Question: I m not really sure either. Sorry :( Second Question: Neurons often release more than one transmitter. Until relatively recently, it was believed that a given neuron produced only a single type of neurotransmitter. There is now convincing evidence, however, that many types of neurons contain and release two or more different neurotransmitters. Hope that helps! =D", + "video_name": "Tbq-KZaXiL4" + }, + { + "Q": "At around 14:07, Sal points out that if a K+ pump is triggered, K+ ions will flow out. Why would it go out and not in?\n", + "A": "Sal mentions they move out according to the concentration gradient meaning it moves from the area of high concentration K+ to low concentration K+", + "video_name": "Tbq-KZaXiL4" + }, + { + "Q": "At 4:41 he said water can dissolve more molecules than any liquid. What makes it better than lava?\n", + "A": "It has to do with the polarity of water, it causes ionic compounds to dissociate because there s an attraction between the molucules. Lava isn t dissolving things, it s burning or melting them because of the intense heat instead of interacting with them on a molecular level like a solvent would. Melting something is not the same as dissolving something.", + "video_name": "QymONNa5C6s" + }, + { + "Q": "\nAt 5:38, since we started with a ketone, shouldn't the compound be called a hemiketal?", + "A": "It could (and maybe should) be called a hemiketal. Some people use hemiacetal for both types of intermediates. SInce this reaction type works for both aldehydes and ketones, I guess they just used the more general term hemiacetal .", + "video_name": "8-ccnvn9DxI" + }, + { + "Q": "I haven't understood why the final velocity is negative (1:24) and neither why the gravitational acceleration is negative too... (2:02)\n", + "A": "Because we said that up is positive.", + "video_name": "15zliAL4llE" + }, + { + "Q": "\nAt 1:36, Sal says velocity is a scalar quantity but isn't velocity a vector quantity since it requires both magnitude and direction?", + "A": "Yeah,they corrected it later,you see?", + "video_name": "15zliAL4llE" + }, + { + "Q": "At 2:23, I don't get why acceleration due to gravity is negative because acceleration is a scalar, so it does not have direction?!\n", + "A": "Acceleration is a vector, not a scalar.", + "video_name": "15zliAL4llE" + }, + { + "Q": "\nAt 6:28, I am confused on how you found the momentum of the car.", + "A": "The momentum of the car is it s mass (1,000kg) multiplied by it s velocity (9m/s eastward). The units of momentum are kg-m/s The momentum of any object is it s mass multiplied by it s velocity vector.", + "video_name": "XFhntPxow0U" + }, + { + "Q": "In Right hand rule, doesn't the index finger indicate the direction of magnetic field and the middle finger the direction of current? Then why does the video say otherwise? (at 9:45)\n", + "A": "Try it your way and try it the way it s described in the video and see what happens.", + "video_name": "jQ2nD8ZGeEw" + }, + { + "Q": "\nThe particles in the experiment, shown in 7:51, seems to have an increased radius. How come? The particle is experiencing a constant acceleration due to the electrical force - is it really true that the absolute value of v stays the same? Should the radius in our example really be constant?", + "A": "If the speed is constant, the radius is constant.", + "video_name": "b1QFKLZC11U" + }, + { + "Q": "\nAt 2:13, what's an arduino?", + "A": "A programmable computer chip.", + "video_name": "VnfpSf6YxuU" + }, + { + "Q": "At 2:08, I am not getting why he divided the concept into chiral molecules and chiral atoms, while in the end they are chiral molecules and not atoms and have the same concept?\n", + "A": "Chiral atom is a potentially confusing term - chiral centre is a better expression. It s important to be able to identify a chiral centre because that leads to the identification of a chiral molecule. Understanding the exact configuration of groups around the chiral centre is also necessary for naming the molecule.", + "video_name": "tk-SNvCPLCE" + }, + { + "Q": "\nAt 9:57, what eactly does it mean to exert a repelling chage of Fe=5N/C in this case? Does the charge that's being exerted this force move away from the other positive charge at a rate that we can compare to F=ma?", + "A": "If the charge is 1 C, it will experience a force of 5N. if there are no other forces on it, it will accelerate accordingly. If it is 2 C it will experience a force of 10 N", + "video_name": "elJUghWSVh4" + }, + { + "Q": "\nat 2:46, Sal said that we need an equal and opposite force to lift the mass but wouldn't the force we've just applied and the gravitational force cancel each other?", + "A": "Yes, and that would enable the mass to maintain its velocity, whatever that velocity is.", + "video_name": "elJUghWSVh4" + }, + { + "Q": "around 9:10 sal says that to get the charge moving downwards, we have to exert a force of 10N. But if we exert that force in the downward direction, seeing that the metal plate is ALSO exerting a force by the same amount, won't the charge just stay stationary over there (like suspended in the electric field)???\nPLEASE HELP ME ON THIS ONE :(\nVERY IMPORTANT\n", + "A": "The force you actually have to exert is 10.000000000(etc)1 N, which is basically 10, so that s the answer people give. Theoretically, yes it would float if they were both exactly 10N.", + "video_name": "elJUghWSVh4" + }, + { + "Q": "At 11:06 David says that the height is -3m\\s, using the area formula for the second triangle, i-e Area of Triangle = 1/2(Base)(height) . So how is this possible that height can be measured using a negative sign, after all Height ain't no Vector quantity\n", + "A": "Above the axis is positive, below is negative. Scalars can be positive or negative But in this case the height represents displacement, which is a vector", + "video_name": "DD58B2siDv0" + }, + { + "Q": "at 6:24. how is it possible to have infinitely small rectangles?\n", + "A": "It s not, but we can imagine that we can get as many rectangles as we want, as small as we want. And then we can imagine what the limit of that is as the number of rectangles goes up and up and up.", + "video_name": "DD58B2siDv0" + }, + { + "Q": "\nAt 9:00 to 10:40 he keeps subtracting the initial (positive) velocity from the change in velocity, yet ends up with a greater number. Why or how is this?", + "A": "He adds 1m/s to 10m/s on the right side of the equation so that it cancels out on the left side so you are left with the velocity at 6 seconds equals 11 m/s.", + "video_name": "DD58B2siDv0" + }, + { + "Q": "what is meant by \"6 followed by roughly 230's of molecules\" at 1:50 ?\n", + "A": "Well, a mole of any element is equal to 6.022*10^23 atoms. So, if we ignore .022, it means roughly 6*10^23 atoms. This means that there are roughly 6 followed by 23 zeroes(6000.....) atoms. That s what Sal meant at 1:50. Hope this helps :)", + "video_name": "5B1i26dUwME" + }, + { + "Q": "at 3:45 why didn't Sal just write C6H8O2 in stead of HC6H7O2 for sorbic acid?\n", + "A": "Both formulas are correct for sorbic acid! Sal wrote it with one of the hydrogen atoms at the beginning to make it a little more clear that the underlying structure of sorbic acid has one proton (or hydrogen ion) that is reactive, since it can be donated to a base. By writing it as HC6H7O2 and knowing that is an acid, one can figure out that once sorbic acid donates a proton, you are left with H+ and C6H7O2-.", + "video_name": "jzcB3faNdq0" + }, + { + "Q": "\nat 8:18 sal says that helium is smaller than hydrogen because it has 2 electrons oin the valence shell but in the case of helium , how can the nucleus attract the valence electrons ,it is a noble gas\nplease explain ?", + "A": "Valence electrons are the electron in the outer shell of an atom. Helium and hydrogen both have valence electrons: hydrogen has 1, helium has 2. Why does the nucleus attract electrons? Because the nucleus is made up from protons (positively charged) that are attracting electrons (negatively charged) and opposite charges attract. Whether or not it is a noble gas is irrelevant. Note that the valance electrons are simply those in the outer most layer and nothing more.", + "video_name": "q--2WP8wXtk" + }, + { + "Q": "At 8:10 Sal mentions Coulomb attraction; Exactly what is that?\n", + "A": "It s the attraction between two opposite charges due to Coulombs law. Law of electrostatics: The force between two point charges (e.g. proton & electron) is proportional to the product of their charges, and inversely proportional to the square of the distance between them. So the more charged particles are there, the higher is the charge pulling the electrons to the nucleus, the smaller becomes the distance between them", + "video_name": "q--2WP8wXtk" + }, + { + "Q": "at 9:35 why does sal make a diagonal line? I understand the horizontal line but why is there anything vertical involved?\n", + "A": "Each element in the table has one more proton than the last and that means one more electron if the element is not ionized. So as you go down the table, you get more and more electrons, and more importantly, more orbitals. The more orbitals, an element has, the larger it will be.", + "video_name": "q--2WP8wXtk" + }, + { + "Q": "\nAt 2:40 Sal draws this putting two atoms together WITHOUT bonding / sharing electrons. Then he draws the other example WITH bondings(electrons share the same atom) ... At the first example you can take half of it and the second you even though can take half of it. So it seems to be that there isn't a difference in Bonding or Not Bonding?!", + "A": "No, these are different ways of estimating an atomic radius. They give different results because atoms do not have a fixed or definite boundary.", + "video_name": "q--2WP8wXtk" + }, + { + "Q": "\nDo we have a line diagram for methane as Sal explained for Propane at 6:42", + "A": "There s no way to represent it using a line structure.As each line represents a carbon-carbon bond, and methane only has carbon-hydrogen bonds, there is no line structure.", + "video_name": "pMoA65Dj-zk" + }, + { + "Q": "At 4:30, do you need to show all electrons for propane.\n", + "A": "Unless you are drawing a dot structure no it s a waste of time. That s why we almost always draw structures like he does at 5:35, it tells us exactly the same information as the other structures it just saves time.", + "video_name": "pMoA65Dj-zk" + }, + { + "Q": "\nAt 11:35, why does the horizontal velocity stay the same? Doesn't the object horizontally slow down as it goes further in space (by which the velocity would decrease)?", + "A": "In the real world the horizontal velocity would decrease because of air resistance but usually in problems like this air resistance is ignored to illustrate the concept without complicating it with extra details.", + "video_name": "ZZ39o1rAZWY" + }, + { + "Q": "\nAt 6:44, why is the delta velocity be -10?", + "A": "What are the values that determine the change in velocity, and what numbers represent them in this video?", + "video_name": "ZZ39o1rAZWY" + }, + { + "Q": "\n6:45 why is velocity -5 m/s and not 0 m/s?", + "A": "Why would it be 0? Because the projectile hits the ground and stops? What we are trying to find out is how fast the projectile is going when it hits the ground. We wouldn t need to do any work to know that after it hits the ground it just sits there.", + "video_name": "ZZ39o1rAZWY" + }, + { + "Q": "\nAt 4:05, Sal takes only the MAGNITUDE of the vert component of the velocity vector. What happens to its Direction ?", + "A": "The direction is up which is what has been chosen as the positive vertical direction", + "video_name": "ZZ39o1rAZWY" + }, + { + "Q": "At around 6:48, why is the final vertical velocity -5 m/s? Wouldn't the final velocity be 0, since the ball momentarily comes to a complete stop when hitting the ground?\n", + "A": "You re right, but at the very instant that the ball hits the ground, before the ground stops it, it will be moving at -5 m/s. Just like how the ball isn t moving before it is thrown, but its initial velocity is still 5 m/s.", + "video_name": "ZZ39o1rAZWY" + }, + { + "Q": "\nAt 06:26, why does Sal say the final velocity is -5 m/s? Surely it would be 0 m/s when it hits the ground as it inevitably will?", + "A": "We are interested in its velocity right before it touches the ground. It is pretty obvious that the body will be at rest when it touches the ground, so calculating the velocity at that time is pretty useless. Since we d rather take into account the velocity with which the body strikes the ground, we consider -5 m/s (which is the velocity RIGHT before the body touches the ground).", + "video_name": "ZZ39o1rAZWY" + }, + { + "Q": "\ni am confused about the initial velocity and the final velocity when you talked about it in 5:50. how do you figure it out?", + "A": "The initial velocity is the velocity you start with (in this case, in the vertical direction). The final velocity is the velocity you finish with, which is exactly the same one as you started with but in the opposite direction (going down, instead of going up).", + "video_name": "ZZ39o1rAZWY" + }, + { + "Q": "At 6:28 Sal says that the final velocity is -5m/s. I thought it would be 0 since it hits the ground and at that moment in time, it will have no velocity.\n", + "A": "We re studying projectile motion. It s not a projectile when it s lying on the ground,.", + "video_name": "ZZ39o1rAZWY" + }, + { + "Q": "At 7:34 I am still confused on how the acceleration in the vertical direction became -9.8 meter per second squared...?\n", + "A": "Downward direction is always taken a negative acceleration, a deceleration and is thus represented by a -ve.!", + "video_name": "ZZ39o1rAZWY" + }, + { + "Q": "\nAt about 8:14 in video, both sides are divided by -9.8m/s/s. The left side has a -10m/s unit, but when the division is done the units are ignored. Can you explain why it is ok to divide m/s by m/s/s?", + "A": "It s just algebra. (m/s) / ((m/s)/s) = 1/ (1/s) = s", + "video_name": "ZZ39o1rAZWY" + }, + { + "Q": "\nat 10:20 how is it that the velocity of the object in the horizontal direction remains the same. i can't seem to put my head around this one.", + "A": "Why would the velocity in the horizontal direction change? Is there a force in the horizontal direction? When you are in an airplane and you drop your peanuts, they land right at your feet, don t they? Their horizontal velocity remained the same.", + "video_name": "ZZ39o1rAZWY" + }, + { + "Q": "\n11:00\n\nSal simplified 10*cos30 to 10*((squareRoot of 3)/2) to 5*squareroot of 3... wouldn't it still be 5*((squareRoot of 3)/2)?\n\nSorry, it's late and maybe I need to take a break...", + "A": "No it would not. 10/2 is 5 so 10(square root of 3)/2 = 5(square root of 3).", + "video_name": "ZZ39o1rAZWY" + }, + { + "Q": "\nAt 3:21 why does Sal put two lines in the front and back of the unknown magnitude?", + "A": "That is a way to indicate take the magnitude of the vector in between these bars . It s sort of like the vector version of an absolute value sign.", + "video_name": "ZZ39o1rAZWY" + }, + { + "Q": "\nAt 6:25 why is the final velocity equal to -5m/s and not 0 m/s ?", + "A": "He is talking about the vertical velocity at which it falls back down to the ground. You know the old saying, what goes up must come down . Well, in order to come back down, it must do so at some speed. Assuming no loss of energy due to air resistance, it will come back down at the same speed at which it went up, except in the opposite direction, hence negative rather than positive.", + "video_name": "ZZ39o1rAZWY" + }, + { + "Q": "\nAt about 7:42 Sal said that vertical velocity = acceleration x change in time. Then he said that 10m/s = -9.8m/s2 x t I do not understand why the acceleration equals -9.8m/s2. I know that -9.8m/s2 is the acceleration of an object falling, but couldn't a projectile be thrown up at ANY acceleration? (For example, if the projectile is thrown up at an acceleration of 7.3m/s2 then 10m/s2 = 7.3m/s2 x t and t = 1.37 seconds, not 1.02 seconds)", + "A": "No, a projectile will accelerate at 9.8 m/s^2 downward as soon as it is released. We can give it whatever initial upward velocity we want, but the moment it is released, there s no upward force on the object, so gravity takes over.", + "video_name": "ZZ39o1rAZWY" + }, + { + "Q": "\nThroughout this lecture series, (at this video time 0:37) you state that a chiral carbon is \"usually\" a carbon bonded to four different groups. This begs the question, when is a carbon chiral, that is not bonded to four different groups? Thank you, Mike Johnston", + "A": "A chiral carbon always has four different groups. But you can have a chiral molecule that contains no chiral atoms.", + "video_name": "0XSSPow5oAc" + }, + { + "Q": "\nI love the part when Sal is looking for a spot to draw the flipped molecule at 3:55", + "A": "I like that part, too. :)", + "video_name": "0XSSPow5oAc" + }, + { + "Q": "\nat 5:14 why does it produce 2 halid groups and not a alcohol group?", + "A": "Answered starting at 2:15.", + "video_name": "1k6MUeM-pEo" + }, + { + "Q": "At 7:16 what are the names of those molecule?\n", + "A": "It can be named 3-aminopropanal or 3-aminopropionaldehyde", + "video_name": "GuaozMpFS3w" + }, + { + "Q": "\nI also wanted to ask that though in the eg at 7:00, we figured out that the S.N. of oxygen and I have clearly understood the concept of finding the steric no. but I wanted to know that how can oxygen with its elec. confi. 1s2 2s2 2px2 2py1 2pz1 excite its electron(or by any other means) form 4 sp3 hybridised just as we have seen so clearly in the case of carbon.", + "A": "You don t excite the electrons. You hybridize the orbitals first and then puts the electrons in. So you hybridize the s orbital and two 2pz orbitals. This gives 2sp\u00c2\u00b2, 2sp\u00c2\u00b2, 2sp\u00c2\u00b2 and an unhybridized 2pz. The 6 electrons of O give the configuration (2sp\u00c2\u00b2)\u00c2\u00b2, (2sp\u00c2\u00b2)\u00c2\u00b2, (2sp\u00c2\u00b2)\u00c2\u00b9, (2pz)\u00c2\u00b9. The filled sp\u00c2\u00b2 orbitals are the lone pairs, the half-filled sp\u00c2\u00b2 orbital forms the \u00cf\u0083 bond to C, and the half-filled pz orbital forms the \u00cf\u0080 bond to C.", + "video_name": "GuaozMpFS3w" + }, + { + "Q": "\nThis might be a silly question, but at 8:45 when he draws in the H - does it matter that he draws it down? Could it drawn up?", + "A": "The carbon bonding with the H you mentioned is sp3, so it tetrahedral geometric. It is a common way to draw the H like that", + "video_name": "7p2qfyqiXHc" + }, + { + "Q": "At 2:53 it is mentioned that in this example carbon only has 6 electrons around it, but what about the single electron in P orbital that is not bonding?\n", + "A": "With a carbocation there is no electron in that p orbital. Another atom has taken it when the carbocation was formed.", + "video_name": "7p2qfyqiXHc" + }, + { + "Q": "When he was talking in the pic about 1:25 your mouse shifted over long waves what are they?\n", + "A": "long waves are the lowest part of the electromagnetic radiation scale even less than your tv and radio produce", + "video_name": "PX_XSnVWlNc" + }, + { + "Q": "\n5:38 What does cohesion mean?", + "A": "Cohesion is the intermolecular attraction between like-molecules.", + "video_name": "6G1evL7ELwE" + }, + { + "Q": "\nwhy is oxygen a electronegative element at 3:16- 3:18?? and why is it way more electronegative that hydrogen at 3:23-3:25??", + "A": "See the electronegativity values for oxygen and hydrogen and you ll see that the difference is great that s why oxygen is more electronegative than hydrogen. Also, as you go through the periodic table, from right to left, electronegativity increases. See the periodic trends for electronegativity for better understanding.", + "video_name": "6G1evL7ELwE" + }, + { + "Q": "\n2:18 Why are only 4 electrons shown? There should be 8 electrons shown.", + "A": "Each bubble represents either a lone pair of electrons or a covalent bond in both cases they represent 2 electrons therefore 8 in total", + "video_name": "6G1evL7ELwE" + }, + { + "Q": "\nat 5:31 sal mentions \"action potential\". what is it?", + "A": "An action potential is a short-lasting event in which the electrical membrane potential of a cell rapidly rises and falls, following a consistent trajectory. You will see this often in physiology, particularly is neurons because this is how signals travel through our bodies", + "video_name": "ob5U8zPbAX4" + }, + { + "Q": "at 4:22, sam says the axon is covered by schwann cells which form the myelin sheath. but as far as i know myelin sheath have cells called schwann cells. i am confused. please help.\n", + "A": "The myelin sheath is made by Schwann cells. The Schwann cells wrap around the axon and produce myelin around it, creating the myelin sheath", + "video_name": "ob5U8zPbAX4" + }, + { + "Q": "why does sal say temperature changes at 1:50, if PV is the only thing determining it? i mean, if PV is constant throughout the process, and there is no loss of kinetic energy, how can temperature become lower?\n", + "A": "Temperature will change because PV is determining it. So you logic is right, and so is Sal s. I think you just misinterpreted the way Sal said it.", + "video_name": "lKq-10ysDb4" + }, + { + "Q": "At 0:26 can we determine the value of this pressure? If so, how?\n", + "A": "i think it is P = t/v (temp/volume) as volume is inversely proportional to pressure i.e if p increases v decreases and vice-versa", + "video_name": "lKq-10ysDb4" + }, + { + "Q": "\nAt 03:06 Sal says\"the temperature also probably went down\" Why would that be?", + "A": "When the volume increases, the pressure and temperature usually both go down. Both pressure and temperature are products of molecular motion. When the same amount of molecules occupy a larger space, then they bounce off the walls less frequently. Therefore, the pressure and temperature are lower.", + "video_name": "lKq-10ysDb4" + }, + { + "Q": "If calories, or kilocalories, (3:00) are heat or energy in your body, why is it unhealthy to have to many calories in your body?\n", + "A": "The energy is stored in fat, and evidence suggests that excess fat is not good for your health.", + "video_name": "h-31O7CaF2o" + }, + { + "Q": "\nAt 6:00 you said that sand heats up faster than water due to less specific heat. could that also be because the sun heats up the top inch or so of sand but penetrates deeper into the water? So the sun is heating up a greater volume of water than sand per area? Just curious.", + "A": "If you take the same amount of sand and water (and place it with the same shape), still sand is going to heat faster. You should see the last part of the video when Sal talks about the friction of the hydrogen bonds in water.", + "video_name": "h-31O7CaF2o" + }, + { + "Q": "\nAt 7:40 Sal shifts the parallel component down and joins it up to the Fg component. My question is, how can you know that this line will meet up exactly with the Fg component and therefore become a right angled triangle? If you don't know the length(force component) of the perpendicular line, how can you assume that it will be at a 90deg angle to the Fg line?", + "A": "The projected force is skewed by the angle theta of the ramp. Meaning if the ramp wasn t inclined then Fg1 would be a line perpendicular with the ground. Since the ramp is inclined we know that the force is displaced by the same angle, as Sal proved in the video. Thus, Fg1 forms a right angle with the ramp whether the ramp in inclined or not.", + "video_name": "TC23wD34C7k" + }, + { + "Q": "\nAt about 2:30, he draws the force due to gravity and the force of the gravity of the perpendicular. I'm confused on which one of those is the force of gravity normal.", + "A": "I don t get it", + "video_name": "TC23wD34C7k" + }, + { + "Q": "\nIs the sign of parallel. || . and magnetude same?? Becuz in 7:56 sal tells the parallel lines as magnitude??", + "A": "parallel: || magnitude: ||x||", + "video_name": "TC23wD34C7k" + }, + { + "Q": "At 8:56 Sal refers to the perpendicular component Fg as the adjacent but I thought that was supposed to be the opposite component which kinda throws off all the calculations after this. Did I miss something because I am really confused.\n", + "A": "A side is termed as Adjacent or Opposite in reference to the the Angle you are considering. Here, Sal refers \u00d1\u00b2 (Theta). So the Fg\u00e2\u008a\u00a5 is the Adjacent side here. Hypotenuse is constant in position. But Adjacent and Opposite are variable, Because they change with respect to your preferred Angle.", + "video_name": "TC23wD34C7k" + }, + { + "Q": "At about 2:30, he draws the force due to gravity and the force of the gravity of the perpendicular. I'm confused on which one of those is the force of gravity normal.\n", + "A": "The normal force is always perpendicular to the surface of contact.", + "video_name": "TC23wD34C7k" + }, + { + "Q": "At 7:52, it is stated that v+ = v_in. But isn't v_in = v+ - v-? How are these two statements consistent with each other?\n", + "A": "In this video, v_in is the name of the voltage created by the voltage source on the left side of the circuit. It is connected directly to the v+ input of the opamp. In other opamp videos, the same variable name might be assigned a different meaning. like v_in = v+ - v- as you suggest. There are no standard rules or conventions for which signal gets to be called v_in. It all depends on the person who draws the schematic.", + "video_name": "_Ut-nQ535iE" + }, + { + "Q": "At 3:05 he said \"the water isn't exerting force on anything.\" but isn't it exerting force on the molecules around it?\n", + "A": "Everything has gravity, so yes. However, the gravity of a molecule of water is so minuscule it can largely be ignored.", + "video_name": "NGpJPz44JYc" + }, + { + "Q": "At 10:50, when do you use the kb value or the ka value?\n", + "A": "When you set up the equation for the equilibrium constant, the products are on the top line and the reactants are on the bottom line (for example, K = [NH4+][[OH-]/[NH3]). If the reactant is a weak base (ie, NH3 in this example) then K is Kb. But if the reactant is a weak acid (eg, CH3COOH), then K is Ka. (For example, K = [H3O+][CH3COO-]/[CH3COOH].)", + "video_name": "223KLPnJCBI" + }, + { + "Q": "\nAt 9:50 we have 0.35 M NH4NO3, but how is that the same as having 0.35 M NH4? How come we just completely ignore the NO3 part of the compound?", + "A": "because nitrate ions are mainly found as free ions on both sides of the equation, i.e, they are not bonded to any other ion while they are in solution, and thus are called spectator ions and can be neglected while writing a net ionic equation.", + "video_name": "223KLPnJCBI" + }, + { + "Q": "\nAt 11:14, would I be correct if I said that increasing the resistance decreases the volume (I'm guessing that more resistance means less current to the speaker, and less current means less volume). Am I correct?", + "A": "you are correct it like water, a small rock would have low resistance but a big rock would have high resistance and so would let less water through", + "video_name": "xuQcB-oo-4U" + }, + { + "Q": "\nAt 13:10, what is the material they use to etch away the area that isn't protected?", + "A": "It depends. There are many, and I mean VERY many materials on the market that can do this, but I personally use a non-corrosive drying paste that protects certain areas from the acid, although this is time-taking and is not favored by most industries -The Weekend tinkerer", + "video_name": "xuQcB-oo-4U" + }, + { + "Q": "\nAt 12:56, he mentions this photo emulsion process, but I couldn't tell what he meant. What is it?", + "A": "please do check the information and confirm: when a photograph (NON DIGITAL) is taken, photo-chemical compounds react and produce different colours and shades. i guess it is quite similar...", + "video_name": "xuQcB-oo-4U" + }, + { + "Q": "\nIn the diagram at 10:13 , u say that the top ones are correct for IUPAC naming system .I would request u to please state that whether both are applicable or only one ? If one please state which one and also why ?", + "A": "The top 2 would be named exactly the same way: 3,4-diethyl-2-methylheptane", + "video_name": "F8RCR_1jIAk" + }, + { + "Q": "At 0:26 why is the oxygen said to get the plus one charge instead of the hydrogen. If oxygen is more electronegative than the hydrogen, wouldn't it make more sense to say the hydrogen is positively charged. Is this because when you draw these molecules, you usually leave out the hydrogens?\n", + "A": "The oxygen will have a +1 formal charge. To find formal charge, you take the number of valence electrons of a free atom, subtract 1/2 # of shared e-, and subtract #of lone e-. In this case for oxygen in H3O+: Oxygen has 6 valence e- , has three bonds, and has 2 electrons that fill its octet but aren t involved in bonding. Therefore the formal charge is 6-3-2=+1.", + "video_name": "BeHOvYchtBg" + }, + { + "Q": "\nat 4:35, the equation had a value d. what is it?", + "A": "The d in the capacitor and inductor equations is an expression used in calculus. You can read it as a tiny change in ... something . So dv means a tiny change in voltage , and dt means a tiny change in time . The quotient dv/dt represents the rate of change (slope) of voltage with respect to time.", + "video_name": "l-h72j2-X0o" + }, + { + "Q": "\nWhen, at ~ 2:41 Sal is talking about the specific heats of water is it assuming atmospheric pressure? Just wondering because I've been taught that it'll have lower boiling and evaporating points at lower pressures and higher ones at higher pressures.\nOn a separate note, should I do the section on the gas laws before this section?\n\nI'm not trying to be a smart Alec.\nThanks.", + "A": "Specific heat has nothing to do with boiling. It is the amount of heat you need to add to 1 kg of the material to get the temperature to go up by 1 K.", + "video_name": "zz4KbvF_X-0" + }, + { + "Q": "What is potential energy? I'm confused since you mentioned it at 1:48.\n", + "A": "Any form of stored energy is potential energy. Most commonly in physics you have gravitational potential energy and electric potential energy. You can also have elastic potential energy (the energy stored in a spring) and chemical potential energy (stored in chemical bonds), A physicist might tell you those are ultimately forms of electric potential energy but don t worry about that for now.", + "video_name": "zz4KbvF_X-0" + }, + { + "Q": "\nShouldn't we always calculate with K in the equation not C? Especially @6:11 because that's how the K's cancel out.", + "A": "When you re talking about change in temperature, C is actually the same as K. The difference between -10 C (263 K) and 0 C (273 K) is the same in both cases: 10 degrees. It s important to note the difference when you re talking in absolute values (0 C vs. 273 K) but when you re talking in relative values, the amounts will be the same. (Note that this does NOT apply to F. Each degree F is about half a degree C or K.)", + "video_name": "zz4KbvF_X-0" + }, + { + "Q": "\nat 4:19 shouldnt x approach zero\nthen and only,'I think ' we might get closer to zero\nPLEASE correct if i am wrong\nI am talking about the slope at point 'a' on the second graph", + "A": "Since x = a+h, when h approaches 0, x approaches a.", + "video_name": "Df2escG-Vu0" + }, + { + "Q": "So, for resistors in parallel, the circuit experiences no drop in voltage when the current reaches the resistors (11:19)? And for resistors in series, there is a voltage drop? Also, are the formulas for total resistance for resistors in parallel and for resistors in series different?\n", + "A": "There is a voltage drop, but it is identical for each resistor. The equations are very different. Series: Rtotal = R1 + R2 +...+Rn Parallel: 1/Rtotal = (1/R1 +1/R2 + ... +1/R3)", + "video_name": "ZrMw7P6P2Gw" + }, + { + "Q": "9:37 - Could you not also use the formula R(total) = 1 / ((1 / R1) + (1 / R2) + ... (1 / Rn)) , where \"Rn\" is the last resistance that is compiled into the equation?\n", + "A": "Hello Swaggy, Yes! Personally I prefer this the equation you mentioned as it is very fast to solve using a calculator and the 1/x key. Regards, APD", + "video_name": "ZrMw7P6P2Gw" + }, + { + "Q": "\nIf the voltage difference between two points in the circuit is always the same as long as the resistence is between these two points,is there no voltage difference between two points which are both in the blue region, for example (04:43)? So, in a circuit without a resistence, wouldn't there be a voltage difference? But then there would no current at all... I don't understand this at all. Also, isn't the voltage difference which provokes the movement of the electrons?\n\nThanks!", + "A": "Virtually all conductors have resistance, albeit very small. If you short a battery with a wire, you will get a very large amount of current flowing (likely the largest that battery can output). There will be a voltage drop across that wire that is equal to the voltage increase across the battery. Also batteries do have some built in internal resistance which also limits the maximum output current and results in a small voltage drop within the battery when current is flowing.", + "video_name": "ZrMw7P6P2Gw" + }, + { + "Q": "\nAt 9:25 in the video the resistance comes out to be 4 ohms. While the mathematics behind this makes perfect sense, the physics doesn't. The smallest resistor on the entire circuit is 5 ohms. I understand that most of the electrons will want to pass through this, but wouldn't that mean that the total resistance should never come out to be less than the smallest resistor?", + "A": "No, the resistance of two resistors in parallel will always be less than the resistance of either of the two. Think about it this way. Take the bigger resistor out. Now the resistance is just 4 ohms, right. Now put it back. There s another path for current to go through that wasn t there before. Therefore more current is going to flow, therefore the total resistance is less than it was before.", + "video_name": "ZrMw7P6P2Gw" + }, + { + "Q": "\nAt 0:07, Sal mentioned that at higher temperatures you get a 4th state(plasma). But doesn't our blood contain plasma, and isn't our average temperature is 37C?", + "A": "good question. blood plasma has nothing to do with the fourth state of matter. It s just has the same (inaccurate, of course) name.", + "video_name": "pKvo0XWZtjo" + }, + { + "Q": "At 0:06, what is the fourth state of matter Sal refers to?\n", + "A": "Plasma would be the fourth state of matter that Sal is referring to.", + "video_name": "pKvo0XWZtjo" + }, + { + "Q": "\nAround 14:00 minutes, the temperature goes up but the state does not change (yet). So does that mean that there is some ice that can be colder or warmer that other ice?", + "A": "Sure, ice can be -10 C, or -20C, or -100C, or 0C.", + "video_name": "pKvo0XWZtjo" + }, + { + "Q": "At about14:50, Sal said that the steam will get hotter. However, is there a limit to that, or does it just heat up forever?\n", + "A": "No, you cannot heat steam forever . Like all molecules, when sufficiently hot it will decompose. There is not a set temperature at which it decomposes, it is more of a gradual process as the temperature increases. You start getting significant quantities of water decomposing at around 2500 K. At about 3000 K you get around 50% of water molecules decomposing. Of course, this is a rather hot temperature and it is rather impractical to generate, much less create a container to house the reaction.", + "video_name": "pKvo0XWZtjo" + }, + { + "Q": "\nat 10:07 he said that the months stay the same. Is that what causes leap years?", + "A": "No AegonTargaryen is right, a year is not completly 365 days. If it were, there wouldn t be February 29th...which BTW is my birthday, but we usually celebrate it on February 28th", + "video_name": "2o-Sef6wllg" + }, + { + "Q": "\nAt 1:40, why must those electrons also attack? Why can't we just be left with a halogen ion and 1-halogen-ethane?", + "A": "We could. If the molecule is ethane, the attack of the \u00cf\u0080 electrons would give a halide ion and a 1\u00c2\u00b0 2-haloethyl carbocation. But the 1\u00c2\u00b0 cation is less stable than the cyclic halonium ion, so the reaction does not use that pathway.", + "video_name": "Yiy84xYQ3es" + }, + { + "Q": "At 3:00 shouldn't both carbon atoms have a partial + charge?\n", + "A": "Yes, they should. He just put the \u00ce\u00b4\u00e2\u0081\u00ba on one of the carbons to illustrate the mechanism.", + "video_name": "Yiy84xYQ3es" + }, + { + "Q": "At 3:42, does the halide ion attack the carbon that is most substituted or can it attack any carbon equally? I know in the halohydrin reaction the H2O attacks the most substituted carbon and the halogen goes on the least substituted.\n", + "A": "The halide ion preferentially attacks the more substituted carbon, just like water does in the halohydrin reaction.", + "video_name": "Yiy84xYQ3es" + }, + { + "Q": "\nAt 3:08 Hank says Ground tissue does photosynthesis but how can it get light if there is Dermal Tissue on the outside layer? Is the dermal tissue transparent?", + "A": "Very good question. I might not be the right person to answer this, and I could be wrong, but I think photosynthesis does not require all of the visible light, but only some energy from the light. There are wavelengths of the light that will continue through the dermal tissue. I suppose the energy from those light waves contain enough energy to keep the photosynthesis going.", + "video_name": "VFtOcdXeP0Y" + }, + { + "Q": "At about 10:18, the sap Hank is talking about gives the Ponderosa (spelling??) its delicious smell. In a maple tree, is that sap we turn into maple syrup produced in the same way the Ponderosa-scent-sap is? Thanks! :D\n", + "A": "Maple sap is very watery and needs to be boiled down into what you can buy in the store.", + "video_name": "VFtOcdXeP0Y" + }, + { + "Q": "At 0:44 sec in the video how is the slope coming from positive infinity at negative four?\n", + "A": "At x = -4, the slope is vertical and has a positive infinity slope, thus, the graph is going from that positive infinity amount to 0 at y=4.", + "video_name": "NFzma7NsHtI" + }, + { + "Q": "Shouldn't Hydrogen be the one with the partially positive charge and Fluorine with partially negative charge? Then why in the video did Sal do oppositely at 10:09 mins?\n", + "A": "You are correct, the H would be partially positive and the F should be partially negative due to the differences in electronegativities. Also, Fluorine has chemical symbol of F, not Fl. Fl is now the symbol for Flerovium, element number 114.", + "video_name": "8qfzpJvsp04" + }, + { + "Q": "\nAt 11:00, why is the partial positive at fluorine? If the fluorine is more electronegative, why does it have a partial positive?", + "A": "I believe that is the video s mistake, because generally in hydrogen bonds it is the hydrogen side that is slightly positive and the more electronegative element is slightly negative. You are correct, probably just a small mistake on the video s end.", + "video_name": "8qfzpJvsp04" + }, + { + "Q": "\nIf the sides of atoms become negative and positive (4:26), then that means at one moment in time, one side of the neon atom will be attracted to another neon atom. As the atoms change charges again, the neon atom will be attracted in the other direction. But that would mean, even at absolute zero, the particles would be moving. How can this be? This would mean the presence of kinetic energy even though the gas has no heat.", + "A": "It is not correct to say that atoms are not moving at 0 K. If that were the case. we would then know both the position and the momentum of the atom. That would violate the Heisenberg Uncertainty Principle. Just as an electron in a hydrogen atom has a certain minimum allowed energy (a 1s orbital), an atom at 0 K must have a certain minimum energy. For example, liquid helium does not freeze under atmospheric pressure at any temperature because of its zero-point energy.", + "video_name": "8qfzpJvsp04" + }, + { + "Q": "At 7:24, why isn't the hydrogen-chlorine bond a hydrogen bond?\n", + "A": "Because a hydrogen bond is a weak intermolecular bond i.e between two or more molecules due to dipole-moment. The H-Cl bond is simply a bond between two atoms to form a molecule. Hope that helps.", + "video_name": "8qfzpJvsp04" + }, + { + "Q": "\nAt 7:33, if the bond is between two atoms that are the same such as a C-C bond, which way would the dipole moment go towards?", + "A": "when equally electronegative atoms form a bond the electrons do not prefer to go more towards either of the atoms i.e., they are shared equally between the atoms giving a zero dipole moment", + "video_name": "q3g3jsmCOEQ" + }, + { + "Q": "What's the relation with center of mass, at 2:51?\n", + "A": "The molecule has different centers of charge and mass, meaning that the position where charge is zero is not the same as the average mass position.", + "video_name": "q3g3jsmCOEQ" + }, + { + "Q": "\nat 5:18, why do you care about the lone paris? Bc then wouldnt Sf2 be non-olar as well?", + "A": "By Sf2 do you mean SF2 (sulfur difluoride)? If so it s polar. The lone pairs around S mean that the molecule is NOT linear, it looks sort of like a V instead. This means that the polar bonds between S and each F do not cancel one another out and the molecule is polar.", + "video_name": "q3g3jsmCOEQ" + }, + { + "Q": "At around 7:20, I don't understand how you can replace V with 4 m^3.\n\nmeters^3 is not a unit for volume so it is confusing.\n", + "A": "meters^3 IS a unit for volume. cubic meters. any length cubed is a measure of volume.", + "video_name": "d4bqNf37mBY" + }, + { + "Q": "\nat 9:50 sal said 101,325Pa=1atm , I thought it was 101.3Pa=1atm, thats what i remember learning in chemistry, or am I wrong.", + "A": "1 atm = 101.3 kPa, that is kiloPascals, or 101 325 Pa", + "video_name": "d4bqNf37mBY" + }, + { + "Q": "At 8:04 Sal mentions multiple values or R in PV=nRT, but my science book only has one. How do you know which to use?\n", + "A": "You use the version of R that contains the same units that you have for volume and pressure.", + "video_name": "d4bqNf37mBY" + }, + { + "Q": "\nAt 4:33 he says no net work due to no change in kinetic energy. Is there not a change in potential energy that would account for work being done?", + "A": "When PE increases, no NET work is done. For example, when you lift a 1 kg book 1 meter in the air, you did 1 Joule of work on it, but gravity did -1 Joule of work, so the net work is zero, and thats why the book is not moving. This is called the work-KE theorem.", + "video_name": "udgMh3Y-dTk" + }, + { + "Q": "\nAt 7:32 to 7:45 If an object gets to the center of some massive object will it be moving back and forth because gravity is pulling and pushing it or will it stay at center?", + "A": "It will stay at the center as the gravity is 0 at that point.", + "video_name": "RpOHZc6cDIw" + }, + { + "Q": "\nAt around 3:20, Sal is talking about how, the faster the projectile is thrown, the further it goes before falling back down. How is this so? I thought that objects accelerated downward at the same rate regardless of initial horizontal velocity. Does this only apply to objects projected perfectly horizontally?", + "A": "The downward acceleration is the same, so the fall time is the same, but the horizontal velocity is faster, so it goes further in the same amount time.", + "video_name": "oIZV-ixRTcY" + }, + { + "Q": "At 1:56, Sal said, \"I'm making these numbers up on the fly, so bear with me.\" What did he mean? Did he mean that he's inventing these numbers temporarily and without preparing carefully before recording this video?\n", + "A": "yes, that is what it means.", + "video_name": "_k3aWF6_b4w" + }, + { + "Q": "\nAt 5:15, how did he get the excluded values?", + "A": "he just found what values of x would make the denominator equal zero.", + "video_name": "dstNU7It-Ro" + }, + { + "Q": "\nI think that I am on the wrong topic, but I really don't understand what Sal was doing at 1:16-1:28. Can someone please explain what he just did?", + "A": "Adding on to what Jerry said, you would get the factors of 5 and -1. You could then plug it into the equation like this. x^2 + 5x - x - 5. Form here, you can solve it to this. x(x + 5) - 1(x + 5) Finally you would get (x + 5) and (x - 1) as your final answer", + "video_name": "DRpdoZQtvOM" + }, + { + "Q": "So we are supposed to guess at 2:16?\n", + "A": "No, that side definitely goes there. Could wasn t the best choice of word.", + "video_name": "m1ZTnl4CNQg" + }, + { + "Q": "At 3:38, how does Sal get (1 - 4x^2)? I understand the -4x^2 part, but not how he gets the 1 preceding it when he factors out the e^-2x^2...\n", + "A": "All he did is factor out the e^(-2x^2). e^(-2x^2) - 4x^2 * e^(-2x^2) = e^(-2x^2) * (1-4x^2) It is the same as factoring out the x term in this expression: x -2x^2 = x * (1-2x) When factoring it out, there is still the e^(-2x^2) * 1 term that you need to take into account.", + "video_name": "MUQfl385Yug" + }, + { + "Q": "at 4:28 why the e^-2x^2 cant be zero ?\n", + "A": "The exponential function (when considered a function of real numbers) is always positive. That is, for every real number u, we have exp(u) > 0. Now let u = -2x\u00c2\u00b2, which is a real number whenever x is a real number. It follows that exp(u) = exp(-2x\u00c2\u00b2) > 0. Hence never zero. The fact that exp(u) > 0 for every real number u requires a proof in itself, but I will not provide one here (unless you really want me to).", + "video_name": "MUQfl385Yug" + }, + { + "Q": "\nAt 2:50, shouldn't d/dx e^-2x^2 = -2e^-2x^2*(-4x)?", + "A": "f(x) = e^(-2x^2) f (x) = d/dx(e^(-2x^2)) Apply Chain Rule: f (x) = e^(-2x^2)*d/dx(-2x^2) Remove constant: f (x) = e^(-2x^2)*-2*d/dx(x^2) Apply Power Rule d/dx(x^n) = n*x^(n - 1): f (x) = e^(-2x^2)*-2*2*x^(2 - 1)*d/dx(x) f (x) = e^(-2x^2)*-2*2*x^(2 - 1)*dx/dx f (x) = e^(-2x^2)*-2*2*x^(2 - 1) f (x) = e^(-2x^2)*-2*2*x^(1) [ f (x) = -4x*e^(-2x^2) ]", + "video_name": "MUQfl385Yug" + }, + { + "Q": "\nwhat is the associauive property again? Sal says it on 2:05 to 2:10", + "A": "In the context of the video, Sal was talking about 3*a^1*a^7. The Associative Property refers to grouping numbers in a particular way to make solving the problem easier. It means that 3*(a^1*a^7) = a^7*(3*a^1) = a^1*(3*a^7). In the video at 2:10, Sal is choosing to make 3*a^1*a^7 into 3*(a^1*a^7) so he can simplify it into 3*(a^8) and into 3a^8.", + "video_name": "-TpiL4J_yUA" + }, + { + "Q": "\nAt 2:53 why is it that at most 1 Sals out of 100 may die in order for the insurance company not to loose money? What's the explanation? Sal didn't give any here.", + "A": "Because each Sal only pays 1% of the insurance payout over the life of the policy. So in this case 100 Sals each pay $10,000 for a total of $1,000,000. For each Sal that dies, the insurance company needs to pay that Sal s family $1,000,000. So if 2 Sals die the Insurance pay out $2,000,000 but have only collected $1,000,000 so they are losing money.", + "video_name": "NSSoMafbBqQ" + }, + { + "Q": "what does denote mean at 0:08?\n", + "A": "Denote means: to show, mark, or be a sign of (something). In his case, he is denoting or marking that the two lines are parallel.", + "video_name": "Ld7Vxb5XV6A" + }, + { + "Q": "Why would Sal not just subtract 34 degrees from one-hundred eighty and get the angle for the other side at 3:58?\n", + "A": "Good eye. When I come up with an alternate correct answer to a problem, as I m learning, I consider it a good sign -- you re thinking.", + "video_name": "Ld7Vxb5XV6A" + }, + { + "Q": "\nAt 5:13, couldn't you have just found the total area of all the triangles and the square and have it equal to c^2?\n\n(1/2 ab)*4= area of 4 triangles\n(b-a)^2=area of square\n\n2ab+(b-a)^2=c^2\n2ab+b^2-2ab+a^2=c^2\nb^2+a^2=c^2\nWhat's wrong with this why do we have to shift all the triangles and stuff", + "A": "I think its essentially the same thing. While you ve penned down an equation and played about with the variables algebraically, Bhaskara has played about geometrically and gotten the same answer. Also (correct me if I m wrong), you wrote down two equations before you arrived at the theorem, and Bhaskara shifted two triangles before he arrived at the theorem! Pretty neat I think.", + "video_name": "1ul8g55dYA4" + }, + { + "Q": "\nI REALLY don't understand why we rewrite (7x - 5) for a second time on the right hand side (2:59) sec in to the video?? why?", + "A": "What sal is doing is the distribution property. He is distributing the value (7x-5) to g(x) s components. Recall: (a)(b+c) = ab+ac", + "video_name": "JKvmAexeMgY" + }, + { + "Q": "At 0:25 He say (f*g)(x). then says f of x and g of x is the same thing, why is it like that? Also why doesn't he use y?\n", + "A": "Because you are doing what he also says to do in the video, distributing. You are distributing the x in (f*g)(x) to f and g, thus getting f(x)+g(x)", + "video_name": "JKvmAexeMgY" + }, + { + "Q": "At 2:28 why is it that 7x * x^3 equals to x^4 ?\n", + "A": "Diego, 7x^3 means 7*x*x*x 7x^3 * x = 7*x*x*x * x 7x^4 means 7*x*x*x*x That is why 7x^3 * x = 7x^4 I hope that helps", + "video_name": "JKvmAexeMgY" + }, + { + "Q": "at 1:17 how do you determine that x =2?\n", + "A": "Because u need it to equal zero so u must replace x with what is necessary witch was 2 in that case.", + "video_name": "7QMoNY6FzvM" + }, + { + "Q": "\n4:52 He labeled the postulate as AAS but once he made it clear BE was congruent to EC doesn't it become SAS after that is marked?", + "A": "He used AAS to prove that the two triangles are congruent, which by definition means that all corresponding sides/angles are congruent, including \u00f0\u009d\u0090\u00b5\u00f0\u009d\u0090\u00b8 \u00e2\u0089\u008c \u00f0\u009d\u0090\u00b6\u00f0\u009d\u0090\u00b8 (which means that \u00f0\u009d\u0090\u00b5\u00f0\u009d\u0090\u00b8 and \u00f0\u009d\u0090\u00b6\u00f0\u009d\u0090\u00b8 are of equal length, which is what we wanted to prove).", + "video_name": "RFesGHsuFZw" + }, + { + "Q": "\nat 4:21 Did you mean angle side angle?", + "A": "NO because Angle Side Angle mean the side is in between the 2 angles. Since the side is not between them so it SSA. Hope this help.", + "video_name": "RFesGHsuFZw" + }, + { + "Q": "\nI'm a little confused on how he got 3 at 5:12... how did he get that?", + "A": "Statement #3 - triangle-BEA is congruent to triangle-CED, comes from angle-angle-side. The first angle is from statement #2 (ABE = DCE via alternate interior angles), the second angle is from statement #1 (AEB = DEC via vertical angles), and the side is given in the original drawing (AE=DE).", + "video_name": "RFesGHsuFZw" + }, + { + "Q": "\nAt 6:50, so for every eigenvector there is also a corresponding eigenvalue?", + "A": "Actually, that s a good question. Some matrices transform vectors so that some of the vectors don t rotate (they re eigenvectors ). If a transformed vector x isn t rotated, what is x , the transformed vector? x is a scalar (called lambda - the eigenvalue ) times the original vector x - that is, Ax = x = lambda*x. So: Does every eigenvector have an eigenvalue?", + "video_name": "PhfbEr2btGQ" + }, + { + "Q": "At 4:11, Sal assumes he can draw a line through B, C, and D, making BCD a transversal of the two parallel lines, an assumption which allows him to solve the whole problem. I understand how that all works out. But unless I'm mistaken, it's never stated that points B, C, and D all lie on the same line. Sure, they look like they do, but without that being explicitly stated, isn't it possibly an erroneous assumption?\n", + "A": "Let s say that BC and CD are subtly off kilter. The technique will still work because you can extend line segment BC along (infinite) line BC, and there will be a new point (call it Q) to use instead of D. From there, the technique will be the same. The important element is that AB and CE are parallel, which means that BC (not necessarily BC and CD) is the transversal.", + "video_name": "0gzSreH8nUI" + }, + { + "Q": "\nAt 5:04, instead of finding the corresponding angle for 4x, couldn't we find the corresponding angle for 2x and solve? I know you get the same answer, but I'm just clarifying if you can't.", + "A": "there is more than one way to solve most problems. You can do it both ways in this problem.", + "video_name": "0gzSreH8nUI" + }, + { + "Q": "Also, can you get a definite answer for part 2:30 where the area is going to be x?\n", + "A": "Yes and No, it depends on what you mean. No if you do not know anything like in thew video. What Sal is showing is like a format. (you can fill out the sides and the inside) Yes if you know the side L*W. What he is trying to show you is that for a square each side, if it is squared will get you the area. Hope this helped!", + "video_name": "87_qIofPwhg" + }, + { + "Q": "At 1:14, he mentions imaginary and complex numbers.\n\nWhat does he mean by \"imaginary\" numbers?\n", + "A": "Imaginary numbers are complex numbers in the form a + bi, in which a = 0. So, you d simply have i and its coefficient.", + "video_name": "87_qIofPwhg" + }, + { + "Q": "at 5:08 where does the tan function come from?\n", + "A": "tan theta = opp/adj opp = sin theta adj = cos theta A simple proof: I dont know how to do theta symbol, so just pretend the no. 0 is theta show that: tan0 = sin0/cos0 RHS = opp/hyp divided by adj/hyp = opp/hyp times hyp/adj (when dividing fractions, invert and multiply) = opp/adj = tan0 = LHS", + "video_name": "8RasCV_Lggg" + }, + { + "Q": "sal why are you dividing when you could be subtracting at 00:55\n", + "A": "Because you wouldn t get the correct answer. Whenever dealing with decimals and percents, in situations like Sal had in 00:55, divide.", + "video_name": "gKywkLHV6Ko" + }, + { + "Q": "Hi Sal, at 4:44 it says a mean of 7.5 is impossible for a sample of size n=2. But, wouldn't a mean of 7.5 be achieved by a random sample with values 6 and 9, which was a mean of (6+9)/2 = 7.5? Thanks, Chris Broski\n", + "A": "Hi I just saw the answer to my questions below. I understand now, yes, it is possible to get 7.5 as the mean for a sample of size n =2. Thanks, Chris Broski", + "video_name": "NYd6wzYkQIM" + }, + { + "Q": "\nat around 4:25, Sal says we are never going to get 7.5 when n=2. But if 6 and 9 are randomly selected, then 7.5 would be the average, so I'm not quite understanding his reasoning here?", + "A": "You re totally correct, Mike G! Your logic is solid; Sal made a mistake.", + "video_name": "NYd6wzYkQIM" + }, + { + "Q": "\nAt 1:46, shouldn't Sal have noticed he wrote \"Armaan\" when it should be Arman?", + "A": "This is a known problem with the video. A box pops up with the correction.", + "video_name": "W-5liMGKgHA" + }, + { + "Q": "The third problem, The \"Bizarre looking shape\" at 5:09, would it be possible to find the area of that dodecagon?\n", + "A": "Yes. Since the dodecagon is made up of all right angles, as Sal said, finding the area would be easy. All you need to do is cut it up into rectangles, find the rectangles areas, and add them up.", + "video_name": "vWXMDIazHjA" + }, + { + "Q": "\nI'm really confused about why the top equation was multiplied by -2 at 17:20. Surely it's not an arbitrary number, right?", + "A": "Sal was setting up the elimination step. The next thing he does is add the two equations and the C_1 variable is eliminated allowing us to solve for C_2. Multiplying by -2 was the easiest way to get the C_1 term to cancel. Another question is why he chooses to use elimination. The first equation is already solved for C_1 so it would be very easy to use substitution. He may have chosen elimination because that is how we work with matrices.", + "video_name": "Qm_OS-8COwU" + }, + { + "Q": "\nAround 13:50 when Sal gives a generalized mathematical definition of \"span\" he defines \"i\" as having to be greater than one and less than \"n\". Is this because \"i\" is indicating the instances of the variable \"c\" or is there something in the definition I'm missing?", + "A": "Its because we are looking at the Span of the Vectors v1 to vn, so for every vi there is a ci. Thats why i has to be between 1 and n.", + "video_name": "Qm_OS-8COwU" + }, + { + "Q": "At 1:10 why does he ask that question?\n", + "A": "he was adding the number thats it", + "video_name": "Oe1PKI_6-38" + }, + { + "Q": "at time 9:10 when he puts the boundary conditions, he replaces each of the y variables with -1. i do not get this point as boundary condition means the whole function should evaluate to -1 as x=0. some one please help me with that.\n", + "A": "thanks a lot i got it now....!!!....", + "video_name": "C5-lz0hcqsE" + }, + { + "Q": "\n1:10 I don't understand Sal's explanation of the vertical tangent as having infinite dy. I know that a vertical line has an undefined slope because there's no change in x so dy is being divided by zero, but what does infinity have to do with that?\nAlso, how does a small change in x give an undefined slope when it's still a defined number that returns another real number when divided by a defined change in y?", + "A": "But we don t have a defined change in y for a vertical line. The change could be anything. If we have a vertical line, then y is not a function of x. Would you be happier if we said dy was undefined for a vertical line, rather than infinite ? To be honest I m not sure if you think a vertical line is differentiable with respect to x or something else is troubling you.", + "video_name": "pwh1dK3vTkM" + }, + { + "Q": "\nat 0:53 it is said that a point having a vertical tangent is not differentiable because for a change in x there is an infinite change in y at that particular point . how is it so?", + "A": "Sal is a tad off with his wording there. The change in y is finite but it doesn t get smaller as x gets smaller so you have a limit of dy/dx where dy decreases much slower than dx as dx --> 0 so the limit is unbounded.", + "video_name": "pwh1dK3vTkM" + }, + { + "Q": "At 2:52 how can we be sure that the three angles equal 180 degrees? It may appear to be a straight line, but without any notation ensuring that it is, how can we be sure?\n", + "A": "Hi J, Right at the very beginning of the video, at 0:01, Sal uses the words in this larger triangle here as he outlines triangle ABE. If this was a straight word question however, the question would start out with something like, Given triangle ABE, prove that ... Hope that helps!", + "video_name": "aDCXPdzyS0s" + }, + { + "Q": "At \"3:12\" I do not exactly understand how Sal pinpoints point C in the designated location? Please explain how he knew where to find all of the points of the hexagon given the special set of values for y, thank you.\n", + "A": "because the hexagon had to be convex and with all sides equal.", + "video_name": "Ec-BKdC8vOo" + }, + { + "Q": "At 3:07 why does he add 16?\n", + "A": "I ve just looked at this video and cannot find any 16 mentioned. Did you reference the correct video?", + "video_name": "PupNgv49_WY" + }, + { + "Q": "\nat 7:11 why do you all of a sudden flip 81 into 1/81", + "A": "Sal was substituting into A / C. A was 1 / 9 and C was 81. So, A / C = ( 1 / 9 ) / 81 which is the same as ( 1 / 9 ) * ( 1 / 81 ). In words, dividing by a number is the same as multiplying by its reciprocal.", + "video_name": "PupNgv49_WY" + }, + { + "Q": "In 2:14, we have the same bases on one side of the equation but what if there was a value on the other side of the equation without the same base. For example, logbase3 of 5 +logbase3of 2= 8 How would you approach the problem?\n", + "A": "First you would combine the bases. Then you will exponentiate both sides of the equation. What this means is you make all of those numbers into a power. For example, x = y. When you exponentiate it, you will get something like 3^x = 3^y. You can use this to your advantage to eliminate logs.", + "video_name": "PupNgv49_WY" + }, + { + "Q": "is any number in the sequence of numbers 1 2 4 8 16 32 64 128 256 512 etc... able to some how convert into a higher number in the sequence? this question came from 3:33 in the video, it might have been before, when you converted the number 8 in the sequence into 25, because i have noticed that many numbers are multiples of those higher numbers.\n", + "A": "I m not exactly sure what you are asking but the sequence you wrote down is the sequence you get by multiplying by 2 to get the next number. Another way to write that sequences is 2^0,2^1,2^2,2^3,2^4,2^5,2^6,.... I m not sure what you mean by converting 8 into 25.", + "video_name": "PupNgv49_WY" + }, + { + "Q": "Why does Sal change colors, like at 4:37?\n", + "A": "It lets the viewer understand things more easily. He also does it so that it isn t boring and he color codes some things. Try to learn things the KHAN way!!", + "video_name": "PupNgv49_WY" + }, + { + "Q": "at 1:58 why did u divide the number ab=-3 by a , why not multiplied it by a?\n", + "A": "Sal is solving the b . To move the a , we look at the relationship between the a and b in ab . It is multiplication. Then we always use the opposite operation to move the a . The opposite operation to multiplication is division. If you multiplied both sides by a , you would get a*ab = -3a or a^2b = -3a . The b is not by itself. Hope this helps.", + "video_name": "3_DxJwDTbyQ" + }, + { + "Q": "at around 4:25 he says that you can manipulate it to make one variable seem more DEPENDENT then another. What does he mean? If anyone could help me that would be nice, thanks.\n", + "A": "m=n/7, m/n = 1/7, n = 7m, n/m = 7. The only thing I can come up with is that whichever variable has the number 7 on the same side with it might seem to be the independent variable, as in y = f(x) , y = 3x .", + "video_name": "3_DxJwDTbyQ" + }, + { + "Q": "\ncan anyone hrlp me. at 2:15 he says 1/10/x = 1/10x. I can't see how he got there..", + "A": "(1/10)/x is the same as multiplying 1/10 by the reciprocal of x i.e. 1/x. So, (1/10)/x = 1/10 * 1/x = 1/10x. HOPE THAT HELPED YOU!", + "video_name": "3_DxJwDTbyQ" + }, + { + "Q": "At 3:41 I didn't understand how it is neither\n", + "A": "Cause the funcion has a sign minus (-) and is not clear if a is negative or is a sustraction. If you see the direct/inverse variation has no addtions or sustractions, just multiplication and divisions. I hope being helpfully", + "video_name": "3_DxJwDTbyQ" + }, + { + "Q": "\nwhat does he mean at 1:11 when he says constant?", + "A": "Well, what he means by constant is that when one side of a function goes up or down, multiplying or dividing, the other side will go up by the same amount, since it is a direct variation. If the function was a inverse variation, it wouldn t be a constant, because when one side of the function goes up, the other side of the function goes down, so therefore the variable isn t constant, because it doesn t do the same thing for both sides, it does the opposite. HOPE THIS HELPS!!", + "video_name": "3_DxJwDTbyQ" + }, + { + "Q": "At 2:53, why doesn't y = -2x count as inverse variation? The values move in opposite directions; as x increases y decreases. Thanks for any help.\n", + "A": "Inverse variation is when the letter is under, so divides the coefficient and doesn t multiply it.", + "video_name": "3_DxJwDTbyQ" + }, + { + "Q": "\nDid you know that the reason things float to the edge of a overfilled cup if you put something in it (say, a penny) is because that the middle of the water is actually just a teeny bit higher then the sides, so the penny automatically goes to the lowest point in the cup.\nVice Versa, if you were to underfill a cup, and put a penny on the side, it would automatically go towards the middle because that is the lowest point (3:02)", + "A": "Yep. Surface tension is an amazing thing, isn t it? In science, when you re measuring liquid in a beaker or graduated cylinder, you would call the lowest point the meniscus", + "video_name": "lOIP_Z_-0Hs" + }, + { + "Q": "\nCan you explain the sentence written at 2:12 to me: \"Of all the integers, 1 is the integeriest.\"?", + "A": "She is saying that some people say that saying that phi is the most irrational number is like saying that of all the integers 1 is the most integer-y.", + "video_name": "lOIP_Z_-0Hs" + }, + { + "Q": "\nAt 9:10 to 9:33 Sal says that a rational can be a repeating decimal but it can't go backwards. But his answer was backwards. Is he wrong or am I not getting something.", + "A": "Sal is completely right! What he meant was that you can t say (by that statement) that a number is rational because it can be written as a repeating decimal. To conclude that a number that can t be written as a repeating decimal is not rational, he didn t goes backwards. He did use a strait foward reasoning to deduce. If all rationals can be expressed that way, a number that can t be written as a repeting decimal is not rational.", + "video_name": "GluohfOedQE" + }, + { + "Q": "\nSal converted the fractions into improper fractions in 1:38. Is that the easiest way?", + "A": "converting mixed fractions into improper fractions helps in comparing mixed fractions", + "video_name": "QS1LMomm0Gk" + }, + { + "Q": "At 1:57, Why do we need to find a common denominator? Can't we just add 25/8 + 3/4 directly?\n", + "A": "Cause a common denominators solves all of life s problems", + "video_name": "QS1LMomm0Gk" + }, + { + "Q": "\nReferencing the Banach-Tarski Paradox made my day. (2:24)\nIf only physics wouldn't get in the way of my math!", + "A": "I know, right? Physics rocks UNTIL it gets in the way of doing things like the Banach-Tarski paradox!", + "video_name": "F5RyVWI4Onk" + }, + { + "Q": "\n2:27 If I had this sort of problem on a test, what are other ways of stating that there's no solution? I'm assuming the symbol for the empty set would be one of them? Or is that basically it?", + "A": "Yes, the symbol for the empty set would be an acceptable way of saying there is no solution.", + "video_name": "ZF_cZ-GX9PI" + }, + { + "Q": "At 8:54, why is tan theta described as sine theta/ Cosine theta?\n", + "A": "You will need to know these definitions: sin\u00ce\u00b8 = y/r cos\u00ce\u00b8 = x/r tan\u00ce\u00b8 = y/x Since we re in a unit circle, r = 1, so sin\u00ce\u00b8 = y and cos\u00ce\u00b8 = x. Since tan\u00ce\u00b8 = y/x, y = sin\u00ce\u00b8, and x = cos\u00ce\u00b8, we can make the substitutions. y = sin\u00ce\u00b8 x = cos\u00ce\u00b8 tan\u00ce\u00b8 = y/x = sin\u00ce\u00b8/cos\u00ce\u00b8", + "video_name": "1m9p9iubMLU" + }, + { + "Q": "At 2:34, shouldn't the point on the circle be (x,y) and not (a,b)? [Since horizontal goes across 'x' units and vertical goes up 'y' units--- A full explanation will be greatly appreciated]\n", + "A": "It would be x and y, but he uses the letters a and b in the example because a and b are the letters we use in the Pythagorean Theorem a\u00c2\u00b2+b\u00c2\u00b2 = c\u00c2\u00b2 and they re the letters we commonly use for the sides of triangles in general. It doesn t matter which letters you use so long as the equation of the circle is still in the form a\u00c2\u00b2+b\u00c2\u00b2 = 1.", + "video_name": "1m9p9iubMLU" + }, + { + "Q": "\nat 4:29, why do we find cosine?", + "A": "Sal is just demonstrating how all of the trig functions work as they are defined on a unit circle.", + "video_name": "1m9p9iubMLU" + }, + { + "Q": "At 3:48, how do we know that side b of the triangle is the same as the chord \"b\", like Sal says?\n", + "A": "He never says that the length of the chord you are creating is equivalent to the length of side b. He s simply saying that the length of side b, or the height as he says, is the y-value, b, which is what he marks on the y-axis. He s not creating a chord b, it s just a dashed line to show that the y-value corresponds to the height of side b of the triangle. Hope this helps!", + "video_name": "1m9p9iubMLU" + }, + { + "Q": "At 7:05,Sal said \"bottom boundary\" as z=2-2/3*x-y/3 but from graph it seems\nz=0 to z=z=2-2/3*x-y/3. I think the bottom limit for dz is zero? i am confused?\n", + "A": "Here is the clarification: Review from 1:13 where Sal defines the plane (via x,y,z intercepts). Then at 2:11 he says he cares about the volume above the plane (to make the problem more complicated). So he is asking for the volume between this plane and the plane z=2.", + "video_name": "ZN2PfqZ4ihM" + }, + { + "Q": "\nAt 10:10, I don't get it", + "A": "There is an exact same question at the back, with the same point of time reference which has some good answers. You should have a look at them.", + "video_name": "ZN2PfqZ4ihM" + }, + { + "Q": "at 4:35 cant the x and y axi, axises, axis(multiple axis) be a line and go on forever in any direction and seems how forever is a relative term go on in both directions in so far it is impossible to reach the end what so ever.\n", + "A": "The axes do go on forever, so to speak, in both directions, and it is indeed impossible to reach the end (if we progress by finite distances). Did it seem to you that Sal was implying something different? Is your question related to the restriction in the domain of arctangent?", + "video_name": "QGfdhqbilY8" + }, + { + "Q": "\nAt 0:43 what did mean by 90 degrees. Do you mean that all sides are the same length for a square?", + "A": "It is true that all sides of a square have equal length but when he said the square had 90 degrees he meant that all the angles of the square were equal to 90 degrees. Have an awesome day!\u00f0\u009f\u0098\u008a", + "video_name": "1pHhMX0_4Bw" + }, + { + "Q": "At 0:34-0:39, did he also mean to say that all sides are of equal length? A rectangle is also a quadrilateral with only 90-degree angles, but all the sides aren't always the same length.\n", + "A": "Yes, rhombus is a quadrilateral with 4 sides of equal length. So rectangles are not always rhombus.", + "video_name": "1pHhMX0_4Bw" + }, + { + "Q": "\nShouldn't it be (2x-2y) - (2x-2y)(dy/dx) instead of (2x-2y)+(2x-2y)(dy/dx) at 2:15", + "A": "He has switched the order of the variables, so that it is (2x-2y)+(2 y-2 x)(dy/dx). -(2x-2y) = 2y-2x", + "video_name": "9uxvm-USEYE" + }, + { + "Q": "At 2:12, why does Sal simply multiply (2x-2y) *1 and then by the (dy/dx), instead of FOIL'ing it out and getting something like 2x-2x(dy/dx)-2y+2y(dy/dx) ?\n", + "A": "He could have done that. Then he would have had to put the dy/dx s back together: 2x - 2y + 2y(dy/dx) - 2x(dy/dx) 2x - 2y + (2y - 2x)(dy/dx) He wants to get all the dy/dx s together such that he can manipulate them into one instance of dy/dx multiplied by a factor (in this case that factor ends up being (2y - 2x - 1)), such that he can isolated dy/dx on the left and have his answer.", + "video_name": "9uxvm-USEYE" + }, + { + "Q": "at 3:05 shouldnt it be (2y-2x) time negative dy/dx but why is there no negative\n", + "A": "at 2:15 - 2:25 he explains that instead of doing -(2x - 2y) he chose to do (2y - 2x) (they are equal).", + "video_name": "9uxvm-USEYE" + }, + { + "Q": "At 0:52, why does he say she wants to divide the blueberries into 6 groups? That number doesn't take Kali into account, and we don't know how many berries she may want. She could want 1 blueberry, or 0, or 12. Why then, does he not at least say \"we can assume that Kali doesn't want any berries, if she is giving them all too her friends.\"?\n", + "A": "That s right. I agree", + "video_name": "QXNg_u5Tv8Q" + }, + { + "Q": "so it ends at 4:42 ?\n", + "A": "Yes. Why wouldn t it its the end of the video.", + "video_name": "vAlazPPFlyY" + }, + { + "Q": "at 0:22, what is a better under standing of what adjacent is?\n", + "A": "It just means next to", + "video_name": "vAlazPPFlyY" + }, + { + "Q": "\nAt 4:00 Sal cancels out the terms that approach zero as if they dont exist and states that the limit is 3/6 or 1/2.\n\nI dont understand how he can be sure the function isn't defined for 1/2.\n\nAs it approaches infinity it is (3 minus a tiny fraction) over (6 minus a tiny fraction)\n\nAs I see it, unless those tiny fractions are exactly the same, the limit will be a tiny amount greater or less than 1/2, making the function defined for the point Sal claims it never reaches.\n\nIs there something I'm misunderstanding?", + "A": "I think you just answered your own question without realizing it. The value will always be a tiny amount greater or less than 1/2. It will never be exactly equal to 1/2.", + "video_name": "P0ZgqB44Do4" + }, + { + "Q": "\nAt 7:55, there was a reference to the function g:R^2-->R. How did that function morph into g(x1,x2)=2.", + "A": "so you have a vector space that is R^2, and a vector space that is R. the R^2 vector space simply has more data than the vector space R. the transformation G fits vectors from the R^2 vector space into vectors in R, or at least attempts to.", + "video_name": "BQMyeQOLvpg" + }, + { + "Q": "\n@ 4:00 why is the exponent -10?", + "A": "At around 2:10 you will see that it is counting the number of places from the standard decimal place, and it is negative because you re moving it to the right, towards the negative side of the number line.", + "video_name": "6phoVfGKKec" + }, + { + "Q": "At 9:45, how does \u00e2\u0088\u009a10 . \u00e2\u0088\u009a10 = 10 in the denominator?\n", + "A": "That equals 10 because at 9:04, he says that 1/radical 10 is irrational. If you wanted to get rid of the radical, you would have to multiply square root 10 over square root 10. 1x square root 10= 10. Square root 10x square root of 10=10 because 10 times 10 is 100. 100 is a perfect square so it simplifys back to 10 again. If my explaination dosen t help much, watch other videos on this topic.", + "video_name": "BpBh8gvMifs" + }, + { + "Q": "\nWhy in example D @ 4:37 the square of 2*2=2 and in example E @ 6:24 the square of 2*2=4? What makes the two identically appearing values different?", + "A": "Because in D There was only one 2*2 and in E there are two: (2*2)*(2*2)*5*5*5 And we can simplify that as 4.", + "video_name": "BpBh8gvMifs" + }, + { + "Q": "At 8:36, how come the fraction isn't reduced?\n", + "A": "Zoe.daniele, you can either reduce the fraction, or you can put it into decimal form. Either way, your answer will be correct (make sure to check with your teacher whether he or she wants you to use fractions or decimals in your answer). Hope that helps!", + "video_name": "BpBh8gvMifs" + }, + { + "Q": "\nat 6:30 why we can't write \"36 35 34 33 32 1 1 1 1\" instead of \"1 1 1 1 32 31 30 29 28\"", + "A": "Because knowing you have all the 1s, you can t have the whole 36 options. The 1s are part of the 36 unique cards, so you can t pick one of them and then add them again, that would make it five 1s. So once you locked the 1s to be in your hand, you only have 32 cards left as the first choice for the non-1s card.", + "video_name": "ccrYD6iX_SY" + }, + { + "Q": "In 0 4:04 Sal tells about a factorial. What is the definition of a factorial\n", + "A": "In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, 5! is 5*4*3*2*1. 76! would be 76*75*74*73*72*71*...*3*2*1. They are essential in probability.", + "video_name": "ccrYD6iX_SY" + }, + { + "Q": "\nat 03:55 , why does it equal to 36!/(36-9)!9! ??", + "A": "Before that in the numerator we have 36*35*...*28, and 9! in the denominator. 36! is 36*35*....28*27...*2*1. So in writing 36! as the new numerator, we have to multiply by 27*26...*2*1 both the numerator and denominator. (36-9)! = 27!, which is exactly that factor.", + "video_name": "ccrYD6iX_SY" + }, + { + "Q": "From minute 5:07 to 5:53, why does it have to be 1x1x1x1x32x31x30x29x28 instead of 36x35x34x33x32x1x1x1x1? Obviously the end result will be different but I'm asking why or what is the rule, idea, concept or whatever that says to go with the former rather than the latter.\n", + "A": "Even if you used your logic, you are still saying that the 4 ones are drawn at the end, so the first 5 cards could not be ones, so it is still 32*31*30*29*28*1*1*1*1.", + "video_name": "ccrYD6iX_SY" + }, + { + "Q": "\nat 1:26, i think you meant to write DCE = BAE. (You wrote DEC = BAE)", + "A": "Indeed, it should be DCE = BAE.", + "video_name": "TErJ-Yr67BI" + }, + { + "Q": "I really don't get it. At 1:42, why do you have to do f(x) times g(x)^-1?\n", + "A": "Dividing by a number is the same as multiplying by the inverse of that number, which you can get by setting the exponent equal to -1 : Thus, the inverse of B is B^-1 since B^-1 = 1/B^1 = 1/B. Therefore, A/B = A*B^-1. That s why f(x)/g(x) = f(x)*g(x)^-1.", + "video_name": "ho87DN9wO70" + }, + { + "Q": "\nAt 3:54 Sal says f(x)=1/(2+2cos(theta)), but it should be f(theta)=\u00e2\u0080\u00a6.\nIt's not a function of x, but it is a function of theta.", + "A": "Yup You got it right Sal Made A Mistake, it should be f(theta).", + "video_name": "d8qtbGMB2gI" + }, + { + "Q": "2:12 to 2:23 is so unclear, why do they take out the 2s and 3s? How did they get the numbers? I took the test and did it another way...\n", + "A": "that is how it goes", + "video_name": "-UagBvxCReA" + }, + { + "Q": "\nAt 1:30, how did he get x((4x)2", + "A": "You mean, how he got to x( (4x)^2 + 2*4*3 + 3^2) ?", + "video_name": "BFW2lHobO4E" + }, + { + "Q": "\nWould using a different trig identity work @4:00. For instance, we could use the \"Product-to-Sum\" trig I.D of Sin(t-Tau)Cos(Tau). Then we could just split the integrals and it would make life a bit nicer right?\nTrig I.D.: sin(u)cos(v) = sin(u + v) + sin(u \u00e2\u0088\u0092 v)", + "A": "Yes, you can use that identity, and the integration does indeed is simpler. But that identity is not so easy to memorise, Sal decided to use only the most basic of identities.", + "video_name": "IW4Reburjpc" + }, + { + "Q": "in the first example at 0:42, what where the m's and the b's?\n", + "A": "Here, m and b are constants; in a linear equation, m is traditionally used to represent slope, and b is used to represent the y-intercept. In other words, they re just the good old slope-intercept form pieces from algebra.", + "video_name": "zid7J4EhZN8" + }, + { + "Q": "\nat 3:14, can you explain the use of the chain rule that results in 2y * y'? thank you.", + "A": "The derivative of y^2 is 2y * (dy/dx). (dy/dx) = y so then 2y * (dy/dx) = 2y * y", + "video_name": "ZtI94pI4Uzc" + }, + { + "Q": "At 6:09, Sal describes taking the integral at a specific value c. What would happen if you took the derivate of the Dirac delta function combined with a certain function at value c and then applied the Laplace transform?\n", + "A": "The derivative of the Dirac delta function is undefined at c, so it would not work very well.", + "video_name": "vhfjEpQWWeE" + }, + { + "Q": "In the first equation, Sal simplifies the equation to: (7x - 2) / (15 - 5/x). He states at 2:32 that 7x will approach negative infinity, however he simplified this value from 7x^2 which by definition will always turn negative numbers positive. Shouldn't he have simplified the equation to state: 7|x|?\n", + "A": "Sal simplified the expression down to it s dominate terms: 7x/15. If you are going to use the 7x^2, then you also need to use the 15x in the denominator. Yes, 7x^2 would be positive, but 15x would be negative. A positive / a negative = a negative. Hope this helps.", + "video_name": "Vtcmyr5IGYY" + }, + { + "Q": "\nAt 2:00, why would I need to see if the sides are parallel to each other?", + "A": "To know if any of the shapes are the right answer. And to know for sure that what you think is right", + "video_name": "vsgrWDLEzcQ" + }, + { + "Q": "\nAt 7:17, how does Sal choose the starting point? Does it matter? Could it be the other point?", + "A": "The starting/ending points could certainly be any as long as they are on the line c. I think these were chosen because they both had integer values for x and y and thus made the computation a little easier.", + "video_name": "Iqws-qzyZwc" + }, + { + "Q": "At 2:27,Can it still be -12 over -4? (-12/-4)\n", + "A": "yes it can be (-12/-4)", + "video_name": "Iqws-qzyZwc" + }, + { + "Q": "At 2:29 isn't it suppose to be y2-y1 over x2-x1?\n", + "A": "Yes . . . and that s what Sal did. y2 is 6, and y1 is -6, so we get y2 - y1 = 6 - (-6) = 12 For the change in x Sal basically just counted the number of squares horizontally between the two points, but that s the same as finding x2 - x1.", + "video_name": "Iqws-qzyZwc" + }, + { + "Q": "At 4:39, Sal didn't label the x values as x1 and x2, and the y-values as y1 and y2. Why is that?\n", + "A": "You don t need to label the points as x1, x2, y1 and y2. You just need to know which is which.", + "video_name": "Iqws-qzyZwc" + }, + { + "Q": "In the end of 10:00 , we can see, slope of one line is -2 (negative two) and another is +1. So which one's rate of change will be higher ?\n", + "A": "The higher rate of change should be -2 as the rate of change deals with the magnitude of the slope.", + "video_name": "Iqws-qzyZwc" + }, + { + "Q": "\nAt 2:11, isn't it a change of -4 because y=-4?", + "A": "y=-4 is like y= 0x -4. In order for the x to be gone you would need a zero at its coefficient. since the coefficient of the x is the slope then the slope is zero.", + "video_name": "J43CIbKpdWc" + }, + { + "Q": "\nAt 3:45 he points out that there's a new slowest time, and uses that to determine that the 4th bullet point is wrong. Does that new slowest time even matter though? Even if that new slowest dot wasn't there (ie, it had been at the 52 mark in the final round), does that change anything regarding the 4th bullet point question?", + "A": "It does matter because, as pointed out, one swimmer did swim slower so the statement all swam faster cannot be true.", + "video_name": "KXDOOmquZag" + }, + { + "Q": "At 4:35, I still don't get why -(-e)/f is equal to e/f.\n", + "A": "When there are 2 negatives, it equals to a positive. When someone says Jump , it s a positive. When someone says Don t eat , it is negative. Meanwhile, if someone says Don t not eat , that s back to saying Eat which is a positive.", + "video_name": "9eSPhvhuInw" + }, + { + "Q": "at 1:08 he says that the sin of 7pi/12 is the length of the magenta line however isn't that the sin of pi/2 and shouldn't that length be one considering it is a unit circle?\n", + "A": "Sal has drawn a right triangle. The hypotenuse (the diagonal line, or the green line furthest to the left) is = 1 because it goes from the center of the circle out to the circle. The angle 7pi/12 goes up to the hypotenuse. You are trying to make the angle into 90 degrees (pi/2)rather than the 7pi/12. Next, it is hard to see, but the magenta line is slightly shorter than 1. This is why it doesn t = 1. Hope this helps.", + "video_name": "2RbKfRfzD-M" + }, + { + "Q": "At 6:16, why do you need to collect multiple data points to determine if a question is a statistical question?\n", + "A": "Statistics is the comparison of data at different points. If you have a single data point then there is nothing to compare it to. So you need multiple points so you can compare the data, an thus be using statistics.", + "video_name": "OjzfQDFf7Uk" + }, + { + "Q": "\nAt 3:31, Why does Sal multiply 6x5x4x3?", + "A": "nPr is used because nPr counts all answer sets (including duplicate unordered sets, which is what we want since the duplicates have different meaning than the ordered version) theres 6 total items so n=6 we re picking 4 items so r=4 the formula is n!/(n-r)!=6!/2!=6*5*4*3", + "video_name": "oQpKtm5TtxU" + }, + { + "Q": "\nhow is 1 m = to 100 cm 02:57", + "A": "Centi refers to 100. The root is the same as in century (100 years). A centimeter is one one-hundredth of a meter (1/100). So 100 centimeters are equal to 1 meter. Note that a decimeter is 1/10 of a meter. That word looks a little like decade, doesn t it?", + "video_name": "byjmR7JBXKc" + }, + { + "Q": "\nwhy does it say the problem reads 80:1 scale but should read 1:80 scale", + "A": "They corrected it", + "video_name": "byjmR7JBXKc" + }, + { + "Q": "i am confused, is the 80 in 80:1 centimeters as well?\n", + "A": "It is saying that 80 centimeters in the real world is 1 centimeter on the blueprint", + "video_name": "byjmR7JBXKc" + }, + { + "Q": "\nat 1:21 i never understand how he got y/x 3/1 6/2=27/9 im soooooooooooooooooooooooooooooooo lost right now", + "A": "A proportional relationship just means that the 2 fractions are equal. Your 3 fractions are all equal fractions. Start with 3/1 If you multiply 3/1 * 2/2 = 6/2. If you reduce it, you get back 3/1 If you multiply 3/1 * 9/9 = 27/9. If you reduce it, you get back 3/1. Hope this helps.", + "video_name": "qYjiVWwefto" + }, + { + "Q": "\nIn the charts that Sal makest at 3:36, is the y side always going to be numerator in fraction form?", + "A": "It doesn t matter which side you use as the numerator, as long as the proportions are consistent. So if you have x/y = 2x/2y = 3x/3y, that will work for sure. But if you have x/y = 2y/2x = 3x/3y, that won t work. Sure you can place the y on the top but make sure it stays on the top.", + "video_name": "qYjiVWwefto" + }, + { + "Q": "At 7:34, why are all the sides equal to the square root of a^2 + b^2?\n", + "A": "If one of the sides is equal to the square root of a^2 + b^2 (using Pythagoras theorem), then all of the sides are equal to it (since all the sides of a rhombus are equal).", + "video_name": "jpKjXtywTlQ" + }, + { + "Q": "\nAt 12:19, Sal simplified (2a)^2 to 4a^2. Wouldn't it just be 4a?", + "A": "(2a)^2 = (2a)*(2a) = 2*2*a*a = (2*2)*(a*a) = 2^2*a^2.", + "video_name": "jpKjXtywTlQ" + }, + { + "Q": "at 12:23 , he said 50=5a^2 , then he divided by 5 and got 10=a. what about that squared symbol?\n", + "A": "The equation was 50a=5a^2. He then took each side divided by 5a, which came out to be 10=a, or a=10.", + "video_name": "jpKjXtywTlQ" + }, + { + "Q": "at 0:42 , how do we get to know if an equation is homogeneous equation. i mean what is the working rule for homogeneous equation?\n", + "A": "For a first order equation you can determine it s not separable because an x term is added to a y term. Homogeneous is probably the next thing to try. It works because the exponent on the x and y terms are the same. I don t know of any perfect test to determine if it s homogeneous. I would say it s trial and error and, of course, practice.", + "video_name": "6YRGEsQWZzY" + }, + { + "Q": "\nI have an dummy question, but at minute 1:03, i dont get why the multiplication (1/x\u00c2\u00b2)/1/x\u00c2\u00b2 makes the after result.\nThanks", + "A": "Distribute the 1/x^2 on top to both terms, then multiply the bottom term by 1/x^2. You ll get the same result as the video.", + "video_name": "6YRGEsQWZzY" + }, + { + "Q": "I believe at 2:23 and other instances during previous videos he makes the mistake of putting the 'approx. equal to' sign. It is exactly equal to e^x.\n", + "A": "Well, technically, yes and no, since we are summing something to infinity, it can never be exact exact, because it has to go on forever(e is transcendental anyway), but he probably could have used equals, or approx. equals, the definitions get quite similiar while summing things to infinity.", + "video_name": "JYQqml4-4q4" + }, + { + "Q": "at 0:24 cant you just do -31+(1-1)-7 ?\n", + "A": "yes, you can but the way Sal did it is simpler.", + "video_name": "GA_yxxeFYBU" + }, + { + "Q": "During 0:21, he screen became blurred and it was tough to concentrate. Still, love your videos( Your ScratchPad makes me jealous)!!\u00f0\u009f\u0098\u0083\n", + "A": "HaCk(ERROR<1>) X>0 Y<0{heading 0 Ipx} =hAck", + "video_name": "qW-Ce44ll0Q" + }, + { + "Q": "\nAt 2:09 he basically tells us we can't assume and we don't know the angels.\nWell.. We know the angle bisector is equal (no duh...) But doesn't that mean that the 2 angels at D are 90 degrees. And if we know that we also know that the Angle A and Angle C are equal am I right?", + "A": "We actually don t know that the 2 angles at D are 90\u00c2\u00b0. They look like they could be, but that information wasn t given in the question. If they were, then you re correct that we could find the other angles and prove that the triangles are congruent by ASA (or AAAS).", + "video_name": "TpIBLnRAslI" + }, + { + "Q": "How did Sal know to divide by two at 2:04. Thats part of taking the average... right?\n", + "A": "Sal was trying to find the midpoint of thouse two points. He averaged the coordinates to find a new set of coordinates exactly in the middle. The midpoint formula is... (x+x/2, y+y/2)", + "video_name": "63mWxNXQQAk" + }, + { + "Q": "\nI still don't understand. e.g. Sharing $20 in the ratio of 2:3. How would you do it? As well as both numbers wouldn't be equal if you separated. Any advice?", + "A": "Well ratios don t have to be equal that is the thing.2+3=5 so 20\u00c3\u00b75=4 so the first person who got 2 would get 4x2=8 so that would be 8 for the first person then 4x3=12 and so to check do 8+12=20 tada", + "video_name": "bIKmw0aTmYc" + }, + { + "Q": "\nInstead of using \"to\" for the ratio, we could also tell it as \"is to\"....For example 6:9 could be told as 6 is to 9 too...", + "A": "Yes, I think using is to is the same as using to", + "video_name": "bIKmw0aTmYc" + }, + { + "Q": "\nIn ratio when you write something like 6:10, why do you have to write a colon??", + "A": "The colons are used to seperate two different amounts of something/item.", + "video_name": "bIKmw0aTmYc" + }, + { + "Q": "If the problem is like this one where it says find the ratio to apples and oranges 6:9 does it matter which one goes first could it be 9:6\n", + "A": "It matters which goes first and it is very important. In your example, we have the ratio of apples to oranges so the number of apples will be first, 6:9 (I assume that 6 is the number of apples). If you write it as 9:6, you also need to switch your sentence into the ratio of oranges to apples or it won t be the same.", + "video_name": "bIKmw0aTmYc" + }, + { + "Q": "\nat 3:13 what does he say", + "A": "This is what he said 3:1= Here we 9 oranges for every 6 apples. This can also be shown as 6 apples for every 9 oranges Hope this helps.", + "video_name": "bIKmw0aTmYc" + }, + { + "Q": "\nAt 3:54,is 9:6 the same as 6:9,is it only switched around?", + "A": "Uh, no. For example, you d have 9 red cars for every 6 blue cars, while if it was 6:9, it would be 6 red cars for every 9 blue cars.", + "video_name": "bIKmw0aTmYc" + }, + { + "Q": "At 3:09, Sal said that 0^0th power = 1. But I used my calculator and saw that 0^0 = undefined.\nIn the previous videos, he showed that decreasing the index/exponent would mean dividing by the number whose power is taken. In other words, 0^1 to 0^0= 1*0/0=0/0=undefined.\nBut then there is the case of other powers. what is actually going on?\n", + "A": "Well, what Sal is saying is that 0^0th power could equal one, depending on what theory you think is correct. It comes out undefined, because the true answer to 0^0 power could be 0 or 1: we just don t know. Because theorists can t agree, they settled with undefined, which pretty much means, we don t know for sure .", + "video_name": "PwDnpb_ZJvc" + }, + { + "Q": "At 0:12, what is the answer\n", + "A": "Zero, because multiplying ANYTHING by zero is going to be zero.", + "video_name": "PwDnpb_ZJvc" + }, + { + "Q": "At about the time frame 5:20 to 5:40 you told us that the dot plot would probably be the easiest to use. did you mean for everything as it was stressed that way in \" and this is once again where maybe the dot plot is the most (pause), the most, it jumps out at you.\" So do mean that it is the easiest for all the questions or just those few? -thanks\n", + "A": "No, he was talking about those that were shown there. So, the dot plot was the best for that in comparison with the list and the table. Hope this helps!", + "video_name": "gdE46YSedvE" + }, + { + "Q": "I thought I understood this but at 6:18 I stopped understanding it.:(\n", + "A": "What exactly did you not understand? The range is a measure that helps you figure how large the difference between the smallest and largest values of your data set is, and to calculate it you take the smallest value and subtract it from the largest one. It s really just a way to figure out how spread out your data is. Hope this helped, if not don t hesitate to ask away :)", + "video_name": "gdE46YSedvE" + }, + { + "Q": "I am wondering if it's possible to raise a number to a power to result in 0. x^x = 0 I've been graphing functions with the variable in the exponent (i.e. y = 4^x) and was wondering if it ever actually reaches zero. @ 4:13 Sal says it never quite reaches zero, so is it impossible? The line keeps going on forever in the X direction?\n", + "A": "It s my firm belief that infinity doesn t exist. As you can see by the graphs of y = a^x, y is always positive, and can only get close to zero where x is negative. No matter how large a negative number -x you get, you can always find another so large that the first one is negligible in comparison. And a^(-x) = 1/(a^x) is never zero. (Kind of crazy, insn t it?)", + "video_name": "9SOSfRNCQZQ" + }, + { + "Q": "\n1:30 how can 5^0=1?", + "A": "You have to think of it in groups a bit, but also considering the increase/decrease. Ex: 2^3, or 2x2x2=8 2^2, or 2x2=4, with a decrease/increase of 4. 2^1 or 2 = 2, with a decrease/increase of 2. So the number is basically halved each time, specifically only for 2s. For 3s it would be divided in to thirds, 4s would be fourths and so forth. So what s one half of 2? 2 x 1/2 cross multiply: 1 x 1/1 = 1. for 3s: 3 x 1/3 cross multiply: 1 x 1/1= 1. and so forth. Posted this above, hope it helps :D", + "video_name": "9SOSfRNCQZQ" + }, + { + "Q": "on 4:11 it says to the 3rd power but how because in the formula it says to the 2nd power so I don't know how he got 3rd power\n", + "A": "The units of volume is to the third power because it is related to multiplying length \u00e2\u0080\u00a2 width \u00e2\u0080\u00a2 height. Radius squared provides two, height is the third direction.", + "video_name": "hC6zx9WAiC4" + }, + { + "Q": "\nI know at 3:04 he gave the formula for finding the radius, but how do you change it to find the height?", + "A": "If you already know the volume and the radius, to find the height, the formula wound be the following: h = 3 time v divided by pi times r squared.", + "video_name": "hC6zx9WAiC4" + }, + { + "Q": "\nAt 15:20 Would we be wrong if we write \u00e2\u0088\u00ab f cos\u00ce\u00b8 dt?", + "A": "You would want \u00e2\u0088\u00ab ||f||.||r|| cos\u00ce\u00b8 dt, with the magnitude of f and r, and \u00ce\u00b8 all defined as functions of t, which given the way Sal has set up the problem (with f and r defined as rectangular functions of t) would be difficult.", + "video_name": "t3cJYNdQLYg" + }, + { + "Q": "\nHolla. At 06:00, \"add one to itself and times.\" I know, sounds silly, but cannot get it, since adding one to itself is two. What am I missing here?", + "A": "He actually said (or at least he meant) add one to itself n times . If n = 4 then it would be 1 + 1 + 1 + 1 = 4 = n.", + "video_name": "sRVGcYGjUk8" + }, + { + "Q": "\nIsn't the \"proof\" for the equivalence of the angles formed by a transversal across two parallel lines (4:09) simply that if the angles were not equivalent the lines would meet and not be parallel? Is that not considered a proof? If not, why not?", + "A": "Yes it is. People think it isn t but Khan knows better\u00f0\u009f\u0098\u009c", + "video_name": "H-E5rlpCVu4" + }, + { + "Q": "At 6:49, what does \"deduce\" mean?\n", + "A": "Deduce means to make a conclusion given the evidence that you have,", + "video_name": "H-E5rlpCVu4" + }, + { + "Q": "\nAt 1:46, do the lines have to be parallel for the line to be a transversal?", + "A": "No, not necessarily. A transversal is a line/line segment/ ray intersecting two other lines/line segments/ rays.", + "video_name": "H-E5rlpCVu4" + }, + { + "Q": "at 3:30 when Sal is discussing lim x--> c for f(x)/g(x), you can only calculate the limit if the bottom is not zero!\n", + "A": "That is true until you learn L Hospital s rule and then it will be possible to calculate the limit of a function when g(x) is zero or when f(x) and g(x) are both infinity", + "video_name": "lSwsAFgWqR8" + }, + { + "Q": "At 2:52, Sal said, \"anything divided by anything is just one.\" I think what he meant to say was \"anything divided by itself is just one.\" :)\n", + "A": "Yeah, Sal was referring to the first anything when he said anything the second time : )", + "video_name": "UquFdMg6Z_U" + }, + { + "Q": "\nAt 0:30, why couldn't long division work?", + "A": "That is another way to do basically the same thing. Whichever way is easiest for you!", + "video_name": "UquFdMg6Z_U" + }, + { + "Q": "At 2:14 to 2:32, could the -\u00c2\u00bdx also be written as -x/2?\n", + "A": "Yes, they are the same.", + "video_name": "UquFdMg6Z_U" + }, + { + "Q": "at around 1:15 you say that you subtract 4x from each side so wouldn't it be 2y = 8-4x not 2y=4x-8\n", + "A": "The equation was 4x + 2y = - 8 You simply missed out the negative signs. Subtracting 4x from the equation above will give us: 2y = -8 -4x which is the same as 2y = -4x -8 If you cannot understand why changing orders will still be the same, try taking -2 -4 and -4 -2. Either way, you will get -6! Same analogy here :) Hope this helped", + "video_name": "V6Xynlqc_tc" + }, + { + "Q": "10:40. How can you define a function S such that S(y) is the unique solution in X to f(x) = y? How can you know such a function even exists?\n", + "A": "Sal assumed that for any point in Y there is a unique solution to f(x) = y. That means that there must be a function. Remember, a function is anything that maps each value of y to a unique x.", + "video_name": "7GEUgRcnfVE" + }, + { + "Q": "\n@ 3:16 I didnt get how' 2 is the same thing as e to the natural log of 2 ' ?can someone please explain?", + "A": "e^x and lnx are opposite functions. It would be akin to multiplying by some number and then dividing by that same number. The operations cancel one another out. e to the natural log of elephant = elephant.", + "video_name": "C5Lbjbyr1t4" + }, + { + "Q": "At 2:42 Sal says he wants to multiply the length of vector v by the vector itself (||v|| v), but then immediately after he defines the unit vector as \"1/||v|| v\". Where did he get the \"1/\" from?\n", + "A": "If a vector v has a length of e.g. 5, then v/5 has length 1.", + "video_name": "lQn7fksaDq0" + }, + { + "Q": "At 0:50,why is it that dividing is the same as multiplying the fractions?\n", + "A": "Dividing by a fraction is the same as multiplying by that fraction with it s denominator and numerator swapped.", + "video_name": "yb7lVnY_VCY" + }, + { + "Q": "\nAt 2:32 you say that 5 + 5 cannot represent a vector. (5 represents a possible starting point on the number line and the additional 5 can represent a distance in the positive direction on the number line.)", + "A": "A vector has to have BOTH a magnitude and a direction. As is, it is just a magnitude. Had there been a direction attached then it would be a vector.", + "video_name": "n8Ic2Oj-zvA" + }, + { + "Q": "I haven't had the time to find the video to explain this type of equation so I'll just ask it here. If I had an equation such as 6t3rd + 9t2nd \u00e2\u0080\u0093 15t(that's 6t to the third plus 9t to the second minus 15t)how would I factor this to a form similar to the one shown at 3:35?\n", + "A": "first factor out 3t so you get 3t(2t2nd+3t-5). Then factor (2t2nd+3t-5). to factor it, you need to find 2 numbers that multiply to make -10 (2*-5) and add together to make 3 (the middle number). those two numbers are 5 and -2. Split the middle term into those 2 numbers which gives you 3t(2t2nd-2t+5t-5). Then factor by grouping. that gives you 3t(2t(t-1)+5(t-1)). Simplify to 3t(2t+5)(t-1). The next video is very helpful in understanding this. Hope that helps!", + "video_name": "u1SAo2GiX8A" + }, + { + "Q": "\nAt 3:25, I'm confused about where the 5 came from. Can someone shed some light on this?", + "A": "They divided 10y-15 by two and got 5(2y-3).", + "video_name": "u1SAo2GiX8A" + }, + { + "Q": "In 3:49, how does he know that the triangle is equilateral?\n", + "A": "EC = EB as he has proven in 3:17 , and EB and CB are radiuses of the same circle, therefore EB = CB. And, if you think about it you will find out that you can say EC=EB=CB by combining the two relationships above. That s why it is equilateral.", + "video_name": "3n0LvI99-KM" + }, + { + "Q": "\nat 5:18 were did he get 9/3?????i understand the 3 but not the 9 plz help me", + "A": "i am the helper", + "video_name": "Zn-GbH2S0Dk" + }, + { + "Q": "\nAt 3:00 i didnt get how he got 8", + "A": "Sal doesn t seem to arriving at an 8 at 3:00. Maybe you mean how he gets -8 at 2:00? At that point he is adding -3 to both sides of the equation so he can isolate the term with x (i.e. the variable) on the left side of the = sign and the contants on the right side. When adding -3 to -5 you get -8.", + "video_name": "Zn-GbH2S0Dk" + }, + { + "Q": "At 5:41, Sal says that he could define the f(x) as -x^2-3x+28 or (x+7)(x-4), as they are the same thing.\nWhen you graph -x^2-3x+28 you get a parabola opening up\nWhen you graph (x+7)(x-4) you get a graph opening down\n\nHow can they be the same thing if their graphs are not the same?\n", + "A": "Ok, so I think he misspoke when he said he could use either one, yes? Or is the sign for some reason not important in this case?", + "video_name": "xdiBjypYFRQ" + }, + { + "Q": "\n7:47 Is there a video where Sal proves this? Thanks", + "A": "using the same diagram as in the video, imagine the following: draw segment AD and segment BC, angle AED is congruent to angle BEC by vertical angles theorem, angle DAE is congruent to angle BCE because angles that subtends the same arc are congruent (arc DB) so, triangle ADE is similar to triangle CBE by aa similarity postulate. corresponding sides of similar triangles are proportional, so AE/CE = DE/BE, cross multiply and you get the CHORD-CHORD PRODUCT THEOREM, AE*BE = CE*DE.", + "video_name": "FJIZPvE3O1A" + }, + { + "Q": "at 4:18, couldnt you go over 6 THEN up 4? if not why? please help! i just joined the pre-algebra class, and im way behind.\n", + "A": "no because 6 would be a negative number (moving to the left) and 4 would be a positive number. If you did that,then you would have a negative slope. The answer, is a positive slope. Hope that helps :)", + "video_name": "R948Tsyq4vA" + }, + { + "Q": "\nOn 3:36 he goes to the right but it still comes out negative. Why? If anyone knows the answer to this, please reply.", + "A": "At 3:36 he goes 6 units to the left (-6) - he doesn t go to the right.", + "video_name": "R948Tsyq4vA" + }, + { + "Q": "can you go up first? So like at 3:24 he is going down first then over six. But from the point at -3 could you go up 4 and then over 6 to get to your other point?\n", + "A": "Yes you can. Sal likely was more comfortable going down then over, but it will work either way.", + "video_name": "R948Tsyq4vA" + }, + { + "Q": "\nAt 2:57 Sal said that the change was -4. Why can't that number be 4? Does that change the outcome of the answer? Thanks!", + "A": "You basically switched one of the values in y2-y1/x2-x1 so you made it y1-y2 as long as you switch the x value as well to x1-x2, then nothing changes but if you only switch the y, then it changes the slope.", + "video_name": "R948Tsyq4vA" + }, + { + "Q": "at 1:21, Sal draws a line going across, but I thought it was rise (which is going up), then run, (go across). Am I misunderstanding something?\n", + "A": "Slope is rise/run, but it doesn t matter what order you calculate them in. If you find the run (x) first, just make sure you are putting that value in the denominator of your slope.", + "video_name": "R948Tsyq4vA" + }, + { + "Q": "At 0:25, why is it y over x and not x over y?\n", + "A": "Slope is always rise over run.", + "video_name": "R948Tsyq4vA" + }, + { + "Q": "\nAt 1:04 how can a numerator be equal to 0 when there is only a value such 4/x-2", + "A": "Well... When does 4 = 0? Let s keep an eye out for pigs on the wing.", + "video_name": "fvC0dm2wzIo" + }, + { + "Q": "3:19 Shouldn't it be commutative instead of associative, since commutative is about switching orders? Thanks.\n", + "A": "Idk! I m just a fifth grader, so... -Brianna-", + "video_name": "vr0sTKbV7lI" + }, + { + "Q": "At 5:54 is the trapezoid the same thing as a trapezium?\n", + "A": "This is a very good question. If you are american then the accepted answer would be no. By american definition a trapezium has no parralel sides while a trapezoid has 1 set of sides that are parallel to each other. The British definition states that a trapezium has 2 sides that are parallel which would be the same thing as a trapezoid.", + "video_name": "10dTx1Zy_4w" + }, + { + "Q": "\nI dont understand 3:17?", + "A": "You can t have a domain that maps to more than 1 number in the range.", + "video_name": "Uz0MtFlLD-k" + }, + { + "Q": "At 1:05, I was wondering if there was an actual name for the type of function which maps 2 numbers in the domain to just 1 in the range, e.g. f(x)=x^2\n", + "A": "Good question! We say that functions are not one-to-one. :) Therefore, what we actually say is that one-to-one functions are functions for which each element in the domain is paired with its own unique element of the range (or, that each element of the range is paired with exactly one element from the domain). Hope that helps!", + "video_name": "Uz0MtFlLD-k" + }, + { + "Q": "\nat 1:37 why did he multiply 5x5 ?", + "A": "He evaluated what was inside the parentheses first: (9-4) = 5 So, 5(9-4) = 5(5) = 25", + "video_name": "Badvask-UDU" + }, + { + "Q": "I dont get what he says at 2:05\n", + "A": "That 74.7 is one sigma away from the mean. What he should have said maybe would be like this. Where does that get us?Well, 81-6.3 is 74.7 which is one standard deviation from the mid", + "video_name": "Wp2nVIzBsE8" + }, + { + "Q": "second q is 1/4??? Paused @ o2:42\n", + "A": "there are 13 hearts in a 52 card standard ddeck of playing cards...1/4.....13/52", + "video_name": "obZzOq_wSCg" + }, + { + "Q": "\nin 00:20, what did Sal mean by Suits??", + "A": "thanks a lot!", + "video_name": "obZzOq_wSCg" + }, + { + "Q": "\nGreat video! but just a word not clear... at 5:48 what is being said..four fifty what?", + "A": "4/52=1/13 is the probability of a jack being drawn.", + "video_name": "obZzOq_wSCg" + }, + { + "Q": "This is where the ray terminates.\n1:40\nIt's an endpoint.\nLOOK at the above statement In regarding to the ray, he messed up as there is not the end point but rather the commencement point or the source of the ray ,that is not where it terminates but starts were it a line transfoming into a ray then we would say thats where it terminates and an end point but since its genesis is where there is a point it is wrong to refer it as an end or use terminate what do you think?\n", + "A": "It starts there, endlessly going in whatever direction. But it ends there, because when the ray reaches that part, it ends.", + "video_name": "DkZnevdbf0A" + }, + { + "Q": "At 0:40, he puts a zero as a place holder. my teachers at school say to just drop the number. Wouldn't that change the answer? Could you tell me which one is correct and why?\n", + "A": "i think you have gotten confused. you can only do that while you are adding decimals. but i guess you can also do that if the number is at the top and it is the larger one over zero hope this helps!", + "video_name": "MufbvU4tGh8" + }, + { + "Q": "\nWait I do not get it do you have to do what he said at 0:55", + "A": "You sort of do. Since 3 is larger than 0, you need to borrow. The 1 ten is the same as 10 ones. So if you add them together, you d get ten. Now you can subtract with 10 and 3.", + "video_name": "MufbvU4tGh8" + }, + { + "Q": "\nAt 5:00, all I have to do is graph is x=5 and x=-1 correct?", + "A": "I don t believe you would graph x=5 and x=-1 because the solutions are points, not lines. What you have are vertical lines, and we don t really want that, because the solutions to the quadratic are one x with one y only. When asked for the answers, you are correct to say that x=5 and -1. But do not actually graph that.", + "video_name": "VTlvg4wJ1X0" + }, + { + "Q": "At about 7:56 Sal simplifies 2x^2 - 3x^2 into -1x^2... How come the outcome isn't -1x^4?\n", + "A": "If we let x\u00c2\u00b2 = y Then our problem becomes: 2y - 3y Which is obviously equal to: -1y But since y = x\u00c2\u00b2 We have: 2x\u00c2\u00b2 - 3x\u00c2\u00b2 = -1x\u00c2\u00b2 = -x\u00c2\u00b2", + "video_name": "aoXUWSwiDzE" + }, + { + "Q": "\n@ 4:43 #6 Why is \"\" + -4 \"' The same as \"\" - 4 \"\" ?", + "A": "The plus and the negative sign before that four immediately cancel each other out. Same as -(-4) : the minus negative x become a plus x.", + "video_name": "aoXUWSwiDzE" + }, + { + "Q": "\nat 00:41, where did you get the x and it shows 2 x11r?", + "A": "it is actually an x it looks like an r", + "video_name": "aoXUWSwiDzE" + }, + { + "Q": "\nAt 18:30 al finishes a problem as 40x10^-7 could that be simplified?", + "A": "Yes it can, the number is really 0.000040, he simply wrote it in scientific notation (which should be explained in the video). You could think of scientific notation like a kind of shorthand. 0.000040 equals 40 \u00c3\u0097 10^-7, so you can write is either way, it s simply easier, and less cumbersome, to write it in scientific notation.", + "video_name": "trdbaV4TaAo" + }, + { + "Q": "\n20:26 wouldnt 6.022x7.23 be att least 42 because 6x7=42", + "A": "Yes, you are correct. Well done for noticing Sal s mistake :)", + "video_name": "trdbaV4TaAo" + }, + { + "Q": "\nAt 6:01, what is avogadro's number?", + "A": "it s the number of atoms in one mole of a substance, and it s equal to 6.02214179 x 10^23", + "video_name": "trdbaV4TaAo" + }, + { + "Q": "at 12:44 Sal says with negative exponents with a base of 10 (unlike positive exponents) it cannot be thought of as the number of zeroes. (i.e. 10^5 = 10 000, but 10^-5 = .00001) That only has 4 zeroes. :(\nBut couldn`t you write the answer to 10^-5 as 0.00001? That has 5 zeroes. (Sorry this has been really bugging me for a while. :) )\n", + "A": "No, the decimal is supposed to move 5 times. Think about it. 10^-5 can also be written as 1/10^5. 10^5=100000, and you do 1/100000. When you divide, you find the quotient to be 0.00001. Hope this helps!", + "video_name": "trdbaV4TaAo" + }, + { + "Q": "\nWhat is the difference between estimating and guestimating? 4:57", + "A": "An estimate is more certain than a guestimate", + "video_name": "trdbaV4TaAo" + }, + { + "Q": "At 0:18 how do you know the difference between a large and a very large number?\n", + "A": "One is BIG and the other is SMALL", + "video_name": "trdbaV4TaAo" + }, + { + "Q": "\nat 18:36 sal added two powers 10^-3 and 10^-4 = 10^-7. should it not be 10^7 ?", + "A": "No, Sal is correct. -3 + -4 = -7. A negative plus a negative equals a bigger negative. (You may be getting confused with multiplication; a negative TIMES a negative is a positive.)", + "video_name": "trdbaV4TaAo" + }, + { + "Q": "\nIn problem #10, minute 1:56, wouldn't the triangles be called RTP or PTR or just T for the one in purple, and the other to be called APT or TPA or just P. I thought that the major/main angle of the triangle needed to be in-between the other two letters when naming it?", + "A": "I m not aware of defining a triangle based solely on the reference to the major angle.", + "video_name": "bWTtHKSEcdI" + }, + { + "Q": "at about 3:30, the instructor states that (a^b)^d=a^bd. How is it possible for the exponent to shift down a degree?\n", + "A": "This is how exponents work. It doesn t shift it down a degree. Here are a few cases and examples: (2^3)^2=8^2=64 (2^3)^2=2^(3*2)=2^6=64 (2^1=2,2^2=2,2^3=8,2^4=16,2^5=32,2^6=64) (3^2)^3=9^3=729 (3^2)^3=3^(2*3)=3^6=729 (3,9,27,81,243,729) This is not unlike what happens when you multiply two numbers with the same base raise to different powers. In that case you add the exponents: 2^2*2^4=2^(2+4)=2^6=64 2^2*2^4=4*16=64 Good question. It is confusing at first, but when you get the hang of it, it s not too hard.", + "video_name": "Pb9V374iOas" + }, + { + "Q": "I understood the video, but one part confused me. When he's talking about B = -B at 1:12 through 1:53, that confused me. Wouldn't B equal -B because it is after the zero? Thanks in advance!\n", + "A": "No. If you assume the scale is one then B = -1. -B would then be - -1. Two negatives is a positive so B= -1 and -B = 1. 1 is not equal to -1 so B=-B is not true. Just because there is a negative in front of the variable does not mean it is negative. It just means that it is multiplied by -1. I hope this clears up your confusion.", + "video_name": "vRa6XxykfbY" + }, + { + "Q": "\nAt 5:38, does Sal mean Law of Sines?", + "A": "yes you are definitely correct that is a funny mess up on Sal part", + "video_name": "VjmFKle7xIw" + }, + { + "Q": "At 3:36, you said that we should take a reciprocal to the both sides of the equation. But can't we just cross multiply the equation to get a=4xsin105 degrees\n", + "A": "Either way works. The answer is the same.", + "video_name": "VjmFKle7xIw" + }, + { + "Q": "\nI calculated the sides using the Pythagorean Theorem, and I came up with a = 3.47, which is .4 off the answer they said at 4:14. When I calculated the side of b from the given answer (3.86) I got 3.3, also about .4 off the listed answer at 5:14 (2.83). Is this just because of rounding, or was something wrong?", + "A": "Hello GoMcLucky, The Pythagorean Theorem doesn t apply to this problem as we do not have right triangle. Instead we want to set up a ratio: SIN(105) / a = sin(30)/2 a = 3.86 Regards, APD", + "video_name": "VjmFKle7xIw" + }, + { + "Q": "At 1:04 why is Sal Subtracting those numbers?\n", + "A": "Remember that the sum of a triangle s three angles is 180 degrees. You can see that we know two of the angles already, 45 and 30. To find the final unknown angle, Sal simply subtracts the other two angles from 180, the sum of a triangle s angles.", + "video_name": "VjmFKle7xIw" + }, + { + "Q": "At around 5:03 how does he go from 4*\u00e2\u0088\u009a2/2 to 2\u00e2\u0088\u009a2?\nSolving both problems on the calculator give the same answer so they are both the same thing, but how did he simplify it from 4*\u00e2\u0088\u009a2/2 to 2\u00e2\u0088\u009a2?\n\nEDIT: Ok... its pretty obvious It just didn't click for some reason. He just simplified the 2 in 4*\u00e2\u0088\u009a2/2 to convert it to 2\u00e2\u0088\u009a2.. idk how I didn't see that.\n", + "A": "that got me as well", + "video_name": "VjmFKle7xIw" + }, + { + "Q": "At 8:34, does it matter where you place your coordinate letter points? Like for example, can you put point T at the top left of the isosceles trapezoid instead of the bottom left?\n", + "A": "Yes, as long the the diagonals correspond and the letters are in order going around the trapezoid. The answer would still be the same!", + "video_name": "4PPMnI8-Zsc" + }, + { + "Q": "At 0:13, what does 'hone in' mean?\n", + "A": "To hone in means to sharpen or make something more precise", + "video_name": "ojFuf9RYmzI" + }, + { + "Q": "\nAt 1:34, why are the points 2,0 and 0,2?", + "A": "how does that help", + "video_name": "wyTjyQMVvc4" + }, + { + "Q": "\nAt 8:14, when Sal says this curve actually has another point where the slope is equal to the average slope, I was wondering whether there are as many such points as the number of inflection points in the graph, or atleast in the closed interval we are concerned about.\nIs this true? Are there really as many such points as the number of inflection points?", + "A": "You re almost right. If n = the number of inflection points, then there will be n + 1 points where the slope is equal to the average slope. Except straight lines, of course, where the slope of every point is equal to the average slope.", + "video_name": "bGNMXfaNR5Q" + }, + { + "Q": "why was it that one corner was 30* and one was 49* at 8:44? I still don't understand :(\n", + "A": "It was because when you add up 101 (the measure of corner 1) and 30 (measure of corner 2), you get 131. In a triangle, when you add up all 3 of the angles, you get 180*, no matter what. So, 180-131=49. Therefore, the measure of the other angle would be 49*. Hope that helped! ^_^", + "video_name": "kqU_ymV581c" + }, + { + "Q": "At 9:55 shouldn't the sqrt of 1 be +1 and -1 and then say that its because its in the first quadrant we can drop -1?\n", + "A": "Sal took the positive square root of 1 because ds(the length of a small segment of the curve) is always positive because it is a length.", + "video_name": "uXjQ8yc9Pdg" + }, + { + "Q": "\nAt 1:55 isn't it supposed to be 3.14159", + "A": "Sal used 3.14 as an approximate value for \u00cf\u0080. (3.14159 is also an approximate, but a little more precise.)", + "video_name": "ZyOhRgnFmIY" + }, + { + "Q": "why did you divide by 2 at 1:10\n", + "A": "because the diameter is twice as big as radius. so you divide 2 from diameter to find the radius", + "video_name": "ZyOhRgnFmIY" + }, + { + "Q": "\nat 1:29, why is it 64 pi not 16 pi because dont you multiply pi and the diameter to get the answer", + "A": "pi * diameter (same as 2*pi*radius) would be the circumference of the wafer which is 16 pi. The question wants us to compute the area so we need to use pi*r^2.", + "video_name": "ZyOhRgnFmIY" + }, + { + "Q": "How do you get 64 at 1:27? Do you just multiply the number that's the radius by itself or something? I'm confused with this.\n", + "A": "Yes. pi*r^2 means radius in second power. What s power? How many times the number needs to be multiplied by itself. If power is 2 than the number needs to be multiplied twice. If radius is 8 than r^2 is 8^2 which is 8*8 (multiply by itself twice) which equals 64.", + "video_name": "ZyOhRgnFmIY" + }, + { + "Q": "\nAt 3:50, How does 8*8*8 simplify to just 8?", + "A": "good question. this simplifies to 8 because all those 8s are inside of a cube root symbol. so we had \u00e2\u0088\u009a8*8*8. this simplifies to just 8. sry if this doesn t help :( its kinda hard to explain in words.", + "video_name": "DKh16Th8x6o" + }, + { + "Q": "0:32 You need to use prime factorization to help you with finding cube roots?\n", + "A": "The prime factorization of the base is rather important in finding any type of root (whether square root, cube root, 5th root, or whatever). Do you need instruction on how to do this?", + "video_name": "DKh16Th8x6o" + }, + { + "Q": "At 3:48, I don't get it how Sal got the square root of 8*8*8 to get the answer 8.....Can someone explain to me what happened there?\n", + "A": "well he was answering the cubed root of -512 thats how he got 8 so -8*-8*-8 is -512", + "video_name": "DKh16Th8x6o" + }, + { + "Q": "\nAt 4:33 was Sal meant to write \"X2 +2\" or am I confused ?", + "A": "You re right, he should have written X2 +2 instead of X1 +2", + "video_name": "r4bH66vYjss" + }, + { + "Q": "At 5:09, shouldn't it be (x1-1, x2+2)?\n", + "A": "Yes it should", + "video_name": "r4bH66vYjss" + }, + { + "Q": "\nAt 21:32, Khan says that the vector \"y-x\" is equal to (-6, -5) and graphs it by going six points down and five points to the left. Shouldn't he graph it by going six points to the left and five points down?", + "A": "Good catch. You are correct.", + "video_name": "r4bH66vYjss" + }, + { + "Q": "At 25:07, it looks like he accidentally enabled the smudge tool on the tablet. Do vectors like these have anything to do with matrix algebra?\n", + "A": "Yes, you could actually see the columns of matrices as vectors (if I am not mistaken).", + "video_name": "r4bH66vYjss" + }, + { + "Q": "At 5:35 how did Sal know that the two areas are equal? The problem doesn't say that they function has x intercept at 1.5, and picture isn't necessarily to scale\n", + "A": "looking at the graph and where the coordinates are given and marked, we can clearly see that the two areas are equal", + "video_name": "OvMBNVi5bLY" + }, + { + "Q": "\nAt 1:38 ,does he have to write out all of the possibility's like that . i tried that and it took a long time (not to mention how tricky it was). Can't he use a possibility diagram/probability space diagram?", + "A": "It is just a way to show every possible outcome, like with truth tables. A shorter way to represent this is to determine the rule governing the outcomes and simply calculate mathematically. I think Sal is trying to show all possibilities so that even students witj no prior exposure to probabiliy can understand.", + "video_name": "xSc4oLA9e8o" + }, + { + "Q": "At 2:32 you said 240x^2. Why and How is it squared?\n", + "A": "It s squared because you are multiplying 30x and 8x. When multiplying variables, you write the variable, (x), and add what powers that they are each to together, (x^1 times x^1).You will end up with x^2. Here is an example. x^3 times x^2. First, write the variable, (x), and then, add their powers together, (^3+^2)=^5. Your answer will be x^5. :)", + "video_name": "bamcYQDzVTw" + }, + { + "Q": "I think he said that 3-dimensional object volumes were the products of the base and the height, somewhere around 1:00. That probably is a mistake, or I heard incorrectly, because pyramid volume has a different formula. So, are we just supposed to assume that the tank is not a pyramid? I've never heard of a pyramid-shaped tank, so that might be it.\n", + "A": "He said a three-dimensional object like this referring to a cylinder, and in this case, and with similar 3D objects (like prisms), base x height applies.", + "video_name": "bamcYQDzVTw" + }, + { + "Q": "(3:33)\nThe C(A) is (1, 2, 3) and (1, 1, 4). We know this because X1 and X2 are the pivot variables?\nand columns 3 and 4 are not part of the column space because X3 and X4 are free variables?\n", + "A": "C(A) is the span of v1 = (1, 2, 3) and v2 = (1, 1, 4). Why? Because by setting x3 and x4 in turn to 0 we can show that v3 and v4 are each in the span of v1 and v2. Then clearly all 4 column vectors are in the span of the 1st two, and by closure the span of any vectors within a span is in the span.", + "video_name": "EGNlXtjYABw" + }, + { + "Q": "\nAt 2:25 Why isn't y = 2sin(t)?\nThen again at 7:12 Why isn't x = 2cos(t)?\nWe were given these values in the beginning of the question (previous video), and yet Sal made these up? How?", + "A": "It could be, if you wanted it to be. The point is that on the c2 path y needs to go from 2 down to 0. On the c3 path x needs to go from 0 up to 2. How it gets there isn t that important, and doesn t have to be the same or even related to the c1 path parametrization, so Sal just picked the simplest possible way to do what he wanted.", + "video_name": "Qqanbd3gLhw" + }, + { + "Q": "\nAt 12:18, when Sal is simplifying x^4 = 81, he straightaway puts x^2 = 9. It could have been -9 as well, but wouldn't have worked in the end, since it would yield complex values for x.\nWhat do you think - was that unintentional (a mistake), or he knew it would not be helpful in the end?", + "A": "Could have been either of those, you can t really know for sure. You re right that it wouldn t have been useful though, as at 6:30 Sal even mentions that we re assuming that we re dealing with real numbers. Had he put x^2 = +- 9, the only thing that would have changed would be the length of the video, as he d have probably explained what you ve just covered in your post. :)", + "video_name": "zC_dTaEY2AY" + }, + { + "Q": "\nat 12:00 did he factor out 4x^2 correctly? it doesn't look right for some reason.", + "A": "It s correct. 4x\u00c2\u00b2*81 - 4x\u00c2\u00b2*x^4 = 27 * 12 * x\u00c2\u00b2 - 4x^6", + "video_name": "zC_dTaEY2AY" + }, + { + "Q": "\nAt 2:36, Sal said that the function of the graph is y = | x - 3 |. Can someone please explain this?", + "A": "Two things can make the graph of functions shift, a change in the x or a change in the y. For absolute value functions, the shifts are defined by y = | x - h | + k, so a y shift is outside the absolute value and follows the sign. Inside for the x shift, however, the graph shifts in the opposite direction, so a -3 shifts it in the positive x direction. The other way to think about is that if x = 3, then the value inside the absolute value is 0.", + "video_name": "Wri26sPEBoI" + }, + { + "Q": "At around 2:30 in the video Sal invokes the chain rule: d/dx(ln(e^x))=d/dx(e^x)*d/d e^x(ln(e^x))=d/dx(e^x)*(1/e^x)=1. The derivative of the composite function ln(e^x) is the derivative of the inner function w.r.t. x multiplied by the derivative of the outer function w.r.t. e^x. I don't recognize this chain rule. I always thought the chain rule was: d/dx(e^x)*ln(e^x)+d/d e^x(ln(e^x))*e^x. Furthermore, is there a more direct proof; without starting from the composite function d/dx(ln(e^x))?\n", + "A": "Well, you could define e^x such that d/dx e^x = d/dx e^x, and then show that the e in question actually is the e. However, in rigorous calculus they first define a function ln x to be \u00e2\u0088\u00ab{0,x}(dt/t), such that its derivative clearly is 1/x (and d/dx ln(f(x)) = f\u00c2\u00b4(x)/f(x)) and then define e^x to be its inverse function.", + "video_name": "sSE6_fK3mu0" + }, + { + "Q": "At 0:56 I don't know why he added the four there, but I see how it works with the equation. Where does the four come from?\nThanks for your help!\n", + "A": "Hi, I would be happy to help you; is the 0:56 time reference that you made correct? (That part of the video is long division)", + "video_name": "Y2-tz27nKoQ" + }, + { + "Q": "What does Sal mean at 2:01 when he says \"Any of those - well that's just going to give you 3.\"? I also don't understand how he got 15 either. I've been stuck on this lesson re-watching it trying to figure out what he is saying, but it doesn't make sense!\n", + "A": "The square root of 3*3 is 3. 3*3 = 9, and the square root of nine is three.", + "video_name": "cw3mp8oNASk" + }, + { + "Q": "in 2:06 to 2:14 -- why wasn't the square root of 3*3 simplified to the square root of 9 to get 81\n", + "A": "You are taking the square root of 9 not squaring 9. When you do 9 square or 9^2 you get 81. When your taking square root , you finding which number you have to multiply twice to get to 9. By which your answer will be 3, since 3*3 = 9", + "video_name": "cw3mp8oNASk" + }, + { + "Q": "At 1:55 why did he write 13 separately?\n", + "A": "The \u00e2\u0088\u009a(117) is split into 2 square roots: \u00e2\u0088\u009a(9) * \u00e2\u0088\u009a(13). The reason we do this is we can simplify \u00e2\u0088\u009a(9). It = 3. So, the radical will go away on that piece. We can not simplify \u00e2\u0088\u009a(13), so it stays in that form. Hope this helps.", + "video_name": "cw3mp8oNASk" + }, + { + "Q": "\nKahn takes the derivative at 2:17, but what is the purpose of that? Does that signify the rate of change of the area or is that the area from (x,x+\u00e2\u0088\u0086x)?\n\nPlease answer both questions.", + "A": "It would indeed signify the rate of change of the area, but that is not why he is doing it. Sal is demonstrating that the integral (in terms of area under a curve) happens to coincide with a sort-of inverse operation of taking a derivative. This concept is at the core of the Fundamental Theorem of Calculus.", + "video_name": "pWtt0AvU0KA" + }, + { + "Q": "I don't understand the factoring. At 1:09 when Sal starts simplifying and factoring everything out, how did he get that (x2+3x+2) was the same thing as (x+2) (x+1) and that x2-4 was the same as (x+2)(x-2)?\n", + "A": "He noticed that the factors of 2 (1 and 2) add up to 3, and that (x^2-4) is a difference of squares, which has a simple factoring rule. If you re having trouble with factoring, you may want to go back and review your algebra before going further. If your algebra is rusty, calculus will be very difficult.", + "video_name": "oUgDaEwMbiU" + }, + { + "Q": "\nAt 1:58. isn't the question mark supposed to be on top of the equals sign, to indicate that we are not sure that the equation is equal to -11, instead of next to -11?", + "A": "You could do either the way he does it in this is more informal", + "video_name": "SkMNREAMNvc" + }, + { + "Q": "\nAt 0:33, how did he know that i squared equals -1?", + "A": "Hi Anushka, Recall that i is defined as sqrt(-1). if we square this we get liberate radicand yielding -1. Here is a challenge for you. Calculate i squared, i cubed, and i squared. Look for the pattern. It will help you in the future. Regards, APD", + "video_name": "SP-YJe7Vldo" + }, + { + "Q": "\nat 0:51 y would u cross out the division and turn it into 2/3\nPLEASE ANSWER THIS QUESTION I WANT TO STUDY THIS TOPIC", + "A": "what i dont understand what that means can u be more specific", + "video_name": "Io9i1JkKgN4" + }, + { + "Q": "could somebody explain to me which formula is Sal using at 6:00? is it the Heron's formula?\n", + "A": "it is the distance formula", + "video_name": "GiGLhXFBtRg" + }, + { + "Q": "At 1:41, why are angles C and B 90 degrees? I know it was explained in the video, but I didn't really understand it.\n", + "A": "AB and AC are tangents, meaning that they intersect the circle at one and only one point. One property of tangents are that if you draw a radius to the tangent point, the tangent will be perpendicular to that radius.", + "video_name": "ZiqHJwzv_HI" + }, + { + "Q": "\nJust a quick question, at 9:38 you cannot cancel the top vector v and the bottom vector v right? Is this because they are dot products and not multiplication signs?", + "A": "You get a different answer (a vector divided by a vector, not a scalar), and the answer you get isn t defined.", + "video_name": "27vT-NWuw0M" + }, + { + "Q": "\nAt 2:08, he says \"sin^2(theta)\" why didn't he say \"sin(theta)^2\"?", + "A": "sin ^2 theta is the more formal way to write out the equation, as it avoids the possibility of mistaking the theta as theta^2 .", + "video_name": "HnDvUaVjQ1I" + }, + { + "Q": "At 0:35, Sal said a greatest common factor and a greatest common divisor are \"kinda\" the same thing. Does he mean exactly the same?\n", + "A": "Yes GCF & GCD are the same thing", + "video_name": "jFd-6EPfnec" + }, + { + "Q": "\n4:59.", + "A": "i get it", + "video_name": "jFd-6EPfnec" + }, + { + "Q": "\nat 2:37 arent the base and height souposed to be switched? or they can stay the same?", + "A": "well, at 2:37, the base is supposed to be one of the sides, and the height should be inside the triangle.", + "video_name": "ukPjc3Oyad4" + }, + { + "Q": "\nWhat is happening at 4:27 when Sal states that Cos(theta) = -1 can be viewed as (2n + 1)pi? Why add the one to that function, when the previous function \"2n(pi)\" does the same thing?", + "A": "(2n+1) where n is an integer, is the standard way of specifying any odd integer. Whereas 2n is even. So, cos \u00ce\u00b8 = \u00e2\u0088\u00921 only when \u00ce\u00b8 is an odd integer multiplied by \u00cf\u0080.", + "video_name": "SdHwokUU8xI" + }, + { + "Q": "at 3:50, why is it that it goes pi, 3 pi, 5 pi for cos (-1) rather than o, 2, 4 pi...?\n", + "A": "The cosine is just the x-value of a point on the unit circle. At 0, 2pi, 4pi, etc, the x-value is 1. But at pi, 3pi, 5pi, etc, the x-value is -1.", + "video_name": "SdHwokUU8xI" + }, + { + "Q": "\nI don't get it... At 4:08 5/9 was given as the answer for cleaning the entire bathroom. I just cannot wrap my head around it because I feel like 5/9 is for cleaning 3/5 of the bathroom still? Please help. Thanks", + "A": "Anon is right... just break it down on a scratchpad", + "video_name": "2DBBKArGfus" + }, + { + "Q": "at 1:56 what do you mean by bottles an bathroom?\n", + "A": "at 1:56 he is just using this ratio as an example nothing too important", + "video_name": "2DBBKArGfus" + }, + { + "Q": "\nAt 2:13 Sal said lets see how they look an a ___ diagram. Does anyone know what he said? \"Argan\"\nThanks!\nI am assuming it is named after a mathematician.", + "A": "It s called an Argand Diagram.", + "video_name": "BZxZ_eEuJBM" + }, + { + "Q": "At 2:34 Why does Sal draw the number Z with an arrow like a vector?\n", + "A": "It is not an arrow, but simply a line on top of Z, it stands for conjugate of Z in this case.", + "video_name": "BZxZ_eEuJBM" + }, + { + "Q": "\nAt 2:14, he referenced a z*. What does that mean? Additionally, is an Argand diagram just an imaginary coordinate plane?", + "A": "z is the conventional variable for a complex number. a z with a bar over it, or a z with an asterisk means the conjugate of z, which is what the video is all about.", + "video_name": "BZxZ_eEuJBM" + }, + { + "Q": "\nAt 8:15 is the reason that ||a-b||=||b-a|| because the length is always a positive value?", + "A": "Yes. Remember that when you subtract two things (x - y) it is equal to -1 * (y - x). Since the magnitude only deals with the absolute value, the magnitudes will be the same, but the direction will be exactly opposite.", + "video_name": "5AWob_z74Ks" + }, + { + "Q": "\nThere is one but. In the video (2:43) it said that after the price for topping became 2$, the equation must be 8+2(p+8)/p+8. While I was doing the exercises I got the same problem, but in the hints the answer was that the second part should be 24+2p/p+8. Where did they get 24 and how?", + "A": "The answer is (24+2p)/(p+8), because when you simplify [8+2(p+8)]/(p+8), that s what you get. Here s the process: [8+2(p+8)]/(p+8) (8+2p+16)/(p+8) -- used distributive property (24+2p)/(p+8) -- added together; 8+16=24", + "video_name": "jQ15tkoXZoA" + }, + { + "Q": "At 1:14, why is it the square root of x+2? I know that the square root of x looks like that, but how can you determine if it is x + 2?\n", + "A": "If x+2 is substituted for x, then the graph is centered at x= -2. That s because the general format is x-c, where c is where the graph is centered. For example, If x-2 was substituted in, then the graph would be centered at x=2.", + "video_name": "IJWDyPFXGyM" + }, + { + "Q": "\nisnt the slope of the first graph on the left corner negative..and how at 2:17, does SAL say that the slope is close to 1?.?", + "A": "it s positive because as x increases y increases, too", + "video_name": "nZrxs-U9d8o" + }, + { + "Q": "\nAt 11:26 he forgets to write a line above the x2 (the standard deviation of the difference of the sample 'means'). Right?", + "A": "Yes, he does, as commented in the next video and as you can see from his calculation of the confidence intervals, he gets a little confused sometimes in videos that are longer than 10 minutes ;D After all, its not that easy to talk about so serious stuff for quiet long, without making any small mistakes :)", + "video_name": "hxZ6uooEJOk" + }, + { + "Q": "7:45 Sal says there's a 95% chance that 1.91 is within 1.96 standard deviations. Shouldn't the interpretation be that \"we are 95% confident...etc.?\" Because this isn't really about probability, right?\n", + "A": "Yes, because he is talking about the specific value that was observed (1.91). If we re still talking theoretically, we can talk about probability. So we can say there is a 95% chance that xbar will be within 1.96\u00cf\u0083 of \u00ce\u00bc. When we start plugging in numbers and get, say, that xbar is 9.31, then we no longer have a random variable, and the observed mean either is or is not (100% or 0%) within 1.96\u00cf\u0083 of \u00ce\u00bc.", + "video_name": "hxZ6uooEJOk" + }, + { + "Q": "\nAt 3:34, Sal drew a distribution of the difference of sample means. This looks like it's a normal distribution? In the last video, the distribution of the difference of sample means he drew looked normal, too. How do we know this is normally distributed? If you add two normal r.v.s together, is the resulting distribution normal, and why?\n\nThanks! Beth", + "A": "Central Limit Theorem. Sal has vids on it.", + "video_name": "hxZ6uooEJOk" + }, + { + "Q": "at 4:23, how do you find the height and acquaint as srt2 over 2? I cannot understand.\n", + "A": "What do you mean by acquaint ? Numbers don t get acquainted with each other, people do. Regarding how did Sal find the sine and cosine of -45 degrees... 45 degree angles are a very common occurrence. Sal has memorized these values from the unit circle. You might want to search the internet and find a good picture of the unit circle to use as reference.", + "video_name": "Idxeo49szW0" + }, + { + "Q": "\nat \"9:00\", Why do you include the first quadrant in your restriction of Theta? Why wouldn't you restrict your range of Theta to only the fourth quadrant?", + "A": "You need to have all the positive and all the negative possibilities. If you exclude Q1 you can t have any positive answers. Q1 covers the positive angles and Q4 covers the negative angles.", + "video_name": "Idxeo49szW0" + }, + { + "Q": "\nThe restrictions on this test seem redundant.\n\nfrom 0:53 to 1:33, Sal gives three restrictions on the series:\n\n1) Bn \u00e2\u0089\u00a5 0 for all relevant n (namely positive integers n).\n2) lim as Bn\u00e2\u0086\u0092\u00e2\u0088\u009e = 0\n3) {Bn} is a decreasing sequence.\n\nDon't the first two rules imply the third?", + "A": "Consider the function f(n) = x*e^(-n). This will be our Bn. What do you get at n= 0, n=1, n=2? f(0) = 0, f(1) = e^-1 = 0.37, f(2) = 2/e^-2 = 0.27 So the first 3 terms of the sequence are: [0, 0.37, 0.27]. Notice the b2> b1 this function is not always decreasing! Yet all terms are greater than zero. And the limit as n\u00e2\u0086\u0092\u00e2\u0088\u009e = 0. Some functions like this rise a little bit, then fall back down as they go on. So the third rule is necessary.", + "video_name": "91qVGeyTl44" + }, + { + "Q": "At 0:38-0:48: Why is it necessary that the alternating sign be expressed by either (-1)^n or (-1)^(n+1). Aren't there a whole slew of other ways to produced an alternating sign? What about (-1)^(n+2), (-1)^(n^2), or any polynomial exponent with odd integer coefficients?\n", + "A": "We are only talking about the form the series takes on. We know that it alternates, so the question is, is a negative term first, or a positive term. Given n goes from 1 to infinity, the first term of the (-1)^n series will be negative, and the first term of the (-1)^(n+1) series will be positive. That is all that is meant by the form of the series. Why make it any more complicated? It is an alternating series, either the first term is positive, or the first term is negative.", + "video_name": "91qVGeyTl44" + }, + { + "Q": "\nat 3:25 he said twice,but ment two times", + "A": "Twice is the same as two times. Once, twice, thrice are still used occasionally.", + "video_name": "N1X0vf5PUz4" + }, + { + "Q": "2:41 alligator eats the bigger number\n", + "A": "Im finally done this thing!", + "video_name": "nFsQA2Zvy1o" + }, + { + "Q": "\nAt 3:41 can you explain how you went from 4(y^2-4y+4) to 4(y-2)^2?", + "A": "Sal factored the trinomial. Find 2 numbers that multiply to +4 but also add to -4. The numbers are -2 and -2 This creates the factors 4(y -2)(y - 2). If you write it using exponents, you get: 4 (y-2)^2 Hope this helps.", + "video_name": "cvA4VN1dpuY" + }, + { + "Q": "\nAt about 1:14 he starts writing the \"number tree\". Do you always put the larger number on the right?", + "A": "The order of the numbers don t change the actual math. Usually people will use one side or the other for the prime numbers which makes a clear picture where it is easy to find all the primes. However, it is not fixed and when working with students I ll break it up by whatever factors they can think of and circle the primes as we get them. (For example, when factoring 48 a student may say 6*8 initially)", + "video_name": "znmPfDfsir8" + }, + { + "Q": "\n@ 7:43 why and how did you guess 'y' to be = Ae^(2x) ?", + "A": "Because we knew that after some algebra with both the second derivative, the first derivative and the original function, the result must be 3e\u00c2\u00b2\u00cb\u00a3, so a good candidate that will maintain that exponent but with enough room to play with the coefficients was Ae\u00c2\u00b2\u00cb\u00a3", + "video_name": "znE4Nq9NJCQ" + }, + { + "Q": "@ 8:38 ish, what happens when the left side all adds up to 0?\nex: y''(x)-6y'(x)+9y(x)=5e^3x is the equation and my guess would be Ae^3x\ni'd end up with coefficients of 9-18+9=5e^3x\n", + "A": "In that case, you ve proved your guess wrong by contradiction. That means you must change your guess accordingly. For example, I would change y(x) = Ae^3x to y(x) = Ae^Bx instead. This gives y(x) = Ae^Bx, y (x) = ABe^Bx and y (x) = AB^2e^3x y (x) - 6y (x) + 9y(x) = AB^2e^3x - 6ABe^3x + 9Ae^3x = 5e^3x Therefore, AB^2 - 6AB + 9A = 5. Solving for A, we have A = 5/(B - 3)^2; B =/= 3 That s it. Hope that helps!", + "video_name": "znE4Nq9NJCQ" + }, + { + "Q": "\nAt 2:34, could you replace the outermost parentheses with brackets so it can be 4+[2(7- 2x)] instead of 4+(2(7-2x)?\nAre both expressions valid or is one expression more correct than the other?", + "A": "Yes, they both mean the same thing. The brackets would be understood to be parentheses; they are usually used to set the groups of things you multiply first apart.", + "video_name": "xLYVo_k0_us" + }, + { + "Q": "I don't understand at 1:25 what falls out of the pythagorean theorem\n", + "A": "The video states that the distance formula falls out of the the Pythagorean Theorem. The distance formula is A squared plus B squared equals C squared. C represents the length of the hypotenuse of a right triangle (The longest side). A or B can represent the length of one of the sides that make a right angle in a right triangle.", + "video_name": "9ASWQi14FlE" + }, + { + "Q": "At 8:15, when he proves T(V) is a subspace, is he proving simultaneously that R^m is a subspace as well??\n", + "A": "If R^n is a vector space (which it is, as it is easy to show), then yes, because T(x) = Ax maps R^n to R^m.", + "video_name": "hZ827mfh1Jo" + }, + { + "Q": "AT 8:00 shouldn't it be PLUS zero not MINUS?\n", + "A": "Actually during 5:43 and 5:53", + "video_name": "fyJkXBvcA2Q" + }, + { + "Q": "At 7:24, Sal said g(x) = 3 (1/3)^x\nCould this be simplified down to 1^x?\n", + "A": "No, you need to retain the base of 3, but you could simplify it to 3^(1-x) Like this: 3*(1/3)^x = (3^1)*(3^(-1))^x = (3^1)*(3^(-x)) = 3^(1-x) But it s harder to see what this will do than in the earlier form.", + "video_name": "gFdh_rE2XgU" + }, + { + "Q": "\nAt 5:07 in the equation ar^-1, does -1 apply to r only or both a and r. I'm not sure because Sal didn't put any parentheses in.", + "A": "if no parentheses => applies only to one symbol which it is written after, (r)", + "video_name": "gFdh_rE2XgU" + }, + { + "Q": "At 6:40 how to get from r^2=1/9 to r=1/3. What was done to get this answer. I don't get it. I'm confused. Could someone explain please?\n", + "A": "You need to take the square root of both sides. The square root of r^2 = r. The square root of 1/9 = 1/3.", + "video_name": "gFdh_rE2XgU" + }, + { + "Q": "\nAt 0:23 Sal says \"literally\". Is that a math term I am not aware of or something?", + "A": "He means that it s condensed to basic numbers. Like a regular equation is 6743-2340 but a literal equation is (6000+700+40+3) - (2000+300+40)", + "video_name": "RRk5qLd__Ro" + }, + { + "Q": "In 0:32, How did he get 200cm squared for the height of the cereal box?\n", + "A": "It was the area of the front of the cereal box, so he did 20cm(height of box) times 10cm (width of front of box) which equals 200 cm which is the area of the front of the box.", + "video_name": "1iSBNSYhvIU" + }, + { + "Q": "At 0:00, is the bead counter actually an 'Abacus'? Thank you if you answer.\n\n-TheAmericanBerserker\n", + "A": "Yes , at 0:00 , the bead counter is an abacus.-facepalm- Stop doing this just for badges.", + "video_name": "v3gdX07Q6qE" + }, + { + "Q": "In discussing reflections at 4:38, why does not Sal place the reflection line through the origin? This approach would better help novice learners of the concept.\n", + "A": "I agree especially if you do not have a computer program to do these reflections - along the line y=x makes easy reflections, the line on the graph does not appear to be precisely defined, but it sort of looks like y = x + 1/2.", + "video_name": "XiAoUDfrar0" + }, + { + "Q": "Do units in this case kilometers (km) cancel each other out? At 3:06 Sal mentions km cancel km to just get hours.\n", + "A": "Yes, the km units cancel creating a final unit in hours.", + "video_name": "Q0tTfe2lKIc" + }, + { + "Q": "\nMr Sal At 3:43\nhow can square root of X-3 be greater or equal to 0\nif i plug 0 in place of x i would -3 which is wrong", + "A": "If x=0, then it would be sqrt(-3). Then would be an imaginary number. That s why domain comes in handy.", + "video_name": "U-k5N1WPk4g" + }, + { + "Q": "\nHey there! I'm new to Khan Academy and I've got a doubt regarding inequalities involving modulo, i.e, |x|.\n\nAt 5:58, Sal says that when |x|>=3 ---> x<=(-3) or x>=3, But what if x was positive, how then would x<=(-3)?\n\nThanks!", + "A": "First |x| represent the absolute value not modulo (modulo is a very different thing). As for your question, the solution is that x<=3 OR x>=3 so if x is positive, it satisfies the right half of the inequality and since it is an OR it doesn t need to satisfy the other side, likewise for a negative number <-3. If the solution was instead x<=-3 AND x>=3 then we would have a problem since anything that satisfied one half could not satisfy the other, thus resulting in no valid solution.", + "video_name": "U-k5N1WPk4g" + }, + { + "Q": "At 6:04 when hes discussing that x can < or = to -3, im lost. If x was -4 and then you subtracted 3 youd get -7. If x has to be = or > than 0 then i dont understand how it can be -3 or less. Some body please explain this.\n", + "A": "i understand now thank you", + "video_name": "U-k5N1WPk4g" + }, + { + "Q": "\nAt 6:21, Sal asks, \"Is 'such that' the colon or the line?\" I've always used those interchangeably. Is there actually a difference?", + "A": "Well I ve always used the pipe ( | ) symbol there (e.g { x in R | x \u00e2\u0089\u00a0 -2 } ) out of laziness, but Sal s comment in this video made me question that practice...", + "video_name": "U-k5N1WPk4g" + }, + { + "Q": "\n4:28 It is to my understanding that if f(x)=radical x-3 then the x cannot be any less than three, which means x greater or EQUAL TO 0* cannot be so it is just x is ONLY greater than or equal to zero. If I am missing something please let me know.\n*just putting an emphasis", + "A": "Sal said it was greater than or equal to zero, so I don t know what you mean", + "video_name": "U-k5N1WPk4g" + }, + { + "Q": "\nAround 6:10, I don't undersand how x could be smaller than -3.\nSay x= -4, than we get square root of -4 -3 = square root of -7, which isn't possible, or at least doesn't make sense to me..", + "A": "It is because you are taking the absolute value of x. So, for x = -4, we would get: \u00e2\u0088\u009a( |x| - 3) = \u00e2\u0088\u009a( |-4| - 3) = \u00e2\u0088\u009a( 4 - 3) = \u00e2\u0088\u009a( 1) = \u00c2\u00b1 1 It is only when x is between -3 and 3 that we would get a negative number under the square root.", + "video_name": "U-k5N1WPk4g" + }, + { + "Q": "\nAt 9:12 why can't we make the trasformation R2+R3 and then R3+R2 to recover two zero rows as in the case lambda=3? This way at the end I would get an eigenspace that is equal to the span of the vectors (-1,1,0) and (-1,0,1). And if you sum them up you actually get the same vector Sal recovered in the video! Are they simply two \"equivalent\" solutions or is there something wrong about mine?\nThanks in advance for any answer :D", + "A": "You can replace any row with a scalar multiple of itself, or with itself minus another row (or equivalently, another row minus itself ). There are different paths to the same result. If you don t interchange any columns, you should end up with the same equation Sal got, otherwise you made an error.", + "video_name": "3Md5KCCQX-0" + }, + { + "Q": "At 2:56 while dividing 54 by 4, why did 4 went to twenty while it is written as 2.0? I see that it is number two because the decimal is just next to it on the right hand side. In the other words 2.0 is equals to 2 x 10^0. While the number twenty is equals to 2 x 10^1. Also, the number twenty is equals to 20.0, which looks different than the twenty that is written when we added a zero at 2:54.\n", + "A": "Ah, I believe that Sal was carrying the decimal point down so you can see where it would be.", + "video_name": "jTCZfMMcHBo" + }, + { + "Q": "\nAt 4:24, 3=2 has no solutions but what about if x =0? Then 0=0 would be one solution.", + "A": "If you are asking if X=0 can be a solution to the middle equation, the answer is no. It really has no solution. To verify whether or not X=0 is solution, substitute into the equation. -7x + 3 = 2x + 2 - 9x -7(0) + 3 = 2(0) + 2 - 9(0) 0 + 3 = 0 + 2 + 0 3 = 2 This is false, so X=0 is not a solution. Hope this helps.", + "video_name": "qsL_5Y8uWPU" + }, + { + "Q": "At 3:20 the symbol Sal used, is that the sign of infinite?\n", + "A": "Yes \u00e2\u0088\u009e is the infinite sign. Great educated guess!", + "video_name": "qsL_5Y8uWPU" + }, + { + "Q": "5:40 Why that line is called secant line?\n", + "A": "A secant line is a line that intersects a curve of some sort, at two points. A secant line is what we use to find average rates of change.", + "video_name": "f4MYCepzLyQ" + }, + { + "Q": "\nAt 0:50 what does sal mean by with respect to time?", + "A": "Sal meant . what will be the change in distance with respect to time . Example :- you car moves with a speed of 80/kmph , so what do you mean by this, your car moves with a speed of 80 km, per hour and that is your speed . if you want to write it in meter/ sec it would be 22.2/sec . =)", + "video_name": "f4MYCepzLyQ" + }, + { + "Q": "\nI still don't understand why at 1:36 you have to multiply both sides by Pi to simplify the equation.", + "A": "He multiplied both sides by the reciprocal.", + "video_name": "tVcasOt55Lc" + }, + { + "Q": "\nAt 0:51 he said 9/5 is equals to 1 4/5, but why?", + "A": "9/5 = 5/5 + 4/5 = 1 + 4/5 = 1 4/5. Have a blessed, wonderful new year!", + "video_name": "-lUEWEEpmIo" + }, + { + "Q": "\nAt 0:19 why does Sal say that we can get a 1 coefficient? Why do we need to get a 1 coefficient?", + "A": "Your 1st step in factoring should always be to look for and remove the greatest common factor. The reason this should be your 1st step is that it makes doing any other factoring technique easier to do. Think of it has cleaning out the clutter, all the other numbers get smaller and easier to work with. And, you have to factor it out sometime, so do it as your 1st step and make the rest of the work easier.", + "video_name": "R-rhSQzFJL0" + }, + { + "Q": "\nI'm really confused. Where does Sal get the 21 from @1:18? O_O", + "A": "He multiplies 7 by -3. He factored the polynomial, then applied the product/sum theorem for quadratic polynomials to get the answers for their roots.", + "video_name": "R-rhSQzFJL0" + }, + { + "Q": "What is the difference between a square root and a principle square root? 0:49 3:00\n", + "A": "A square root can be negative or positive, but the principle square root is always positive.", + "video_name": "s03qez-6JMA" + }, + { + "Q": "\nAt 1:50 to 1:57, is the reason why that following that logic you would get i^infinity 2\u00e2\u0088\u009a13 or am I missing something?", + "A": "I m confused where you got the idea of i^infinity from. Sal is explaining why sqrt(+52) cannot be sqrt(-1) \u00c3\u0097 sqrt(-52). When you simplify this, you end up with i \u00c3\u0097 i\u00c3\u0097sqrt(52), which is -sqrt(52). This is not the correct answer; therefore it doesn t work.", + "video_name": "s03qez-6JMA" + }, + { + "Q": "At, 2:12 Sal says the property does not work if both nos. are negative. I wanted to know why?\n", + "A": "If both numbers are negative, you get something like what he showed in the video. To recap: if sqrt(1) = sqrt(-1) * sqrt(-1) <-- both numbers are negative then 1 = -1 <-- you already know sqrt(1) = 1, and sqrt(x) * sqrt(x) = x As you can see, it just doesn t work. Because of this, both numbers can t be negative.", + "video_name": "s03qez-6JMA" + }, + { + "Q": "\nAt 2:03 , Sal says u cant separate a principal square root number into the product of two numbers with the principal square root of a negative number. But you can, if you take the only the square root (not principal square root ) of the number ,say 4 , right? Cuz, u'll end up with i^2 sq.root(4) which\nalso can be written as [ -sq.root(4) ] which will give you the same two answers. Jst need a confirmation. Thanks.", + "A": "I can understand what you are trying to say, but -2 x -2 = 4 not -4, likewise 2 x 2 is not = -4 hopefully this helps if you still need the question answered after 2 years.", + "video_name": "s03qez-6JMA" + }, + { + "Q": "When you are answering the question for credit on a test or something, would you write the constraints explained at 3:12 along with your answer?\n", + "A": "yes, you would its part of the answer", + "video_name": "XChok8XlF90" + }, + { + "Q": "\nIs the constraint a \u00e2\u0089\u00a0 -9 at 3:47 really necessary? The simplified expression is already undefined at a = -9, so it looks as if it doesn't have to be restated.\n\nAdditionally, the original context of the word problem provides a rectangle whose width and length are rational expressions. Can't you not have a negative number in the simplified expression anyway?", + "A": "1) Yes, it s obvious. 2) Set the area > 0. You get a^4+6a^3-36a^2-54a+261 > 0", + "video_name": "XChok8XlF90" + }, + { + "Q": "what is that sound at 3:40 ?\n", + "A": "some one laughing", + "video_name": "X2jVap1YgwI" + }, + { + "Q": "At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?\n", + "A": "It s because from Earth the moon is closer than the sun therefore it looks like it is blocking it.", + "video_name": "X2jVap1YgwI" + }, + { + "Q": "\nAny one knows the answer for this it would be so helpful\nA Squate and a rectangle have the same area.\nThe sides of the rectangle are in the ratio 4:1. It's perimeter is 200cm.\nWhat is the length of the sides of the Square?", + "A": "For problems like this, it is useful to write one of the unknown in terms of a symbol or letter. (i ll go with x) Here, length of shorter side of the rectangle is x. (Since the longer side is 4 times longer, i ll call it 4x) perimeter of rectangle= length+width+length+width = 200 Therefore, x+4x+x+4x =200 10x=200 x=20 Now to find the area of the rectangle, area= lengtth * width =20*80 =1600 area of square = 1600 = length*length length= sqrt(1600) =40 (fill in the units everywhere when you work on paper)", + "video_name": "4ywTWCaLmXE" + }, + { + "Q": "\nAt 4:55 , how is that multiplying 9 times 9 times cancels each other?\n9*9=81....am so confuse", + "A": "Ah I see whats going on. Alright, theres 2/3 = x/9. Lets change this just a tiny bit to 2/3 = x * 1/9, now multiplying both sides by 9. we get 9 * 2/3 = x * 1/9 * 9. On the right side it s One Divided by 9 that gets multiplied by 9. Or if I just swapped it around. 9 * 2/3 = x * 9 * 1/9 = x * 9/9. So now multiplying and dividing it all out it is. 6 = x", + "video_name": "4ywTWCaLmXE" + }, + { + "Q": "At 2:010 in the video above, is the pink loop twice the size of the smaller loop?\n", + "A": "It should be, since the pink loop was going around the original loop twice.", + "video_name": "Am-a5x9DGjg" + }, + { + "Q": "At 1:50, why did it divide like, into two loops? How come they aren't the same? Help me!\n", + "A": "Because there is only one edge on a M\u00c3\u00b6bius strip, when she cut the edge off, it completely separated. Because of the twist in the M\u00c3\u00b6bius strip, the longer edge curled around the thicker center.", + "video_name": "Am-a5x9DGjg" + }, + { + "Q": "At 2:04. Why does Sal say, \" third of the way around the triangle \". What does it mean?\nThanks.\n", + "A": "A triangle s three angles measure up to 180. Since it is a equilateral triangle Sal is constructing, each angle is 60 degrees. Many people become confused when Sal says 120 degrees is one third of the triangle, but he is talking about the arc of the circle. To find the arc or the angle formed by the arc, use this equation: arcX = 2 angleX. Thus, the angle is 60 degrees and one third of a triangle, due to what I said earlier. (60 x 3 = 180)", + "video_name": "gWMTTP58_J0" + }, + { + "Q": "\nAt 1:02, what does Sal mean with the fact that the sum of 1/n is unbounded, but that the sum of 1/n^2 is bounded?", + "A": "i think an unbound sum is basically like a divergent integral and a bound sum is like a convergent integral one goes to infinity and the other has a fixed value", + "video_name": "u1UKIljUWuc" + }, + { + "Q": "At 6:33 -- Does Sal mean\n(1 + def-integral from 2 to inf of 1/(x^2)) instead of (1 + def-integral from 1 to inf of 1/(x^2))?\n", + "A": "No, it is the indefinite integral from 1 to infinity. The series does start at n=2 and goes to infinity, because we took out the 1. But both the integral and the series, that starts at n = 2, start at x = 1. The only difference is that the series is an understimate (a right Reimann Sum) of the actual area of the curve (the indefinite integral).", + "video_name": "u1UKIljUWuc" + }, + { + "Q": "\nAt 5:35, why does Sal define the range of the Volume function according to the height (x) and width (20 - 2x) of the box? Why that specific combination of dimensions and not say height (x) & length (30 - 2x) or width & length instead?", + "A": "At that point he isn t defining the range of the volume, he s defining the realistic range for x, where x will ultimately represent the height of the box. Eventually some value of x will result in an optimum volume relative to its height (where the height is a direct function of x), width and length, all of which have been defined in terms of x.", + "video_name": "MC0tq6fNRwU" + }, + { + "Q": "Towards the end of the video at around 19:00, didn't Sal mean to write rank(A) = n?\n", + "A": "I believe he did", + "video_name": "M3FuL9qKTBs" + }, + { + "Q": "\nAt 4:22, Sal said that there is variability in the data. can you please explain this?", + "A": "Variability means that something changes. So, if your set of data has values that differ from each other or change, then there is variability in the data.", + "video_name": "qyYSQDcSNlY" + }, + { + "Q": "7:54... Shouldn't the new vector have \"m\" components? One for each row?\n", + "A": "Yes (mistake).", + "video_name": "7Mo4S2wyMg4" + }, + { + "Q": "At 0:36 could the sequence be written instead as the sum from n=0 to infinity of (1/2)^n? and if so which one is used most commonly?\n", + "A": "Sure - both versions are widely used.", + "video_name": "rcRg_gO7-7E" + }, + { + "Q": "\n3:04 she says that circles can be defined by three points, can't a circle be defined by more than three?", + "A": "No. A circle is only defined by three points. If you have three points, then there is only one circle that can pass through all three (unless they are collinear in which case no circle can). A fourth point would either be redundant or make the circle previously defined invalid.", + "video_name": "DK5Z709J2eo" + }, + { + "Q": "\nat 0:56, vi says a camel is only a third of the page, but if so, couldn't you just mark 1/6 of the page, and 1/12, 1/24, & so on?", + "A": "Yeah, she could ve just acted like the 2/3 left was 1 page, then made the camels half of that, then half of that, and so on. She could ve also made the camels bigger or only used 2/3 of the page for camels, making the 1/2 of 1/2 of 1/2\u00e2\u0080\u00a6 again and used the extra for a circle game shape.", + "video_name": "DK5Z709J2eo" + }, + { + "Q": "At 3:57, couldn't you just make the intervals on 0 and 3 and not include the numbers -1 and 4?\n", + "A": "Remember, there are lots of numbers (fractions and decimals) that are located between the integers. If you make the interval 0 to 3, you lose all the real numbers from -1 to 0 and 3 to 4 (numbers like -0.5, -1/4, -0.999999, 3.6; 3.999, etc.). So, you have a completely different set of numbers and a much smaller set of numbers. Thus, the interval needs to be (-1, 4)", + "video_name": "UJQkqV2zGv0" + }, + { + "Q": "\nAt 8:13 could it also be expressed as {X \u00cf\u00b5 R | 1 < X < 1 } ?", + "A": "Sorry, but no. 1 < X < 1 is the notation for and , not or . 1 < X < 1 is the null set since both 1 < X and x < 1 must be true. There is no number that is both greater than one and less than one.", + "video_name": "UJQkqV2zGv0" + }, + { + "Q": "When you work out the problem at 3:55, wouldn't it be f(x+1)/f(x)=1/4*2^x+1/1/4*2^x=1? Because 1/4 and x's cancel and you are left with 2/2 which is equal to 1.\n", + "A": "First off, be careful how you write it, you need extra sets of parentheses or your equation is totally different so f(x+1)/f(x) = 1/4 * 2^ (x+1) / (1/4*2^x). The 1/4 cancel so you are left with 2^(x+1)/2^x x s do not cancel, we have to use exponent rules where dividing same bases require us to subtract the exponents, so as Sal noted x + 1 - x is just 1, so we have 2^1 or just 2", + "video_name": "G2WybA4Hf7Y" + }, + { + "Q": "\nAt 2:43, what does the word arithmetic mean in general? I've heard people use the word a lot.", + "A": "The worldwide definition of arithmetic is: the branch of mathematics relating to the manipulation of numbers. Fractions, addition and subtraction, division and multiplication fall into this category.", + "video_name": "uhxtUt_-GyM" + }, + { + "Q": "In this video about Statistics in 8:04 and 10:42 when Sal was talking about The median does this type of rule apply When there is odd numbers there is a middle number but when there is an even number you have to divde it by the two middle numbers that is your median.Does that rule apply in Statistics? Just want to know.\n", + "A": "Thanks Andrew for letting me know!", + "video_name": "uhxtUt_-GyM" + }, + { + "Q": "\nAt 11:10 sal, u wrote 115 /6 what is that supposed to mean were talking about arithmatic not fractions and also your example for the mode did not make sense may you clarify that for me", + "A": "He was calculating the mean of the data set {3,3,3,3,3,100}, which is found by taking the sum of all those numbers (=115) and dividing by the number of elements in the set (6). Hence 115/6, which is, as he says, 19 1/6. You could also write it as 19.7, but 115/6 is more precise, as you don t have to round. For that same data set, the mode is pretty straightforward. The number 3 is clearly the most common number in that set (thee are five 3 s but only one 100), so the mode is 3.", + "video_name": "uhxtUt_-GyM" + }, + { + "Q": "At 18:10 when Sal says/writes \"set X spans subspace V and X has 5 elements you now know that no set than spans the subspace V can have fewer than 5 elements\", isn't this statement incorrect? The set X didn't claim to be a BASIS for V, just span V. (I know Sal continues with \"even better if X is a basis...\" but it sounds like he's going on to make a separate statement).\n", + "A": "Indeed. This threw me for a loop. Sal needs to correct this with a pop-up.", + "video_name": "Zn2K8UIT8r4" + }, + { + "Q": "At 4:41, why are you using the last equation?\n", + "A": "It doesn t matter what equation of the 3 is used to find out the value z. Any of the three equations can be used.", + "video_name": "f7cX-Ar2cEM" + }, + { + "Q": "at 2:30 why is he adding all the numbers when he could be subtracting?\n", + "A": "so that he can eliminate the z variable.", + "video_name": "f7cX-Ar2cEM" + }, + { + "Q": "at around 15:40. Are you allowed to just say dx*(1/dt) = dx/dt and have it be the derivative of x with respect to t??\n", + "A": "I m not sure what you are asking, but remember that since dx and dt were on different sides of the radical, you d have to deal with them slightly differently.", + "video_name": "_60sKaoRmhU" + }, + { + "Q": "Okay, I guess Sal is using Synthetic Division at 10:20, but I don't see how he's doing it.\nFor example, when he uses the 1:\n\u00e2\u0080\u00a2 We write down the 1\n1, ...\n\u00e2\u0080\u00a2 1 x 1 + (-3) = -2\n1, -3, ...\n\u00e2\u0080\u00a2 1 x (-2) + (-9) = -11\n1, -3, -11, ...\n\u00e2\u0080\u00a2 1x (-11) + 27 = 16\n1, -3, -11, 16\nNow this doesn't add up to zero, but it still doesn't make any sense to me.\nUsing 3 I get:\n1, 0, -9, 0\nWhat am I doing wrong?\n", + "A": "I don t use synthetic division. It s quicker when you get used to it, but harder to understand. Long division (what he used in this video) always works. You don t have to relearn it whenever you haven t used it for a while.", + "video_name": "11dNghWC4HI" + }, + { + "Q": "At 2:18, I didn't get what the speaker meant by \"that multiplies the rest of the term\". Can anyone explain?\n", + "A": "A number is a coefficient, which defines how much there is. In maths , especially algebra, numbers get an x or another letter. When you put a 5 before a x you get 5x. Whereby 5 is the coefficient and x the rest of the term . It s get tricky when you add multiple variables to one coefficient. Like this 4xy or 57abc.", + "video_name": "9_VCk9tWT0Y" + }, + { + "Q": "\nAt 1:03, Sal says that the term is 7y, but isn't it -7y ?", + "A": "Whether it s negative (7y) or not, it really depends on what the value of y is. : If y is negative, then 7y will be a negative number too : However if y is positive, then this term will be positive", + "video_name": "9_VCk9tWT0Y" + }, + { + "Q": "\non 5:34 that expression the last 3 factors are x, y, z what would be the coefficients of that term?", + "A": "The coefficient would be 1. It doesn t have to be stated that 1*x*y^2*z^5 for 1 to be the coefficient as the 1 multiplies way to x*y^2*z^5. Also the 1 is not a factor of that term.", + "video_name": "9_VCk9tWT0Y" + }, + { + "Q": "At 4:08, Sal's final expression (2rp - 4\u00cf\u0080r^2) had three terms : r, p, and r^2. But didn't the question ask for a binomial, which has two terms? I'm confused....\n", + "A": "This expression has two terms. I think you counted the types of variables in the expression instead of the terms. A term is an expression that doesn t have the operations of addition and subtraction. 2rp<---One term 4\u00cf\u0080r^2<---Second term There are two terms in this expression; therefore, it s a binomial. I hope this helped!", + "video_name": "EvvxBdNIUeQ" + }, + { + "Q": "5:42: How did he get 2x squared?\n", + "A": "during the Pythagorean theorem he had x^2 + X^2 = c^2 right? Well when u put x^2 and x^2 together u get 2x^2", + "video_name": "McINBOFCGH8" + }, + { + "Q": "Why do you not express the ratio of the 30,60,90 as 3:4:5? I seems a lot less confusing.\n", + "A": "Just because 3:4:5 immediately relates to pytha. thereom... which isn t always the case with 30.60.90 s.", + "video_name": "McINBOFCGH8" + }, + { + "Q": "What does delta mean like at 5:08?\n", + "A": "Delta means the change in a quantity. It is a Greek letter that looks like a triangle. It is used in Math, Science, and others to show that you re looking at how something is changing without having to write out: the change in... . Kinda like when you re laughing out loud and you text someone lol .", + "video_name": "9wOalujeZf4" + }, + { + "Q": "\nI dont get it. Any equation on how 0.2 becomes 1/5? at 8:03?", + "A": "0.2 is equal to 1/5. A simple way to explain it is how many 0.2 s in 1.0. There are 5. 0.2 is just 1 of those 5, so 1/5.", + "video_name": "9wOalujeZf4" + }, + { + "Q": "I still don't get how to find x and how you know that it is automatically zero based on something else at 9:12 and why is it that when y=-x that equeals M but when y=3.75 that equeals b. is x always zero?\n", + "A": "i think you subtract,add, divide,or multiply 3.75 to both sides of the equation depending on what the sign is you do the opposite :)", + "video_name": "9wOalujeZf4" + }, + { + "Q": "\n5:20 Why is it written n greater than or equal to 2?", + "A": "In the formula being used, the nth term = the (n-1)th term + a common difference. In other words, the value of the nth term depends on the value of the term before it If n were 1, the term before it would be the 0th term --- which doesn t exist. So n is restricted to 2 and above in order that the term before will be no less than the first term.", + "video_name": "_cooC3yG_p0" + }, + { + "Q": "At 4:19, Sal pronounces \"arithmetic\" wrong.\n", + "A": "That was defiantly Worth pointing out", + "video_name": "_cooC3yG_p0" + }, + { + "Q": "\nat 6:41, is there not a way to write the third question in an explicit from? If there is, can someone show me how?", + "A": "Actually you re asking for the common formula that is taught in the next lessons: a_n = (n * (n + 1))/2", + "video_name": "_cooC3yG_p0" + }, + { + "Q": "On 0:08, is it first first quadratic formula? Yes or no?\n\nAnd on 2:27-2:28, what's binomial? Anyone tell me??\n", + "A": "The equation shown at 0:08 is the standard form of a quadratic expression or equation, not the quadratic formula. A binomial is a polynomial having only two terms. Hope that helped.", + "video_name": "r3SEkdtpobo" + }, + { + "Q": "At 1:17 Sal divides \"everything by a\" but writes ... x(b/a) instead of (b * x) / a. Why does x not get divided by a?\n", + "A": "x(b/a) is exactly the same as (b * x) / a Here are the steps: x (b / a) = x/1 * (b / a) = (b * x) / (a * 1) = (b * x) / a", + "video_name": "r3SEkdtpobo" + }, + { + "Q": "At 6:30, why couldn't you take \"b^2\" out of the radical? Because the square root of b^2 is just plus/minus b ? Or am I missing something?\n", + "A": "You can only take factors out of root signs if they re factors, but in this case it s being added not multiplied so you can t split it up.", + "video_name": "r3SEkdtpobo" + }, + { + "Q": "\nAt 5:00, How do you already know that the sin^2(a) plus the cos^2(a) equals one?", + "A": "let us imagine a right triangle \u00ef\u00bc\u008co=opposite\u00ef\u00bc\u008ch=hypotenuse\u00ef\u00bc\u008ca= adjacent. sin\u00ef\u00bc\u0088a\u00ef\u00bc\u0089=o/h\u00ef\u00bc\u008ccos\u00ef\u00bc\u0088a\u00ef\u00bc\u0089=a/h\u00ef\u00bc\u008cright\u00ef\u00bc\u009fso \u00ef\u00bc\u009a sin \u00c2\u00b2\u00ef\u00bc\u0088a\u00ef\u00bc\u0089=o\u00c2\u00b2/h\u00c2\u00b2 and cos\u00c2\u00b2\u00ef\u00bc\u0088a\u00ef\u00bc\u0089=a\u00c2\u00b2/h\u00c2\u00b2 we can add up these\u00ef\u00bc\u008cand get\u00ef\u00bc\u009a sin \u00c2\u00b2\u00ef\u00bc\u0088a\u00ef\u00bc\u0089+ cos\u00c2\u00b2\u00ef\u00bc\u0088a\u00ef\u00bc\u0089=\u00ef\u00bc\u0088o\u00c2\u00b2+a\u00c2\u00b2\u00ef\u00bc\u0089/h\u00c2\u00b2 \u00ef\u00bc\u008c we know that \u00ef\u00bc\u009a\u00ef\u00bc\u0088o\u00c2\u00b2+a\u00c2\u00b2\u00ef\u00bc\u0089=h\u00c2\u00b2 \u00ef\u00bc\u008cthen we can get the answer\u00ef\u00bc\u008chope that could help you\u00ef\u00bc\u0081", + "video_name": "a70-dYvDJZY" + }, + { + "Q": "At 12:06pm, How do i verify csc^4 (x) - cot^4 (x) = 1 + 2 cot^2 (x)\ni got to (csc^2 (x) + cot^2 (x))1 = 1 + 2cot^2 (x) (i think the right side can convert to 2cscx but im stuck)\n", + "A": "Identity to use: 1 + cot\u00c2\u00b2 x = csc\u00c2\u00b2 x We need to square this. Thus, [1 + cot\u00c2\u00b2 x]\u00c2\u00b2 = [csc\u00c2\u00b2 x ]\u00c2\u00b2 1 + 2cot\u00c2\u00b2 x + cot\u00e2\u0081\u00b4 x = csc\u00e2\u0081\u00b4 x Let us then use this to substitute for csc\u00e2\u0081\u00b4 x in your equation: csc\u00e2\u0081\u00b4 (x) - cot\u00e2\u0081\u00b4 (x) = 1 + 2 cot\u00c2\u00b2 (x) (1 + 2cot\u00c2\u00b2 x + cot\u00e2\u0081\u00b4 x) - cot\u00e2\u0081\u00b4 (x) = 1 + 2 cot\u00c2\u00b2 (x) 1 + 2cot\u00c2\u00b2 x = 1 + 2 cot\u00c2\u00b2 (x) As, both sides of the equation are now the same thing, we have proved the original.", + "video_name": "a70-dYvDJZY" + }, + { + "Q": "\nat 2:01, vi said \"hamentashe\" or something. What are those?!", + "A": "Hamantash is a triangular cookie or pastry, often associated with the Jewish holiday Purim.", + "video_name": "o6KlpIWhbcw" + }, + { + "Q": "\nat 1:09 did she say ''beacaus you have to navigate your triangle stack around your nose''?\nor ''beacaus you have to navigate your triangle stack around your notes''?", + "A": "I heard nose but notes is probably more correct", + "video_name": "o6KlpIWhbcw" + }, + { + "Q": "At 2:49, how did she make the triangle look upset when she didn't even change sides?\n", + "A": "it was a short smile she just made a big arch and the she got a frown", + "video_name": "o6KlpIWhbcw" + }, + { + "Q": "at 5:17 do you multiply positive numbers the same way you multiply regular numbers..? if so do the positive numbers cancel out and the awnser become negative..?\n", + "A": "ok but what I don t understand is how negative x negative =positive but positive x positive =positive how does that work..? shouldn t it be positive x positive =negative...?", + "video_name": "47wjId9k2Hs" + }, + { + "Q": "\nAt 2:48 why does pos times neg have to be neg? is there a reason for that?", + "A": "If you tell yourself that Multiplication is the same as repeated addition, then: 4x -9 is the same as saying four times -9 , or: -9 + -9 + -9 + -9 -> -9-9-9-9 = -36", + "video_name": "47wjId9k2Hs" + }, + { + "Q": "\nAt 0:25 - what's the point of writing down \"a^2 + -ab...\"? Why not just \"a^2 - ab\"? The teachers I've had would have marked the way you'd used as wrong.", + "A": "You could do that, and you re correct, it is proper form. Sal just did that to keep everyone on the same page, and solve the problem step by step. Later in the video, it did get simplified down to a^2 - ab, and as long as your final answer is simplified properly, it won t really matter where you do it.", + "video_name": "YahJQvY396o" + }, + { + "Q": "\nAround 9:13, what type of function would it be if there was an x value that wasn't mapped to a y value?", + "A": "Such a scenario doesn t really exist. Say we had f: {a, b, c} -> {1, 2}, defined by f(a)=1, f(b)=2, and f(c)=7. Then either it is a typo where (whoever gave such a problem) forgot to put 7 in {1, 2}, or the object f is not a function, because a function f: A->B must be a subset of AxB. Since 7 is not in B, such an f wouldn t be a subset of AxB, so it wouldn t be a function.", + "video_name": "xKNX8BUWR0g" + }, + { + "Q": "\nAt 0:40, Sal starts thinking about the question. Maybe that makes sense but what I was thinking was different. What I did was, x^5 simplify with x^5, x^2 with x^2 and then I tried solving the question. I got a very different answer.....-0.03......That is way off 2/3! I know 2/3 is an approximation but having a difference of signs is a big difference! Why?", + "A": "Ack! NEVER, EVER, EVER, cancel out anything next to a plus or minus sign! This is a very bad algebra mistake. Here s an example so you can see why this is not okay: Consider (x + 1) / (x + 2). If you could just cancel out the x s, you would be left with 1/2. But, try plugging in some values for x and you will see that this can t be right. For instance, if you plug in x = 1, you will get (1+1)/(1+2) = 2/3, not 1/2. Different values of x would give you different ratios.", + "video_name": "gv9ogppphso" + }, + { + "Q": "i didn't understand at 2:40 why x squared was x. I thought this was radicals not square roots. Or is x just 1\nHelp Please :/\n", + "A": "In the video, it actually shows the square root of x squared, not just x squared. So, if you think of the equation as the square root of x*x, you get x. Hope this helps!", + "video_name": "egNq4tSfi1I" + }, + { + "Q": "\nAt 2:47, Sal says that sqrt(x^2) is the absolute value of x, and I get that. How come at 3:14, he says that sqrt(4) would be 2? Shouldn't he also consider -2?", + "A": "He qualified his answer by saying that the principal square root of 4 is 2. The principal square root is the unique nonnegative square root of a nonnegative real number.", + "video_name": "egNq4tSfi1I" + }, + { + "Q": "Why at 9:45 do we use n! in the denominator instead of just the n. I understood up to the second derivative why we introduce 1/2 but then on the third it I do not understand why we have 1/3! as this is 1/6 and not 1/3 which means that it will not cancel out. I hope you understand my questions.\nThank you very much for your help :)\n", + "A": "For the second derivative, it s not 1 / 2 it s really 1 / 2! It s just that 2! happens to be equal to 2. The factorial works well for repeated differentiation: d/dx x^5 / 5! = x^4 / 4! d/dx x^4 / 4! = x^3 / 3! d/dx x^3 / 3! = x^2 / 2! d/dx x^2 / 2! = x / 1! d/dx x / 1! = 1 / 0! d/dx 1 / 0! = 0", + "video_name": "epgwuzzDHsQ" + }, + { + "Q": "at about 3:09, Sal adds an \"x\" after f '(0). Why?\n", + "A": "It s so p (0) still equals f (0) after he takes the derivative of his expression f(0)+f (0)x. If the x wasn t there, then the f (0) would end up equaling zero when he took the derivative, just as the f(0) did. Reviewing power rule may be helpful in clarifying this.", + "video_name": "epgwuzzDHsQ" + }, + { + "Q": "\nWhat is the function approaching as x=1? At 3:30 could anyone explain or phrase that in a different way or ways?", + "A": "What is the y-value of the line (or function) approaching as x gets closer to 1? This example is simple as y is always 1 except on the exact point of (1,1) since we cannot divide by zero. when x=0, y=1. when x=0.5, y=1. when x=0.9, y=1.", + "video_name": "riXcZT2ICjA" + }, + { + "Q": "At 5:06 Sal drew a curve like thing after writing g(x).What is that curve?\n", + "A": "Braces ( curly braces ), it is the same of using { .", + "video_name": "riXcZT2ICjA" + }, + { + "Q": "\nAt 10:34, Sals calculator said that 1.999999999999^2 was 4. Well it is actually 3.999999996...but close enough.", + "A": "Listen again, he said his calculator rounded the result to 4 but that the result wasn t exactly 4, but it was really really really really close to 4. And that is the whole deal with limits. What is the value of a function as you get really really really really close to the limit value. Keep Studying!", + "video_name": "riXcZT2ICjA" + }, + { + "Q": "Hey @4:15 This might sound stupid but why is the answer 1 and not zero?\n", + "A": "I think I was thinking about slopes and derivatives. I was a little rusty on my calculus at the time I watched this video.", + "video_name": "riXcZT2ICjA" + }, + { + "Q": "at 5:22, Sal says \"it\" what is he referring to?\n", + "A": "His it is referring to g(x) , and yes he is trying to say g(2) = 1 , or at the x-value 2, g(x) outputs a 1.", + "video_name": "riXcZT2ICjA" + }, + { + "Q": "\nAt 6:39 he says the discontinuity is when X=2, why can't it also be at X=-2?", + "A": "That is the whole point of limits, x cannot equal 2 because that is your limit!", + "video_name": "riXcZT2ICjA" + }, + { + "Q": "at 7:08 on the y=f(x) axis you put an open circle at 4 the top why\n", + "A": "Putting an empty circle in a graph of this kind indicates that the function does not have a value on the curve at that point. Often this is because the function is undefined at that point, but in this case it is because the function has a quirky definition stating that the function has a different value, not on this curve, at that particular point.", + "video_name": "riXcZT2ICjA" + }, + { + "Q": "\nAt 2:44 why did he draw an open circle and not an asymptote?", + "A": "Good question. It s because there is a finite limit as x approaches 1. He uses the open circle to show that the function is undefined at that point. If you graph something like 1/(x-1) you ll notice that it goes to +infiniti as you approach 1+ and -infiniti as you approach 1-. So there is an asymptote at 1. In the example of (x-1)/(x-1) the function is 1 at every x value except 1 so there is no asymptote.", + "video_name": "riXcZT2ICjA" + }, + { + "Q": "\nAt 0:10, Sal said that limits are the ideas that calculus is based upon. How important are limits for anyone more familiar with calculus? (just curious)", + "A": "Limits are very important to calculus. Derivatives and integrals use calculus and many modeling applications in calculus use limits. Limits are very important in calculus because many concepts are based on that sole aspect.", + "video_name": "riXcZT2ICjA" + }, + { + "Q": "At 4:40 , f(x) must tend to one but why it is equal to one?\n", + "A": "It is the two-sided limit of the function as x approaches 1.", + "video_name": "riXcZT2ICjA" + }, + { + "Q": "At 6:27, why is he using g(x)? Can't it be something else?\n", + "A": "What do you mean? It is just used to write a function.", + "video_name": "riXcZT2ICjA" + }, + { + "Q": "At 0:35, Sal explains another way of finding the determinant, by taking each value of the first row terms in the original matrix and multiplying it by the corresponding terms in the cofactor matrix, and taking the sum of those products. Why does this work?\n", + "A": "This is called rule of Sarrus, only applies to the 3 x 3 matrices. It s just a coincidence of the traditional minor and cofactor method.", + "video_name": "ArcrdMkEmKo" + }, + { + "Q": "At 0:57, 2i-7i is -5i. Based on this, is i a coefficient?\n", + "A": "No, the coefficients are the 2, -7 and -5. i is like a variable. But, it is unique because we know its value. i always = sqrt(-1).", + "video_name": "SfbjqVyQljk" + }, + { + "Q": "\n6*3 is 3 times larger than 2*3. how is this in-between as Sal says @1:30\nI can perform the computation, I just don't know why it works. Can someone help.", + "A": "Note that if we multiply 2 \u00e2\u0080\u00a2 3 by 3, we can have 3 \u00e2\u0080\u00a2 2 \u00e2\u0080\u00a2 3. Then, we can use the associativity of multiplication to find that this is equivalent to (3 \u00e2\u0080\u00a2 2) \u00e2\u0080\u00a2 3 = 6 \u00e2\u0080\u00a2 3. Therefore, 6 times 3 is thrice 2 times 3.", + "video_name": "j3-XYLnxJDY" + }, + { + "Q": "At 1:36,why the point (1,-1) is the center?\n", + "A": "you set each numerator equal to zero. so x-1=0 ==> x=1 and y+1=0 ==> y=-1 If you want to know why setting the each numerator finds the center... I think about it like this. (x-1)^2 is symmetric about x=1. That is if you add or subtract the same number from x, say 1 (x=2, x=0), then you will get the same output. (2-1)^2=(0-1)^2. The same goes for (y+1)^2. ***this may not be the exact terminology but is a way to think about it.", + "video_name": "lGQw-W1PxBE" + }, + { + "Q": "\nIn 3:35, why didn't Sal factor x^2/4-4 in (x/2+2)(x/2-2)?", + "A": "He s taking the square root of everything except the constant anyway, so it makes more sense and is easier to square root in the end.", + "video_name": "lGQw-W1PxBE" + }, + { + "Q": "At ~6:20, shouldn't the second multiple choice said \"If \u00e2\u0088\u00a0AOC is rotated...\", not \"If Ray OA and Ray OC are rotated...\"? Because you can't rotate points, rays, lines, or line segments due to them not having a vertex, right?\n", + "A": "Yes, you can rotate those around a point/origin, actually.", + "video_name": "uYXhga17q1g" + }, + { + "Q": "\ni don't understand 2:20", + "A": "its just saying that 70% is equal to 100% - 30%", + "video_name": "d1oNF88SAgg" + }, + { + "Q": "\nWhy are we subtracting 0.30 from x at 1:59?\nI don't get it\nThis algebra is a bit confusing", + "A": "x would be considered the full price of the guavas, and you are subtracting 0.30 from it, as you are finding 30% of the full price. 0.30 is 30% in decimal notation, so by subtracting x by 0.30, you are finding the price after the 30% discount", + "video_name": "d1oNF88SAgg" + }, + { + "Q": "\nI noticed Sal uses x in his previous video, and then he uses it here at 1:40. I know x is the same as 1x, but why is 1 used instead of 2 or 3? Is 1 supposed to be the opposite of 0? Because in a number line, the numbers between 0 and 1 would be 0.01 to 0.99. Does 1 represent 100% in this case?", + "A": "Yes, x here represent 100%, that s why x is the same as 1x. Sal is just using x as a variable. You can use whatever letter you like, y, z, a, b, etc...", + "video_name": "d1oNF88SAgg" + }, + { + "Q": "At 3:21, why can we divide 12.60 by 0.7 to get the full price?\n", + "A": "The equation has 0.7 times x . To isolate x , we use the opposite operation. The opposite of multiplication is division. This is why Sal is dividing both sides of the equation by 0.7", + "video_name": "d1oNF88SAgg" + }, + { + "Q": "\nIn 1:13, why is sal putting it like -400w+1,100 instead of subtracting it like 1,100-400w?", + "A": "the first looks like slope intercept form, y = mx+ b", + "video_name": "2EwPpga_XPw" + }, + { + "Q": "At about 2:19, what is the word \"constraint\" used for? What exactly does that mean for this problem?\n", + "A": "A constraint is simply another word for a limitation or restriction of the possible set of solutions satisfying both equalities. While either equality will represent visually a different line on a graph or in other words a different relationship to each variable given a set of constants, the solution set is limited to the intersection of the equalities. Thus in a system of equations, additional equalities or equations represent further restriction of the possible set of all solutions.", + "video_name": "2EwPpga_XPw" + }, + { + "Q": "\nAt 0:33 if he did regroup instead of leaving it, would the outcome be the same or would it be different?", + "A": "If by outcome you mean the solution to 65*78 then yes, it would be the same.", + "video_name": "p0jCw2sqZgs" + }, + { + "Q": "At 0:24 why is that shape a parallelogram because I thought it was scalene how come it is a paralleogram I don't get it\n", + "A": "Sal says like a parallelogram . He doesn t mean to say that it IS a parallelogram. Hope that helps you understand! :)", + "video_name": "inlMrf2d-k4" + }, + { + "Q": "\nat 2:14 what does adjacent mean?", + "A": "Adjacent means that the two sides are directly next to each other. Not opposite in any way but connected.", + "video_name": "inlMrf2d-k4" + }, + { + "Q": "\nAt 0:10 Sal said that mathmeticians have looked at the way kites are drawn in cartoons, why would they do that? I thought that the kite that we fly and draw in cartoons was copied off the math kite.", + "A": "They tried to compare kites as a shape to something used in cartoons so they could see the new shape.", + "video_name": "inlMrf2d-k4" + }, + { + "Q": "Using the kite in the video, preferably looking around 2:00 , are the top left and bottom right sides parallel?\n", + "A": "Kites do not usually have any parallel sides. The only exception I know of is the rhombus (which, depending on how kite is defined is a special kind of kite).", + "video_name": "inlMrf2d-k4" + }, + { + "Q": "\nsorry for got time 5:01", + "A": "He said it can be an arbitrarily large number as long as it s greater", + "video_name": "UTs4uZhu5t8" + }, + { + "Q": "Starting at 3:35 sal subtracts to isolate the variable, but in previous videos, any time you subtract from both sides you have to change the inequality sign. Is that only done in a multiply or divide situation or did he just not switch the sign?\n", + "A": "Correct, do not change the direction of the inequality when you add or subtract a negative. Always change the inequality when you multiply or divide by a negative. 3 < 4 -3 > -4", + "video_name": "UTs4uZhu5t8" + }, + { + "Q": "\nAt 4:19 Sal says that sqrt(2) * sqrt(2) is 2. How does that work?", + "A": "We can multiply square roots. sqrt(2) * sqrt(2) = sqrt(4) What is the sqrt(4)? It = 2.", + "video_name": "s9ppnjgmiyk" + }, + { + "Q": "\nAt 3:40 Why does the the square root of 2 times 2 times the square root of 5 times 5 times the the square root of 2 equal 10 times the square root of 2? Shouldn't , sense, the square root of 2 times 2 is 2 and the square root of 5 times 5 is, it be 7 times the square root of 2?", + "A": "you re multiplying the square roots not adding them.", + "video_name": "s9ppnjgmiyk" + }, + { + "Q": "\nAt 3:18 what does Sal mean when he says that each triangle has 180 degrees?", + "A": "All of the internal angles of a triangle will always add up to 180\u00c2\u00b0.", + "video_name": "_HJljJuVHLw" + }, + { + "Q": "\nAt 10:28, why isn't the exterior angle 240 degrees, like a major arc in a circle?", + "A": "all exterior angles add up to 360 in any polygon. in regular polygons all exterior angles are equal. thus one angle=360/6=60", + "video_name": "_HJljJuVHLw" + }, + { + "Q": "At 2:44, Sal says there is a formula, but he doesn't reveal it. What is the formula?\n", + "A": "The sum of interior angles in an n-sided convex polygon is: 180(n - 2)", + "video_name": "_HJljJuVHLw" + }, + { + "Q": "\nAt 0:37, Sal gives a negative number as common ratio, so the terms are alternatively positive and negative. But a sequence usually has terms which keep increasing or decreasing, right?", + "A": "Sequences might usually keep increasing or decreasing, but there s no rule that says they have to. As Sal s example illustrates.", + "video_name": "CecgFWTg9pQ" + }, + { + "Q": "3:28 is there a symbol for not existing or for a false statement ?\n", + "A": "The not-equal-to sign, =/=, means that something does not equal something else. Another one to use is the naught sign, meaning that no possible solutions exist. It is denoted by a zero with a diagonal slash, like (/), only more circular.", + "video_name": "nOnd3SiYZqM" + }, + { + "Q": "3:27 If both limits must be equal for the whole limit to exist, what about in instances where there is a piecewise function like this, but with the filled-in dot continuous on one of the lines? As it is approached from either side, you will get different values.\n\nTherefore, for all piecewise functions, is the limit nonexistent at the discontinuity?\n", + "A": "Yes, if there is a discontinuity, or if the graph asymptotically approaches infinity, there is not limit. However, as you will soon learn (or maybe already have), there is a such thing as a one sided limit. For example the one sided limit of sqrt(x) approaching 0 from the right is 0, even though the whole limit does not exist at that point. I hope this helped.", + "video_name": "nOnd3SiYZqM" + }, + { + "Q": "\nAt 5:30, why does he say that the limit as x approaches 4 is 5 instead of -5?", + "A": "Because he made a mistake.", + "video_name": "nOnd3SiYZqM" + }, + { + "Q": "At 5:30 I think Sal made a speed mistake. The limit as x approaches 4 is equal to -5, not 5. Am I right? :)\n", + "A": "Yes, of course, and the correction is on there now :)", + "video_name": "nOnd3SiYZqM" + }, + { + "Q": "\nAt 3:13, sal says the limit does not exist. Does it mean that the graph is not possible, or that f(X) is not defined for that graph?", + "A": "Another way to think of the limit failing to exist at x=2 is that f(2) cannot be re-defined in such a way that the graph becomes continuous at x=2. In other words, the discontinuity in the graph at x=2 cannot be removed even if the value of f(2) is changed! Have a blessed, wonderful day!", + "video_name": "nOnd3SiYZqM" + }, + { + "Q": "\nwhy is it the matrix vector product and not the dot product at 13:00", + "A": "Because the dot products are for just one row and he s talking about the whole system.", + "video_name": "qvyboGryeA8" + }, + { + "Q": "\nAt 3:34, how does Sal know the triangle is a 30-60-90?", + "A": "Because of the sides. The basic 30-60-90 triangle has sides 2, 1, and sqr 3 (Watch Example: Solving a 30-60-90 triangle , Intro to 30-60-90 Triangles , 30-60-90 Triangles II ...), you can use them to find out angles and points on graphs, with this question, instead of 1 the side is 1/2, so to find the rest of the sides you simply half all the sides of the basic triangle and it is still a 30-60-90 triangle but now it fits the triangle on the graph and you can solve the problem.", + "video_name": "eTDaJ4ebK28" + }, + { + "Q": "can someone explain how sal gets to 3/4 ? at 4:03?\n", + "A": "He subtracts 1/4 from both sides.", + "video_name": "eTDaJ4ebK28" + }, + { + "Q": "\nAt 6:38, Sal says that, \"We need to restrict it's range to the UPPER hemisphere\". Why do we actually need to restrict it only to UPPER hemisphere?", + "A": "it is not mandatory that you have to restrict only the upper hemisphere. Anyways you have to restrict it to one hemisphere as there will be another value equal to it on the other hemisphere. Also as Sal said you could go one full round and have the same trig function value which would be unacceptable", + "video_name": "eTDaJ4ebK28" + }, + { + "Q": "\njust got confused after 9:06 .... HELP!", + "A": "x = f(f^-1(x)) - a minor correction: f^-1 goes before f(x) Cheers", + "video_name": "eTDaJ4ebK28" + }, + { + "Q": "\nfrom 3:30 , when sal defines the error fxn, he uses a term *'bound* how good is p(x) fitting in f(x)...\n\nBut what is meant by Bound and how is the error function bounded ?", + "A": "Being bound simply means that you know that a value is definitely between two limits. For instance, if 10 < x < 15, then x is bound between 10 and 15. You ll actually do that bounding in another video when Sal gets to questions like, how many terms do we need in order to ensure that our approximation is good to one part in a thousand? See my other answer above for an example of when you might look for error bounds in a physical world example as opposed to pure math.", + "video_name": "wgkRH5Uoavk" + }, + { + "Q": "\nis 3 x = 8 i at 1:01", + "A": "Not quite, actually 3 x = 9 at 1:01", + "video_name": "kbqO0YTUyAY" + }, + { + "Q": "\nAt 0:57 why does Sal write down 6 with a 1 above it and say six squared-isn't it(the drawing of six squared) supposed to be a six with a 2(instead of a 1) above it?", + "A": "it is a 2, but as the quality is low, it looks like a squished up 2 or a 1.", + "video_name": "nMhJLn5ives" + }, + { + "Q": "At 1:35 you said radical is 85 the radical?\n", + "A": "also i don t know about perfect squares but the square root of 85 can be simplified to 7 square root of 17", + "video_name": "nMhJLn5ives" + }, + { + "Q": "At about 3:12, do you mean James Grime from Numberphile?\n", + "A": "Yes, that is exactly what Vi meant.", + "video_name": "lA6hE7NFIK0" + }, + { + "Q": "\n@ 3:05, she mentions a type of infinity called \"aleph null\". Could someone help me out because I understand that there are multiple infinities, but what is \"aleph null\"?", + "A": "Aleph null is the smallest infinite cardinal number. A cardinal number is the type of number we normally think of when counting things: three videos, six A s, one question, and aleph null integers. Aleph null is defined to be the number of natural numbers.", + "video_name": "lA6hE7NFIK0" + }, + { + "Q": "How come at 1:28 it sounds like her voice is echoing?\n", + "A": "beacuse it is she is in an open room", + "video_name": "lA6hE7NFIK0" + }, + { + "Q": "At 3:11, what is listable infinity and who is Jason Grime?\n", + "A": "James Grime is a mathematician. He is often seen in several Numberphile videos, and his website is singingbanana.com. Listable infinity is his way of saying countable infinity, because the idea is that you can list the elements of a countable set, but you can t actually count them, because there are an infinite number.", + "video_name": "lA6hE7NFIK0" + }, + { + "Q": "\nWhat does the small hand represent in 13:11:4", + "A": "The small hand represents the hour; in this case it is pointing to nine.", + "video_name": "ftndEjAg6qs" + }, + { + "Q": "What is the elapsed time in start time 2:30 endtime 6:30\n", + "A": "the answer is 4:00", + "video_name": "ftndEjAg6qs" + }, + { + "Q": "\nat 2:57 how did you come up with x+y= 5?", + "A": "Looking at the scale to the right, you can see that one side of the scale has 5 blocks(of 1). The other side has a X block and a Y block. The scale is not tipped, therefore a X and a Y have the same weight/ equal 5. So x+y=5", + "video_name": "h9ZgZimXn2Q" + }, + { + "Q": "3:03 but how are you supposed to do this in the real world if you don't have a scale?\n", + "A": "x+y=5 is just a given, a tool for solving the original problem. Sal simply skips over explaining that fact. On a test or worksheet the problem might be presented as something like... Solve 2x+y=8 for x if x+y=5", + "video_name": "h9ZgZimXn2Q" + }, + { + "Q": "At about 3:00, where did he get the 5 from?\n", + "A": "On the left side of the scale, there is an x and a y cube. That s where he gets x + y from. On the right side of the scale, there s 5 yellow cubes. That s where he gets 5 from. x + y must equal 5, because that s how the scale is balanced.", + "video_name": "h9ZgZimXn2Q" + }, + { + "Q": "\nAt 1:40 why do you divide x^3-1 by x-1?\nWhy don't you divide it by x+1? Does it make a difference?", + "A": "Two reasons. First, factoring by (x + 1) doesn t get us anywhere, because our problem is how to find the limit at x = 1, which means we need to get rid of a factor of (x - 1), because that s the factor that gives us a zero in the denominator at x = 1. And second, (x + 1) isn t a factor of x^3 - 1. Try dividing it and you ll see that you get a remainder.", + "video_name": "rU222pVq520" + }, + { + "Q": "\nat 5:43, do the answers to the \"b\" value always end up as weird fractions (i.e. in the video 13/3)?", + "A": "Not always. The y-intercept can be any real number.", + "video_name": "XMJ72mtMn4Y" + }, + { + "Q": "At 4:28, would the answer be the same if you used other set of points?\n", + "A": "I am not sure what you are asking because through any two points there is only one line. If you give different points, unless they are on the same line, then you would get a different line.", + "video_name": "XMJ72mtMn4Y" + }, + { + "Q": "\nwhat did at sign that sal made mean? at 3:41?", + "A": "That the bisector was congruent to itself...i think..", + "video_name": "7UISwx2Mr4c" + }, + { + "Q": "\nAt 0:57, Sal mentioned angles ABC and ACB. How do I know what order to put the letters in? For example, how do I know to write angle ABC instead of angle CBA?", + "A": "no, order matters. the middle letter has to be the vertex", + "video_name": "7UISwx2Mr4c" + }, + { + "Q": "\nStarting around 2:40, I entered the same exact numbers into my calculator, 5*tan(65), and I got -7.350191288, instead of 10.7225346025. Any suggestions to what I could have done wrong?", + "A": "Your calculator is using radians, not degrees. You can probably change it in your calculator s settings (but I can t help you with that without knowing what calculator you have). You could could convert 65 degrees into 65*\u00cf\u0080/180 radians and enter 5*tan(65*\u00cf\u0080/180) to get the correct value.", + "video_name": "l5VbdqRjTXc" + }, + { + "Q": "\nAt 1:01 Sal says to use a trigonometric function. Since this is a right triangle, why can't you just use the Pythagorean Theorem?", + "A": "In order to solve for a side using the Pythagorean theorem, you would already have to know the lengths of 2 sides of a right triangle. In this case, you only know 1 length, so you must use the trig functions to solve for a side.", + "video_name": "l5VbdqRjTXc" + }, + { + "Q": "Wait a second.. what is the definition of the tangent of a number, what do you do with it? For example, at about 2:30, Mr. Khan finds the tangent of 65 degrees on his calculator. How does that work?\n", + "A": "If you have a right triangle with a 65 degree angle in it, then the tangent of 65\u00c2\u00ba is the ratio of the side opposite the 65\u00c2\u00ba angle to the side next to it.", + "video_name": "l5VbdqRjTXc" + }, + { + "Q": "At 2:50, Professor Khan used a TI-85 calculator to find the answer as 10.7. But, when I used my TI-84 calculator at home to find the answer, I got -7.4 (rounded to the nearest tenth). I also searched up on google \"5*tan 65\" and got -7.4 (rounded to the nearest tenth). Is there a reason for this?\n", + "A": "Make sure your calculator is set to use degrees. It is likely set to radians which would cause it to produce a different result.", + "video_name": "l5VbdqRjTXc" + }, + { + "Q": "\nat 2:50 he enters 5 times tangent of 65 into calculator and gets 10.72....\nwhen I enter the exact same thing.. I get -7.35....\nhave re-entered it over and over to ensure it's the same thing.\nsame result... yes it's the plain old \"tan\" function (not tan-1)", + "A": "Make sure you aren t in radian mode.", + "video_name": "l5VbdqRjTXc" + }, + { + "Q": "\nAt 5:54 , I believe Sal should have used the approximately equal sign (\u00e2\u0089\u0088) as opposed to the equal sign (=). Of course, it's a small difference so it could be my eyes, but did anyone else see it like I did?", + "A": "actually, he is correct because the problem clearly states to round to the nearest tenth. So his answer is exact when rounded to the nearest tenth.", + "video_name": "l5VbdqRjTXc" + }, + { + "Q": "Why is it, at 2:33, that the tangent was multiplied by 5?\n", + "A": "It was multiplied so the variable a would be isolated. It is just like in solving a regular algebraic equation- you isolate the variable first, then solve for it.", + "video_name": "l5VbdqRjTXc" + }, + { + "Q": "At 1:32, why didn't Sal use the Law of Sines?\n", + "A": "I don t know why. Using the Law of Sines would seem to make doing this problem quicker and easier. However, there are often several ways to do a problem, and maybe Sal just wanted to illustrate how to do this problem from basics (SOH CAH TOA).", + "video_name": "l5VbdqRjTXc" + }, + { + "Q": "\nat 1:30 does it matter if I use I use sin,cos,tan? in which situation would I use each one? If it does NOT matter, can I be sure that it's the same way with every other trig problem?", + "A": "In this situation, we know the length of the adjacent side, we know the angle is 65 degrees, and we want to find the length of the opposite side. It matters very much which trig function we use in every trig problem. Here, the tan of 65 degrees = opposite / 5, so we can solve for the length of the opposite side with opposite = 5*tan 65 degrees. Which trig functions we use depends on which parts of the triangle we know.", + "video_name": "l5VbdqRjTXc" + }, + { + "Q": "(at 2:38) Hi, can anyone please tell me how to plug your equation eg. 5*tan 65 into the calculator? I seem to have trouble doing it on the Khan Academy virtual calculator on the practice exercise.\n", + "A": "First, you make sure the calculator is in degree mode. Then, you hit the buttons 5 , x , tan , 6 , 5 , ) , and = and you should get the answer.", + "video_name": "l5VbdqRjTXc" + }, + { + "Q": "\nAt 5:30 you used the calculator to do 5/ (Cos 65) my calculator gets 0.422 when I do that and it is set in degrees.", + "A": "Cos(x) is always between -1 and 1 so you should never get an absolute value below 5.", + "video_name": "l5VbdqRjTXc" + }, + { + "Q": "During 1:34 he uses tangents but insted could you have figured out the other angle and then use law of sines\n", + "A": "He could have done that, but this lesson is using the basic trig functions. Additionally, using the Law of Sines would actually be slower.", + "video_name": "l5VbdqRjTXc" + }, + { + "Q": "1:22 I dont understand how did sal said difference is -2 please help\n", + "A": "Sal didnt mean -2, he meant -1. He said this because the whole number intervals on the graph are every other square and therefore look like its -2 but it is -1. It is negative because the slope goes down 1 unit or looking from the other way it goes left 1 unit.", + "video_name": "hoRISaqp1Po" + }, + { + "Q": "\nat 3:30 Sal says the slope for the limit from the positive direction of 8 is infinite. how does he know that?\nI thought the slop was -1.\ncan someone please help me?", + "A": "You re correct that the slope on the positive side of 8 is clearly -1. I m not sure if Sal worded that 100% correct. I would say the limit as h approaches 0+ would be -1. The limit at 8 does not exist because limit as h ---> 0- does not equal h---> 0+ So the infinite slope he is drawing applies only AT 8.", + "video_name": "hoRISaqp1Po" + }, + { + "Q": "\nA the time of the video, 1:13, it tells you the inverse of the slope. What i was wondering is since you have the coordinates and the inverse slope, why don't you put in into point slope form to satisfy the question? Since the equation is looking for the equation of line B, why cant you do it this way? is it still wrong to do so? Hopefully this has made sense... :)", + "A": "since the question does not say the answer has to be in slope-intercept form - then i guess that yes, simply putting the equation in point-slope form would be a correct answer", + "video_name": "TsEhZRT16LU" + }, + { + "Q": "\nat 2:20 he said 9 and 9 when it was 7 and 9", + "A": "yes, but it was actually at 2:14 hey, nobody s perfect, anyone can make a mistake", + "video_name": "LEFE1km5ROY" + }, + { + "Q": "on 1:50 does he keep adding them all together\n", + "A": "Sal is not adding them all together. What he is doing is using place value to determine what the tens and ones places should be. Re-watch the video from 0:32.", + "video_name": "LEFE1km5ROY" + }, + { + "Q": "2:14 he said 9 twice\n", + "A": "why ask me the same thing in a different way?", + "video_name": "LEFE1km5ROY" + }, + { + "Q": "\nAt 5:00, the whole equation is written and he is describing the point-slope form. In the original equation at 4:11, is it y - y1 and x - x1 or y - y2 and x - x2?", + "A": "Either point (x1, y1) or (x2, y2) (or any known point on the line) will work, because the slope between any 2 points on the line is the same.", + "video_name": "LtpXvUCrgrM" + }, + { + "Q": "At 6:17 and 6:20, Sal says \"-a finite number of values,\". What does finite mean?\n", + "A": "It means that the values are countable and not infinite. The numbers 1 to 10 are finite. Or 1 to one billion are also finite. Contrast that with an infinite number of values where any number up to infinity is allowed.", + "video_name": "dOr0NKyD31Q" + }, + { + "Q": "\nAt 08:32, does the fact that there will only be one value for Z make a difference for our discrete random variable?\n\nI ask because Y will have multiple values for the multiple students. I guess I can answer my own question because if the class contains one student then Y is equivalent to Z in that the random variable can only take on one value.", + "A": "A discrete random variable can have more than one value but the number of values it can be is limited. In the ant example the answer can be one of many whole numbers over a range or interval. If our interval is 0 to 1,000,000 the answer could be an integer in that range (say 52). However, there there cannot be 52.6583 ants born in the universe. Either an ant is born or it isn t. To be a continuous random variable it has be able to take on ANY value in the interval.", + "video_name": "dOr0NKyD31Q" + }, + { + "Q": "At 2:22, why does the Khan Academy guy say pre-algebra is necessary? I'm in Grade 11 summer school and I can barely pass it btw I'm 16 years old and I feel dumb :(.\n", + "A": "You are not dumb. Sal believe s in the growth mindset, a belief that no one is dumb.", + "video_name": "Zm0KaIw-35k" + }, + { + "Q": "\nHow long can pi go for? 30:00", + "A": "are you sure?", + "video_name": "Zm0KaIw-35k" + }, + { + "Q": "\nfigured out the answer at 0:30", + "A": "that is 1:63 newspapers per hour...... ;p", + "video_name": "Zm0KaIw-35k" + }, + { + "Q": "\nAt 0:21, how did you conclude that the sample standard deviation was 2.98? I understood the method you used to arrive at 17.17 for the sample mean, but in in order to find the t-statistic I must know how we got \"S\".", + "A": "The s is the sample s standard deviation.To find this take each data point subtract it by the mean(17.17) and square it. Then add it all together. finally divide that number by 10 and take the square root of that number. If you put into the calculator it would look like this: [ (15.6 - 17.17)^2 + (16.2 - 17.17)^2+.... ]/10 <-then take the square root of it and it will = 2.98.", + "video_name": "D2sMsmL0ScQ" + }, + { + "Q": "At 4:24, how are we able to bring the 5 to the outside of the integral?\n", + "A": "That is a basic property of limits and an integral is a limit problem. You can factor out any constant that is convenient to factor out, though you don t have to.", + "video_name": "QxbJsg-Vdms" + }, + { + "Q": "At around 5:10, Sal applies the power rule to x^-1, making it -x^-1. Should it not actually be -x^-2, since you are supposed to subtract 1 from the exponent. Also, would the expression not turn positive, since there is a negative numerator and a negative denominator? Thanks for any help.\n", + "A": "The power rule for integrals is the reverse of the power rule for derivatives, so you add 1 to the exponent, you don t subtract. There is no negative coefficient in the numerator, so that should be negative. The power rule for integrals, then is: \u00e2\u0088\u00ab u \u00e2\u0081\u00bf du = [ u\u00e2\u0081\u00bf\u00e2\u0081\u00ba\u00c2\u00b9 / (n+1) ] + C", + "video_name": "QxbJsg-Vdms" + }, + { + "Q": "\nwhat if at 4:35 i do not take 5 out of the antiderivative operator and then just operate it simply, it gives me a result -5x^(-1) +C . can anyone tell me why is this wrong?", + "A": "Why would you think it is wrong. You got the same result as Sal by a slightly different method. Whether or not to factor the coefficient outside the integral sign is purely stylistic. I think it makes for less clutter, and anything that reduces the clutter of integration is welcome.", + "video_name": "QxbJsg-Vdms" + }, + { + "Q": "\nAt 2:52, why is n not allowed to be equal to -1?", + "A": "Because then you would be dividing by zero.", + "video_name": "QxbJsg-Vdms" + }, + { + "Q": "At 3:49, to check to see if the derivative of (x\u00e2\u0081\u00b6/6)+C is in fact x\u00e2\u0081\u00b5, why don't you use to quotient rule? Shouldn't the derivative be 6(x\u00e2\u0081\u00b6/6) * [(6*6x\u00e2\u0081\u00b5- 0*x\u00e2\u0081\u00b6)/ 6\u00c2\u00b2]? Which equals x^11, not x\u00e2\u0081\u00b5.\n", + "A": "There is no reason to use the quotient method here, but the rules will always work is used correctly (unless you end up with an undefined answer) The problem with your math is that when you multiply x\u00e2\u0081\u00b6 times zero that term goes away. So you end up with 36x\u00e2\u0081\u00b5/36", + "video_name": "QxbJsg-Vdms" + }, + { + "Q": "\nat 1:15, why did you not apply the derivative rule for division? It is supposed to be (f'(x)g(x) - f(x)g'(x))/(g(x))^2", + "A": "keep in mind n is a constant, so n+1 is a constant f(x)=((x^(n+1))/(n+1) by quotient rule: f (x)=(x^(n)*(n+1))-(0*x^(n+1)) f (x)=((n+1)(x^n))-0 f (x)=(n+1)(x^(n) same, see?", + "video_name": "QxbJsg-Vdms" + }, + { + "Q": "So at around 5:18, if you ended up with -5x^-1 + 5c, would that still be correct?\n", + "A": "Yes, and I think Sal mentions this around 5:15 in the video. However, since 5 times a constant C is just another constant, we get in the habit of writing a different variable name (C_1) instead of 5C.", + "video_name": "QxbJsg-Vdms" + }, + { + "Q": "\nWhen he explained about the CF is equal to 9, i did not understand that well. I did not understand how CF is equal to 9 at 6:31. Please help me as my english isn't good", + "A": "CF corresponds to AB (which has a length of 9) on a similar triangle. Therefore, there is a proportional relationship between the two. CF is actually equal to 36/7, not nine, but it is proportional to nine.", + "video_name": "7aGEvpHaNJ8" + }, + { + "Q": "\nThere is a \"Acute\" angle in 5:35. A to C and E :)", + "A": "Rays EA and EC do make an acute angle. You would call it angle AEC. Always put the letter of the center point of the angle in the middle of the angle name.", + "video_name": "w9jEq6dmqPg" + }, + { + "Q": "at 2:53, can the rays CE and CF also be written CEF or FEC?\n", + "A": "No because you only use two points to identify a ray, using all three points means you are talking about an angle", + "video_name": "w9jEq6dmqPg" + }, + { + "Q": "\nAt 2:38, can you express the ray as ray CEF?", + "A": "No. You only use two points to express a ray. For example ray CF or ray EF or ray EC. If you use three points you are expressing an angle, in this case a straight angle.", + "video_name": "w9jEq6dmqPg" + }, + { + "Q": "\nFrom 0:34 and onward, he starts to talk about how you can tell if it is an axis of symmetry. Can you do this with any shape? How about with a circle??", + "A": "You don t need to worry. From 0:34, Sal started talking about that cause the topic is axis of symmetry. You always find a line of symmetry in every basic shape you find. But it is not important that there is axis of symmetry in every shape. I hope this helped!", + "video_name": "LrTn4cvsewk" + }, + { + "Q": "\nAt 3:04 why does it continue after that?", + "A": "It doesn t, it ends at 3:04.", + "video_name": "jb8mFpA1YI8" + }, + { + "Q": "\nAt 11:15, Sal mistakenly wrote 2.5, when it was supposed to be 2.9.", + "A": "Good catch! If you look, you ll even see a little note in the lower left corner about the mistake.", + "video_name": "i6lfVUp5RW8" + }, + { + "Q": "At 11:15 instead of 2.5 isn't it suppose to be 2.9\n", + "A": "That is a known error in the video. A box pops up and tells you the error and provides the correct value of 2.9", + "video_name": "i6lfVUp5RW8" + }, + { + "Q": "\nAt 0:25 I wanted to know when was scientific notation even invented?", + "A": "not hepfull flaged", + "video_name": "i6lfVUp5RW8" + }, + { + "Q": "At 10:10 we have 5 digits. Is there any limit as to the total number of digits we can have? How does this affect significant figures?\n", + "A": "Nope. There are no limits. The more digits you have, the bigger the exponent of 10 needs to be. The rules for significant figures aren t affected.", + "video_name": "i6lfVUp5RW8" + }, + { + "Q": "\nAt 0:47, Sal says 15 to 25.\nShouldn't he say 25 to 15 ?", + "A": "He can say 15 to 25 or 25 to 15, it depends on him, because the order in which you say ratios doesn t really matter.", + "video_name": "jNUz0P5MG9M" + }, + { + "Q": "at around 3:30, Sal siad for the second equation that why is ewual to NEGATIVE 1x +5. Why is that? Shouldn't it be positive?\n", + "A": "No, it should not, the reason for this is that the x(1x) was already negative in the equation. The original form of the equation looked like this y<5 -x(1x) , the only thing Sal did was rewrite the equation to look like the one above it. So he moved the x(1x) to the front of the equation taking the negative sign with it y< -x(1x) +5. When you rearrange an equation the signs of numbers remain to keep the problem balanced.", + "video_name": "CA4S7S-3Lg4" + }, + { + "Q": "\nAt 3:14 Sal said that y is equal to 5-x even though it said y is less then 5-x?", + "A": "At 3:14 Sal is talking about the boundary line, not the area. That s why he says equal to.", + "video_name": "CA4S7S-3Lg4" + }, + { + "Q": "At 4:30, when zero is said to be undefined, how come no one of the many mathematicians over the years were able to define it? Why is it so disputed over? Humans as a whole, over the many years of their existence weren't able to do so?\n", + "A": "Sal says a number divided by zero is undefined, not zero itself. The reason a number divided by zero is undefined is because no such number exists. The value of a number divided by zero is infinite.", + "video_name": "bQ-KR3clFgs" + }, + { + "Q": "At 4:45 he says zero is undefined. Does that mean its not negative of positive?\n", + "A": "Its neither. An integer is a whole number that can be either greater than 0, called positive, or less than 0, called negative. Zero is neither positive nor negative. Two integers that are the same distance from the origin in opposite directions are called opposites.", + "video_name": "bQ-KR3clFgs" + }, + { + "Q": "In algebra, why just not use the letter X so you can still use it for multiplication? 2:05\n", + "A": "It s just that x happens to be very common, if you don t like the use of x, you can use any other variable, like j .", + "video_name": "bQ-KR3clFgs" + }, + { + "Q": "\nAt 0:42 why is the answer negative if the bigger number is positive?", + "A": "It doesn t matter if the bigger number is positive or not. If you re dividing (or multiplying) and exactly one of the two numbers is negative then the answer is negative.", + "video_name": "bQ-KR3clFgs" + }, + { + "Q": "At 2:30, what does \"factoring out the negative sign\" mean? How do you factor out a negative sign? I also had a problem with this in \"Manipulating linear expressions with rational coefficients,\" in Algebra. I never understood how to do it.\n", + "A": "area of each interior angle = 180 (5-2)/5 = 108, so area of each exterior angle = 180-108 = 72, so area of five exterior angle = 72*5 = 360, Am I on the right track?", + "video_name": "95logvV8nXY" + }, + { + "Q": "at the time 2:02 in the video, i don't understand what he was doing? Can anyone help me please!\n", + "A": "In this section at 2:02, he is finding the 4th root of 16 or \u00e2\u0088\u009c16 The 4th root of something is a number multiplied by itself 4 times to equal that something Well, at that time after factoring 16, he has \u00e2\u0088\u009c2\u00e2\u0088\u00992\u00e2\u0088\u00992\u00e2\u0088\u00992 written and he is talking about finding the 4th root of 2 times 2 times 2 times 2 We are looking for a factor that occurs 4 times, and there it is! We can see that 2 is a factor of 16 four different times, so \u00e2\u0088\u009c16 = \u00e2\u0088\u009c2\u00e2\u0088\u00992\u00e2\u0088\u00992\u00e2\u0088\u00992 = \u00e2\u0088\u009c2\u00e2\u0081\u00b4 = 2 And that is how he got the 2", + "video_name": "iX7ivCww2ws" + }, + { + "Q": "I do not entirely understand the rules in regards to a specific exponent being rewritten as a specific corresponding square root. Ex: The square root of 25= 25^1/2 power. I am absolutely lost after this point: 6:35. Are there any videos that explore this further and in greater detail? Thanks!\n", + "A": "Basically, when a number is raised to a fractional power, it is asked for that specific root. EX: 1/2 power= square root 1/3 power = cubed root", + "video_name": "iX7ivCww2ws" + }, + { + "Q": "\nAt 6:20, why does the sixth root of X^6 equal X and not the absolute value of X?", + "A": "It depends on whether or not the radical is given in the equation or if you need to insert it. If the problem has a radical shown, then you assume it is positive (what Sal did). If you are solving the problem and you introduce a radical, then you could have both the positive and negative option (so the absolute value).", + "video_name": "iX7ivCww2ws" + }, + { + "Q": "\nAt 3:10 Sal says that each of the objects became two groups. Exactly how are they in two groups? I'm having a hard time visualizing the two groups. I get how he divided each circle in half groups, but the 2 groups he mentions at the very end, I cannot see. Please help. Thanks.", + "A": "Oh wait, I just saw it. The four circles were split in two.", + "video_name": "tnkPY4UqJ44" + }, + { + "Q": "\nat 12:47pm. What if you are multiplying a whole number by a fraction", + "A": "Let s do 7 \u00c3\u00b7 3/4 Change the whole number into a fraction: 7/1 \u00c3\u00b7 3/4 Then change division to multiply by using the reciprocal of 3/4: 7/1 * 4/3 Multiply: 28/3 = 9 1/3 Hope this helps.", + "video_name": "tnkPY4UqJ44" + }, + { + "Q": "\nAt 0:21, cant you divide by 5?", + "A": "At 0:21 you could divide =)", + "video_name": "D1cKk48kz-E" + }, + { + "Q": "At 0:33, couldn't you divide by -5?\n", + "A": "You could, however, some people consider it easier to multiply. Dividing by -5 is the same as dividing by -5/1. You can multiply the inverse -1/5 if you find multiplication easier.", + "video_name": "D1cKk48kz-E" + }, + { + "Q": "At 1:13, why does Sal flip the inequality sign? PLEASE HELP!\n", + "A": "We solve inequalities almost exactly the way we solve equations. The one exception is that if we multiply or divide by a negative, we have to reverse the inequality. Let s look at what happens if we don t. Start with: -4 < 12 This is current true. If we divide both sides by -2, what happens? -4/(-2) < 12/(-2) 2 < -6 This is no longer true. 2 is a larger number than -6. This is why we reverse the inequality. It is needed to maintain the integrity (truth) of the inequality. Hope this helps.", + "video_name": "D1cKk48kz-E" + }, + { + "Q": "0:25. Why would it be one fifth and not 5?\n", + "A": "-5 is the coefficient of c, not a subtraction from c. If it were -5+c or c - 5,, then the opposite would be to add 5. since the 5 and c are adjacent, it means multiply (which is what a coefficient is), so the opposite of multiplying by -5 is to divide by -5 which is the same as multiplying by (-1/5).", + "video_name": "D1cKk48kz-E" + }, + { + "Q": "at 1:36 why did you shade in 2 whole halves an only 1/2 on the others?\n--------------------------------------------------------------\n", + "A": "because, we have to add 1/2 (means half) 5 times", + "video_name": "4PlkCiEXBQI" + }, + { + "Q": "\nAt 3:10 he writes the value of pi = 3.14, but Sal uses it as a reference for radians, isn't the 3.14 value in degrees? I mean he says that 3 radians is close to 3.14. So basically I'm asking what measure are we using in normal arithmetic, degrees right? If so, how come he compared 3 radians to 3.14 ,what are presumebly, degrees? Please tolerate any ignorance you come across in my question, I'm simply trying to understand the concepts.", + "A": "Pi is simply a mathematical constant. It does not have any default units attached to it. The number 5 is not in degrees or meters, it is just the number 5. The same with pi.", + "video_name": "fYQ3GRSu4JU" + }, + { + "Q": "\nDoesn't Koch's snowflake and Mandelbrot's famous shape already address your concept of an \"infinigon/zigfinigon\" as seen around 03:09?", + "A": "She does say something fractally at 03:35 which again Koch and Mandelbrot takcle the fractal field with their well known shapes.", + "video_name": "D2xYjiL8yyE" + }, + { + "Q": "\nAt 3:24, your creating a pentagram, right?", + "A": "If you mean the five-sided shape she ended up with after the Zigfinite star then that s a pentagon. If not, can you explain better what you mean?", + "video_name": "D2xYjiL8yyE" + }, + { + "Q": "\u00e2\u0088\u009a4 is 2. But at about 2:45, it says \u00e2\u0088\u009a2 is 2. How is this possible?\n", + "A": "This is a joke, sometimes called sophistry. In fact, angular line will never be straight, so it s proof that the square root of 2 is 2 does not work =)", + "video_name": "D2xYjiL8yyE" + }, + { + "Q": "I did the drawing she does at about 2:50 and then divided the squares I got into right triangles and squares, and divided those squares into right triangles and squares, and so on... The top half ended up looking like Serpinsky's triangle. I encourage you to try it for yourself. Also, does anyone know why it looks like Serpinsky's triangle?\n", + "A": "She is really good at doodling :P", + "video_name": "D2xYjiL8yyE" + }, + { + "Q": "Why can't you just square root the whole hypotenuse formula? For example, at 1:50, instead of squaring 15, 8, and x, why can't you just use 15+8=x?\n", + "A": "That will not get us the right answer. 15+8=23, but x=17. You have to square both numbers, add them together, and only then take the square root.", + "video_name": "T971zHhZ3S4" + }, + { + "Q": "\nat 4:08, why did he flip the left side?", + "A": "He did that to get t up top . He inverted both sides of the equation which is a valid thing to do. Here is why the flip is valid: start with a / b = c / d => ad = bc (multiplied both sides by b, then by d) => d / c = b / a (divided both sides by c, then by a)", + "video_name": "gD7A1LA4jO8" + }, + { + "Q": "At 3:08 and 5:38, how did Sal know what the graphs of the functions would look like?\n", + "A": "Lots of practice... different types of equations create specific graphs. f(x) = x^2 is a quadratic equation. It creates a U-shaped graph. g(x) = x is a linear equation. It creates a line for a graph.", + "video_name": "96uHMcHWD2E" + }, + { + "Q": "What are oulpuls at 1:45- 1:55\n", + "A": "Outputs , with the crosses on the t s not drawn well.", + "video_name": "96uHMcHWD2E" + }, + { + "Q": "\nAt 4:35, Is zero a \"non-negative\" number? Is it also non-positive?", + "A": "Yes, 0 is neither positive nor negative. If you were to add 0 to any number, let s say x, it would not increase nor decrease its value.", + "video_name": "96uHMcHWD2E" + }, + { + "Q": "\nThe Formula Sal derives for m at 13:00min is not the same as the formula he derived in a previous video for m(Proof part 4 @ 3:00min) They seem to be negatives of each other.. Am I missing something?", + "A": "What would happen if you multiplied both the numerator and denominator by -1?", + "video_name": "ualmyZiPs9w" + }, + { + "Q": "\nWhere exactly did that x+3 go whenever it was originally at the top of the fraction at 2:09? Was is just replaced by A and B? If so how & why...?", + "A": "The answer to your question starts at 7:20.", + "video_name": "S-XKGBesRzk" + }, + { + "Q": "\nAt 1:20, is Sal taking the anti-derivative of the derivative of f(x)*g(x) ? So they just cancel out? Like if you had (sqrt(X))^2 and you are just left with X. Is that pretty much the same thing that is going on at that point?", + "A": "Whether they cancel out depends on what f(x) and g(x) happen to be. Integration by parts is quite useful if you need to integrate a complicated function that would be exceedingly difficult to try to integrate altogether.", + "video_name": "dh__n9FVKA0" + }, + { + "Q": "Isnt integral of f'(x) is f(x) just like at 2:42\n", + "A": "yes it is\u00e2\u0080\u00a6as d/dx of f(x) Is f (x)", + "video_name": "dh__n9FVKA0" + }, + { + "Q": "\nAt 0:09, Sal said that 35 doesn't goes into 6. Did he purposely choose a number with a remainder?", + "A": "He likely did. He s trying to demonstrate decimals. Since decimals are fractions, there needs to be a remainder to create a decimal value.", + "video_name": "xUDlKV8lJbM" + }, + { + "Q": "02:29 Why did Sal use K instead of Z?\n", + "A": "I quickly checked the timestamp out. I assume he did so as you can use any letter that isn t already used in this situation. No special reason.", + "video_name": "lHdlHTsXbZg" + }, + { + "Q": "\nAt 1:59 Sal says x can not be equal to zero. Why does x have to be a non-zero number? If it could be zero, couldn't 0/0 = 0? Is there any reasoning as to why x can not equal zero, or is it just to enforce other reasoning as to why 0/0 is impossible?", + "A": "At that point it s just the boundaries of the current proof he was laying out. Later on he does another proof where 0/0=0, however that comes from multiplying the constant on the right side of the equation by 0. That constant can be any number between infinity and negative infinity, so it is indeterminate.", + "video_name": "lHdlHTsXbZg" + }, + { + "Q": "At @6:19 he says that he wanted to come up with a number for k, but k is already defined by 0/0 so shouldn't there be no problem since he already defined k?\n", + "A": "It s because he wants to come up with a single number for k, but he can t seem to find one. So he still technically calls it indeterminate.", + "video_name": "lHdlHTsXbZg" + }, + { + "Q": "\nAt 5:05, why isn't the antiderivative of dw just w? The dw completely disappears, which confuses me.", + "A": "The indefinite integral of only dw is just w (+C, of course). However, he didn t just take the indefinite integral of dw. He took the indefinite integral of (e^w)dw. The derivative of e^w+C is e^w, so the indefinite integral of (e^w)dw is e^w+C. Because there s a -1/5 in front of the integral, we must multiply the whole expression by -1/5. This results in -1/5(e^w)+C (-1/5 times a constant is still a constant). I hope this explains what Sal did!", + "video_name": "ShpI3gPgLBA" + }, + { + "Q": "@ ~2:20-2:33, we have (1/5)\u00e2\u0088\u00ab(1/e^u)du,\n\nwhy can't we use w substitution on the e^u?\n", + "A": "I tried my, and got a different answer, or maybe just another form of the answer? Thanks a bunch for your help :)", + "video_name": "ShpI3gPgLBA" + }, + { + "Q": "6:01 What is the principle root?\n", + "A": "When you take a square root, you have two branches; a positive branch, and a negative branch. For instance, x\u00c2\u00b2 = 9 implies that x = \u00c2\u00b1 3 because (-3)\u00c2\u00b2 = 9 and 3\u00c2\u00b2 = 9 also. The principle square root is the positive branch.", + "video_name": "q7eF5Ci944U" + }, + { + "Q": "At 1:15 did anyone notice that the two smaller right triangles make a bigger right triangle\n", + "A": "Doesn t work as a proof.", + "video_name": "q7eF5Ci944U" + }, + { + "Q": "\nAt 3:00, couldnt you also say that triangle AMO is congruent to triangle CMO by aas", + "A": "If you did that, you d either need to prove that angle A is congruent to angle C or that angle AOM is congruent to angle COM. I don t see any obvious reason to believe that either of those is true, or at least nothing that is as obvious as proving that AO is congruent to CO or that MO is congruent to itself.", + "video_name": "q7eF5Ci944U" + }, + { + "Q": "\nAt 5:00 and on, I still don't understand how you can get a pentagon by slicing it through once.", + "A": "And you would need to have a blade that is bigger than the sides of the cube so there would be parts where the blade can exit the cube before you finish cutting.", + "video_name": "aSokFEpoJFM" + }, + { + "Q": "at 5:35 how do you make that pentigon in one slice\n", + "A": "He uses different cuts to obtain the shape of a pentagon, the sides can be expanded to show a plane cutting into the cube. think of the solid lines as lines you can see, and think of the dotted lines as you cannot see, the front two solid lines on the pentagon you can see are lining up with the faces of the cube and the plane is tilted at an angle", + "video_name": "aSokFEpoJFM" + }, + { + "Q": "\nSal said at 2:34 that the range is limited to the first and fourth Quadrants. Why wouldn't 2.80 radians be excluded from this set?\nPerhaps he misspoke, because all positive values for y, (sin), would actually be in the first or second quadrants, correct?", + "A": "Sal didn t misspeak. If 2.80 were in the range of arcsine, then the arcsine function would be multivalued. If we allowed values in the first and second quadrants, there would be two values that every input could map to; one in the first quadrant and one in the second.", + "video_name": "NC7iWEQ9Kug" + }, + { + "Q": "\nAt 0:42, when Mr. Khan says \"nesting\", is he trying to say a function within a function? This looks almost like combining, but I know it really isn't. So what exactly is composing, and what is the main difference between composing and combining?", + "A": "Composing function- applying one function to the results of another...In other words he s replacing x as the results of another function (eg. replace f(x) with f(g(2)), which is also equal to f(-3)", + "video_name": "wUNWjd4bMmw" + }, + { + "Q": "\nAt 4:39\nlog\u00e2\u0082\u0083(27x) as log\u00e2\u0082\u0083(27)+log_3(x), which is simplified as 3+log\u00e2\u0082\u0083(x)\nI mean why is that? cause log\u00e2\u0082\u0083(27) suppose to be log\u00e2\u0082\u0083(3^3), then =3 log\u00e2\u0082\u00833", + "A": "Your work is ok so far, but is incomplere as 3 log\u00e2\u0082\u00833 can be simplified: `3 log\u00e2\u0082\u00833 = 3*1 = 3. Remember, 3^1 = 3. So, log\u00e2\u0082\u00833 = 1. Hope this helps.", + "video_name": "pkGrXzakRFs" + }, + { + "Q": "\nAt 4:11, how does one know that the arc that subtends 'theta' is equal to r?", + "A": "Sal is just defining what a radian is. It is simply the measure of a central angle that subtends an arc equal in length to the radius.", + "video_name": "EnwWxMZVBeg" + }, + { + "Q": "\nAt 3:13, what does he mean by \"theta\"? I can't seem to understand what it means.", + "A": "Theta is the eighth letter of the greek alphabet. Greek letters are commonly used as variables in higher math.", + "video_name": "EnwWxMZVBeg" + }, + { + "Q": "\nDoes theta at 3:14 mean anything it stands out in a weird way", + "A": "Not really, it s just used a lot in geometry and trigonometry to indicate angles for whatever reason. It s no different than if you d call it angle x or angle z.", + "video_name": "EnwWxMZVBeg" + }, + { + "Q": "\nAt 01:14 sal asks what are the theories. What I guessed was I think that since our earth almost takes 360 days around the sun to complete one revolution thats why we said one complete revolution or rotation is 360 degress. Am iCorrect?", + "A": "Woohoo I placed my guess and it was correct... It was just a guess!", + "video_name": "EnwWxMZVBeg" + }, + { + "Q": "\nat 3:22 he calls the angle theta... what does that mean? does it represent a certain angle measure, position, etc?", + "A": "That is a Greek letter named Theta. In mathematics and science disciplines, Theta is often used as the variable representing an angle measurement. You will see it very often used this way.", + "video_name": "EnwWxMZVBeg" + }, + { + "Q": "\nAt 3:17 what does theta mean? Is it just a name for any angle, or does it have to be a specific angle to be \"theta\"?", + "A": "Theta is just like an angle labeled as x. Mathematicians commonly use letters of the greek alphabet to label angles.", + "video_name": "EnwWxMZVBeg" + }, + { + "Q": "\nSo, basically every degree amount will have the same amount of radians no matter the circle? So every circle is 2pi(r) radians? Is that what this is about? 7:00", + "A": "Yes. Since radians are just a way of measuring angles, like degrees, they stay the same no matter the size of the circle. As a circle always has 360 degrees around the point, it always has 2pi radians.", + "video_name": "EnwWxMZVBeg" + }, + { + "Q": "At 4:23, what does Sal mean when he says that the ratio can be represented as a function of n?\n", + "A": "What Sal means is that your attention should be drawn to the fact that the ratio ((n+1) term over (n) term) dos not simplify to a constant ratio because it has a variable n in it. What it simplifies to is a ratio which is itself a function of the terms in question (the a sub n in question). Hope this helps!", + "video_name": "av947KCWf2U" + }, + { + "Q": "\nYou can't prove that n^10/n! doesn't diverge with the divergence test as stated in 2:40 because lim an = 0 so it can still diverge ou converge. Or am I wrong?", + "A": "Absolutely correct, a series such as 1/n (harmonic series) diverges, even though the limit as n goes to infinity leads to 0 for an, so Sal made a mistake.", + "video_name": "av947KCWf2U" + }, + { + "Q": "At 2:20 what did Sal mean by you can rewrite this.\n", + "A": "What he actually means in 2:20 is that -15.08+526.90 is the same thing as saying 526.90-15.08. If you are careful with the numbers, you can rearrange the numbers in an equation for simplification!", + "video_name": "fFdOr8U4mnI" + }, + { + "Q": "0:07, Sal says that Stewart has a checking account with a balance of -$15. Does this mean that Stewart owes money?\n", + "A": "Yes, he does.", + "video_name": "fFdOr8U4mnI" + }, + { + "Q": "\nAt 3:38, I don't understand why you wouldn't just divide 9 into 2 and have the quotient of 0.22 there instead of \"borrowing\" the 10.\nI calculated 0.22*10^14 which would simplify to 2.2*10^13\nSo i would have gotten it wrong unless i \"borrowed\" the 10 during my calculation.", + "A": "0.22 x 10^14 is numerically correct, but it isn t valid scientific notation. A number which is written in scientific notation must have the mantissa (the bit before the power of ten) greater than or equal to 1, and less than 10. Here, 0.22 is not greater than or equal to 1, so it fails that test. So although 0.22 x 10^14 = 2.2 x 10^13, only the latter is correct scientific notation.", + "video_name": "0lOpqmTdtzk" + }, + { + "Q": "\nAt 1:28, Sal talks about tuples. This makes me think of \"quintuples,\" except the \"tu\" is pronounced differently. Is that where \"tuples\" comes from? Where does the term \"tuples\" come from?", + "A": "From Wikipedia: The term originated as an abstraction of the sequence: single, double, triple, quadruple, quintuple, sextuple, septuple, octuple, ..., n\u00e2\u0080\u0091tuple, ..., where the prefixes are taken from the Latin names of the numerals. Although this treats \u00e2\u0080\u0091tuple as the suffix, the original suffix was \u00e2\u0080\u0091ple as in triple (three-fold) or decuple (ten\u00e2\u0080\u0091fold). This originates from a medieval Latin suffix \u00e2\u0080\u0091plus (meaning more ).", + "video_name": "lCsjJbZHhHU" + }, + { + "Q": "\nAt 2:20 how come you do not get rid of the exponent after you square 2x^2? Is it because it still contains a variable? because after you squared (8)^2 = 64 ...no more exponent, but when you square (2x)^2, it turns into 4x^2?", + "A": "In (2x)^2, both the 2 and the X have to be squared. We can calculate 2^2 = 4. But, we don t know the numeric value for X. So, we can t calculate X*X. We just write it in exponent form: x^2. (2x)^2 = (2x) (2x) = (2*2) (x*x) = 4x^2", + "video_name": "h6HmHjkA034" + }, + { + "Q": "at 1:27 Sal said milli ment 1,000 shouldn`t it mean 1,000,000\n", + "A": "milli means one thousandth, micro means one millionth. :)", + "video_name": "mI84WDfhuYA" + }, + { + "Q": "At 11:40, can (0,0) on a graph be both a x-intercept and a y-intercept?\n", + "A": "Yes. (0,0) is an x-intercept and a y-intercept. We call this point the origin.", + "video_name": "_npwsLh0vws" + }, + { + "Q": "\n1:20 WHAT did it mean infantine set of eyes", + "A": "There are infinite y values.", + "video_name": "_npwsLh0vws" + }, + { + "Q": "4:54 i think he showed wrong direction of resultant vector c it should be from tail of a to head of b which is shown wrong i think\n", + "A": "You might want to listen more closely to what Sal was saying. In the second example he was working, the vector C he was using was NOT the sum of vectors A and B. Once he switched directions as you suggest to create the vector -C he then set up the equation A + B = -C.", + "video_name": "BsBH8nAv5l4" + }, + { + "Q": "\nIf Vector A - Vector B =Vector D in 4:08 then Vector B - Vector A= -Vector D ??", + "A": "Yes it is. Just , you are multiplying -1 to the whole equation.", + "video_name": "BsBH8nAv5l4" + }, + { + "Q": "\nwhere did u get 144 on 03:54????", + "A": "it is given that the side of the square is 12 and hence the area of the square is 12*12=144.....", + "video_name": "vaOXkt7uuac" + }, + { + "Q": "At 8:15, How does Sal get 25 roots of 3, divided by 2? I don't get where 2 came from.\n", + "A": "The 2 comes from the equation for the area of a triangle, 1/2 times the base times the height, or [1/2bh]. He divides it by 2 because that is the 1/2 in action. The base is 5 and the height is 5\u00e2\u0088\u009a3. So, the area is (25\u00e2\u0088\u009a3)/2, which could also be simplified to 12.5\u00e2\u0088\u009a3.", + "video_name": "vaOXkt7uuac" + }, + { + "Q": "\nAt 0:42, Sal says that the two angles are supplementary. In a real proof, wouldn't we not be able to assume that unless it was given?? Or do the opposite arrows show that it is a horizontal line?", + "A": "The arrows do indicate that it is a line. So the angles are supplementary.", + "video_name": "eTwnt4G5xE4" + }, + { + "Q": "At 3:44 Sal mentions the \"Exterior angle of 121 to be equal to the sum of the remote interior angles.\" This somehow confuses me as I don't remember him mentioning it before in previous videos. Is this true? If so does any exterior angle of a triangle mean that its equal to the triangles interior angles? Thanks in advance!\n", + "A": "Yep!! I can t remember the name of the postulate/theorem that says this, but it is definitely true. Any exterior angle of a triangle is equal to the sum of its remote interior angles (the two interior angles that are across from the exterior angle in question). Hope this helps!! :)", + "video_name": "eTwnt4G5xE4" + }, + { + "Q": "\nat 2:46, i notised that the angel he was trying to solve enisally is about the the same as the one he is going to solve.", + "A": "Well ya, but there is an even easier way to solve for x. 180-121 is 59. So now we know the angle next to 121. There is another line with the same slope on the other side, so we know the corresponding angles are the same. Therefore we know that x is 59. So Simple.", + "video_name": "eTwnt4G5xE4" + }, + { + "Q": "\nWhy in the first place, would you need to find for example an inverse of a matrix like Sal said at 3:40, or a determinant, or add or subtract matrixes?", + "A": "The why is the means to find solution(s) to matrix operations.", + "video_name": "0oGJTQCy4cQ" + }, + { + "Q": "At 1:55 in the video, why is it 72 * 7? I understand that 72 is the (9 * 8 * 7) part, but why is it multiplied by seven? Is it because there is only 7 people left after the 3 positions are filled?\n", + "A": "72 is just the 9*8 part. He multiplied it by 7 because he wasn t done with the whole multiplication of 9*8*7.", + "video_name": "l9ft9jpriNA" + }, + { + "Q": "How do you tell the quadrants apart at 0:40\n", + "A": "the quadrants are usually labeled", + "video_name": "Jeh5vudjmLI" + }, + { + "Q": "At 2:55, I cannot understand how does ln(67)=4.205 approximately matches between 2 and 3. plz help:(\n", + "A": "If we let ln67 = a then e^a = 67 by definition of a logarithm e by definition is about 2.71 I think If we round the 4.2 down for approx. 2^4 = 16 and 3^4 = 81 Therefore since e = 2.71 which is in between 2 and 3 we expect e^4 to be in between 16 and 81, which it is.", + "video_name": "Dpo_-GrMpNE" + }, + { + "Q": "At 5:00 in the video, why does Mr. Khan place positive 2 in the x place, if the x value was -2? Was that a mistake or something else?\n", + "A": "The two aren t related, the positive two is the midpoint of the two x-intercepts and the negative two is one of the intercepts of the parabola", + "video_name": "EV57jv7JKCs" + }, + { + "Q": "at 1:57, how is it equal to each other\n", + "A": "it means the answer could be that number or less", + "video_name": "ilWDSYnTEFs" + }, + { + "Q": "At 2:00, it is a little error in video when he writes M_y=cosx+1xe^y ( it should be M_y=cosx+2xe^y).\n", + "A": "No, he wrote it correctly. It s just a low resolution video, like many of the old KA videos are.", + "video_name": "Pb04ntcDJcQ" + }, + { + "Q": "At around 2:30 Sal tell us that -4 / - 1/2 is equal to -4/1 * - 2/1. I am wondering why the 2 becomes a negative when it's going to be multiplied. I would like to know if -4/1 is the same as - 4/1? I hope I'm clear.\n\nTo be clearer: why doesn't Sal multiply -4/1 by 2/-1, and instead multiplies by -2/1\n", + "A": "He could multiply by any of those because - 2/1 = -2/1 = 2/(-1).", + "video_name": "H0q9Fqb8YT4" + }, + { + "Q": "at 1:47 it say greatest common divisor what dose that mean\n", + "A": "It is the largest number that can be divided into both 18 and 20. 18 can be divided by 2, 3, 6, and 9, while twenty can be divided by 2, 4, and 5. The only number that they have in common is 2, so two is the greatest common divisor. Notice that they can each also be divided by 1, but generally we ignore that when simplifying fractions because dividing by 1 gets us nowhere.", + "video_name": "H0q9Fqb8YT4" + }, + { + "Q": "\nWhy switch the numbers at 0:34", + "A": "When dividing, you need to make the second fraction a reciprocal, or flip the fraction so that the numerator ends up as the denominator and the denominator as the numerator.", + "video_name": "H0q9Fqb8YT4" + }, + { + "Q": "at 5:11 Mr Khan says that a 90 degree angle is a right angle so would an 180 degree angle be a straight angle?\n", + "A": "yes, it could be called a straight angle or just a straight line", + "video_name": "92aLiyeQj0w" + }, + { + "Q": "\nWhat if your angle is 0 Degrees? At the end 8:18-8:21, Sal says that if your angle is all the way 180 degrees... it forms a line. But, what if the angle is 0 degrees? What does that form? Is it still an acute angle? Or is there a special vocabulary word to describe this type of angle? Appreciate the help! :)", + "A": "An angle of 0 degrees between two rays forms one ray. Think of the two rays being perfectly on top of each other, going in the same direction.", + "video_name": "92aLiyeQj0w" + }, + { + "Q": "at 6:00 he is talking about < zxy\nwouldn't it be the same if he called it:\n1 when at the top of the screen it says b<0\n", + "A": "It can t. And in the 30 seconds after 5:37, Sal explains that b>1 cannot be part of the solution because b<0 is a restriction.", + "video_name": "0_VaUYoNV7Y" + }, + { + "Q": "\nWhen you divide A out at 4:20 do you always replace the empty side with 1?", + "A": "When you divide any variable out of a equation, you always replace the number or variable with 1. 1 is like the benchmark in math, it always takes the place of the number if the initial number is divided out.", + "video_name": "0_VaUYoNV7Y" + }, + { + "Q": "at the end ( 5:15 - 5:20 ) when sal says b <-1 and b > 1 how does that work b cannot be no number can be b if b was 2 that would violate the first inequality if b was -2 it would violate the second someone please explain.\n", + "A": "You are trying to use b <-1 AND b > 1 . Sal is using b <-1 OR b > 1. You are correct, AND will not work as it means both conditions need to be true. But, OR is more flexible, only one condition need to be true. Hope this helps.", + "video_name": "0_VaUYoNV7Y" + }, + { + "Q": "\nAt 0:49. Don't you mean 19 + 18. You said 19 over 18...", + "A": "Yeah he meant 19 + 18.. It said it in the bottom right corner..", + "video_name": "8Eb5MWwcMMY" + }, + { + "Q": "At 1:10, where did the 6 come in?\n", + "A": "The 18 is bigger than the 3.... so you have to ask yourself what you have to multiply the 3 by to get to 18.... 3x6=18..... Whatever you do to the denominator you have to do to the numerator to arrive at an equivalent fraction... so now you also multiply the numerator by 6 to get the numerator for the equivalent fraction", + "video_name": "8Eb5MWwcMMY" + }, + { + "Q": "What the heck is a caveat? Sal says it at 3:14. I'm guessing that it is the backwards C like object.\n", + "A": "It s the RESTRICTION or the CONDITION. You know how Sal writes p \u00e2\u0089\u00a0 -5 , that s the caveat or condition.", + "video_name": "gcnk8TnzsLc" + }, + { + "Q": "\nAt 3:35, when you cancel out (p - 5), you cross out (p - 6)", + "A": "It looks like a 6, but it is a 5.", + "video_name": "gcnk8TnzsLc" + }, + { + "Q": "\nAt 4:02 when Sal reached the answer, 4(p+3) over 5, providing p does not equal -5, he did not further simplify the equation. Can you not simplify it into 4p+12 over 5, providing that p does not equal -5?", + "A": "In more advanced math, you often have to take your result and do other steps. That is usually easier if the result is in factored form. Sometimes in Calculus you will want to multiply the result all the way out. Practice will help you choose...and also little hints like the instructions you receive with the assignment and choices you are given as possible answers.", + "video_name": "gcnk8TnzsLc" + }, + { + "Q": "\nat 1:02, how did you get 0?", + "A": "He is talking about the denominator: x cannot make the denominator equal to 0 or that would make the problem undefined. No matter what other solutions we come up with, we always have to exclude that value, which in this case is x.\u00e2\u0089\u00a0 -4", + "video_name": "2RnS3fSHVV8" + }, + { + "Q": "In 3:26, Sal said, \"So all I did, got rid of the exponent...\", but I think he meant the negative sign\n", + "A": "Yes, he could have said it that way, but what he means is that he got rid of the negative exponent and replaced it with a positive.", + "video_name": "S34NM0Po0eA" + }, + { + "Q": "At 5:47, why is the answer just 9/4? Can't we just simplify it to 2/1/4?\n", + "A": "You could, but Sal must consider 9/4 a simplified fraction as well, even if it is improper, because you can t simplify it any more (although, you can change it to a mixed number). Sometimes, whatever is considered simplified depends on the standards of your teacher or professor.", + "video_name": "S34NM0Po0eA" + }, + { + "Q": "\ni still don't get it at here the time 0:35\nAnd like M21 how did he got 100/100\nhere the time 0:32\nAnd again help on the last second 1:48", + "A": "because percent is out of a 100,(for EG,80/100) like an exam, it is out of a 100 percent, if you get 1 wrong you get like 98% or something, and for the last one, he is just multiplying 1.501 times 100%, so you move the decimal twice because 100 has two zero. but let say it was out of 1000, so you move the zero....three times.10, that will be one time.", + "video_name": "3_caioiRu5I" + }, + { + "Q": "At 1:36, it says the answer is 150.1%. Doesn't that equal 150.1/ 100? Is that even possible?\n", + "A": "Yes, it s possible. The concept is similar to improper fractions to mixed numbers.", + "video_name": "3_caioiRu5I" + }, + { + "Q": "\nAt 1:03 , can I write -15+j?", + "A": "Yes, you could write it as -15+j", + "video_name": "640-86yn2wM" + }, + { + "Q": "Hi can I please get help Asap Please ?! I understood what sal was saying until he got to the slope part. To sum it up , I don't understand from 1:38 to the end\n", + "A": "If x = 1 what is y? If x = 2 what is y? How much did x change? y? What s (change in y)/(change in x)?", + "video_name": "uk7gS3cZVp4" + }, + { + "Q": "At 0:27, how do you actually tell if -2 equals y? How is x=0 when there is 1/3 next to it?\n", + "A": "A little after your time stamp, Sal states that we know that the y intercept is -2 because the y intercept is where x=0. The idea of putting an equation in slope intercept form is so that we can quickly recognize the slope (m) and the y intercept (b). For the y intercept (where a function crosses the y axis), x will always be zero.", + "video_name": "uk7gS3cZVp4" + }, + { + "Q": "\nAt 0:38, what does he mean by \"the y-intercept occurs when x equals to zero\"?", + "A": "The Y-intercept is the point where the graph crosses the Y-Axis and a line crosses the Y-axis when x=0, since the Y-axis can be thought of as the line X=0.", + "video_name": "uk7gS3cZVp4" + }, + { + "Q": "At 6:22, Sal says that we are going to find the volume of the coin shaped object by multiplying pi times f(x)^2 times dx, but how is this possible because the side of the coin also slightly slopes like the rest of the cone?\n", + "A": "The point of the integral is to take the sum of an infinite number of coins, so in theory the slope is 0.", + "video_name": "btGaOTXxXs8" + }, + { + "Q": "\nThis seems too simple for a 10-minute video, so someone please confirm that I understand. If I fully get the concepts of span, subspace, and a matrix being defined as a set of column vectors, then it's dead simple to grasp the concept of the column space of a matrix, right? So, anyone who gets the videos in this series up to this point can watch up to 1:28, then skip to the next video, right?", + "A": "I believe the point to drive home is that any vector multiplied with the matrix must result in a vector that exists in the column space of that matrix, which in turn is the span of those column vectors. This implies that the column space is a subspace.", + "video_name": "st6D5OdFV9M" + }, + { + "Q": "\nAt 9:48 to the end of the video the lines get confusing", + "A": "Yes, They Do. Don t Worry You ll get the hang of it Good Luck ! And Happy Learning .", + "video_name": "K759mIqpvOU" + }, + { + "Q": "\nat 5:21 How does he know it will be a right triangle?", + "A": "He knows that triangle BDM is a right triangle because point D is on a line perpendicular to line AB. As he says at 5:30, All of the points that are equidistant between A and B are going to be on a line that is perpendicular to AB. Therefore, line DM intersects line BM at a right angle, making BDM a right triangle.", + "video_name": "smtrrefmC40" + }, + { + "Q": "I dont understand, how at 10:37 he got cosx=sin90-x?\n", + "A": "Its just a property of sin and cos. If you look at the unit circle you can see that the sin of say 30 is the same as the cos of 60. The sin of an angle is the same as the cos of the complementary angle.", + "video_name": "smtrrefmC40" + }, + { + "Q": "I dont understand, how at 10:37 he got cosx=sin90-x? Also at 14:39 it is really confusing?\n", + "A": "If you take a right triangle where there are the points A,B,and C(with C being the right angle), you can see that sin(x)=cos(90-x) by looking at the sine of angle A and the cosine of angle B. (90-angle A= angle B)", + "video_name": "smtrrefmC40" + }, + { + "Q": "\nIn 2:15 did he make a mistake?\nYou are supposed to divide with the biggest number inside the box, but he did the opposite. Is that a mistake?\nM&M", + "A": "No, it is not a mistake. The problem is 4 / 16 = 4 \u00c3\u00b7 16. 16 is the divisor, it goes outside. Maybe you need to review decimal division. This usually comes up at that time.", + "video_name": "FaDtge_vkbg" + }, + { + "Q": "\nisn't it 1/2 on 0:47?", + "A": "No, it s 1/4. Simplify 4/16 by going like this: 4 divided by four equals 1 16 divided by four equals 4", + "video_name": "FaDtge_vkbg" + }, + { + "Q": "At 2:37, how do you know the slope of the tangent is one?\n", + "A": "It is given that tan \u00ce\u00b8 = 1 in the problem.", + "video_name": "MABWdzmZFIQ" + }, + { + "Q": "\nAt 7:43, I would have separated it into the span of [.5,0] and [0,1]. Why is that wrong?", + "A": "The span of (1/2, 1) is a line parallel to (1/2, 1). The span of {(1/2, 0), (0, 1)} is the span of {(1, 0), (0, 1)} - the xy plane.", + "video_name": "3-xfmbdzkqc" + }, + { + "Q": "at 9:40, i got 1 and 1 at the bottom row instead because I kept the bottom row the same rather than the top row. Is that also correct?\n", + "A": "Yes, that has the same meaning. You will still end up with v1 + v2 = 0.", + "video_name": "3-xfmbdzkqc" + }, + { + "Q": "why couldn't the five at 0:47 be plus or minus five?\n", + "A": "mj, You re correct. 25x\u00e2\u0081\u00b4-30x\u00c2\u00b2+9 can be factored to either (5x\u00c2\u00b2-3)(5x\u00c2\u00b2-3) or (-5x\u00c2\u00b2+3)(-5x\u00c2\u00b2+3)", + "video_name": "o-ZbdYVGehI" + }, + { + "Q": "Can anyone explain to me where the 2 came from at 1:26? Thanks!\n", + "A": "He s just checking to make sure that it is a perfect square", + "video_name": "o-ZbdYVGehI" + }, + { + "Q": "At 4:34, How did you turn the 370, to a 371?? Why add the 1??\n", + "A": "The solution to the problem was that she should sell 370.3 computers in order to make a profit. However, in real life you can t sell a fraction of a computer. If she sold 370 computers she would make too little money to make a profit, so you have to round up and say that she should sell 371.", + "video_name": "roHvNNFXr4k" + }, + { + "Q": "\nWhy did Sal switch sides 2:28 (the variable and the number)", + "A": "He switched the sides simply because it s customary to write equations with the variable on the left and the number on the right. Switching the sides doesn t change the validity of the equation. For example, if 2 + 7 = 13 - 4, then 13 -4 = 2 + 7.", + "video_name": "roHvNNFXr4k" + }, + { + "Q": "\nAt 2:03, why does Khan leave a blank space?\n\nshouldn't it be; (assume \"///\" is just a space for formatting purpose)\n///////////////////// (4/9)^1 + (4/9)^2 + (4/9)^3 + . . .\n///////////////////// (4/9)^2 + (4/9)^3 + (4/9)^4 + . . .\n//////////////////// ----------------------------------------- -\nnot\n/////////////////////////// (4/9) + (4/9)^2 + (4/9)^3 + ...\n///////////////////////////////////// (4/9)^2 + (4/9)^3 + (4/9)^4 + ...\n///////////////////// ----------------------------------------- -", + "A": "Use code blocking for monospace formatting. (Click the Formatting tips hyperreference below the entry block) (4/9)^1 + (4/9)^2 + (4/9)^3 + ... (4/9)^2 + (4/9)^3 + (4/9)^4 + ... You want the addition to be applied to equivalent exponents: (4/9)^1 + (4/9)^2 + (4/9)^3 + ... (4/9)^2 + (4/9)^3 + (4/9)^4 + ... (4/9)^1 + 2*(4/9)^2 + 2*(4/9)^3 + 2*...", + "video_name": "vBlR2xNAGmo" + }, + { + "Q": "Why does Sal use shorthand at 5:28?\n", + "A": "conserving space.", + "video_name": "aTjNDKlz8G4" + }, + { + "Q": "\n6:39 how did you get 5.6 shouldn't it be 5.3?\nSorry, I'm confused. :/", + "A": "Its basically 336 divided by 60. Your answer is 5.6. Hope that helps :)", + "video_name": "aTjNDKlz8G4" + }, + { + "Q": "You lost me at 6:39 >.<\n", + "A": "Its basically 336 divided by 60. Your answer is 5.6. Hope that helps :)", + "video_name": "aTjNDKlz8G4" + }, + { + "Q": "At 1:01, why is it called the Foil method? Does 'Foil' stand for something or is it just called that?\n", + "A": "FOIL stands for First, Outside, Inside, Last . You multiply together the first term in each binomial, the outside (leftmost and rightmost) terms, the inside terms, and the last term in each binomial. Take those four products, add them up, and you have the expanded expression.", + "video_name": "HLNSouzygw0" + }, + { + "Q": "\nWhy add -11 to the other side when you could add 4 and equal them out 0:31", + "A": "Lauri, The problem was to Use the drop down menu to form a linear equation with no solution. If you chose the 4, you would have a linear equation which is valid for any x and so it has an infinite number of solutions for x.", + "video_name": "uQs100shv-A" + }, + { + "Q": "At 1:20 Sal says that there is only one triangle, but couldn't he have pulled it to the right?\n", + "A": "If you mean, could he have pulled the bottom right point to the right more , then no. If he pulled it to the right more, then the triangle wouldn t have two sides of length 3, which is what the directions are asking for.", + "video_name": "lohMwoq3WFA" + }, + { + "Q": "at 2:37.... someone tell me that was a typo on the transcript.\n", + "A": "Of course it is, it should say when is f of x increasing . A very unfortunate typo.", + "video_name": "KxOp3s9ottg" + }, + { + "Q": "at about 6:45 mins into the video, sal differentiates 6tan(theta). why is 6 not differentiated but tan is?\n", + "A": "hmm.... You know what... a constant can never be differentiated...... !!!", + "video_name": "fD7MbnXbTls" + }, + { + "Q": "\nAt 1:05 for the slope formula of y=6 i thought the slope is 6 and the y intercept is 0? Is that right? If not, why isn't it?", + "A": "If the slope was 6, there would be a x after the 6.", + "video_name": "y5yNi08cr6I" + }, + { + "Q": "At 0:25, doesn't Sal mean \"letters,\" and not \"alphabets\"?\n", + "A": "In the general idea... letters... some people say different things.", + "video_name": "VYbqG2NuOo8" + }, + { + "Q": "At 4:11 when You got the 3rd row did you not make a mistake when you are converting the row, You said it was the 3rd row- 2X the second row. so for the 3rd row shouldn't it be 0 3 3 2 ? Because in the video you did the 3rd- 2x the first row.....\n", + "A": "I guess that was just misspoken, since the first row was the only row kept original. Sal meant to do the 3rd row minus 2 times the first row.", + "video_name": "QV0jsTiobU4" + }, + { + "Q": "\nat 2:32 why does Sal get -xe^-x^2 instead of xe^x^2?", + "A": "Those negatives do not cancel.", + "video_name": "DL-ozRGDlkY" + }, + { + "Q": "In 0:28 sal says 8 goes into 37 three times but can you add the remainder??\n", + "A": "8 goes into 37 4 times, ( because 8 x 4 = 32 ) and that is why he writes 4 on top of the line.. The reminder then is 5, ( because 37- 32 = 5 ) and he then uses that when he brings down another place value - 7.. So the next thing to figure out then is how many times 8 goes into 57, and so on.... Did that make any sense ?", + "video_name": "MbpmP1esh-Q" + }, + { + "Q": "\nCan someone explain to me why the cube root and 3 exponent got erased? at 3:50ish", + "A": "Something raised to the power of 3 is a perfect cube, like: 2^3 = 8 You can simplify cube roots of perfect cubes: cuberroot (8) = 2. The video is just a more complicated version of the example I just did. Sal has cuberoot [(x+1)^3]. The (x+1)^3 is a perfect cube. Take the cube root, and you end up with just (x+1). Hope this helps.", + "video_name": "8GEGnSEJA2s" + }, + { + "Q": "\nat 1:09 he says 100 times the light goes on and off. How long would that take?!?!?!", + "A": "ok... you re weird -Midnite Blaze", + "video_name": "-xYkTJFbuM0" + }, + { + "Q": "\nso would the ratio 9.999... : .999... would be equal to 10:1", + "A": "Yup! just like 1.111\u00e2\u0080\u00a6 to 0.111\u00e2\u0080\u00a6 :) (10/9 to 1/9)", + "video_name": "TINfzxSnnIE" + }, + { + "Q": "\ni just still don't get why .9999..... equals 1 it doesn't make any sense.\nalso starting at 01:28 it starts to get confusing... can someone explain it to me???", + "A": "It s confusing because it deals with infinities, something that algebra and arithmetic are quite incapable of adequately describing. Our brains too, because infinities are actually quite hard for us to accurately imagine. calculus, on the other hand, is full of wonderful things like numbers infinitely close but not equal to other numbers and dividing by zero and such.", + "video_name": "TINfzxSnnIE" + }, + { + "Q": "At around 05:58, what did she write on the left hand side in green?\n", + "A": "Infinity times magnified", + "video_name": "TINfzxSnnIE" + }, + { + "Q": "my qs is two no. are in the ratio 5:6. If 8 is subtracted from each of the no. the ratio becomes 4:5. find the no.s\n", + "A": "the numbers are 40 and 48", + "video_name": "DopnmxeMt-s" + }, + { + "Q": "\nAt 4:34, I know that Sal means the twos cancel out and then it turns to one over one, which equals one, etc. But WHY do the twos cancel out?", + "A": "2/2 means 2 divided by 2, any number divided by itself = 1. To rephrase it: How many 2 s are in 2? One. Works for any number.", + "video_name": "DopnmxeMt-s" + }, + { + "Q": "\nAt 2:50, not enough to solve but we can simply i think,\n15a+15b = 3a+3a+3a+3a+3a+5b+5b+5b\ni guess you see know ...\n\n3a+5b = 2\n3a+5b = 2\n3a+5b = 2 THEN\n\n2+2+2+3a+3a = ?\n6+6a= 6 . ( 1+a)\n\nis it correct ? or am i too wrong in there =)", + "A": "You are right", + "video_name": "CLQRZ2UbQ4Q" + }, + { + "Q": "at 4:27 it shows reflection 0,1 to 1,1 and I see this as Y=1 but for the question y=x\u00e2\u0088\u00922 answered 0,2 to 2,4 and not sure why its wrong.\n", + "A": "You weren t plugging in the numbers correctly. y=x-2 for (0,2) would give you 2=0-2 which is not correct since 2 does not equal -2. Plugging in (2,4) for the second part would give you 4=2-2 which is a false statement as well.", + "video_name": "vO1Ur38PGCY" + }, + { + "Q": "\nwait at 6:39 why did he simplify", + "A": "The sooner you simplify the more extra work you avoid.", + "video_name": "bAerID24QJ0" + }, + { + "Q": "\nat 2:10 what do u mean by recipical", + "A": "a reciprocal is the inverted number. if you have 3/4 the reciprocal is 4/3. if the number is a whole we know the denominator is 1 therefore any whole number a has the reciprocal 1/a. A number like 3 has the reciprocal of 1/3.", + "video_name": "bAerID24QJ0" + }, + { + "Q": "what are conventions? 3:15\n", + "A": "A convention is an unspoken agreement to do something a certain way. Grammar, spelling, the order of operations, etc. are all systems of conventions.", + "video_name": "bAerID24QJ0" + }, + { + "Q": "I always learned the equation was A(n)=a+(n-1)*(d) where a equals the first term, n is the term number, and d is the common difference. So the equation for 3:14 is A(100)=15+(100-1)*(-6)=-579. Is this correct?\n", + "A": "Yes, that is correct (5:53). Good job!", + "video_name": "JtsyP0tnVRY" + }, + { + "Q": "\nWhy did he put the 0 at 2:16?", + "A": "The 0 represents how many times we want to subtract 6 (or add -6, that s the same thing) from our starting value, which is 15. More generally, the value x represents how many times we want to subtract 6 from our starting value of 15. Because the very first value is 15, we don t want to subtract 6 from it, because that would give us 9, which is the second term, so we write 15 - (0)*6. Anything times 0 is 0, so that becomes 15 - 0, but subtracting or adding nothing to an equation doesn t change it s value.", + "video_name": "JtsyP0tnVRY" + }, + { + "Q": "At 5:14, Why would the sqrt of 1/2 be 1/sqrt2 and not sqrt 1/2?\n", + "A": "This is because the sqrt(1/2) is the same thing as saying sqrt(1)/sqrt(2) and since the square root of 1 is just 1 we can simplify the numerator and rewrite it as 1/sqrt(2).", + "video_name": "KoYZErFpZ5Q" + }, + { + "Q": "\nat 5:17 shouldn't it be sqrt 1/2 ?", + "A": "Yes, but you need to go further and simplify the radical. When your radical is simplified, 1) it will not have a fraction inside the radical. sqrt(1/2) = sqrt(1) / sqrt(2) 2) all perfect squares inside the radical will be simplified: sqrt(1) / sqrt(2) = 1 / sqrt(2) 3) there will be no radical in the denominator - rationalize the denominator: 1 / sqrt(2) = 1 / sqrt(2) * sqrt(2) / sqrt(2) = sqrt(2) / 2 hope this helps.", + "video_name": "KoYZErFpZ5Q" + }, + { + "Q": "\nAt around 2:06, how come Sal doesn't put (square root of y)^2 in the denominator? I thought when using the product rule, you put (g(x))^2 in the denominator.", + "A": "I suspect you re confusing the product rule with the quotient rule. Product rule: derivative of uv = u v + uv Quotient rule: derivative of u/v = (u v - uv )/v\u00c2\u00b2", + "video_name": "2CsQ_l1S2_Y" + }, + { + "Q": "His algebra is wrong at 2:37 3*1/4 is not 13/4 and 2*1/2 is not 5/2\n", + "A": "His math is not wrong. You are confusing mixed numbers: 3 1/4 with multiplication of 3 * 1/4. In a mixed number like 3 1/4 of 2 1/2 there is no multiplication symbol between the numbers. 3 1/4 is 3 whole units + 1/4 unit, or 3.25 in decimal. 2 1/2 is 2 whole units + 1/2, or 2.5 in decimal form. Seems like you need to review basic concepts of dealing with fractions and mixed numbers.", + "video_name": "x5EJG_rAtkY" + }, + { + "Q": "\n00:32 when you said 'any m&b on the surface = SE for that line', what does 'that line' exactly mean?", + "A": "That line is referring to a line drawn through your data. If you have your data plotted on a graph, you can draw a line through it to fit to the data. This line will have a gradient, m, and a y-intercept, b. It will also have a squared error - the square distance of each point of data from the line. The aim is to find the line with the minimum squared error.", + "video_name": "u1HhUB3NP8g" + }, + { + "Q": "at around 1:40 how do we know that the top side (c or 2x) in not equal to the right side (b or x=10) ?\n", + "A": "It s because triangle ABC is an isosceles triangle. If 2x was equal to x+10, then it wouldn t be an isosceles triangle, it would be an equilateral triangle, because an equilateral triangle s angles are all equal.", + "video_name": "CVKAro3HUxQ" + }, + { + "Q": "\nAt 2:55 Sal suggests that it is necessary to take the natural log of both sides but I solved it by changing it to e^(ln(x)*x) and then taking the derivative as normal and I got the right answer.", + "A": "There is always different ways to solve the same problems. Sal only mentioned one of the ways by taking the natural log (mentioned at 4:37), but using e is another way.", + "video_name": "N5kkwVoAtkc" + }, + { + "Q": "\nAt 4:11, why does Sal ask us how many times 16 goes into 1388 when we can see the answer on the other side of the screen?", + "A": "Sal is explaining how to do it and he is asking himself he same questions that you will ask yourself.", + "video_name": "R486L0M5cWk" + }, + { + "Q": "\n@3:35 Sal Crosses out the \"hours.\" Why can he do this?", + "A": "Because the hours part can be cutout as it is both at the numerator as well as at the denominator.", + "video_name": "Uc2Tm4Lr7uI" + }, + { + "Q": "\nAt 2:34, Sal arrives at -(sqrt of 1/7)... I tried to simplify this more got -sqrt or 1 / sqrt of 7. I squared the top and the bottom. -1^2 and sqrt 7^2 and got 1/7. Is this correct or incorrect and why?", + "A": "No, you started off ok. -(sqrt of 1/7) = - sqrt(1) / sqrt(7) But, you can not square the fraction. It isn t equivalent to the original fraction. Instead, you should 1) Simplify sqrt(1): - sqrt(1) / sqrt(7) = -1 / sqrt(7) 2) Rationalize the denominator. This means we want to convert the denominator to a rational number. We do this by multiplying top and bottom by sqrt(7) and simplify. -1 / sqrt(7) = -1 / sqrt(7) * sqrt(7) / sqrt(7) = - sqrt(7) / sqrt(49) = - sqrt(7) / 7 Hope this helps.", + "video_name": "suwJmCrSDI8" + }, + { + "Q": "\nWith reference to 9:15 (appx) ,\n\nIs it right to say that all graphs where there is ONLY a discontinuity at one end point, are graphs with removable discontinuity ? By the looks of it, it seems so. Was just wondering if there are any special cases.", + "A": "If you have a piecewise function, and your endpoint is at the point where the function changes, then the discontinuity is not removable. It s not a requirement that a discontinuity at an endpoint must be removable or that a discontinuity should be at the endpoints.", + "video_name": "kdEQGfeC0SE" + }, + { + "Q": "\n4:54 why is rationalizing important?", + "A": "Rationalizing is like simplifying. To always have to simplify your answer unless you re told not to.", + "video_name": "tSHitjFIjd8" + }, + { + "Q": "\nI am confused. I think that this new formula (B=C2/square root 2) is unnecessary. Sal stated at 1:04 that in these 45-45-90 triangels, both non-hypotenuse sides are equal. Therefore, if one non-hypotenuse side of the triangle is 8, we could automatically assume its other congruent side is 8. We could then just use the Pythagorean Theorem to find the hypotenuse. Could someone please explain why we must use a different formula? I'll give a more detailed example of my point in the questions area.", + "A": "For example, in a 45-45-90 triangle where one side is labeled 2 and the hypotenuse is unknown, we can label the other non-hypotenuse side 2 also. From this point, we can simply use the Pythagorean Theorem to find the hypotenuse. We don t need the formula which Sal gives at 4:27 in the video.", + "video_name": "tSHitjFIjd8" + }, + { + "Q": "At 8:30, why is 2 being multiplied by 8, but \u00e2\u0088\u009a2 isn't being multiplied by 8?\n", + "A": "Think of it as 8/1 * 2/\u00e2\u0088\u009a2. In normal multiplication, you just multiply across for example, 2/3 * 3/4 = (2*3)/(3*4) = 6/12 = 1/2", + "video_name": "tSHitjFIjd8" + }, + { + "Q": "At 0:54 , does Sal mean that if a triangle has less then 3 acute angles, it isn't an acute triangle? Is it true? If it is, why?\n", + "A": "Yes, it s true. You must have 3 acute angles to make an acute triangle. You need one right angle to make a right triangle. You need one obtuse angle to make an obtuse triangle.", + "video_name": "PiQxA9O7Rd8" + }, + { + "Q": "\nAt 0:30, The selected answer was side AB, but couldn't side CD also be considered a correct answer?", + "A": "Perpendicular means the two lines are forming a right angle.", + "video_name": "PiQxA9O7Rd8" + }, + { + "Q": "At 11:28, when Sal multiplies by b^2 shouldn't it be b^2 x^2/a^2 instead of b^2/ a^2 x^2 ?\n", + "A": "Actually, both are equivalent. First Case: b^2 x^2/a^2 (b^2*x^2)/a^2 Second Case: b^2/a^2 x^2 (b^2/a^2)*x^2 x^2=x^2/1. (b^2/a^2)*(x^2/1) Multiply the numerators and denominators of the fractions. (b^2*x^2)/a^2 We end up with (b^2*x^2)/a^2 in both cases, meaning that both expressions is equivalent. I hope this helps!", + "video_name": "pzSyOTkAsY4" + }, + { + "Q": "\nAt 2:46 did Sal mean hyperbolas? It sounded like he said parabolas.", + "A": "I think you are correct. He said parabolas , but he should have said hyperbolas .", + "video_name": "pzSyOTkAsY4" + }, + { + "Q": "at 10:32, why is the a sqrt(a), isn't it supposed to me +- a? Because x^2=a^2 and then root both sides, x = +-a? I can't find the report a problem button though. But I might be missing something.\n", + "A": "If you keep playing the video, you should notice that in the bottom right hand corner Sal explains his mistake.", + "video_name": "pzSyOTkAsY4" + }, + { + "Q": "At 2:35, do you have to distribute the y, could you just divide the whole equation by x?\n", + "A": "Keep in mind that we want to solve the equation for x. To do that we have to unlock the parentheses and then gather all the x terms on one side of the equation and everything else on the other side. That s why the y must be distributed. Dividing by x would severely complicate things, as you would end up with [ y ( x + 3 ) ] / x = 2 - 1/x and we would still not have only the x terms on one side of the equation.", + "video_name": "VzWxvDe8TUQ" + }, + { + "Q": "\nAt 3:52, I think Sal forgets the negative sign next to the 1. If this is true, does that mean my answer of (3y+1)/(-y+2) is correct? I took a different approach by leaving the 3y and adding the 1, instead of Sal's method, so I was hoping that it worked both ways.", + "A": "Sal does forget the sign, and a pop-up box in the lower right-hand corner mentions that. Your answer is correct. ( -1 - 3y ) / ( y - 2 ) = -1 ( 1 + 3y ) / [ -1 ( -y + 2 ) = ( 1 + 3y ) / ( -y + 2 )", + "video_name": "VzWxvDe8TUQ" + }, + { + "Q": "\nAt 3:47, shouldn't it be -1-3y instead of 1-3y, so that we get (y-2)x = -1-3y ?? In other words, did he forget to keep the 1 negative?", + "A": "This is a known mistake in the video. There is a box that pops up at about 3:50 that states there is an error and provides the correct value.", + "video_name": "VzWxvDe8TUQ" + }, + { + "Q": "I'm not following what Sal did at 3:18 when he got out the calculator and got a number for r. Did he just rearrange the whole logistic equation in his head and solve for r, or what?\n", + "A": "this is the equation he used: future value / present value = (1+i)^n (growth rate equation google it) i= growth rate n=number of periods. 150/100=(1+i)^20---> i=[(1.5)^(1/20)] - 1", + "video_name": "-fIsaqN-aaQ" + }, + { + "Q": "On 2:32 is scaling a type of measuring? That's all I'm asking thank you!\n", + "A": "Sort of. When you scale something up or down, you are keeping the same proportions, but making it bigger or smaller. So, if you have a 1 cm cube and scale it up by 10, then each of the measurements would increase x10. So, it keeps the same proportions relative to the other sides, but gets bigger. If one side gets bigger out of proportion, then it would lose its original shape.", + "video_name": "yUYDhmQsiXY" + }, + { + "Q": "how does sal know that at 2:10 the graph g(x) ill be equal to f(x)-horizontal shift + the vertical shift and not f(x) + horizontal shift + vertical shift?\n", + "A": "He explains this at 3:00 and on.", + "video_name": "MDav5OMpCto" + }, + { + "Q": "\n0:33 so a derivative of a function for critical points can only either equal to zero or undefined? a derivative can't have both places where it equals to zero and and places where it's undefined?\ncould you please do a video or explain how to identify the minima and maxima for a function where the derivative can be undefined instead of equalling to zero?", + "A": "Some calculus textbooks (perhaps most) refer only to points where the derivative is zero as critical points. Others may include points where the derivative is undefined. Consider this function: y = sqrt(36 - x^2) That s the equation for the top half of a circle. The derivative is zero at x=0, a maximum, and undefined at x=-6 and x=6, which are minima.", + "video_name": "pInFesXIfg8" + }, + { + "Q": "\nAt 3:08 , why did sal crossed the curve of -12 from 2 and -2 ?\nPlease explain.\nThank you", + "A": "I dont understand your question, please explain your problem.", + "video_name": "pInFesXIfg8" + }, + { + "Q": "\n1:00\nSo sin(x)^-1 is not 1/sin(x)? Why is it written this way?", + "A": "It really isn t a well thought out syntax. If it confuses you, you can use arcsin instead of sin^-1. The difference is subtle. Btw, 1/sin(x) can be written as csc(x) (csc stands for cosecant ).", + "video_name": "57BiI_iD3-U" + }, + { + "Q": "\nAt 0:23, the equations were x=3cos(t) and y=2sin(t). Why couldn't we have written x=3sin(t) instead of cosine and y=2cos(t) instead of sine? Would it have made a different graph? Would it have been a hyperbola instead of an ellipse?", + "A": "It would have made the same graph. Try graphing it on your graphing calculator (or a free online one). Be sure that the graph is in parametric mode (or PAR ) and in radians, not degrees. The only difference is in which direction the equation goes. As Sal was mentioning at around 7:45, we don t know which direction the graph was created by simplifying the equation. If sin and cos were switched, then the graph would go in a different direction, but would look the same. Hope this helps!", + "video_name": "57BiI_iD3-U" + }, + { + "Q": "\nAt 1:57, why does Sal say that you divide x^4 by x^4 but then simply divides x^4 by 4?", + "A": "just misspoke. just taking the antiderivative of x^3", + "video_name": "cBi4a1iSaPk" + }, + { + "Q": "At 5:00,\n5/3/2 = 5* 2/3 = 10/3\nI get 5/3/2 = 5/6\n\nWhere am I going wrong?\n", + "A": "The fraction Sal is simplifying is 5 divided by 3/2 . To write it horizontally requires parentheses (5)/(3/2). To divide 5 by 3 before dividing 3 by 2 misreads the problem leading to your wrong answer. The large fraction bar acts as a grouping symbol in common mathematical usage. Thus in order of operations you can think of there being parentheses around the numerator and denominator of any fraction written using the fraction bar.", + "video_name": "cBi4a1iSaPk" + }, + { + "Q": "\nat 1:17 when you try to graph the slope of f(x)'s assumed parabola,how do you know that slope will decrease linearly", + "A": "though Sal didn t want to share it with you here .. but, if you want to know .. a standard parabolic function is of type a x^2 + b x + c .. now help yourself and differentiate the above function .. for x^2, we got the function to be 2x .. when you differentiate the above standard parabolic function, you will necessarily get the function 2ax + b .. this is the equation of a line or a linear relation in x irrespective of the values of a, b and c ..", + "video_name": "eVme7kuGyuo" + }, + { + "Q": "Why doesn't Sal shade in the yellow circle (which marks the beginning of the red line) at 4:04?\n\nEdit: Isn't that point defined (just a jump discontinuity)?\n", + "A": "It is not defined, because the definition of derivative uses limits, and since the limit from the left diverges (meaning, f(x) is the red point, and f(x+e) where e<0 has (f(x+e)-f(x))/e going to infinity), we can t define the derivative here. It just stems from the limit definitions is all.", + "video_name": "eVme7kuGyuo" + }, + { + "Q": "\nAt 0:41 \"How many times does 4 go into 9 ?\" Why do we need to know how many times does 4 go into 9 ?", + "A": "Because that would go in the ones place for long dividing 4 / 9.", + "video_name": "KFzcwWTEDDI" + }, + { + "Q": "\nAt 4:15 why did he flip 3/7?", + "A": "A simpler way to divide fractions is to take the first fraction and multiply it with the reciprocal of the second fraction, example: 5/7 divided by 3/2 is equal to 5/7 times 2/3.", + "video_name": "K2b8iMPY11I" + }, + { + "Q": "7:20 After the summation sign brackets are needed around the two terms following, else the summation sign only applies to the first term?\n", + "A": "You are right. A parenthesis is needed to enclose the two terms in order to include both terms in the summation. Otherwise, it would be ambiguous. Sal sometimes makes mistakes like that. However, judging from this context, even without a parenthesis, it was clear that he intended to include both terms in the sum.", + "video_name": "qUNGPqCPzMg" + }, + { + "Q": "\nSal loses me at about 6:00. I don't understand what he's doing with the\nA+B=0\n2A+B= -2\n-A-B=0\nA= -2\nB=2\nWhat is the thought process here? I don't understand what he did.", + "A": "When you have the same variable on both sides of the equal sign, the coefficients of that variable are going to equal each other so in this case (A + B)n = 0(n) so (A + B) = 0. Same with (2A + B). They are both constant terms and you can rewrite them as (2A + B)n^0 = -2n^0. Then set coefficients of the same variable equal to each other and you get (2A + B) = -2. Now you solve the system of equations (Sal does it here by the method of elimination) and you get A = -2 and B = 2.", + "video_name": "qUNGPqCPzMg" + }, + { + "Q": "\nat 1:00 Sal says, \"We also have to subtract 54 from this side\" When he should have said \"We also have to subtract 5 from this side\"", + "A": "i know. it was just a typo. :D", + "video_name": "VidnbCEOGdg" + }, + { + "Q": "At 0:38, Sal says that we need to get rid of everything on the left-hand side. Why?\n", + "A": "you do this to isolate x, or the other variable, on one side to where x equals a number. :-) hope this helps!", + "video_name": "VidnbCEOGdg" + }, + { + "Q": "At 0:54, what are \"real numbers\"?\n", + "A": "real numbers are a value that represents a quantity along a continuous line. Both plus and minus. like 1, 2, 3, 4, 5, blah blah blah", + "video_name": "GVZUpOm3XUg" + }, + { + "Q": "Why is the integral of cos(x) not -sin(x) at 2:47?\n", + "A": "The fundamental theorem of calculus says that f(x) is a differentiable function, then the integral of f (x) is just f(x). Now if f(x) = sin(x), then f (x) = cos(x). This means that the integral of cos(x) is just sin(x). (Note: I wish I could use integral signs but I can t find a good way to do so).", + "video_name": "xVWCfMe97ws" + }, + { + "Q": "\nAt 0:30 it says that f of negative 6 is 7\nHow did they get 7?", + "A": "f(x) is a function and when you put -6 in for x you get 7. He got it by finding -6 on the x-axis and going strait up to see what was the y-coordinate when the function was at -6 for x. Does that make any sense? Basically, when the function s x-coordinate is -6, the y-coordinate is 7.", + "video_name": "uaPm3Tpuxbc" + }, + { + "Q": "At 7:28 , why are corrseponding altitudes at similar triangles have the same ratio as other corresponding parts such as corresponding sides? perhaps i missed the part where we proves or speaks about corresponding altitudes having the same ratio of the sides? how can we prove this?\n", + "A": "This was proven in Sal s videos on similarity.", + "video_name": "v5SAMuRanGM" + }, + { + "Q": "\nat 1:19 what dose sal say?", + "A": "Here s what Sal is saying between 1:17 and 1:42: Well, we can t subtract the 70 from the 20, but we have other value in the number. We have value in the hundreds place. So why don t we take a hundred from the six hundred, so that becomes five hundred, and give that hundred to the ten s place. If we give that hundred to the ten s place, what is a hundred plus twenty? Well, it s going to be \u00e2\u0080\u00a6 120. (He is explaining how regrouping or borrowing works during subtraction.)", + "video_name": "QOtam19NQcQ" + }, + { + "Q": "\nat 1:27, do you have to take away 100? or can you take away just 1?", + "A": "Well,it depends on what strategy you are using to subtract.If you re just doing standard algorithm then, you would just write that you are borrowing 1 but if you want to say the accurate value of the number then you would say that you re borrowing 100, which is what you are actually borrowing! Hope this helps!", + "video_name": "QOtam19NQcQ" + }, + { + "Q": "\nat 1:33 it just dose not make sence", + "A": "Ok. If you have a calculator on your computer (what you are using right now) I want you to multiply 10 x 32. It will equal 320. If you multiply 100 x 32, you will get 3200. Instead of multiplying by 10 you are multiplying by 100. There are two zeroes in 100, so you take 32 and add zeroes, 3200. Izzy, if this does not help comment below, and I will give you a more detailed answer.", + "video_name": "tHQOAvbyRL0" + }, + { + "Q": "At 23:58 he mentions that parametric equations are the only way to define a line in 3D. Would parametric equations make a line in any dimension from R2 to Rn?\n", + "A": "Yes. Parametric equations will always define a line, assuming you have a parametric equation for each of the dimensions.", + "video_name": "hWhs2cIj7Cw" + }, + { + "Q": "At 20:24 you are making a \"general definition\" in R*3 for a parametric equations for a line.\nL= {P1 + t(P1 - P2)}, t in R but could there also be L={P2 + t(P1 - P2)} . Is that the same line and does it have the same direction? If not then the \"general definition\" is not so general(?).\n", + "A": "They re both the same line with the only difference being which point on the line you re at given a specific value for t. This definition also isn t restricted just to R3. Any line in any R^n vector space can be written in this form.", + "video_name": "hWhs2cIj7Cw" + }, + { + "Q": "\nAt 24:20, the line is represented in terms of x,y and z. And x,y and z are defined in terms of t. If we assume that t is time then each value of t will give a single points on R3 at different times. Are we saying that the points on a 3-dimensional line can be represented in terms of a 4th dimension? t is a scalar, what is the interpretation of t?", + "A": "t is a free variable, getting all values in R.", + "video_name": "hWhs2cIj7Cw" + }, + { + "Q": "why is it vector b - vector a ? at 13:43 ?\n", + "A": "It s to get the slope of the line. The vector b\u00e2\u0083\u0097 - a\u00e2\u0083\u0097 (or a\u00e2\u0083\u0097 - b\u00e2\u0083\u0097) point in the direction of the line we want to represent.", + "video_name": "hWhs2cIj7Cw" + }, + { + "Q": "At 0:04, why does it say \"4,5000 equals 3 thousands plus how many\" in the words when it says \"4,500 = 3 thousands + ? hundreds\" on the board?\n", + "A": "He is correct it at 0:04 it says 45,000 with subtitles on.", + "video_name": "a_mzIWvHx_Y" + }, + { + "Q": "\nAt 6:51 Sal says that it doesn't have to defined at that point, what does he mean by that?", + "A": "He meant that the denominator does not have to be 0.", + "video_name": "igJdDN-DPgA" + }, + { + "Q": "7:34 Sal said that x could not equal -1. But it also cannot equal 2. Did Sal forget it?\n", + "A": "Sal did not forget the condition that x cannot be equal to 2. You know from the resulting equation not to use x = 2 but you would not know that x = -1 would produce a wrong answer. So, if you were to report to someone that she could use either equation, he would know not to use +2 in the first equation but would not know that -1 will cause an error.", + "video_name": "7Uos1ED3KHI" + }, + { + "Q": "at 1:39 in the video, why do you factor out a 3 from the numerator? javascript:%20void%200\n", + "A": "When working with rational expressions (fractions), we always simplify both numerator and denominator so that each of their factors is exposed. This then allows us easily to see what can be divided out in order to further simplify the expression.", + "video_name": "7Uos1ED3KHI" + }, + { + "Q": "At 10:57 why did he write (3x-6) before (x+3)? He didn't do it in previous problems and I wasn't sure if it would have made a difference if he would have written (x+3) (3x-6)\n", + "A": "nope it would not had made a difference how you wrote it cuz in the muliplication property you can switch terms around and get the same answer for example: 2*3=6 3*2=6 or: 3x*4x=12x^2 4x*3x=12x^2 hope this helps:)", + "video_name": "7Uos1ED3KHI" + }, + { + "Q": "at 8:59 you did a harder way then what I was told, could you not just factor the 3 out from the beggining?\n", + "A": "Certainly! That would be easier, faster, and would give you a more thoroughly factored result. (He does some odd things with factoring throughout the videos -- certainly his approach works, but it isn t always the simplest.)", + "video_name": "7Uos1ED3KHI" + }, + { + "Q": "I didn't understand any one thing he explained in this video and it's getting me frustrated!\n\nAt 4:55 you see the whole x squared - 9 = (x + 3 ) (x-3)! How does this make sence? How did u get x+3 and minus 3 in relation to x squared - 9. Help me!\n", + "A": "(x + 3)\u00e2\u0080\u00a2(x - 3) FOIL: x\u00e2\u0080\u00a2x + 3\u00e2\u0080\u00a2x - 3\u00e2\u0080\u00a2x + 3\u00e2\u0080\u00a2(-3) x^2 - 9", + "video_name": "7Uos1ED3KHI" + }, + { + "Q": "At 9:00, what numbers represent a and b?\n", + "A": "a and b represent the coefficients of what you have to split your middle term into when you factor, in order to get the quadratic to factor.", + "video_name": "7Uos1ED3KHI" + }, + { + "Q": "in the example of minute 10:45 wouldn't the proper way to factorize be (3x-3)(x+6) ? sal made (3x-6)(x+3)\n", + "A": "No, Sal was right. The expression 3x(x-3) -6(x-3) has a common factor of x-3. Factoring that out yields (x-3)(3x-6), which is the same pair of factors Sal had..", + "video_name": "7Uos1ED3KHI" + }, + { + "Q": "\nThank you for the lesson. At 15:13, only one restriction is included. Should we also say that x cannot be 1/2 since it would make (2x-1) a zero as well?", + "A": "Yes that would be appropriate.", + "video_name": "7Uos1ED3KHI" + }, + { + "Q": "I stopped understanding at around 4:00 when you started talking about conditions and why x can't equal -3, why can't it equal -3 when both of the (x+3)'s have been cancelled out??\n", + "A": "By being cancelled out, that meant that the (x+3) was divided out of the expression. But if x = - 3, then (x+3) would have equalled zero ---- and division by zero is never permitted. That s why the only way the (x+3) s are allowed to be cancelled out is if the statement that x cannot equal -3 is included with the simplified fraction.", + "video_name": "7Uos1ED3KHI" + }, + { + "Q": "Near 8:36 couldn't you just factor out a 3 and get 3(x^2+x-6) and then factor the rest of it using the quadratic formula or other methods?\n", + "A": "Yes, you could", + "video_name": "7Uos1ED3KHI" + }, + { + "Q": "\n@ 7:17 ish you said the restriction was x cannot equal -1 but there is another restriction too it is x cannot equal 2", + "A": "The only restrictions that need to be stated separately are the ones that are fully divided out of the problem. Because ( x - 2 ) is still visible in the denominator, it is already clear that x cannot equal 2 (since division by zero is never allowed).", + "video_name": "7Uos1ED3KHI" + }, + { + "Q": "\nAt 7:29 don't we also have to add that x does NOT equal 2. Wouldn't 2 make the equation undefined?", + "A": "Yes, but that is obvious from the problem since x-2 is in the denominator. In this case we are reminding ourselves that x cannot be equal to -1 as well. We need the reminder because after we factored the expression, we had in the denominator (x+1) and (x-2), but the (x+1) term cancelled out with a like term in the numerator. So the original expression could not have x=2 and x=-1, but we lost the visual clue when we cancelled the (x+1) terms (see 6:44).", + "video_name": "7Uos1ED3KHI" + }, + { + "Q": "At 8:57, couldn't Sal have made a= -6 and b=+9 instead of the other way round as both of them are divisable by 3 and 18?\n", + "A": "Yes, he could ve had. It doesn t matter whether they are a or b as those are just place holders. As long as the numbers are correct you end up with the same answer.", + "video_name": "7Uos1ED3KHI" + }, + { + "Q": "\nWhat did he do at 1:50 when it was 4/3 pi 27", + "A": "Alegbra. 4/3 * \u00cf\u0080 * 27 or (4 * \u00cf\u0080 * 27)/3. If you multiply it out, 108\u00cf\u0080/3=36\u00cf\u0080 or, what Sal does, is simplify through division because he recognizes 27/3 in his head, so he gets to 4 * \u00cf\u0080 * 9=36\u00cf\u0080 by skipping a bit.", + "video_name": "IXRMVcoqRRQ" + }, + { + "Q": "\nwhile he was rearranging the operations to solve for \"h\" ,at 1:51 why did he divide \"b\" from \"b\" instead of subtracting \"b\" from \"b\" to eliminate it?", + "A": "Yes, you would subtract it from both sides instead of dividing in order to rearrange the equation. That would result in 2A = b + h becoming 2A -b = h", + "video_name": "eTSVTTg_QZ4" + }, + { + "Q": "0:22 how should you divide if your number is a fraction? Like 11 4/6 divided by 5\n", + "A": "To divide 11 4/6 by 5, make 11 4/6 into ana improper fraction, 70/6. Then When diving a fraction like 70/6 divided by 5, Remember KEEP CHANGE FLIP. To do the strategy, first turn teh divide symbol into a multiplying symbol, then make 5 into 5/1. Then flip 5/1 into 1/5, then multiply. Then Simplify, and you SHOULD have the answer.", + "video_name": "Z_NHrwK6ALE" + }, + { + "Q": "at 4:13pm, Solve the following system of linear equations:\n-2x + 4y - z = 8\nx + 7y + 2z = 5\n3x + 3y + 3z = -3\n\nelimination does not seem to work :(\n", + "A": "The first equation, is equal to the second minus the third. So you really have 2 equations and 3 unknowns, and there is not a unique solution.", + "video_name": "GWZKz4F9hWM" + }, + { + "Q": "At 14:10 why can't sqrt of 39/3 be simplified to sqrt of 13?\n", + "A": "Because the 3 is not under the radical. It is \u00e2\u0085\u0093 \u00e2\u0088\u009a39, it is not \u00e2\u0088\u009a(39\u00c3\u00b73)", + "video_name": "i7idZfS8t8w" + }, + { + "Q": "\nOn the second problem (answer at 9:16) couldn't you turn the negative square root into \u00e2\u0088\u009a(84)I?", + "A": "negative square roots are insolvable, and you cannot change intergers at free will. All we can derive is that the equation is insolvable.", + "video_name": "i7idZfS8t8w" + }, + { + "Q": "\nAt 13:36, what happened to the 2 outside of the radical?", + "A": "He simplified the fraction by dividing the top and bottom by 2.", + "video_name": "i7idZfS8t8w" + }, + { + "Q": "at 14:35, why does he divide -12 by 2 as well? Is it because it's a different number than all the stuff with the square root? I thought it would just stay the same because you already divided by two from the top.\n", + "A": "Because (a+b)/c = a/c + b/c. Concrete example (2 + 4)/2 = 6/2 = 3 Right? Now distribute: (2 + 4)/2 = 2/2 + 4/2 = 1 + 2 = 3 Same! What you are trying to do is a/c + b Using our example your way: (2 + 4)/2 = 2/2 + 4 = 1 + 4 = 5.", + "video_name": "i7idZfS8t8w" + }, + { + "Q": "at 4:37, on the final step, the problem is (4 + or - 10)/2. sal divides both terms by two. i thought he could only divide 1 term, and then the 2 would be gone. how did he do that?\n", + "A": "The whole formula must be divided by 2. Think of the quadratic formula as this. [-b \u00c2\u00b1 sqrt(b^2-4ac)] / 2 or in your case it could have been written as (-4\u00c2\u00b110)/2 doing the parentheses first would result in the same answer as dividing both the numbers by two first.", + "video_name": "i7idZfS8t8w" + }, + { + "Q": "\nAt 0:16, Sal mentioned caveat. What does caveat mean?", + "A": "It is a limitation or condition, so he says if you remember this, then you should also remember how to prove it. The condition is the then part of it.", + "video_name": "i7idZfS8t8w" + }, + { + "Q": "At 13:37, how did -12\u00c2\u00b12\u00e2\u0088\u009a39/-6 become -6\u00c2\u00b1\u00e2\u0088\u009a39/-3 ? I don't understand that division/simplification process.\n", + "A": "Think of it as (-12\u00c2\u00b12\u00e2\u0088\u009a39)/-6. If I want to factor out a 2 on the top, I would end up with 2(-6 \u00c2\u00b1 \u00e2\u0088\u009a39)/6, if I divide 2/6, I am left with 1/3, so we would have (-6 \u00c2\u00b1 \u00e2\u0088\u009a39)/3. Be careful how you write it because you do not show the -12 as being part of the numerator, and that is why I added the extra parentheses.", + "video_name": "i7idZfS8t8w" + }, + { + "Q": "At 12:38, why did he chose to stop factoring? Why didn't he continue?\n", + "A": "Because it cant be factored anymore", + "video_name": "i7idZfS8t8w" + }, + { + "Q": "\nAt 10:51 with the yellow matrix Sal just finished, could you add the pivot entries with free variables and finish the reduced row echelon form?\n\nSo something like:\n| 1 1 0 0 | 2 |\n| 0 1 0 0 | s |\n| 0 0 1 2 | 5 |\n| 0 0 0 1 | t |\nInto:\n| 1 0 0 0 | 2 - s |\n| 0 1 0 0 | s |\n| 0 0 1 0 | 5 - 2t |\n| 0 0 0 1 | t |\n\nOr wouldn't schools and universities be looking for something so detailed?", + "A": "Yes, you can reduce it all the way. Don t quote me but... the first form is called Gaussian elimination the second form is called Gauss-Jordan elimination The nice thing about fully reducing the matrix is now you have you re entire solution on the right side.", + "video_name": "JVDrlTdzxiI" + }, + { + "Q": "\nAt 1:58 why is the square root of 74,74", + "A": "That square root of 74 is squared, so you have sqrt(74) and you square it, by definition you get 74.", + "video_name": "T0IOrRETWhI" + }, + { + "Q": "\nAt 00:27, wouldn't we cross off 7 and 49 and simplify them like Sal did at 00:56? I'm a bit confused.", + "A": "Yes, you can. Doing so makes the problem easier as well.", + "video_name": "pi3WWQ0q6Lc" + }, + { + "Q": "\nin the captions of 5:23 - 5:26 it says \"maybeyou\"", + "A": "It might have just been a mistake. It s been sorted out now (it says maybe you)", + "video_name": "DPuK6ZgBGmE" + }, + { + "Q": "at 2:03, what does Sal mean by deviate?\n", + "A": "Sorry I am late but deviate basically means how far the number is from the mean. Where sal uses it, Sophia (I think that was her name) blew 5 bubbles and the mean is 4, so when you deviate, you find the distance away from the mean.", + "video_name": "DPuK6ZgBGmE" + }, + { + "Q": "\nFor this problem I looked at just the equation and solved like in the \"Factoring 5th degree polynomials to find real zeroes\" (pervious) video. I took y=x^3+3x^2+x+3 and split it into two, just like in 4:20, x^3+3x^2 and x+3. When I got to the (x^2+1) (x+3) I factored out the (x^2+1) again and got (x-1) (x+1). Now I have three solutions, x= -3, -1, 1.\nWhy is this not applicable?", + "A": "Because x^2 + 1 is not equal to (x - 1)(x + 1). If you multiply that out, you will get x^2 - 1.", + "video_name": "uFZvWYPfOmw" + }, + { + "Q": "\nAt around 2:20 Sal says that the polynomial function has three roots. Can someone explain how we know that ? :^)", + "A": "Because the polynomial is a 3rd degree polynomial (x^3). 2nd degree polynomials (x^2) have 2 solutions and 1st degree polynomials (x^1) have only 1 solution. Hope this helps. Good Luck.", + "video_name": "uFZvWYPfOmw" + }, + { + "Q": "\nAt 5:23, you say that x^3 divided by x^2 =x , why would that be?", + "A": "Note that: \u00f0\u009d\u0091\u00a5\u00c2\u00b3 = \u00f0\u009d\u0091\u00a5 \u00e2\u0080\u00a2 \u00f0\u009d\u0091\u00a5 \u00e2\u0080\u00a2 \u00f0\u009d\u0091\u00a5 \u00f0\u009d\u0091\u00a5\u00c2\u00b2 = \u00f0\u009d\u0091\u00a5 \u00e2\u0080\u00a2 \u00f0\u009d\u0091\u00a5 Therefore: \u00f0\u009d\u0091\u00a5\u00c2\u00b3/\u00f0\u009d\u0091\u00a5\u00c2\u00b2 = (\u00f0\u009d\u0091\u00a5 \u00e2\u0080\u00a2 \u00f0\u009d\u0091\u00a5 \u00e2\u0080\u00a2 \u00f0\u009d\u0091\u00a5)/(\u00f0\u009d\u0091\u00a5 \u00e2\u0080\u00a2 \u00f0\u009d\u0091\u00a5) = \u00f0\u009d\u0091\u00a5 We could also use exponent properties: \u00f0\u009d\u0091\u00a5\u00c2\u00b3/\u00f0\u009d\u0091\u00a5\u00c2\u00b2 = \u00f0\u009d\u0091\u00a5\u00c2\u00b3\u00e2\u0081\u00bb\u00c2\u00b2 = \u00f0\u009d\u0091\u00a5\u00c2\u00b9 = \u00f0\u009d\u0091\u00a5 Comment if you have questions.", + "video_name": "MZl6Mna0leQ" + }, + { + "Q": "At about \"8:00\" you prove that the linear combination of the two vectors can represent any vector in R^2.And then you set to prove that they are linearly independent.\n\nIsn't it self proving that if two vectors span R^2 (and n vectors span R^n) they HAVE to be linearly independent?\nJust my intuition speaking.\n", + "A": "If n vectors spans R^n, then n vectors are linearly independant and a basis for R^n. So you are right in your intuition.", + "video_name": "zntNi3-ybfQ" + }, + { + "Q": "at the end of the video 18:47 he says that in order for a set to be a basis it has to have the minimum or the most efficient set o vectors that can span R2.\nWhat does he mean for most efficient?\n", + "A": "It means the set with the smallest possible number of vectors. So the set containing <1, 0>, <0, 1>, and <1, 1> is not a basis, since <1, 0> and <1, 1> already span R\u00c2\u00b2. The <1, 0> vector is unnecessary.", + "video_name": "zntNi3-ybfQ" + }, + { + "Q": "In the example that Sal provides around 22:58, is it obvious from the start that the rank of the 3x2 matrix can be at most 2 and therefore less than 3, and therefore not \"onto\" R3?\n", + "A": "That would be a correct observation, yes! :) In his case, the function is not surjective (therefore not invertible), but injective- because rank(S) = n.", + "video_name": "eR8vEdJTvd0" + }, + { + "Q": "\nAt 3:15 on the video Sal starts by doing the subtraction, per order of operations shouldn't the division of /c be done first? If not, why not?", + "A": "Given: 1 1 \u00e2\u0094\u0080 - \u00e2\u0094\u0080 a b 1 \u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080 \u00c3\u00b7 \u00e2\u0094\u0080 c d The 1/a - 1/b is treated has a parenthetical term, which gives it order precedence: \u00e2\u0094\u008c \u00e2\u0094\u0090 \u00e2\u0094\u00821 1\u00e2\u0094\u0082 \u00e2\u0094\u0082\u00e2\u0094\u0080 - \u00e2\u0094\u0080\u00e2\u0094\u0082 \u00e2\u0094\u0082a b\u00e2\u0094\u0082 \u00e2\u0094\u0094 \u00e2\u0094\u0098 1 \u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080 \u00c3\u00b7 \u00e2\u0094\u0080 c d \u00e2\u0094\u008c \u00e2\u0094\u0090 \u00e2\u0094\u0082 b a \u00e2\u0094\u0082 \u00e2\u0094\u0082\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080 - \u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0082 \u00e2\u0094\u0082a\u00e2\u0080\u00a2b a\u00e2\u0080\u00a2b\u00e2\u0094\u0082 \u00e2\u0094\u0094 \u00e2\u0094\u0098 1 \u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080 \u00c3\u00b7 \u00e2\u0094\u0080 c d b - a \u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080 a\u00e2\u0080\u00a2b 1 \u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080 \u00c3\u00b7 \u00e2\u0094\u0080 c d b - a 1 \u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080 \u00c3\u00b7 \u00e2\u0094\u0080 a\u00e2\u0080\u00a2b\u00e2\u0080\u00a2c d b - a d \u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080 \u00e2\u0080\u00a2 \u00e2\u0094\u0080 a\u00e2\u0080\u00a2b\u00e2\u0080\u00a2c 1 d\u00e2\u0080\u00a2(b - a) \u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080 a\u00e2\u0080\u00a2b\u00e2\u0080\u00a2c d\u00e2\u0080\u00a2b - d\u00e2\u0080\u00a2a \u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080\u00e2\u0094\u0080 a\u00e2\u0080\u00a2b\u00e2\u0080\u00a2c", + "video_name": "_BFaxpf35sY" + }, + { + "Q": "At 5:40, why can't you simplify the expression (db-da)/(abc) by cancelling the a variable or the b variable to make it become (d-d)/(c)?\n", + "A": "You cannot do that because the db and the da are being subtracted. If there was a multiplication sign (ex. (db*da)/(abc) ) you would be fine to do that.", + "video_name": "_BFaxpf35sY" + }, + { + "Q": "\nat 4:10, why must we multiply by the reciprocal of c??", + "A": "Multiplication by the reciprocal of c is the same as dividing by c.", + "video_name": "_BFaxpf35sY" + }, + { + "Q": "At 3:25 Sal quickly glosses over how he transforms 1/a - 1/b into b/ba - a/ba. I think an explanation about how these two statements are equivalent would be useful!\n", + "A": "For the 1/a term, multiply it by b/b. Now you have: (1/a)(b/b) = b/ab For the 1/b term, multiply it by a/a. Now you have (1/b)(a/a) = a/ab So you have converted 1/a - 1/b into b/ab - a/ab.", + "video_name": "_BFaxpf35sY" + }, + { + "Q": "\nin the video at 5:00 d is multiplied by (b-a) and c multiplied by ab so whenc is multiplied why is the answer abc instead of acbc", + "A": "The distributive property multiplies across addition or subtraction. d (b-a) = bd - ad But, with c (ab), there is no addition or subtraction. Thus, the distributive property does not apply. You just get abc Note: think about what happens with numbers. 2 (3*5) = 2*3*5 = 6*5 = 30 You just have 3 numbers to multiply, not 4. Hope this helps.", + "video_name": "_BFaxpf35sY" + }, + { + "Q": "At about 8:00, he turns A^2=h^2-h^2/4\nto\nA^2=h^2(1-1/4)\n\nI don't get how he did that.\n", + "A": "That confused me at first too, but then I realised that since h^2/4 is 1/4 of h^2, h^2 - h^2/4 is equal to three quarters of h^2, which is the same as h^2 times 1 - 1/4.", + "video_name": "Qwet4cIpnCM" + }, + { + "Q": "I'm pretty sure this is true, but just want to be sure. When he make the denominators the same in the last problem around 3:30, does the five still remain? For example does 5 4/9 = 5 28/63? This makes sense to me as to why it would be right, I just want to know if actually am.\n", + "A": "Yes. The 5 stays put because you re only changing the 4/9 by multiplying it. The fraction is manipulated, but the whole number is not.", + "video_name": "R8YKuGJ0plI" + }, + { + "Q": "\nWhen you factor it out at 1:46 what becomes of that lonely +x in the middle of the equation?", + "A": "When (x+3)(x-2) is multiplied you distribute the first and last numbers separately, meaning that you have (x^2 - 2x +3x -6) as your answer. After combining the like terms of -2x and +3x we get +1x or simply put, + x. (x^2 + x - 6)", + "video_name": "EAa3J_nDkoI" + }, + { + "Q": "at 2:55 - when it says f(x)= x +3 why did you graph on the y axis... u went up 3 and then u added the limit of 2 in there and said it would be 5 do we do that for all problems?\nso when it says f(x) its only really saying y= x+3 so we go up 2? is that the B in Y=MX +B ??\n", + "A": "In the example f(x)=x+3 the vertical axis is the f(x) axis. Generally f(x ) is the same thing as y. So f(x)=x+3 is the same thing as y=x+3.", + "video_name": "EAa3J_nDkoI" + }, + { + "Q": "at 1:08 sal mentioned radians. what are they ??\n", + "A": "They are another unit of angle measure like degrees. In higher level math, they are much easier to use. You can learn about them in the Trigonometry section of KA.", + "video_name": "1BH2TNzAAik" + }, + { + "Q": "\nAt 1:25, how can you put fraction on top of another fraction?", + "A": "It looks messy, but you can do it. When you put a fraction on top of another fraction it helps to think of it as the numerator fraction divided by the denominator fraction.", + "video_name": "1BH2TNzAAik" + }, + { + "Q": "\nAt 10:14, couldn't have Sal simplified 10y and 4y by dividing it?\nSo if my reasoning is correct (you can correct me if I'm wrong, here to learn :)),\nthe answer should be 5y\u00e2\u0088\u009ay+25y divided by 2y - 25.", + "A": "No, Sal can not reduce the fraction. To reduce fractions we can only cancel common factors (items being multiplied). You are trying to cancel out parts of terms (items being added/subtracted). Since they aren t factors, you can reduce. Hope this helps.", + "video_name": "gY5TvlHg4Vk" + }, + { + "Q": "At 10:11 why didn't he add 10y and 25y to make 35y square root y as the numerator?\n", + "A": "You can t add unlike terms. The expression in the numerator is: 10y\u00e2\u0088\u009a(y) + 25y. These are unlike because y\u00e2\u0088\u009a(y) is not the same as just y . Its like having 10yz + 25y. Hope this helps.", + "video_name": "gY5TvlHg4Vk" + }, + { + "Q": "9:23, Why would I be multiplying as x * x, sqy * sqy , -5*5\nfor the denominator. but in the numerator its\n\n2 * 5, sqrY*y 5*5\nhow come the numerator is being applied to all terms and the denominator is being multiplied by like terms?\n", + "A": "In the numerator since we are multiplying ( 2*sqrt(y)-5 ) by its complement we are using a shortcut. If you multiply a factor by its complement like (x+a)*(x-a) you get x^2-a^2 Proof: (x+a)*(x-a)=x*x+x*(-a)+a*x-a*a=x^2-a*x+a*x-a^2=x^2-a^2 so we can use shortcut on the numerator: ( 2*sqrt(y)-5 )*(2*sqrt(y)+5)=(2*sqrt(y))^2 - (5)^2= 4y-25 or we can do it the long way like: ( 2*sqrt(y)-5 )*(2*sqrt(y)+5)=2*sqrt(y)*2*sqrt(y)+2*sqrt(y)*5-5*2*sqrt(y)-5*5 =4y-25 Both give you the same answer. Hope this makes sense.", + "video_name": "gY5TvlHg4Vk" + }, + { + "Q": "\nAt @2:54 isn't the minus symbol after 8 supposed to be in the green color because of how it's a -12?", + "A": "mabey and do you want to be friends", + "video_name": "GmD7Czmol0k" + }, + { + "Q": "At 3:16, can you always just cross out all the numbers that are congruent in the same equation, or is it better, more accurate, to solve the equation all the way through?\n", + "A": "He did not cross out numbers that are congruent, he crossed out additive inverses, so 3 - 3 = 0. If they were congruent, you would get 3 + 3 to get 6", + "video_name": "GmD7Czmol0k" + }, + { + "Q": "\nAt 2:30 when i solved for the equation 0.7^0 multiplied 0.3^6 my answer was 0.000729 not 0.001.", + "A": "Your calculation is correct but he is rounding to the nearest 1/100. Thus, 0.000729 ~ 0.001.", + "video_name": "eL965_Lscb8" + }, + { + "Q": "\nI think you made a mistake at the end (12:18):\ny = (2/5)*x + (2/5) should be y = (2/5)*x + (4/5)", + "A": "you are correct 4/5 is b*", + "video_name": "QkepM8Vv3kw" + }, + { + "Q": "\nAt around 2:50, do we always have to multiply by negative one? in every system?", + "A": "Not 100% on the context, but it looks like he s eliminating a variable. The answer is no. It depends on the coefficient of the variable you re tying to eliminate. If the first equation was -3x + ... and the bottom was x + ...., you would just multiply by 3. In general terms: You want A + B = 0, where A and B are coefficients of the first term. To do that, you choose some c such that A + cB = 0. The key thing to remember is to multiply both sides of the equation by c. ex) c*(Ax + By) = 10*c", + "video_name": "z1hz8-Kri1E" + }, + { + "Q": "\nAt 0:25 does that mean you can change it around for every operation?", + "A": "No. It only works for multiplication and addition because they are commutative. Communitive means that no matter where your numbers are, you get the same answer. Helpful?", + "video_name": "SfxULALs_u8" + }, + { + "Q": "\n9:20, couldn't he also have used HL Theorem to prove DBE and FBE are congruent?", + "A": "Yes, that is what Sal is calling the RSH theorem at around 9:00. Either strategy is effective for showing that the two triangles are congruent.", + "video_name": "yj4oS-27Q3k" + }, + { + "Q": "At 7:55, Sal begins the proof of the reverse case, where: if a point is equidistant from both sides of an angle, then that point is on the angle bisector. So that is clear, but when I went on to the videos about medians, I thought, if the median bisects the side opposite the vertex, then that point is also equidistant from both sides of the angle from that vertex, so that makes it an angle bisector, right? Well, apparently not, so I'm confused. What is the relationship of angle bisectors and medians?\n", + "A": "As far as I know a median is set to see if the sides are equal to each other, where an angle bisector splits a angle in half making said angle into 2 equal angles. If I am wrong sorry its been awhile seance i went over medians.", + "video_name": "yj4oS-27Q3k" + }, + { + "Q": "At 7:07, Vi says that the cardioid is like an \"Anti-parabola\", and I don't quite understand what that mean. Please explain.\n", + "A": "If you turn positive to negative, infinity to zero while graphing a parabola you get a cardioid", + "video_name": "v-pyuaThp-c" + }, + { + "Q": "at 3:00 whats a prolabala?\n", + "A": "Did you mean parabola? A parabola is basically the opposite of a hyperbola. If you took two identical and perfectly symmetrical cones and lined then up perfectly, one on top of the other, meaning one right-side-up and the one on top upside-down, so it should look some what related to the shape of an hour glass. In a hyperbola, no matter how far you draw out the lines, the ends will never meet. In a parabola it is quite the opposite, or a least that s what I think.", + "video_name": "v-pyuaThp-c" + }, + { + "Q": "how does she do the plaid thing at 4:27\n", + "A": "The circles overlapped over each other, and created a pseudo-grid of shapes. She just alternated colors between them.", + "video_name": "v-pyuaThp-c" + }, + { + "Q": "3:37 - 3: 40 why would you divide by 10 when the scientific notion is 10^-2??\n", + "A": "Actually, Sal was multiplying by 10, so 10^-3 * 10 is 10^-2.", + "video_name": "ios3QL9t9LQ" + }, + { + "Q": "\nWhen you move the decimal point in 4.1 to the right, does it increase or decrease the exponent of 10? How about moving it to the left? At 1:41, Sal is doing it a way I wasn't taught so I am getting confused.", + "A": "When you move the decimal to the right in 4.1, it decreases the exponent by I or how many spaces you move the decimal to the right. When you move it to the left, the exponent of 10 will increase. This is one way you can think about it, when you are moving the decimal point to the right, you are putting a SMALLER number into scientific notation. When you are moving the decimal point to the left , you are putting a LARGER number into Scientific notation.", + "video_name": "ios3QL9t9LQ" + }, + { + "Q": "\nat 3:50, why does he divide by 10?", + "A": "You Cannot have a scientific notation over 10 so he divides 38.4 by 10 to make it valid for a scientific notation, giving you the answer of 3.84 x 10^-2", + "video_name": "ios3QL9t9LQ" + }, + { + "Q": "At 3:13, did Sal just invert and multiply? Also can I cross multiply and then transfer the 4 to divide the other side by 4?\n", + "A": "Yeah it looks to me like he just multiplied the reciprocals of the two numbers. I don t think you could just transfer the 4 to the other side, I think you d have to divide BOTH sides by four which would get X alone, and then you could divide the other side by 4. Hope this helps!", + "video_name": "lEGS5ECgFxE" + }, + { + "Q": "\nWhat about when im trying to solve with fractions or is the form 2:5 the same as 2/5", + "A": "No, it isn t. It should be 2/7 because you re dividing into 7 sections. If you need more explanation, just ask me.", + "video_name": "lEGS5ECgFxE" + }, + { + "Q": "So in one of my questions it says the ratio between AC and BC is 2:3 and to find point B. Then when I click on hint it says the ratio between AC and BC is 2:3 therefore the ratio between AB and AC is 2:5, how does that work?\n", + "A": "AC to BC is 2 : 3 and since they are the only two parts of the line segment AC, the segment has a total of 2 + 3 = 5 parts. Therefore, AB to the whole thing (AC) is 2 : 5.", + "video_name": "lEGS5ECgFxE" + }, + { + "Q": "At 3:29,How did Sal used the chain rule and got the derivative to be (e^((ln a)x) * ln a).\nShouldn't we use the power rule? I mean, if Sal is using the chain rule, (d [f(g(x))]) / dx =f \u00e2\u0080\u00b2(g(x)) g \u00e2\u0080\u00b2(x), then what is the f(x) and g(x)?\nThank you for you reply\n", + "A": "He let \u00f0\u009d\u0091\u0094(\u00f0\u009d\u0091\u00a5) = \u00f0\u009d\u0091\u00a5ln \u00f0\u009d\u0091\u008e and \u00f0\u009d\u0091\u0093(\u00f0\u009d\u0091\u00a5) = \u00f0\u009d\u0091\u0092\u00cb\u00a3. Power rule only works when the power is a constant, not a variable which we are differentiating WRT.", + "video_name": "gHzLHknEk1M" + }, + { + "Q": "At 3:51, how would you write 8^ -1/3 as a radical? Would it be the negative third root (with the three over the root symbol being negative)?\n", + "A": "Any value raised to a negative exponent is the reciprocal of that value raised to the same positive exponent. For example: 8^(-1/3)=1/(8^(1/3))=1/2", + "video_name": "eTWCARmrzJ0" + }, + { + "Q": "\nWow, that was a lot of information to soke in. I don't really get the last example. At 3:36, Sal was giving another example that was very complicate. Can someone help me with it?", + "A": "I got lost when Sal talked about he reciprocal of 2 and then he quickly moved on to 1/3 being -3.", + "video_name": "eTWCARmrzJ0" + }, + { + "Q": "\nAt 1:37 how did you get 1/3 im not really understanding how I would get that?", + "A": "Look ! it was a good question but hear him again . Sal said you need to think in a different manner so, if you look at the question with log 2 with base 8 you have an anti-log or the exponential form as 2= 8^x so for cube Root we have 8 to the power 1/3 . For example 2 to the power 1/2 means an under root of 2 . so same way is for cube root i.e, power 1/3. hope you like the answer", + "video_name": "eTWCARmrzJ0" + }, + { + "Q": "\nat 1:29 he says since 2x2x2=8 so there fore the answer is 1/3 i dont really get this can you help me? ( im not even learning this yet I'm in 7th grade algebra 1 honors, i just want to be prepared)", + "A": "Logx(2)=8 can also be told as 8^x=2. For 8 to be less than itself as 2, the exponent must be a fraction or negative as in powers, fractions and negative integers make the number smaller while whole numbers make the number bigger in this situation. This is not true for all situations. The reason x=1/3 is because it means 8^(1/3)=2. The cube root of 8 is 2 because 2x2x2=8. So that means log 1/3(2)=8, which is true. I m also in 7th grade algebra 1 honors.", + "video_name": "eTWCARmrzJ0" + }, + { + "Q": "At 1:27, how did he get 1/3?\n", + "A": "The question is effectively what power do you need to put 8 to, to get 2. As 2^3=8, 8^(1/3) must equal 2.", + "video_name": "eTWCARmrzJ0" + }, + { + "Q": "At around 5:39 he put 5x-5. But why did he do that? Why didn't he distribute all the way?\n", + "A": "Sal is multiplying the trinomial with a fraction that has the trinominal in the denominator. Thetrinomials cancel out. This is just like if you multiply: 7 * 5/7, the 7 s cancel out leaving just the 5 behind. Hope this helps.", + "video_name": "pLCmwHsDYqo" + }, + { + "Q": "\nat 5:36, Sal canceled the denominator and is only left with the numerator. Why he doesn't distribute the x^2-x+1 into 5x-5 as well? Thanks!", + "A": "The entire fraction is one term, so he is distributing x^2-x+1 into the entire fraction, not just the denominator. Let s say 5x-5 = a and x^2-x+1 = b. Distributing into the last term would leave you with (a/b) * b. Simplifying this would just leave you with a, or 5x-5. This question was asked last year, so my answer is a bit late - you may have already figured it out yourself - but maybe it ll help with someone else who has this question, since there are no other answers here.", + "video_name": "pLCmwHsDYqo" + }, + { + "Q": "@ 0:51 How He Knows That Slope is -4 by just seeing the Equation of Function?\n", + "A": "The equation of a line is y = mx + b. m is the slope of the line. In the video the equation is g(x) = -4x + 7, so -4 is the slope of the line.", + "video_name": "nGCW5teACC0" + }, + { + "Q": "\nAt 3:38, Sal says that the slope will be the same no matter what points are picked in the line. Does that mean the derivative of f or f'(x) will always equal to the slope of the secant line in the function? I just thought even if f(x) and f(x+h) are extremely close (derivative), they would have the same slope as the general slope of the function, therefore derivative equals to the slope.", + "A": "The function Sal is talking about here is linear, so its graph is a straight line. In this case we can t take a secant in the normal sense of the word. Every line that passes through two points on the graph of this function will be the same as the line that graphs the function. This is the only situation where the slope will be the same no matter what points are picked.", + "video_name": "nGCW5teACC0" + }, + { + "Q": "at 0:40 I dont get how did he draw that line...he says the line has a slope of -4 but i dont get how that works...pls help meunderstand this :/\n", + "A": "The slope of a line can be found from its coefficient before x in its equasion. For example, the line y = -4x + 7 has a slope of -4 because it is the coefficient before x. It also represents the tangent of the angle created by the line and the positive direction of the X axis. However, most curves don t behave like that.", + "video_name": "nGCW5teACC0" + }, + { + "Q": "Regarding, the y constraint at 2:30 - 2:44. I don't really get it why it is >= 1...\n", + "A": "If y is a number less than 1, it will make the value sqrt (x - 1) not able to be graphed in the Cartesian plane. (eg you cannot plot sqrt (-4) etc) There s no x-value that would then satisfy the condition sqrt (x - 1) = x + 2. So the constraint for y >= 1.", + "video_name": "aeyFb2eVH1c" + }, + { + "Q": "\nAt 04:28, why don't we take the positive and negative sqrt of ( y -1 ) ?", + "A": "As Sal explained earlier in the video, (x+2)^2 can only be positive, due to the restriction on the function x>=2. Therefore, the square-root of (y-1) can only be positive. The next steps after this are purely algebra, and have nothing to do with a positive or negative square root.", + "video_name": "aeyFb2eVH1c" + }, + { + "Q": "At 1:42, Sal said that if x was greater than or equal to -2 then the underlined expression would be positive, but zero isn't positive.\n", + "A": "So the inverse of y is x it s opposite.", + "video_name": "aeyFb2eVH1c" + }, + { + "Q": "\nat 7:12 what is the range of the inverse O_o ?", + "A": "The range of the inverse is the domain of the original function.", + "video_name": "aeyFb2eVH1c" + }, + { + "Q": "ok,...at 1:04 does anyone understand moving the decimal?\n", + "A": "You multiply like you always do, & when you are done, take that answer and put in the decimal. Oh you want me to also tell you where the decimal goes? Sure, just count how many numbers where behind the decimal in the 2 numbers that you multiplied, and make sure that your answer has the same amount of numbers behind the new decimal. (Hint, when you get harder problems, your going to have to get comfortable putting extra zeros right behind the decimal, before your answer, sometimes!) -Cheers!", + "video_name": "JEHejQphIYc" + }, + { + "Q": "\n@1:26, what do you do if there is a digit instead of a zero? Like say 32.12 multiplied by 35. I'm stuck on that part!", + "A": "You just add as many zero where there are no numbers for example 63.46 +02.59", + "video_name": "JEHejQphIYc" + }, + { + "Q": "at 0:07 the problem has a dot in between 32.12 and 0.5 what does that dot mean?\n", + "A": "It is the same as the multiplication sign. Once you start using variables, it gets really confusing.", + "video_name": "JEHejQphIYc" + }, + { + "Q": "\nAt 1:00 she says \"two separate... um, two separate...\". What does actually result from cutting it like so?", + "A": "its a mobius strip.", + "video_name": "AmN0YyaTD60" + }, + { + "Q": "did anyone notice the mistake in 1:01 - 1:02\n", + "A": "I honestly couldn t because she was talking too fast for me to understand.", + "video_name": "AmN0YyaTD60" + }, + { + "Q": "1:29 shows that vi hart is just awesome\n", + "A": "This should be in Tips and Thanks, not Questions.", + "video_name": "AmN0YyaTD60" + }, + { + "Q": "I calculated the answer to the formula at 12:33, and I got 0.004998. can someone explain the intuition here? I also tried calculating what would be p(x=9), and I got ~0.13\n", + "A": "OK, so I used excel to graph all possible results from X=0 => X=20. I got a nice bell curve, and the sum inside is indeed 1...pretty cool. Indeed 13% (for 9, 10) seems to be the most likely outcome.", + "video_name": "Jkr4FSrNEVY" + }, + { + "Q": "At 1:50 you said that 800 + 0 + 4 is 804. That is correct, but what is the reason to say 800 + 0 + 4 if the 0 doesn't have any value?\n", + "A": "He s trying to reinforce the concept that the numbers have different values based on their place, and how we keep track while we multiply. If it was 231 instead, it would work out to 800 + 30 + 4.", + "video_name": "4BtXvopHXI8" + }, + { + "Q": "\nAt 8:13, he says 1/2^2 is just 1/2. but isn't that 1/4 since it's 1/2 x 1/2?? and he did the same thing for 1/3. shouldn't the answer have been 1/27?", + "A": "it s only squaring one in the numerator, not the quotient as a whole. so (1^2)/2 is just 1/2", + "video_name": "vhMl755vR5Q" + }, + { + "Q": "AT 0:56 on the video you multiply all numbers and how do you get the second number\n", + "A": "When Sal does 6x8x7, instead of doing 48x7, he does 40x7, which is 280, and 8x7, which is 56. Adding the two up gets 336. You get the same answer doing 6x8x7, or 48x7.", + "video_name": "I9efKVtLCf4" + }, + { + "Q": "At 2:08, if the x-axis is inches, and later on it is shown that the area under the curve is the probability, what is the y-axis representative of, as far as units or meaning?\n", + "A": "Y is the rate of change of the area as you change the range of desired outcomes (x). E.g. if y is .5 then probability (area) is increasing at the rate of .5 per additional inch of rain in the interval of chosen outcomes.", + "video_name": "Fvi9A_tEmXQ" + }, + { + "Q": "\nAt 2:00, is .5 a bad example for the height? In a continuous random variable, it's very unlikely any observation is this common. If the y axis is not probability of a particular rainfall level, what is it?", + "A": "the rainfall amounts are on the x axis. The probability is for an interval (range of possible outcomes) and is the area under the curve for that interval. Y is the rate of change of probability (area) for an interval as it changes limits (as x changes).", + "video_name": "Fvi9A_tEmXQ" + }, + { + "Q": "\n8:50 This might be a stupid question, but is a probability distribution function related only to discrete random variables and a probability density function is for continuous random variables?", + "A": "From Wikipedia: The terms probability distribution function and probability function have also sometimes been used to denote the [continuous] probability density function. However, this use is not standard among probabilists and statisticians. I don t believe that a probability distribution of a discrete random variable is referred to as a function. Maybe it could be made into a step function, but I don t know if that is common.", + "video_name": "Fvi9A_tEmXQ" + }, + { + "Q": "At 4:27 it is said that the probability of something happening is \"actually zero\". Which makes sense when you are talking about area under a curve, but it doesn't make intuitive sense because doesn't that mean that the probability of ANYTHING happening in a continuous variable is zero? That doesn't make sense because things are still going to happen, even though we are saying the probability is zero. So if it rains in California, the exact amount of rain that came down had a zero probability of happening?\n", + "A": "This is quite an interesting question! While all impossible events definitely have probability zero of occurring, the reverse is not always true! An event that has probability zero of occurring could still be possible, though extremely unlikely. The probability that a continuous random variable equals any specific, exact value is always zero, but the probability that a continuous random variable lies in a specific interval of real numbers could be greater than zero. Have a blessed, wonderful day!", + "video_name": "Fvi9A_tEmXQ" + }, + { + "Q": "\nat 1:55, why does he do it like a(a+b) + b(a+b) instead of (a x a) + (ab) + (ab) + (b x b)?", + "A": "He is just showing a simpler way of doing it..it looks a little less confusing, :) Hope that helps!", + "video_name": "xjkbR7Gjgjs" + }, + { + "Q": "\nAt 0:23 isn't pretty redundant to point this out this late in the course wouldn't it help to emphasize this point earlier?", + "A": "Well not everyone watches all the videos on order. If people are just watching this specific video because they re not so strong at this topic, you don t know what they already know so it might be a helpful reminder for them", + "video_name": "xjkbR7Gjgjs" + }, + { + "Q": "At 3:15, what was wrong with leaving 7x^2 as is? When he simplified it, he still got 49x^2 so it didn't get rid of the x or the square, so i don't know why he did it. But it seems like it changes the answer, so could someone help me understand?\nThanks in advance.\n", + "A": "He was solving not simplifying. Distribute the ^2 in (7x)^2 and you have 7 squared, which is 49, and x squared, which is x^2.", + "video_name": "xjkbR7Gjgjs" + }, + { + "Q": "\nFrom 6:30 to 6:56, Sal lists non linear equations Why are they nonlinear?", + "A": "A linear equation is only one where x is to the power of 1, generally some form of y=x Its graph is a straight line. In all the equations listed, x was being raised to a power that was either less than or greater than 1 - for example, x^2, or 1/x, which is the same as x^-1. If you look at the graphs of any of those equations, they re curves, not straight lines.", + "video_name": "AOxMJRtoR2A" + }, + { + "Q": "\nat 0:36 he explains that negitive 3p minus p is equal to negative 4 p. how is that possible.", + "A": "To combine like terms, you add / subtract the coefficients (the numbers in front of the variables). The coefficient of -3p is -3 The coefficient of - p is -1 -3 - 1 = -4 If you don t get this part: -- use a number line: got to -3. To take away 1, you move 1 unit to the left. You will now be on -4. -- and, you need to review the lessons on adding and subtracting negative numbers. Thus, -3p - p = -4p Hope this helps.", + "video_name": "SgKBBUFaGb4" + }, + { + "Q": "\nat 1:32 why did sal attach the rope of the mast all the way at the top\nhow does he know where to put the rope on the mast?\nthanks for whoever answers my question in the future!!\nthanks future answers", + "A": "The question clearly states that the rope is attached to the top of the mast.", + "video_name": "JVrkLIcA2qw" + }, + { + "Q": "i don't understand how this works does the dot such as in : 4'5 ( the ' means dot . look at 1:11 to 3:30 ) does that dot system work fo more than 1 digit numbers ??\n\nThanks\nYaz Lightning\n", + "A": "The dot is used for any number, large or small. It is mainly used in algebra, where x could be a variable, not an operator. Hope it helped!", + "video_name": "Yw3EoxC_GXU" + }, + { + "Q": "At 1:14 that looks like a decimal point?\n", + "A": "Yes. The dot, point or period can be used to mean the decimal point, or it can be used instead of the multiplication symbol to mean multiplied by , just like x . You can usually tell from the context what the dot is being used for. As a decimal point, it is normally written at the bottom, where commas and periods go in writing regular sentences. As a multiplication symbol, it is normally written higher up, like the hyphen as in break-dance .", + "video_name": "Yw3EoxC_GXU" + }, + { + "Q": "\nSal keeps on saying Thrill (cola) instead of Thrill (soda), right?\nI think its at 2:02 one of the times.", + "A": "well really that s not the point and it doesn t really matter, but yeah.", + "video_name": "gs-OPF3KEGU" + }, + { + "Q": "\n@ 3:00 we play, what seems to me to be, a dirty trick and move the dx to before the e^x... term. How is that OK? If this is a valid algebraic tool then why not do that every time we have a product so that \u00e2\u0088\u00ab a \u00e2\u0080\u00a2 b \u00e2\u0080\u00a2 c \u00e2\u0080\u00a2 dx can be simplified to \u00e2\u0088\u00ab a \u00e2\u0080\u00a2 dx \u00e2\u0080\u00a2 b \u00e2\u0080\u00a2 c? This of course isn't right because we could just insert a 1 x in the front of any expression and play the same trick, e.g. \u00e2\u0088\u00ab a = \u00e2\u0088\u00ab 1 \u00e2\u0080\u00a2 a dx = \u00e2\u0088\u00ab 1 dx a = x \u00e2\u0080\u00a2 a + C which can't be right.", + "A": "A notationally better version of your equation is \u00e2\u0088\u00ab a \u00e2\u0080\u00a2 dx = \u00e2\u0088\u00ab a \u00e2\u0080\u00a2 1 \u00e2\u0080\u00a2 dx = a \u00e2\u0080\u00a2 \u00e2\u0088\u00ab 1 \u00e2\u0080\u00a2 dx = a \u00e2\u0080\u00a2 x + C , so your example equation is essentially correct, apart from forgetting the dx in the first integral.", + "video_name": "b76wePnIBdU" + }, + { + "Q": "\nAt time 1:44 why do you swap the sign if you aren't dividing by a negative number to solve the right side of the inequality? How come the sign switches from less than or equal to, to greater than or equal to? what is the logic behind that?", + "A": "He moved all of the constants from the right side of the inequality to the left. He left the variable on the right side if the variable is on the right side you swap the sign. I just isolate my variable and bring it to the left and all the constants on the right it s a lot less confusing! Hope that helped!!", + "video_name": "A3xPhzs-KBI" + }, + { + "Q": "\nwhy does he add 4 to every equation at 1:30?", + "A": "He does so to isolate x. By adding 4 to both sides, the x - 4 becomes x because (x - 4) + 4 = x.", + "video_name": "A3xPhzs-KBI" + }, + { + "Q": "\nWait....at like 3:10, in the vid, it says 54/10=5 remainder 4. So...since 4/10=.4, can we write it as 5.4? Are they the same thing?", + "A": "No, you can t. When someone says remainder 4 don t think it s .4. remainder 4 is going to be a whole number!", + "video_name": "STyoP3rCmb0" + }, + { + "Q": "\nAt 7:57, why can we not simply (3 * X ^ 2) - (4 * X ^ -5) ? I know it's a stupid question, but I am really confused. Will the answer not be = -1X^7?", + "A": "You cannot subtract exponents like that. In order to do a subtraction, the exponent needs to match. Take a look below: 2^5 - 2^2 You re saying this would equal: 2^3 = 8 But if you evaluate it: 2^5 - 2^2 32 - 4 = 28 The exponents have to match in order for a subtraction or addition to work.", + "video_name": "mzOBlH32qdk" + }, + { + "Q": "\nSurely, at 0:30, the rule does also works if n = 0, since the derivative will equal 0.x^-1, which equals 0, and that is the derivative of a constant.", + "A": "It s pretty nitpicky, but 0 * x ^ (-1) is not always equal to 0. When x equals 0, it s undefined.", + "video_name": "mzOBlH32qdk" + }, + { + "Q": "\nWhat is the reasoning behind the taking the constant out of the dy/dx at 4:08?", + "A": "It is one of the rules/properties of derivatives so we are allowed to do that. Now, why would you do that? It is to make the computation easier. It is not very noticeable when the constant is a nice small integer and you are taking the derivative of a power. But things can get really messy when you take the derivatives of a quotient with chain rules (just an example). So it is easier to take a constant out. You do not need to take out a constant if you can compute with it.", + "video_name": "mzOBlH32qdk" + }, + { + "Q": "At 4:40, why Sal doesn't make a shortcut, and use the average of the past 4 exams as is? if we solve for - ( 82 + X ) divided by 2 = 88 , we could spare ourselves a step or two. is the number of past exams really necessary to the equation?\n", + "A": "now i noticed that Sal s way didn t work out. if we go the way i mentioned we get that X=92, and 92 + 84 = 176, then finally 176 / 2 = 88. so, if on past 4 exams you got an average of 84, to get an average of 88 - you ll have to get a score of 92 points on the next exam... isn t it?", + "video_name": "9VZsMY15xeU" + }, + { + "Q": "\n42:14=x:2 what does x equal", + "A": "X would equal 6.", + "video_name": "MaMk6-f3T9k" + }, + { + "Q": "So according, to this video,is 2/3 is equal to 2:3\n", + "A": "Yes you are understanding it very well", + "video_name": "MaMk6-f3T9k" + }, + { + "Q": "\nWhat do you do to find out the rate of 14:10?", + "A": "You first find the greatest common factor between the 2 numbers and divide each number by the factor. To find the missing rates your use the unit rate to find the proportional number to the number given.", + "video_name": "MaMk6-f3T9k" + }, + { + "Q": "At 3:23, how is 5 over x (100) + 5 = 5.05? How does the 5 become 0.5?\n", + "A": "I do not see where in the video 5 becoming 0.5, but dividing by powers of 10 moves decimal places, so 5/10 would be 0.5, 5/100 = 0.05, 5/1000 = 0.005, etc", + "video_name": "UvDcEvDC4vg" + }, + { + "Q": "\nAt 1:35, when we count do we always count starting from the right side if the rectangle?\nBecause if you see, when you count from the left side of the first blue rectangle, the total count is 9. But if i start counting from the right side of the firzt blue triangle it adds up to be 8.\nCan someone please explain this to me", + "A": "There are 8 rectangles, counting either from the left or from the right. I guess you re counting the sides rather than the rectangles. By doing so, you ll get 9 walls . Try counting the upper side of each rectangle...", + "video_name": "WeVWv_OEJsY" + }, + { + "Q": "\nNewbie here, how do you decide which side to initially subtract? 1:13 he deducts the left-hand variable using the right-hand equation's first \"9X - 7X\". What is a rule of thumb for deciding which side you are supposed to use? Thanks!", + "A": "It actually doesn t matter which side you subtract first - however, one way is easier then the other. When he subtracts 7x from 9x, he gets positive 2x. If he had subtracted 9x from 7x, he would ve gotten negative 2x, which is more confusing to work with. So, you can work out the equation and come to the same answer either way, but it is generally easier to work with positive numbers. Hope this helps!", + "video_name": "2CZrkdtgeNU" + }, + { + "Q": "At 2:19 how in the world does it equal to 140? I get 248?\n", + "A": "On 9x + 194, you made the mistake of adding, 54 to 194, correct? You should have done 9(-6) + 194 = -54 + 194 = 140 Instead you did 9(6) + 194 = 54 + 194 = 248 hope this helps (sorry I m a bit late)", + "video_name": "2CZrkdtgeNU" + }, + { + "Q": "at 10:44 if we were just asked to write the quadratic function would you just subtract the 61/20 from the right side to get it equal to 0\n", + "A": "If you wanted to set this up to use the quadratic equation, you would have just used the original problem given (10x\u00c2\u00b2 - 30x -8 = 0) and not bothered with all the complete the square stuff.", + "video_name": "bNQY0z76M5A" + }, + { + "Q": "At 10:20 it seems as if Sal forgot to right 3/2x\nI may be worng\n", + "A": "There is no 3/2 x. To complete the square, divide the coefficient of x by 2 and square it. It is just the coefficient that is divided by 2, not the whole middle term. Hope this helps.", + "video_name": "bNQY0z76M5A" + }, + { + "Q": "At 8:54, why would you half the coefficient?\n", + "A": "The easiest way to see why is to work backwards, expand (x+a)^2 to get (x+a)(x+a) using foil, you have x^2 + ax + ax + a^2 or x^2 + 2ax + a^2, so to complete the square, since b term is 2ax, we have to divide whatever coefficient is there by 2 so that 2ax/2 will leave us with ax. Hope this helps", + "video_name": "bNQY0z76M5A" + }, + { + "Q": "I'm confused about the part where he equates things at 01:59. If you have x2-4x+?=x2-2ax+a2\nshouldn't (-4x) correspond to (-2ax), meaning that a=2 (not -2)?\n\n(by \"x2\" I mean x squared)\n", + "A": "You re right. The first time I watched this video I didn t notice the problem because I knew what Sal intended to say and assumed he actually said what he intended -- but there s a mistake here. What he meant to do was set up (x+a)^2 (not (x-a)^2) on the right. That s the normal way to explain the process of completing the square. When he makes the substitution you mention, he does it as if he had written (x+a)^2 on the right, which is what he meant to do.", + "video_name": "bNQY0z76M5A" + }, + { + "Q": "I don't get it why does he do 5+4 instead of 9 ?\n\nat 3:00\n", + "A": "It is 9, but he wants to show that he added 4 to both sides in order to complete the square.", + "video_name": "bNQY0z76M5A" + }, + { + "Q": "Around 6:40, Sal divides the quadratic equation by 5. This process makes the coefficient of x^2 equal to 1. My question is does the coefficient of x^2 need to be 1 to complete the square.\n", + "A": "no it doesn t have to. for example; 2x^2+18x+16 one can factor this by.. (x+8)(2x+2) but if you divide everthing by 2, you can make 2x^2+18x+16 to x^2+9x+8 then you can factor this to (x+8)(x+1) you see, this is the same as (x+8)(2x+1) but simpler. so to answer your question; it doesn t matter, but is s the matter of which one is simpler hope this helps :)", + "video_name": "bNQY0z76M5A" + }, + { + "Q": "Where did Sal get the -2 two from at about 8:45?\n", + "A": "I assume you are referring to where he wrote: a = -3/2 The -3 comes from the equation. It is the coefficient of X Dividing by 2 is part of the process of completing the square. Note: Sal used 2, not -2. The minus sign is from the -3. I suggest you rewatch the video. You will see every time Sal completes the square that he takes the coefficient of X and divides it by 2.", + "video_name": "bNQY0z76M5A" + }, + { + "Q": "\nAround 0:47 he mentions a \"plain vanilla one for real numbers.\" Does that mean there is a square root for negative numbers?", + "A": "There is a square root for negative numbers but it is not yet taught at this level of math.", + "video_name": "4h54s7BBPpA" + }, + { + "Q": "At 0:34, why is the sign \"less than or equal to\"? Shouldn't it be just \"greater than\" because if x was 0, then it'd be the square root of -8?\n", + "A": "Sal IS using the greater than or equal to sign ( not the less than or equal to sign). But he isn t saying that x can equal zero. He s saying that the quantity ( 2x - 8 ) can equal zero. Then he has to solve that inequality to finally find out that x must be GREATER than or equal to 4.", + "video_name": "4h54s7BBPpA" + }, + { + "Q": "\nAt 2:00, why did you subtract 64 from the other side, where in other videos you added 64? What you do to one side you do to the other?", + "A": "Sal doesn t have an equation, so there is no other side. He is working with an expression. To ensure he maintains the original value of the expression, he can only add a value that equal 0 (this is the identify property of addition). This is done by adding the 64 and then also subtracting the 64. 64 - 64 = 0. Thus, he hasn t the expression. He s just making it look different. Hope this helps.", + "video_name": "sh-MP-dVhD4" + }, + { + "Q": "\nAt 3:09, Sal multiplied it by negative 1, but couldn't you just also subtract it with changing it in to a negative?", + "A": "but the can also mess you up right if you interpret it wrong right?", + "video_name": "-nlMXVrgtjw" + }, + { + "Q": "Can this work?\n\n1. First apply a rotation until the projected vector aligns with the vector we want to project to.\n2. Second scale the rotated vector accordingly.\n\nWill the matrix of product of the transformations in 1) and 2) be the same with the one Sal defined at at 13:01?\n", + "A": "This would theoretically work. However, you also require an expression for the angle between every possible vector and the vector you want to project onto. By the time you figure that out and get a way to convert it back into a linear transformation, you may as well have done what Sal did.", + "video_name": "JK-8XNIoAkI" + }, + { + "Q": "\nAt 5:43, Sal says that dx/dy is the slope of the tangent line at any point. I didn't see where it was explained how/why this represents the slope prior to this point; it was just injected as a given into the explanation midstream.\n\nIs this explained elsewhere? How did we go from having d/dx represent the slope to having dx/dy represent it here?", + "A": "I haven t watched the video but... d/dx is a differential operator. d/dx[4x] means take the derivative of the expression 4x with respect to x. If instead we write d/dx[f(x)] we would write df/dx as the derivative (or f (x)). The derivative represents the slope of the tangent line. dx means a very small change in x (infinitesimally small). and dy means a very small change in y. If you write dy/dx and y is your dependent variable then you have \u00e2\u0088\u0086y/\u00e2\u0088\u0086x which is the formula for slope.", + "video_name": "mSVrqKZDRF4" + }, + { + "Q": "\nAt 2:24 why is 4 divided in to 36 and why does 4 become a 1 ?", + "A": "it is because 36/4 equals 9", + "video_name": "RPhaidW0dmY" + }, + { + "Q": "in Gulshan the ratio of private homes to apartment is 3:5.if all apartments are bricks made and 1/6 of the private homes are wooden, that is maximum portion of houses that may be brick...........??\n", + "A": "3+5=8. so apartments are 5/8 of all houses.and all of them are brick made. 3/8 are private homes and 1-1/6 of them may be brick made(1/6 are wooden). that means the maximum of private houses from brick are 3/8 * 5/6=15/48=5/16. adding the apartments we get 5/8+5/16=15/16", + "video_name": "RPhaidW0dmY" + }, + { + "Q": "At 0:07, what does he mean by \"mixed fraction?\"\n", + "A": "no, this is a mixed fraction 5 1/2", + "video_name": "RPhaidW0dmY" + }, + { + "Q": "\nAt 0:08 he meant improper fraction not mixed fraction right?", + "A": "Hi Carolyn, He actually meant mixed fraction. You have to convert 2 mixed fractions to fractions, then multiply them, then convert the result (fraction) into mixed fraction again.", + "video_name": "RPhaidW0dmY" + }, + { + "Q": "At the end (+- 9:00) he says that one of the equations is impractical, because it would entail the calculation of all the pop, is that correct?\n", + "A": "Exactly. It is pretty hard to calculate the heights of all the 150 million people, after all.", + "video_name": "k5EbijWu-Ss" + }, + { + "Q": "At 4:54 how it is 12. The equation is supposed to be 5-(- -7). The answer is supposed to be -2.\n", + "A": "no. It s supposed to be 5-(-7), in which the minus symbol and the negative symbol cancel out each other, making the equation then 5+7, equalling 12.", + "video_name": "XkRD9lv_y44" + }, + { + "Q": "at around 1:17 I don't really understand how at least classic principal root is a defined for a negative number. Can someone please explain it to me?\n", + "A": "Are you trying to find the square root of a negative number?", + "video_name": "n17q8CBiMtQ" + }, + { + "Q": "\nHow did he get that a negative wouldn't work, at 0:56 & 1:15? If it was the absolute value of x, or whatever the number is, wouldn't the absolute value have canceled out the negative ( - ) and turned it to positive, so that it'd work? Also, How did he get -6 < x at about 3:00?? He had just said earlier that it COULDN'T be a negative number, but -6 < x < 6 implies that it could be anything from -5 to 5.", + "A": "At 0:56 and 1:15 he s not saying that a negative value won t work for x, since you are correct -- a negative value would not affect anything since we are taking the absolute value of it anyway. Rather, he s saying that we can t have the expression in the radical -- 6-x -- be equal to a negative, since we would then be taking the square root of a negative of number. This translates to |x|<6 (or -6 +1 BUT If NOT => -1. \u00e2\u0080\u00a2Secondly, any ODD exponent is either -i or +i. i^99 IS i^98 * i => 98 IS NOT divisible by 4 so => -i", + "video_name": "QiwfF83NWNA" + }, + { + "Q": "\nAt 4:10 sal wrote i^i ?", + "A": "He wrote i^i but said i^1, so he meant i^1.", + "video_name": "QiwfF83NWNA" + }, + { + "Q": "At 4:09, Sal wrote i^i. Just out of curiosity, what is i^i?\n", + "A": "Euler s formula says that e^(ix)=cos(x)+isin(x) Let x=\u00cf\u0080/2 and we get e^(i\u00cf\u0080/2)=cos(\u00cf\u0080/2)+isin(\u00cf\u0080/2) e^(i\u00cf\u0080/2)=0+i e^(i\u00cf\u0080/2)=i Now raise both sides to the power of i and we get [e^(i\u00cf\u0080/2)]^i=i^i e^(i\u00c2\u00b2\u00cf\u0080/2)=i^i e^(-\u00cf\u0080/2)=i^i", + "video_name": "QiwfF83NWNA" + }, + { + "Q": "\nAt 1:35-\n5 is also a multiple of 100, so why would i^100 =1 and not i?", + "A": "i^100 can be written as (i^4)^25 which is equal to 1^25 = 1. For what you re asking - even though 5 is a factor of 100 (not multiple) - we could take it like this: i^100 = (i^5)^20 which can written again as (i^5)^4 = i^4 = 1.", + "video_name": "QiwfF83NWNA" + }, + { + "Q": "\nAt 3:02, Sal mentions that K \u00e2\u0089\u00a5 0. I understand that for now K can't be a negative number, but can it be a positive decimal? For example, is it possible to find and answer to i to the 7.89th power? (It is between the 7th and 8th power, so it couldn't follow any of the principles making the value either 1, i, -1, or -i.)", + "A": "You can surely raise any number to a decimal.. I ll tell you what that means... You can convert any decimal number into a fractional number very easily and when you do that understanding the power of decimals becomes meaningful. For eg. If u r saying 2^1.5, you can write it as 2^3/2 which means it is square root of 2^3.. Right? Similarly you can convert any decimal power into a fractional number and understand its meaning...", + "video_name": "QiwfF83NWNA" + }, + { + "Q": "At 9:27 , how did you come up with how many songs and game he would buy?\n", + "A": "Since the shaded area (the darker blueish color) is the solution to both equations (the first being the one about how much money he has and the second being how many songs and games he can buy) any coordinates in that region would satisfy the problem. So 4 games and 14 songs would work, as Sal mentioned. Obviously, the two values need to be integers because you can never buy a half game or song. Hope that helps. : )", + "video_name": "BUmLw5m6F9s" + }, + { + "Q": "\nAt 9:33, Sal says that if you buy 4 games and 14 songs that would work. Sure, on the equation it makes sense but on the graph it looks like it's an impossible point. Or is it just the line....I don't know.", + "A": "no it seems like it could work on the graph too. its just that there is not 14 mark on his graph. but we know 14 is halfway between 12 and 16 so he put his point there.... Hope This Helps =)", + "video_name": "BUmLw5m6F9s" + }, + { + "Q": "Hi,\nI am with you until 2:14 in the video,\nWhere pi \"f\" 1/u du,\nThen that is = to pi ln u (but what happens to the du?)...+C\nAs i understand it there is two term after the \"f\" (1/u) x (du),\nRegards\nPs: thank you very much for all the math help :)\n", + "A": "When you integrate with respect to u, the du disappears, just as dx disappears when you integrate with respect to x. For example, the integral of 2x dx is x\u00c2\u00b2 (not x\u00c2\u00b2 dx). There are different ways to think about why this happens. One is to consider dx or du as part of the integral symbol. It s probably more helpful, especially when doing u-substitution, to understand dx or du as a distinct element, but one that gets incorporated into the answer when you integrate.", + "video_name": "OLO64d4Y1qI" + }, + { + "Q": "\nI get all that happened, but wouldn't the answer at 2:48 be \u00cf\u0080(ln |lnx| + C) = \u00cf\u0080(ln |lnx|) + \u00cf\u0080C instead of \u00cf\u0080(ln|lnx|) + C?", + "A": "It could be, but the two C s would have different values. Imagine if the pi had been left inside the integral--that s the way Sal is handling it. Typically we choose the constant to be the thing added on after computing the integral as a whole rather than at an intermediate step.", + "video_name": "OLO64d4Y1qI" + }, + { + "Q": "\nAt 5:33, Sal said that the area of the parallelogram is 5x6, whereas before, following the previously spoken format it would be 2x5x6. Is this right?", + "A": "Yes! Correct! 2x5x6 is pretty much the same thing as what sal previously said.", + "video_name": "tFhBAeZVTMw" + }, + { + "Q": "\nat 1:22 doesn't that sign mean delta as well?", + "A": "You re right, it s capital delta (at least it looks like it). Here it just means triangle of course.", + "video_name": "tFhBAeZVTMw" + }, + { + "Q": "At 0:54, Khan says to factor out the 2. Is that necessary?\n", + "A": "We factor out 2 to bring expressions in the brackets to similar form. Thus, you can easily see that parts inside the brackets are similar on both sides of the equation. In this form it is quite easy to identify and make a substitution. You don t have to do this step if you can identify similarities right away, remember (4x-6)=2(2x-3).", + "video_name": "ZIqW_sXymrM" + }, + { + "Q": "\nAt 3:48 of the video why does he want to multiply and take 1/3 ?", + "A": "He s trying to get the x by itself on one side of the equation and as long as you do the same thing to both sides then everything equals out. So to get from 3x to x you divide by 3 which is the same as multiplying it by 1/3. Since want to do the same thing to both sides you multiply 12 by 1/3 (which is the same as dividing it by 3). 12 * 1/3 = 12/3 = 4. So x=4.", + "video_name": "_y_Q3_B2Vh8" + }, + { + "Q": "\nAt 4:11, why does he multiply by 1/3? Wouldn't it be easier to divide by 3?", + "A": "Multiplying with 1/3 is the same with dividing by 3.", + "video_name": "_y_Q3_B2Vh8" + }, + { + "Q": "I just noticed at 4:26, there is 6 yellow blocks on the right when there's supposed to be 4 blocks on the right.\n", + "A": "The video has amended this. If you watch it again, you should notice the box in the lower right corner.", + "video_name": "_y_Q3_B2Vh8" + }, + { + "Q": "at 4:23 There were 6 boxes on the right side. WAs that on purpose or what.\n", + "A": "that was an accident", + "video_name": "_y_Q3_B2Vh8" + }, + { + "Q": "\n@4:26 he left 6 on the right did anyone else notice that?", + "A": "Yeah. I noticed it.", + "video_name": "_y_Q3_B2Vh8" + }, + { + "Q": "Any one else notice Sal repeats himself a lot? 2:40 to 2:53\n", + "A": "Repetition is the mother of learning :)", + "video_name": "_y_Q3_B2Vh8" + }, + { + "Q": "\nFor 1:40 of the video, how do you know if all three are 30 degrees? How do you find those angles if they were different angles? If they weren't the 30, 60, 90, then how would you find the angles? I get the 90 degrees part, but what about the rest?", + "A": "The reason that Sal knows those angles all equal 30\u00c2\u00b0 is because the problem states that the 90\u00c2\u00b0 angle is trisected or split into 3 equal parts. So 90\u00c2\u00b0/3=30\u00c2\u00b0.", + "video_name": "dgHksfBFbjk" + }, + { + "Q": "I understand this topic until the last part. I thought that the opposite of the 60 degree angle was supposed to be sqrt(3) and that the side opposite the 90 degree angle is 2 times the number. I don't understand how he got 2/sqrt(3) and 1/sqrt(3). I become confused around 3:16.\n", + "A": "Yes, you multiply the short side by sqrt(3) to find the side opposite the 60\u00c2\u00b0 angle. This problem is different because they gave the you side opposite the 60\u00c2\u00b0 angle and you need to find the short side. So essentially you are saying that the short side times sqrt(3) = 1; therefore to find the length of the short side you have to divide by sqrt(3) to find the short side. This gives you the 1/sqrt(3) for the short side and you multiply this by 2/sqrt(3).", + "video_name": "dgHksfBFbjk" + }, + { + "Q": "How did Sal get 3sqrt(3) from just sqrt(3) at 6:05. Can someone please explain and link the appropriate khan lesson for that.\n", + "A": "Sal actually got 3sqrt(3)/3 because he multiplied both the numerator and denominator by 3.", + "video_name": "dgHksfBFbjk" + }, + { + "Q": "at 3:59, why do we have to subtract 6100 from 400 & 6100?\n", + "A": "Yes, we are isolating the cosine of theta (at 3:59) . You are right.", + "video_name": "Ei54NnQ0FKs" + }, + { + "Q": "\nI have a question about when you are doing the equation and you are crossing out and everything when you was getting on the part when you add on one side and then you subtracted on the other why did you do that? I have always been taught that what you do to one side that you do to the other can you please explain that to me? I do believe it is on minute 5:04 Thank you for the help in advance", + "A": "I don t really understand what you are asking, but I think I have an idea. When the equation was -5700 = -6000 cos (Theta) It also meant -5700 = -6000 times cos (Theta). He divided -6000 from the right, so he did the same to the left. It equaled -5700/-6000 on the left, which is the same as 5700/6000. I think you were just confused by the way he drew the positive signs. I hope I helped! Good luck!", + "video_name": "Ei54NnQ0FKs" + }, + { + "Q": "\nAt 2:14, Sal says,\"The best way to get 12x on the left is to subtract.\" Was he implying that there's more than one way to balance the equation? If so, how?", + "A": "It was just a figure of speech. The only way to move that 12x from one side to the other is to subtract it. However, you could add 9x to both sides instead. Your x s will end up on the right hand side instead of the left but that s OK. x = -1 means the exact same thing as -1 = x", + "video_name": "YZBStgZGyDY" + }, + { + "Q": "At 2:12, Sal says that -12x is the best way to do it. I thought that was the only way- have I been missing something?\n", + "A": "You could also add 9x to both sides.", + "video_name": "YZBStgZGyDY" + }, + { + "Q": "At 6:21 how come pi as a coefficient is allowed? Isn't pi an irrational number?\n", + "A": "Coefficients can be any real number including Pi.", + "video_name": "Vm7H0VTlIco" + }, + { + "Q": "\nAt 3:45, Sal says that he could change it to x to the power of zero. Is this incorrect ? Anything to the power of zero is one, and 9x is not always equal to nine.", + "A": "9x^0 does not be come 9x. 9x means 9x^1 Having x to the 1st power is not the same as x^0 power. x^0 = 1, not x 9x^0 = 9(1) = 9 Hope this helps.", + "video_name": "Vm7H0VTlIco" + }, + { + "Q": "\nAt 8:15 Sal mentions that the highest degree will be the degree of the polynomial. What if there was an equation where there were two terms and they both had the same degree? What will the degree of the polynomial be?", + "A": "The degree of the entire polynomial would just be that degree", + "video_name": "Vm7H0VTlIco" + }, + { + "Q": "At 1:40 why did he multiply 4 * 0 ?\n", + "A": "In the original equation it was 4*Y and since he was solving for the X intercept, Y would be equal to 0 and so 4*0", + "video_name": "xGmef7lFc5w" + }, + { + "Q": "at 1:40 what is the somthing ?\n", + "A": "The something is x , what you re solving for.", + "video_name": "tuVd355R-OQ" + }, + { + "Q": "\nAt 12:34 Sal said ten minus -2.35 but he had a plus sign next to -2.35? Im confused, can someone help me?", + "A": "adding a negative number and subtracting a positive number are the same thing :)", + "video_name": "tuVd355R-OQ" + }, + { + "Q": "\nin 8:18 he say 7 can be written 35/5 , how is that?", + "A": "35 divided by five equals seven, he was simply just showing another way to write whole numbers. But by using fractions! Like 25/5 equals 5, so that s a way of representing five. In my mind, it looks like you know pretty cool things then you put this stuff on a test!", + "video_name": "tuVd355R-OQ" + }, + { + "Q": "at 3:34 how did he get the negative 2\n", + "A": "here is the full equation: 5x -1(3x + 2) = so then you distribute the -1 and you get: 5x - 3x - 2 = hope this helps!", + "video_name": "tuVd355R-OQ" + }, + { + "Q": "At 5:34 why did you or how did you rewrite it to 8/8?\n", + "A": "So that he could subtract his number that was over 8. You probably know that 1=8/8, as well as 4/4 etc... So by making the denominators the same, therefore being able to subtract a number from 1. Hope this helps! :)", + "video_name": "tuVd355R-OQ" + }, + { + "Q": "@ 4:43 how did he end up with 3/2?\n", + "A": "The problem was 5x-(3x+2)=1. He first, to get rid of the parentheses, reversed the sign inside (because the sign outside was negative). He then subtracted 3x from 5x, and got 2x. So far it is 2x-2=1. You can then add 2 to both sides, to get 2x=3, and divided both sides by 2, to get x=3/2. You can look at the previous videos if you re still confused. Hope it helped!", + "video_name": "tuVd355R-OQ" + }, + { + "Q": "\nAt 3:35, where does he get the -2 from? Using the Distributive property doesn't change the sign, right? Why would re-arranging the numbers turn a +2 into a -2?", + "A": "Because, he is having to multiply EVERYTHING in the parenthesis by a negative. There is no number written, but in between the negative and parenthesis symbol is an imaginary number 1. So it is a negative 1.", + "video_name": "tuVd355R-OQ" + }, + { + "Q": "\nat 5:28 why does he change it to 1S to S(1-3/8)", + "A": "He is using the distributive property to combine like terms. He isn t changing 1S to S(1-3/8) he s changing 1S-3/8S to S(1-3/8).", + "video_name": "tuVd355R-OQ" + }, + { + "Q": "\nAt 3:35, how did you change (3x+2) into -3x-2?", + "A": "He distributed -1 to the expression. There was a - before the 3x+2. That s actually a hidden -1. -1(3x+2)=-3x-2. Hope this helps!", + "video_name": "tuVd355R-OQ" + }, + { + "Q": "And why 8/8 on 5:43?\n", + "A": "Because he was subtracting 3/8 from one so 1 - 3/8 = 1/1 - 3/8, since he needs a common denominator he multiplied the denominator by 8 and whatever you do to the denominator you must do to the nummerator thus he got 8/8 - 3/8", + "video_name": "tuVd355R-OQ" + }, + { + "Q": "\nAt around 4:50, you say that x^l * x^m = x^(l+m)\nI thought it would be 2x^(l+m)\n\nWHat am I missing?", + "A": "Where would you get the 2 from? You are multiplying, not adding. Try this with some actual number, maybe that might make the concept more clear: 4\u00c2\u00b2 * 4\u00c2\u00b3 = 4*4 * 4*4*4 = 4\u00e2\u0081\u00b5 = 1024", + "video_name": "FP2arCfAfBY" + }, + { + "Q": "at 7:08 Sal does not multiply (a+b) squared and then on the right sides multiplies ab x 2. Why?\n", + "A": "You can t multiply two different variables.", + "video_name": "EINpkcphsPQ" + }, + { + "Q": "at around 7:00 how and where did he get the 2's with?\n", + "A": "Those are power of twos, the formula for pythagorean theorem is a^2+B^2= C^2", + "video_name": "EINpkcphsPQ" + }, + { + "Q": "\nAt 7:44 in the video when you were solving the equation you managed to get a \"2ab\" after solving (a+b)^2. Why is that? Please explain.", + "A": "Try rewriting (a+b)^2 as (a+b)(a+b) instead. Then, use FOIL and see what happens. First: a times a equals a^2. Outer: a times b equals ab Inner: b times a equals ab Last: b times b equals b^2 Add them all up, and you get a^2 + 2ab + b^2. That s where the 2ab came from.", + "video_name": "EINpkcphsPQ" + }, + { + "Q": "at 2:16 what is that symbol he drew and what does it do?\n", + "A": "It s a greek symbol called theta", + "video_name": "EINpkcphsPQ" + }, + { + "Q": "what do you mean at 2:19 ?\n", + "A": "She protested with a sign. That s all", + "video_name": "sxnX5_LbBDU" + }, + { + "Q": "at 3:06, what is a mobius strip?\n", + "A": "A two dimensional object that can exist in three dimensional space.", + "video_name": "sxnX5_LbBDU" + }, + { + "Q": "At about 5:45, what's a frieze pattern?\n", + "A": "They are patterns that have all the kinds of symmetry, I think. Go to Vi s video about freizepatterns called : Math Improv:Fruit By The Foot.", + "video_name": "sxnX5_LbBDU" + }, + { + "Q": "(0:35) - specifically the word placeholder gave me this question\nIf you were to \"say\" 1 is \"y\", and anything times 1 is the same, would 1 actually represent the \"laws of physics\"? Like, the laws of physics is based on \"common perception/observation\", which should always equal the same thing(s)... Like when you multiply by one... Is this an accurate/logical way to look at it?\n", + "A": "And does 567x1 is. 567", + "video_name": "6nZp2QGeQ9k" + }, + { + "Q": "\nwhat is the in don't know what to call it but at 6:44 when u ad the numbers together what if its 5/4 how do u divide", + "A": "Well when you divide a fraction you must flip the denominator (Bottom number of the fraction) , but when you flip it has to be the SECOND fraction. Ex 4/5 \u00c3\u00b7 6/7 to 4/5 \u00c3\u00b7 7/6 A lot of people forget to add the \u00c3\u0097 sign when you are dividing. If this sounds confusing then let me show you Ex 4/5 \u00c3\u00b7 6/7 to 4/5 \u00c3\u0097 7/6", + "video_name": "GdIkEngwGNU" + }, + { + "Q": "\nAt 1:19 when he wrote P-2w/2 = l, why can't sal divide 2w/2 to just get w?", + "A": "The way he arranged the equation (which is hard to represent here because you can t represent a fraction with a horizontal bar) is L= (P-2w)/2....so both the P and the 2w need to be divided by 2. Think of it with just numbers... - let P=6 and w = 1 so the way you wrote it: P-2w/2 = L says that 6- 2(1)/2 = 5 but the way he represented it L= (P-2w)/2 : again let P=6 and w = 1: L = (6-2)/2 = 2 not the same expression without the ( )", + "video_name": "fnuIT7EhAvs" + }, + { + "Q": "At1:09 when we divide both sides by 2. It cancells out the 2 on the right so we are left with (l). Why doesn't it cancel out on the left and leave us with (p-w)??\n", + "A": "You are dividing both sides by 2. Another way to write the final answer would be: l = P/2 - w", + "video_name": "fnuIT7EhAvs" + }, + { + "Q": "\nat 3:40 Sal writes yos does that mean yards?", + "A": "Yes at 3:40 he wrote yos but it actually meant yards.", + "video_name": "ZS1OZj_oWao" + }, + { + "Q": "\nAt 2:07 Sal substitutes (4x^3 dx) for du. But why does he not have to write another dx at the end of the Integral?", + "A": "Because of du. When you use u-substitution, you basically are writing the integral in terms of u instead of (in this case) x. du and dx ultimately serve the same function as well as representing an infinitesimal change in x or u and also being the dummy variable that integrates to +C .", + "video_name": "Zp5z0wa0kgo" + }, + { + "Q": "\nIn 8:35 - isn't it supposed to be -(34/3)? So that A will equal -(5/17)?", + "A": "Actually I think it should be -5/17, he dropped the minus sign when he subtracted 9 from -25. It should be -34/3 which reduces to -5/17.......right??? :/", + "video_name": "hbJ2o9EUmJ0" + }, + { + "Q": "If you had a ratio of 3:5, would you plot it a (3,5), (6,10), etc...\n", + "A": "Yes, because the ratio of x:y is 3/5.", + "video_name": "dmcVzFbXMCU" + }, + { + "Q": "\nat 1:20 what does numerical expression mean?", + "A": "A numerical expression is a mathematical phrase that involves only numbers and one or more operational symbols. The expression represents a particular number. For instance the numerical expression 10 + 6 \u00e2\u0080\u0093 8 simplifies to the number 8.", + "video_name": "arY-EUZDNfk" + }, + { + "Q": "For the last example at 5:30 can I also define like that? Is it true?\n{x \u00e2\u0088\u0088 \u00e2\u0084\u009d | x = \u00cf\u0080 or x=3}\n", + "A": "You could, but it s a bit more complicated than it needs to be since the set has only 2 values.", + "video_name": "-DTMakGDZAw" + }, + { + "Q": "Hi, Can somebody please explain in \"domain and range of a function\" video (at 5:02 minutes). How can y-6 >= 0 because greater than i understood but how can it equals to 0 as if y= 6 than the equation goes like 6-6 which is equals to 0 and 0 is not defined output.\n\nPlease answer.\n", + "A": "sqrt(0) is defined. It = 0. So, there is no issue have a zero inside the square root. You don t want a negative inside the square root after you have simplified because it is not a real number.", + "video_name": "-DTMakGDZAw" + }, + { + "Q": "\nAt 4:58 can't ti also be 4.5 instead of 4 1/2?", + "A": "Since 4.5 = 4 1/2, yes you can write it the way you prefer.", + "video_name": "hq1bUM2tyg0" + }, + { + "Q": "\nCould you include a fraction in the answer in 4:24? Could you also get a rational number?", + "A": "Fractions are rational numbers. Yes, there s no reason why you couldn t use fractions here.", + "video_name": "hq1bUM2tyg0" + }, + { + "Q": "\nAt 1:59 Sal took the triangle to the other side of the parallelogram to make a rectangle, can't you just multiply base times height to get the area?", + "A": "Yes you can. Sal most likely did that move so that you could visually see why multiplying base times height works.", + "video_name": "hm17lVaor0Q" + }, + { + "Q": "\nWhat is the name of the notation \"S-like\" figure Sal describes at 2:36?", + "A": "The integral symbol or the integral sign. (I know, it seems almost too obvious.)", + "video_name": "MMv-027KEqU" + }, + { + "Q": "\nAt 2:13, how did he convert 3/10 into 30/100?", + "A": "He multiplied them both by 10. don t worry, you l get used to it. its a common technique.", + "video_name": "YZD5ifHZILE" + }, + { + "Q": "\nAt 5:24, how would you solve the C part? Do you spread it out like you did? Or is there another way?\nCan anyone help me quick? Sal... you there?", + "A": "When you say the C part, do you mean the formula for a combination? Sal actually explains that in the following video. But perhaps you meant something else?", + "video_name": "iKy-d5_erhI" + }, + { + "Q": "can anyone explain what sal tried to do after 4:00 ??\n\u00e2\u0096\u00baQ2 whats the difference between permutations and combinations.. ?\n", + "A": "He was showing how to find the number of ways to choose a subset of a set of things. In this case how many ways you can choose 3 people from a pool of 6 people (where order doesn t matter). In permutations order matters, in combinations it does not.", + "video_name": "iKy-d5_erhI" + }, + { + "Q": "\nI have a word problem it says \"the angle of the roof on Wendy's dollhouse is 56 degrees. She built a scale model of the dollhouse with a scale ratio of 1:4. What is the angle of the roof of the model she built?\" I'm curious on how I would work this out. Do I do the same as on this video?", + "A": "Well If You think it is correct then you do it but I think you should do the video", + "video_name": "tOd2T72eJME" + }, + { + "Q": "At 1:00 Sal talks of \"g of negative 6.999.\" Does he mean to say \"negative?\" Isn't the 6.999 positive?\n", + "A": "He said g of negative 6.999 but it should be g of 6.999 . I m guessing what he was trying to say that g of 6.999 is still negative but got mixed up. Report it so he can add an annotation for correction.", + "video_name": "hWJLd6bRthI" + }, + { + "Q": "\nAt 3:40 ish wouldn't the probability be a dependent event since there is a set amount of fish in the pond/lake?", + "A": "Fish after catching are being released back into the pond that is why the probability is independent of what was caught.", + "video_name": "86nb02Bx_5w" + }, + { + "Q": "At 1:12, Sal defines the random variable X as \"what your profit is from bet 1.\" He then goes on to define a function E(X) that gives the expected profit from taking the first bet. Shouldn't X be defined as the outcome of Jeremy's next three fish?\nAgain at 6:55, Sal similarly defines Y as the expected profit from the second bet, which is what E(Y) is. Shouldn't Y be defined as the outcome of my next three fish?\n", + "A": "He makes a small mistake at 6:55 when he says Y is the expected profit. Y should be defined the same as X as just the profit of the bet. E(Y) is the expected profit.", + "video_name": "86nb02Bx_5w" + }, + { + "Q": "\nAt about 0:50, give or take, in the video, Sal figures out the square root so easily. Now, I know this is an easy example, but it there a formula for finding the square root?", + "A": "a square root of a number a is a number y such that y^2 = a, in other words, a number y whose square (the result of multiplying the number by itself, or y \u00c3\u0097 y) is a. For example, 4 and \u00e2\u0088\u00924 are square roots of 16 because 4^2 = (\u00e2\u0088\u00924)^2 = 16. Wikipedia", + "video_name": "ROIfbUQrSY4" + }, + { + "Q": "\nAt 0:45 Sal explains that the square root of 100 is 10 times 10. This is pretty simple to do figure out because if you know your times tables, you will have this memorized. But what if I'm trying to find the square root of a larger number? Any tried and true methods OTHER than a calculator? Thanks!", + "A": "Use factoring. Break the number down into prime factors. For example: 2025 = 3*3*3*3*5*5 Each pair of matching factors is a perfect square. Group the pairs. 2025 = (3*3)*(3*3)*(5*5) OR, you can think of this as 2025 = 9*9*25 This number contains 3 perfect squares. You can take the square root of each perfect square, then multiply the results. sqrt(2025) = sqrt(9) * sqrt(9) * sqrt(25) = 3*3*5 = 45 Hope this helps.", + "video_name": "ROIfbUQrSY4" + }, + { + "Q": "At 0:46 why does Sal say the answer would be a positive number? B could be -3 and A could be -2 and the answer would we -1 which is NOT a positive value.\n", + "A": "We always measure distances in positive numbers. We have no rulers with negative numbers. We don t say we just walked -3 miles. We don t measure the objects and come up with negative inches or negative centimeters. The absolute value of any number represents its distance from zero. We use it to help ensure we create distances in positive values. If A = -2 and B = -3, the distance between them is 1 unit (a positive number. You can find this by doing: | -3 -(-2)| = |-1| = 1 or |-2 -(-3)| = |1| = 1 Hope this helps.", + "video_name": "t4xOkpP8FgE" + }, + { + "Q": "\nAt 6:05 - 6:10, I believe you meant to say that the subject terms are equivalent to the Identity Matrix time vector 'a' as opposed to the Identity Matrix times 'a1'.", + "A": "yup, i m pretty sure he meant matrix a", + "video_name": "PErhLkQcpZ8" + }, + { + "Q": "At 0:45, why does Sal draw the Vertical Line?\n", + "A": "It s kind of working as the = signs of the equations, so it separates the variable constants from the number on the other side of the equation. I think it s just so you remember which are which.", + "video_name": "lP1DGtZ8Wys" + }, + { + "Q": "5:05 Which ordered pair I know that is on the y or x axis?\n", + "A": "For points on a graph, you define them by (distance on the x-axis, distance on the y-axis). So even if you didn t know which point it was, you would figure out how far it was on the different axis, put them in x, y order and in parentheses, and you ve got the point. Hopefully that helps!", + "video_name": "WkspBxrzuZo" + }, + { + "Q": "\nwhat does the triangle mean at 2:10.", + "A": "The triangle is denotes change. So, slope equals the change in the y values divided by the change in the x values.", + "video_name": "WkspBxrzuZo" + }, + { + "Q": "At the 4:24 mark in the video, shouldn't you say \"this is our rise\" instead of \"this is our run\"?\n", + "A": "Yes. If you look at it again, you ll see a box pop up in the lower right corner with the correction.", + "video_name": "WkspBxrzuZo" + }, + { + "Q": "\nAt 6:22, Sal writes r(theta). Does he mean f(theta) as r = f(theta) or am I getting mixed up?", + "A": "Yup he just used both r (theta) and f (theta) as representations of the polar function.", + "video_name": "qVn_Lfec-Ac" + }, + { + "Q": "At 0:00, we learn?\n", + "A": "Yes, we learn!", + "video_name": "daCT_24RnIY" + }, + { + "Q": "I already know what wide is, but what does it mean by 'deep'? Sal was saying it at 5:05.\n", + "A": "anything with 3 dimensions. A rectangle has length and width , a box has depth as well. Think of a swimming pool , depth would be the bottom to the top although normally a pool isn t filled to the brim. In khan you will see swimming pool questions and you have to watch out for the depth of the water as well as the depth of the container", + "video_name": "daCT_24RnIY" + }, + { + "Q": "Why does Sal include a number line at 2:30 to represent is process to tackle this problem when he could just do count to 73 from 68 to show that we added 5 to get there?\n", + "A": "Because Sal just wanna show how we get 73, by breaking up 5 into 3+2, you can add 2 to 68 first,and then add 3 to 70 to get 73. This is an easy method of solving the problem like that, technically. If we just count from 68 to 73, how could we do if we need to add 68 to 29? continue to count?", + "video_name": "DzJvR56Suss" + }, + { + "Q": "\nAt 1:28 into the video you wrote a symbol which had a = sign and something that looks like a vertical line and a greater than symbol. Would you please explane what it is? Thanks", + "A": "I think Sal is just drawing an arrow to show that he is changing the expression into a simplified form.", + "video_name": "Q1vMNyIP4Us" + }, + { + "Q": "\nWhat the heck is a reciprocal? 4:00", + "A": "Example : 1/2 and 2/1= 2/2=1", + "video_name": "f3ySpxX9oeM" + }, + { + "Q": "\nat 0:28,why is 5+5+8,5+8+5,and 8+5+5 exactly the same?", + "A": "how do you have 100,00 and you joined 2 m ago??", + "video_name": "HwSszh3L358" + }, + { + "Q": "At 2:30 he says that the shape can be a rhombus. I thought rhombuses could not have any right angles!?\n", + "A": "Definition of rhombus is all sides are equal, and opposite sides are parallel. So a square is a particular type of rhombus.", + "video_name": "wPZIa3SjPF0" + }, + { + "Q": "\nAt 1:36, Sal says the lines are parallel. How do you know for sure that they are parallel?", + "A": "Great point. We do not know for sure. However, we can take it as a given from the problem.", + "video_name": "wPZIa3SjPF0" + }, + { + "Q": "At 1:38 she said that they found the highest prime number so far? How have they not found more?\n", + "A": "Because finding primes is hard. I could explain exactly why it is hard, but I will instead ask you a question: is 1000000007 (one billion seven) prime? If you try to find it out without a computer, you will soon see the difficulties behind finding primes.", + "video_name": "Yhlv5Aeuo_k" + }, + { + "Q": "\nat 2:31 what is a prespictipal", + "A": "Simply put, a reciprocal of a fraction is when you flip the fraction upside down. For example, the reciprocal of 5/7 is 7/5. The reciprocal of 3/4 is 4/3.", + "video_name": "d8vvVjfTbYY" + }, + { + "Q": "At 8:10, you integrate (5/2)(1/x+1) to 5/2*ln(x+1) explaining that the derivative of the denominator (x+1) is equal to the numerator 1 . Could you please explain this further as I am still very confused?\n", + "A": "F(x) = \u00e2\u0088\u00ab(5/2\u00e2\u0080\u00a21/(x + 1))dx F(x) = 5/2\u00e2\u0080\u00a2\u00e2\u0088\u00ab(1/(x + 1))dx u = x + 1 (d/dx(x + 1))dx = du (d/dx(x) + d/dx(1))dx = du (d/dx(x) + 0)dx = du (d/dx(x))dx = du (dx/dx)dx = du (1)dx = du dx = (1)du dx = du F(u) = 5/2\u00e2\u0080\u00a2\u00e2\u0088\u00ab(1/u)du F(u) = 5/2\u00e2\u0080\u00a2ln(u) + C u = x + 1 F(x) = 5/2\u00e2\u0080\u00a2ln(x + 1) + C", + "video_name": "7IkufOBIw5g" + }, + { + "Q": "\nAt 1:42, Sal says \"the fewest number of candy bars we can buy is zero candy bars\". Why is this so? The definition of a purchase is receiving goods in exchange for money. Surely no money and no candy bars equals no purchase. Do all functions just have to accept zero as an input?", + "A": "Not all functions have the same words like purchase so this makes it easier to understand so in a less mathy way of saying it is you can buy No candy bars for $0.00( my keyboard does not have the cent symbol). So manly all functions have different meaning of the words so they can all accept 0 to make it easier to understand p(0) completely means 0 candy bars so $0.00 was spent for it. Hope this helps..........Sorry if you already had it. It been a month xD.", + "video_name": "AiW7syKXfJM" + }, + { + "Q": "At 3:26 why did Sal put the x's on the right and not the left?\n", + "A": "It doesn t matter which side you move the x s to. Either side will work. Sal likely moved the x s to the right side because it keeps the value positive (which some people prefer).", + "video_name": "EHR-YDwrrhM" + }, + { + "Q": "\nAt 6:43, when you did 8/5 times -5 how did you end up with -8?", + "A": "8/5 (-5) = 8/5 * (-5/1 ) = 8 (-5) / (5 * 1) = -40/5 = -8 hope this helps.", + "video_name": "EHR-YDwrrhM" + }, + { + "Q": "Hello! Okay, so at 1:03 in the video, how did he know that y>= -2? I get how he got it from the graph, but how would one find that algebraically? Please respond quickly, thank you so much!\n", + "A": "Algebraically, the equation was y = ( x - 1 )^2 - 2. Whatever value of x is substituted, the quantity ( x - 1 )^2 will be positive or zero; it will never be negative. Therefore, we ll always be adding a positive number (or zero) to -2, so the total value will be getting larger than (or staying equal to) -2.", + "video_name": "Bq9cq9FZuNM" + }, + { + "Q": "At 6:53 in, shouldn't the point be (3,-1), not (2,-1)?\n", + "A": "The point must be (3,1), not (-1,2).", + "video_name": "Bq9cq9FZuNM" + }, + { + "Q": "At 5:05 Sal mentions interval. Can someone explain to me what this 'interval' means? I keep on hearing this term more and more often.\n", + "A": "In this context, interval just refers to the section of points (along the x-axis) between x1 and x2. If it were an interval of time, for example, it could be the segment of time between two events. Hope this helps!", + "video_name": "8r8Vp_1iB4k" + }, + { + "Q": "\nWhy is he multiplying the -(3x - 4) @ 1:10? Can he not also just add that?", + "A": "The minus in front of the (3x - 4) says to subtract the entire binomial. The minus sign must be distributed to accomplish that subtraction. If you just drop the parentheses and add, then the -4 is being added, not subtracted (you have +(-4) when you need -(-4)). Hope this helps.", + "video_name": "DMyhUb1pZT0" + }, + { + "Q": "\nAt 3:08, Vertically, I don't see 2 blocks.\nThanks\n---- Moon trainer", + "A": "I code on Scratch too! My username is Song_of_the_Cats", + "video_name": "gkifo46--JA" + }, + { + "Q": "\n@ 4:50 - I would have thought that since we are solving for where the greater change occurs, g'(4) < g'(6) would be correct, as the change at g'(6) is far more 'steep'. Its obviously that -1 > -3, however I thought that we're really solving for here is the rate of change.", + "A": "It is descending more at 6 but the derivative gives how much something increases as we move along the graph. So if it decreases then it will be negative.", + "video_name": "S-dcMvJlMJs" + }, + { + "Q": "\nAt 0:33, what does translate mean?", + "A": "Moving the entire figure, without changing its size or orientation.", + "video_name": "6p1lweGactg" + }, + { + "Q": "At 5:36, the outer radius is defines as 2-y^2.\nCan anybody explain why ones takes 2 - the function. My first guess was the function + 2 so that i would reach the line where x =2. This is wrong, but i can\u00c2\u00b4t say i really understand why.\n\nAnd, taking 2-y^2 would that be the gap between the undefined point on the x-axes and x=2? Where is this on our shape?\nThanks.\n", + "A": "At this stage in the process we re trying to find the radius of the outer disk. The radius is the distance from the center of the disk to the perimeter. At the beginning of the video we re told that the figure is created by rotation around the line x=2, so we know the center of the disk is at x=2. The outer edge of the larger disk is at the point x=y^2, so the distance between the two points is 2-y^2.", + "video_name": "WAPZihVUmzE" + }, + { + "Q": "\nAt 5:29, I was taught to do it in the reverse order like (y^2-2), is that wrong?", + "A": "In that case the radius would be negative, but it is just a distance, it shouldn t be negative, but it has the same magnitude so when you square it, I guess it works out just the same. Anyway how Sal does it is the most intuitive and rigorously correct manner.", + "video_name": "WAPZihVUmzE" + }, + { + "Q": "At 5:15,what is associative property?\n", + "A": "The associative property of multiplication just means that when you multiply the numbers, it doesn t matter what order you do it in. (4 x 5) x 6 is (20) x 6, which is 120. 4 x (5 x 6) is 4 x 30, which is also 120.", + "video_name": "VXrn5HOQmHQ" + }, + { + "Q": "At 2:00, what are they trying to say?\n", + "A": "in the whole column there are 8 balls but it is divided into 2 groups of four. So 2 times four = 8", + "video_name": "VXrn5HOQmHQ" + }, + { + "Q": "At 1:38, I got kinda lost.\n", + "A": "Andrew i can t find where you got stuck on show me pls.", + "video_name": "VXrn5HOQmHQ" + }, + { + "Q": "\n10:51pm solve for w in the formula -2.4=w/8+10.4", + "A": "-2.4 = w/8 + 10.4 -2.4 - 10.4 = w/8 + 10.4 - 10.4 -12.8 = w/8 8*(-12.8) = w/8 * 8 -102.4 = w", + "video_name": "Aig1hkq3OsU" + }, + { + "Q": "\n@ 3:54, Sal says there are other ways to write w = (P-2l)/2.\nWhy can't you cancel the 2's and have w = P - l?", + "A": "(P-2l)/2 = P/2 - (2l)/2 = P/2 - l", + "video_name": "Aig1hkq3OsU" + }, + { + "Q": "at 3:36, sal has his formula for W written as p-2l / 2 = W\ncouldn't you just do the division and make the formula into 1/2P - L = W?\n", + "A": "Yes, you can simplify it that way. Sal just decided to leave it as (P-2l)/2.", + "video_name": "Aig1hkq3OsU" + }, + { + "Q": "At 4:25, what does 'factoring out a two' mean?\n", + "A": "He explains it as reversing the distributive property. 2(L + W) = 2*L + 2*W = 2L + 2W He is reversing this and since 2 is a factor of both terms, it is called factoring out a 2.", + "video_name": "Aig1hkq3OsU" + }, + { + "Q": "How come you do not divide by two on the other side? Like I 3:15\n", + "A": "It s a matter of preference. Personally, I prefer Sal s way: (p-2l)/2 However, you seem to prefer this way: (p/2)-l The question is whether you want there to be one big fraction or one little fraction.", + "video_name": "Aig1hkq3OsU" + }, + { + "Q": "At 4:28, instead of 9 minus -49, Sal writes 9 minus 49. Why is this? Doesn't the -7 multiply the 7, making it -49?\n", + "A": "I think you are using the minus sign twice and trying to get -9 -(-49)? It s not clear from your words. The problem has -9 -7 (7). There is one minus sign with the 7 s. You either use it as part of the multiplication and create -9 -49. Or, you multiply 7(7) = +49, then apply the minus and get -9 - (+49) = -9 -49. Hope this helps.", + "video_name": "TIwGXn4NalM" + }, + { + "Q": "at 4:38 you say you can factor out a -9 but why is it a negative? If the original equation is a+b+c = -1 then you would need to factor in a positive 9, right? I'm so confused\n", + "A": "can i just say probably try to rewatch the video and pay attentiion close to what he is saying and watch his steps and if that still doesnt answer your question try to research it", + "video_name": "TIwGXn4NalM" + }, + { + "Q": "\nI am still confused about the speed and velocity thing at 7:12. What is that about?", + "A": "Speed indicates how fast something is moving. Velocity indicates how fast something is moving in a certain direction. Hence, speed is a positive number while velocity is positive or negative depending on the direction.", + "video_name": "ppBJWf_Wdmc" + }, + { + "Q": "At around 1:20: What is the magnitude?\n", + "A": "Remember, velocity is a vector quantity, so it has both direction and magnitude. In the example at 1:20, the particle said to be moving in the negative direction and with a magnitude of 5.", + "video_name": "ppBJWf_Wdmc" + }, + { + "Q": "At 1:37 sal talks about a magenta curve, what does he mean by that\n", + "A": "There is a box that pops up and tells you Sal is talking about the magenta line, not curve.", + "video_name": "xR9r38mZjK4" + }, + { + "Q": "At 5:19, why does Sal divide 350 by 2?\n", + "A": "(1994/2) * 350 was changed to 1994 * (350/2) for easier multiplication", + "video_name": "0-wa7voc0uM" + }, + { + "Q": "\nAt 4:00, why doesn't he multiplicate mu with i squared?", + "A": "i isn t squared in this instance, it remains an imaginary number. Additionally, when the general solution is written, mu plays an important role, so keeping it separate allows you to plug it in without doing extra work.", + "video_name": "6xEO4BeawzA" + }, + { + "Q": "I got confused at 1:03, can u help?\n", + "A": "So first, you multiply x and y which is 3 * 2 = 6. Then you subtract y which is 2. So, 6 - 2 = 4. Then you add 3 * x which is 3 * 3 = 9. So, the answer is 13 as stated at 1:59.", + "video_name": "S_OX3ByvBSc" + }, + { + "Q": "\nAt 3:25 the equation x+180-x+z=180... Wouldn't you put 180-x in parentheses so it would look like x+(180-x)+z=180? Wouldn't that make more sense?", + "A": "Yes, using the parenthesis makes it clearer. You will still get the same answer either way.", + "video_name": "9_3OxtdqmqE" + }, + { + "Q": "At around 2:55: Why do you subtract 3 sin(5x-3y) from both sides?\n", + "A": "You want to get all values of dy/dx isolated on one side.", + "video_name": "-EG10aI0rt0" + }, + { + "Q": "\nat 5:49 why does he choose -2 to multiply both a and b by? Is it only to be rid of the 2b?", + "A": "simultaneous equations. You multiply one of the equations by a number, so that when you add the two equations, one of the variables is cancelled out. You can then solve for one variable, and use it s answer for solving for the other variable. You have to do the same thing on both sides of the equals sign, otherwise it wouldn t be an equation!", + "video_name": "EdQ7Q9VoF44" + }, + { + "Q": "\nat 4:00 how do i make it a fraction", + "A": "have an equal shape to make an equal fration", + "video_name": "jgWqSjgMAtw" + }, + { + "Q": "At 2:30 that golden thingy looks a lot like a hexaflexagon. Does anyone else see that?\n", + "A": "Yep. I bet you could make an interesting snowflake pattern with a hexaflexagon.", + "video_name": "toKu2-qzJeM" + }, + { + "Q": "At 1:38, how ca Vi say she is lazy!?\n", + "A": "She said she was lazy, but it was a joke, because right after that she said they are the binary expansion of pi. That shows she is not lazy.", + "video_name": "Gx5D09s5X6U" + }, + { + "Q": "How do those snake modules at 0:45 add to the middle of the chain? It doesn't seems like she attaching them on. It is so cool!\n", + "A": "The part where she adds them is cut from the video.", + "video_name": "Gx5D09s5X6U" + }, + { + "Q": "At 1:18 you multiply the fraction by the denominator, I understand that this in the inverse of x/4 but I don't understand how it isolates the x. It feels like the two operations would cancel eachother out eliminating the x instead of isolating it. ?\n", + "A": "The inverse of x/4 is actually 4/x. Multiplying these together does give 1, eliminating the x, as you suggested. However, Sal is multiplying x/4 by 4/1, which gives 4x/4, allowing us to cancel the 4 leaving x by itself. On the other side -18 x 4 gives -72.", + "video_name": "p5e5mf_G3FI" + }, + { + "Q": "\n0:28 i don't know how to solve the X over 4 fraction.", + "A": "Using the inverse property, you can multiply any number by its inverse to get 1. Therefore, x/4 *4 = x", + "video_name": "p5e5mf_G3FI" + }, + { + "Q": "At 1:04 how did he get -18 when subtracted -16-2? Sorry I know this is a stupid question.\n", + "A": "When you subtract, you count down. Because it s in the negatives, you count down twice. -16 to -17 and then to -18.", + "video_name": "p5e5mf_G3FI" + }, + { + "Q": "\nIn the video; Patterns in raising 1 and -1 to different powers, I believe there is a mistake. Starting at 5:41 we are shown that (-1) to the 1,000,000 power = 1. At 5:43 we are told that \" \"1,000,000 is an even number so the answer is positive 1\". But, to the left of the problem we see that (-1) to the 1 power = -1, my point being; 1,000,000 is an odd number, is it not?. (-1) x 1= -1 then add the six zeroes. So, (-1) to the 1,000,000 power = -1. correct?", + "A": "Can 1,000,000 be evenly divided by 2? If so, then 1,000,000 is even. 1,000,000 /2 = 500,000 therefore 1,000,000 is even.", + "video_name": "jYOfMszfzAQ" + }, + { + "Q": "At 3:46, Sal says that -1 squared equals one. So every answer above squaring is positive? I don't get how it changes when its squared.\nInstead, it changes to a positive number. How can that be possible when we are squaring a negative number?\n", + "A": "Multiplying two negative numbers always results in a positive product- think of the two negatives as canceling each other out. So, it s the same if you multiply a negative by itself.", + "video_name": "jYOfMszfzAQ" + }, + { + "Q": "\nAt 2:58, wouldn't (-1)^0 equal -1?. Its 1*-1 which equals -1 right?", + "A": "if (x < 0) {Yes your right! }", + "video_name": "jYOfMszfzAQ" + }, + { + "Q": "\nAt 0:26, how do you know which dot is x and which one is y? Would they be labeled, usually?", + "A": "A dot (or point) isn t x or y. A point is just a location. Using the Cartesian coordinate system (the x,y-grid), we assign the point a x-coordinate and a y-coordinate, which describes the location of the point. Hope this helped.", + "video_name": "6_9xNMtwnfs" + }, + { + "Q": "At 6:45 , can't it be like we are in a building , & are trying to get to the exit of the building.\n", + "A": "Yes, its basically like your in a building, but not quite. It does however look like you are trying to exit the building.", + "video_name": "wRxzDOloS3o" + }, + { + "Q": "in 1:49 it said plus or negative square root of 8, I see the point because you can get it either negative or positive square root of 8 but why don't you do the same thing in the left side? like + or - 4x+1\n", + "A": "You don t need to because you would still end up with the same 2 equations. Sal shows 4x+1 = Sqrt(8) or 4x+1 = -Sqrt(8) If we did the same for the left side we would also have -(4x+1) = Sqrt(8) and -(4x+1) = -Sqrt(8), but you can see if you just multiply these though by -1 you end up with the same 2 equations we already had.", + "video_name": "55G8037gsKY" + }, + { + "Q": "where does the +1 come in at5:00\n", + "A": "Colby, The original problem was (4x+1)\u00c2\u00b2 - 8 = 0 Then at about 4:50 he said he was going to put his answer ((-1+2\u00e2\u0088\u009a2)/4) in for the x in the original equation to prove the answer actually works. And the +1 he wrote at 5:00 is the +1 in the original equation (4[x}+1)\u00c2\u00b2 - 8 = 0 When he put the answer in for x he had (4[(-1+2\u00e2\u0088\u009a2)/4}+1)\u00c2\u00b2 - 8 = 0 I hope that helps.", + "video_name": "55G8037gsKY" + }, + { + "Q": "At 8:45, what is the step-by-step procedure to solving (x-8)(x-2)=0 when solving for x? How did Sal immediately know that the answer would be x=8 or x=2? The only way I see him working it out is if he divided the expression up into two parts like so; (x-8)=0 and (x-2)=0 and then solving for x. If so, why is this allowed? It doesn't make intuitive sense.\n", + "A": "Basically the expression (x+8)(x+2)=0 means that one of those two factor [you have to look at (x+8) as one factor and at (x+2) as another factor] must be equal to zero to satisfy the equation. Either (x+8) must be zero or (x+2) must be zero, or both. Therefore if x+8=0 then x = -8 and this is one valid solution, similarly if x+2=0 then x= -2 and this is the second valid solution. When you tackle problems like this remember that, for a product to be equal to zero there must be a factor which is 0. Hope it helped", + "video_name": "55G8037gsKY" + }, + { + "Q": "at about 10:53 why is (x+8)(x+10) equivalent to x= -8 and x= -10? if you add -8 and -10 together u get -18 not +18, shouldn't it be x= +8 and x= +10?\n", + "A": "Because if you are trying to make them both equal 0 you have to do this: (x+8) if you replace x with 8 you get 16, so you replace x with -8 and you get zero. That is why you get -8 and -10", + "video_name": "55G8037gsKY" + }, + { + "Q": "I do not understand at 1:43 why Sal said it could be both the positive and negative square roots of 8?\n", + "A": "When you square any real number, either negative or positive, you always get a positive number. So the sqrt of 4 can either be -2 or 2. Therefore the square root of any number can be either negative or positive. You do not know for a fact that it is the principle square root (i.e that the answer is just 2 squared), it could easily be -2!", + "video_name": "55G8037gsKY" + }, + { + "Q": "At 1:25, he square roots both sides. If you had another equation like (4x + 1)^2 = 0,\ncan you just square root both sides into 4x + 1 = 0?\n", + "A": "Yes you can. Another way to solve it which produces same result as square rooting both sides: (4x+1)^2 =0 is the same as (4x+1)(4x+1) = 0 One of the factors has to be 0 for the expression to equal 0 as anything multiplied by 0 is 0. So we end up with 4x+1=0, you can then use simple algebra to solve for x.", + "video_name": "55G8037gsKY" + }, + { + "Q": "\nAt 1:50, isn't the square root positive?", + "A": "Square roots can be positive or negative, so he marks it with the correct symbol", + "video_name": "55G8037gsKY" + }, + { + "Q": "At 3:19 when you subtracted 1 from both sides, how did you get -1 on the right side?\n", + "A": "Since he can t really subtract it, he just keeps it there for when he does find out what x is equal to.", + "video_name": "55G8037gsKY" + }, + { + "Q": "\nat around 3:37, sal says 56cm squared but puts the exponent 3 [A.K.A. cubed] when he should have put 2 [A.K.A. squared.]", + "A": "I think it was an accident. I think they meant to put a 2.", + "video_name": "b8q6i_XPyhk" + }, + { + "Q": "At 0:28, Sal said that kites are symmetrical. Does this mean that all rhombuses are also kites?\n", + "A": "Yes. A kite can become a rhombus In the special case where all 4 sides are the same length, the kite satisfies the definition of a rhombus.", + "video_name": "b8q6i_XPyhk" + }, + { + "Q": "At roughly 4:40, you cubed the centimeters instead of squaring them\n", + "A": "The maximum length of the video tape is 3:48. How come you said at 4:40?", + "video_name": "b8q6i_XPyhk" + }, + { + "Q": "\nAt 0:21, is calling the length a diagonal proper terminology?", + "A": "If Sal says that, then it certainly seems right.", + "video_name": "b8q6i_XPyhk" + }, + { + "Q": "at 1:00 i don't understand how u would find the height if you copy only half of the kite\n", + "A": "Because if you find halve of the height then you can multiply it by 2 and get the height of the full kite :3", + "video_name": "b8q6i_XPyhk" + }, + { + "Q": "\nAt 1:00 does he mean the 0 vector in R2?", + "A": "Yes, that was Sal s mistake.", + "video_name": "qBfc57x_RSg" + }, + { + "Q": "At 0:55, he says the ratio for a 30-60-90 triangle is x/2: x*square root of 3/2: x. however, my math book says the ratio is x*square root of 3/2: x: 2x....Am i misunderstanding something?\n", + "A": "The video: x/2 : (x\u00e2\u0088\u009a3)/2 : x The book: x : x\u00e2\u0088\u009a3 : 2x Both are equivalent statements. Multiply the terms of the video s ratio by 2 and you will get the book s ratio. Multiplying by all terms by a common factor will not change the value of a ratio.", + "video_name": "SFL4stapeUs" + }, + { + "Q": "At 6:20, Sal mentions taking the \"principal root\" of something. What is a principal root, and how is it different than square root? Thanks!\n", + "A": "The square root of a number is both positive and negative: \u00e2\u0088\u009a9 = \u00c2\u00b13 Because both 3 and -3 squared give you 9. The principal root is just the positive answer. So the principal square root of 9 is 3.", + "video_name": "SFL4stapeUs" + }, + { + "Q": "\nAt 5:59, how did you get (4x^2)/(4)?", + "A": "He changed x^2 to (4x^2)/(4) for calculation purposes, he will subtract (x^2)/(4) later, and changing x^2 will make the subtraction easier to visualize. (4x^2)/(4) is the same thing as x^2 because the 4 in the numerator and 4 in the denominator cancel out (4 / 4 = 1)", + "video_name": "SFL4stapeUs" + }, + { + "Q": "At 3:21, what does the side-angle side, etc. congruence mean?\n", + "A": "That between the two triangles, 2 sides are congruent, and the angle between them is also congruent. It is referred to as SAS There is AAS, SSS, ASA, and HL These will come up in geometry typically in your first or second year of high school.", + "video_name": "SFL4stapeUs" + }, + { + "Q": "\nAt 3:14, what does \"postulates\" mean when Sal says \"...of our congruence postulates.\"", + "A": "A postulate (or axiom) is just a simple statement that is accepted as true. It is similar to theorems, but theorems must be proven, while postulates do not.", + "video_name": "SFL4stapeUs" + }, + { + "Q": "At 1:30 does he mean equal in length\n", + "A": "Yes. equilateral triangles have exactly the same measures of sides and the same angles.", + "video_name": "SFL4stapeUs" + }, + { + "Q": "\nI don't understand how the one comes in at about 4:51 . How does Sal get 1.08?", + "A": "The chain is increasing at a rate of eight percent so, you have .08. You also have the original 100 percent of 200, that is where he gets the 1.", + "video_name": "m5Tf6vgoJtQ" + }, + { + "Q": "\nAt 5:00, how did Sal get 1.08?", + "A": "If in 1999 Nadia had 200 stores and it increases by 8% per year, all you have to do is turn 8% into a decimal (by moving the decimal place 2 places to the left) you get 0.08. So for one year past 1999, you have 200 + 200(0.08), or a way to simplify this because they have the same base you simply multiply 200 by 1.08.", + "video_name": "m5Tf6vgoJtQ" + }, + { + "Q": "\nat 5:37, what does gist mean?", + "A": "Here s the etymology way to understand it: From French gist en = lie in consist in ; from Latin jacet = to lie, rest (as when boards lie on a wooden beam) Now means the real point , important part . (See the Online Etymology Dictionary and Oxford English Dictionary .)", + "video_name": "m5Tf6vgoJtQ" + }, + { + "Q": "\n0:10 isn't it 2 units wide?", + "A": "Yes. This mistake has been noticed and now a pop up on the screen informs you that it is really 2 units 0.10", + "video_name": "1UQ5IbihJNI" + }, + { + "Q": "\n0:01 ... that is ... very easy sir.", + "A": "for some,yes but others, not as much.", + "video_name": "4IWfJ7-CYfE" + }, + { + "Q": "\nAt 02:24 why not 291/100*32/10 be equal to 291*32/(100/10)=291*32/(10)", + "A": "No, actually when you have 2 fractions being multiplied together (in this example 291/100 and 32/10) you multiply the numerators, then multiply the denominators. So in this case it would end up looking like this: (291/100)*(32/10)= (291*32)/(100*10= (291*32)*(1000)", + "video_name": "4IWfJ7-CYfE" + }, + { + "Q": "\nAt 4:37, Sal said that (-48x\u00e2\u0081\u00b4-42x\u00c2\u00b3-15x\u00c2\u00b2-5x)/(8x+7)(3x+1) is the final answer. But isn't possible to factor it by grouping to simplify the answer to (-6x\u00c2\u00b3-5x) with this as the solution:\n(-48x\u00e2\u0081\u00b4-42x\u00c2\u00b3-15x\u00c2\u00b2-5x)/(8x+7)(3x+1)\n-6x\u00c2\u00b3(8x+7)-5x(3x+1)/(8x+7)(3x+1)\n=(-6x\u00c2\u00b3-5x)", + "A": "Factors are items that are being multiplied. When you get to: -6x\u00c2\u00b3(8x+7)-5x(3x+1) you have terms (2 items being added or subtracted). Each term is made up of factors. But, you haven t fully factored the polynomial. Since you don t have factors, you can t reduce the fraction. Hope this helps.", + "video_name": "evmDZkDvlNw" + }, + { + "Q": "\n@6:08 Probability of A and B are independent of each other.\n\nA --> Select a Blue garment\nB --> Select a Shirt\n\nThere is a Blue Shirt in the Sample Space. So if A happens to select the Blue shirt. Then for sure the chance of B selecting a Shirt is impacted since there is one less shirt to select from.\n\nIn this case, how is it that A and B are independent events ?", + "A": "Tomas chooses a garment at random. So if he happens to choose the blue shirt, then A and B are true. A and B are groups of possibilities, not selections. To be clearer, Tomas doesn t select a blue garment, and then select a shirt, he simply picks one at random. So A and B can be independent events. Tell me if you still have questions, or if this wasn t clear enough, please. :)", + "video_name": "R-NeYKSEqns" + }, + { + "Q": "At 0:21. Why are radian angles much smaller than degree angles?\n", + "A": "Actually, 1 radian is much larger than 1 degree. You can equate the two as: \u00cf\u0080 rad = 180\u00cb\u009a", + "video_name": "C3HFAyigqoY" + }, + { + "Q": "\nWhy does Sal move the graph 2 units to the right when it says -2 at 1:05?\n\nShouldn't he move it to the left by 2 units?", + "A": "Think about it on a coordinate plane: if I shift 0 two to the right, I get 2. Because you have to think about it in terms of 0, not 2, you subtract 2 instead of adding 2.", + "video_name": "5DLkB-g8Rr8" + }, + { + "Q": "\n5:31 what is 80 divided by 2/5", + "A": "80/2/5=80*5/2=40*5=200", + "video_name": "xoXYirs2Mzw" + }, + { + "Q": "\nIn the video at 3:09 , the subtitles say c (comedy) instead of (c, d). Someone should fix that.", + "A": "The subtitle is auto-generated by youtube I believe. Sal said, c comma d which I guess it picked up as comedy", + "video_name": "S-agS4YaxxU" + }, + { + "Q": "At about the 5:40 sec mark, Khan talks about the product of dividing:\n\n9.2 * 10^5\n11.5 * 10^2\n\nI worked the equation before Khan. Instead of dividing 9.2 by 11.5 * 10^2, I said divide by\n1.15 * 10^3 (.) We came up with the same answer; 8 * 10^2.\n\nMy doing scientific math problems that way (changing any multiplication involved in the numerator or denominator to correct scientific notation, will that cause me any problems down the road (?))\n", + "A": "I think it is good to know how to do a math question two different ways, so if you learn to do it both ways and remember how to do it, then I think you are set!", + "video_name": "EbmgLiSVACU" + }, + { + "Q": "At 3:45, Sal talks about the \"orientation\" and \"magnitude\" of a vector. So, is \"orientation\" the direction of a vector? And is \"magnitude\" the length of a vector?\n", + "A": "Yes, that is correct. Sometimes you will hear angle instead of orientation or direction, but it is all the same.", + "video_name": "gsNgdVdAT1o" + }, + { + "Q": "\nWhere does the 9/3 come from at 2:32 ?", + "A": "Since you need common denominators in order to subtract two fractions, what he did is that after simplifying 12/4 to 3, he changed it into a fraction that equals 3, 9/3=3, in order to subtract the two fractions.", + "video_name": "BOIA9wsM4ok" + }, + { + "Q": "Why cant we directly substitute and find at 2:28 where 3y+3=y+7\n3y-y=7-3and y=2\n", + "A": "Add 18r to -2r and add 12s to 6s", + "video_name": "vkhYFml0w6c" + }, + { + "Q": "at 0:43 where did you get 0 from\n", + "A": "You get the zero when you do not move either way on the x axis.", + "video_name": "5a6zpfl50go" + }, + { + "Q": "At 0:58, Sal draws a line segment instead of a line. Is this supposed to be the case?\n", + "A": "Should be a line, he just didn t draw the arrows.", + "video_name": "5a6zpfl50go" + }, + { + "Q": "\nDo you get the 1 in the rise over run from 3/1? 5:37 in the video", + "A": "3x is the same as saying go over 1 and up 3 which is like saying 3/1, so yes, you are corect", + "video_name": "5a6zpfl50go" + }, + { + "Q": "Are rates and ratios the same as fractions?\nFor example, 35:1 can also be written as 35/1, which is a fraction.\n", + "A": "Fractions explain how much a number is out of something, whereas ratios compare numbers", + "video_name": "qGTYSAeLTOE" + }, + { + "Q": "At 4:09, why is decameter spelled wrong? Or am I wrong?\n", + "A": "Decimeter and Decameter are actually 2 different things. Decameters are bigger than Meters but smaller than Kilometers and are used less often in math.and science and such.", + "video_name": "I3kQJvR7ZIg" + }, + { + "Q": "At 4:40, how did someone found out all this?\n", + "A": "As Sal says, exponential functions and logarithmic functions are inverses so they appear as reflections on the graph. Basically, the x values and y values are swapped.", + "video_name": "K_PiPfYxtao" + }, + { + "Q": "at 8:10 and 9:21 why is he multiplying by 1/2 ?\n", + "A": "He is finding the area of the triangles. The formula for finding the area of a triangle is 1/2 times base times height.", + "video_name": "EqNzr56h1Ic" + }, + { + "Q": "\nWhy does Log2(2t) become zero at 3:01?So confused", + "A": "Have a look in Top Questions for Theresa Johnson s answer (currently 14 votes) to dugee23 s question. She explains how Sal simplified log_2(2^t) and got t. (Note that there is no zero at 3:01.)", + "video_name": "7Ig6kVZaWoU" + }, + { + "Q": "\nAt around 4:04, why does Sal say \"pi over 2\"? It's supposed to be pi over 4, right?", + "A": "yes", + "video_name": "JGU74wbZMLg" + }, + { + "Q": "Can someone explain to me why at 1:33 Sal says that the unit circle is sqrt2/2!!\n\nI don't understand, looking at the circle, knowing that 180 degrees equals pi, how what looks ro ME as pi/4, is actually the sqrt2/2!\n\nHELP!\n", + "A": "@1:33, you re right that the ANGLE is pi / 4 (or 45 degrees), but Sal was solving the equation for the length of the non-hypotenuse SIDES of the right triangle, each of which turned out to be sqrt2 / 2. @7:32, Sal indicates - sqrt3 / 2 on the Y-axis because the problem given is arcsin(-sqrt3/2). In other words we re looking for the angle whose sin (its measure on the Y-axis) is - sqrt3 / 2.", + "video_name": "JGU74wbZMLg" + }, + { + "Q": "At 6:10 the domain arcsin is restricted to the 1st and 4th quadrant. So far I follow. It starts at Pi/2 - ok I follow. the other range is - Pi/2 ? I do not understand. On the unit circle diagram I pulled up the point (0,-1) is 3pi/2. and I do not see - 2/pi any where on the unit circle. What gives?\n", + "A": "3pi/2 is the same place as -pi/2.", + "video_name": "JGU74wbZMLg" + }, + { + "Q": "At 1:13, how did Sal know that radius of the circle is 1? Like where did he get the 1 for the hyponthensus\n", + "A": "He refer to the unit circle radius 1", + "video_name": "JGU74wbZMLg" + }, + { + "Q": "\n@ 3:22 Couldn't he factor out (s-a) (s-b) and (s-c) to just s(-a*-b*-c)?\nI'm not sure. I'm rusty with my factoring...", + "A": "It would seem that way, but actually, if we factor it out that way, we get -s*a*b*c which is much different from (s-a) (s-b) and (s-c)", + "video_name": "-YI6UC4qVEY" + }, + { + "Q": "at 4:22 Sal gets to the square root of \"7\" and stops and says, \"you don't deal with the negative square roots . . . so this is just the square root of 7.\" The square root of 7 is not negative, it's 2.645... So, why did he stop and not figure out the square root of 7?\n", + "A": "He said negative not about the square root of 7 but about all of those numbers because square root of a positive number can be either positive or negative eg. square root of 4 can be either 2 or -2 ( -2 *-2=4 ). He did not want it to be negative because you are dealing with area, which is not negative. Also by the way there is no need to calculate root of 7 unless you need to find cost of anything.", + "video_name": "-YI6UC4qVEY" + }, + { + "Q": "For the triangle at 3:17, with lengths 9, 11 and 16, can you divide that in half and use pythagoras, so one side becomes 8,11 and x or 8,9 and x? and find the value of x, and that is your height?\n", + "A": "When we look at the triangle at 3;17, you cannot divide it in half and use the Pythagorean Theorem, because we don t know if it is a right triangle. So with a question were they don t give you the 90\u00c2\u00b0 right angle symbol, you can never assume anything in math. Hope this helps.", + "video_name": "-YI6UC4qVEY" + }, + { + "Q": "hey isn't that any number to the 0th power is always 1 including negative number at 1:42\n", + "A": "Yes, but that is not what was in the problem \u00e2\u0088\u0092 b\u00e2\u0081\u00b0 means the same as \u00e2\u0088\u0092 (b\u00e2\u0081\u00b0) = \u00e2\u0088\u0092 (1) = \u00e2\u0088\u00921 However (\u00e2\u0088\u0092b)\u00e2\u0081\u00b0 would be equal to 1", + "video_name": "gR8-vRg6Yp0" + }, + { + "Q": "\nAt 3:42 when it says the radical sign means the principle square root; what's the notation for either square root, or for the negative square root, in that case?\n\nAlso when talking about the third root, you wouldn't have to distinguish between principle and negative, right? Do you have to distinguish for all even roots, but not for odd roots?", + "A": "The notation for both square roots is \u00c2\u00b1\u00e2\u0088\u009ax. If you want only the negative square root, then you would say -\u00e2\u0088\u009ax. As for odd roots, you still have to distinguish between principal and non principal roots. The only difference is that a non principal odd root is not simply the negative of the principal root. For instance, the cube root of -8 is -2, but it can also be 1\u00c2\u00b1\u00e2\u0088\u009a3 i.", + "video_name": "rYG1D5lUE4I" + }, + { + "Q": "\nwait.. at 1:11, Sal says (principal square root = psr) psr of (a*b) = psr of a *psr of b, when in the last video he states that it does not work when the numbers are both negative, and in this case they are. so therefore, this is wrong, right?", + "A": "Square roots generally have two roots: the principal root and the negative root. For example: \u00e2\u0088\u009a9: psr = 3; negative root = -3. The default is to use the psr. If the negative root is wanted, then a minus sign is placed in front of the square root symbol. -\u00e2\u0088\u009a9 = -3", + "video_name": "rYG1D5lUE4I" + }, + { + "Q": "at 3:50 sal says that each number has a positive and negative square root. And i was thinking, if that was the case, couldn't the square root of -1= -i, which is i to the 3rd power. If this was true then i to the 1st power would eqaul i to the 3rd power. in essence -i=i. I'm a little cunfused so could someone please explain this to me.\n", + "A": "Sal says that 4 has 2 square roots. Positive numbers have two square roots. Negative numbers do not.", + "video_name": "rYG1D5lUE4I" + }, + { + "Q": "\nAt 3:23, does that mean that every number actually has two square roots? Wouldn't that make algebra nearly impossible?", + "A": "Not really, it just means you have two possible solutions if you have a function with a square root. example: x^2=9 -> x=sqrt(9) -> x=3 or x=-3. After all 3*3 = 9 and -3*-3 = 9.", + "video_name": "rYG1D5lUE4I" + }, + { + "Q": "How did you get the porabla at 3:02\nI'm still confused..\n", + "A": "I think I understand your question. The line describing the parabola is curved, not straight, but with only a few points drawn in, it s hard to see why. If you went through the equation and filled in x with all the points in between the points that he graphed, you would see a curve shape appear. When you only have two points it s easy to see why it looks like it should be straight. Sal just skipped over doing 2.5, and then 2.25, and so on. The more points you graph, the more it looks l", + "video_name": "hjigR_rHKDI" + }, + { + "Q": "\nWhy is the R^n space not straight? I thought it was made up of vectors. At 1:47?", + "A": "It is straight . The wiggly circle that Sal drew should be viewed very abstractly. Within that wiggly loop is all the vectors in R^n.", + "video_name": "pMFv6liWK4M" + }, + { + "Q": "\nsall, in 13:40 - 13:56, I think I don't get it. -a is a subset of R^2? since R^2 is all the cartesian plain . What we are saying here is -a is not a subset of our restriction of R^2 that we made and not R^2. Is this right? So we are saying that -a is not a subset of R^2 when x_1>0 right?", + "A": "I think I need to rethink what a subspace is, Thank you.", + "video_name": "pMFv6liWK4M" + }, + { + "Q": "At 4:00.. why do you use 2pi for the period?\n", + "A": "2pi is once around a circle. Going around a circle makes a sine wave or a cosine wave.", + "video_name": "SBqnRja4CW4" + }, + { + "Q": "At 5:46, how does Sal determine what the slope is? How does he know it's -(1/2)? Isn't -(1/2) the y-intercept?\n", + "A": "Both the slope and the y-intercept are - \u00c2\u00bd When a function of a line is in the form of mx +b, the slope is m. Since -x/2 = -\u00c2\u00bd(x) the slope is -\u00c2\u00bd", + "video_name": "wSiamij_i_k" + }, + { + "Q": "\nhow do we come to know wheter a curve is 1:1 function and does its has an inverse?", + "A": "The horizontal line test is the easiest way. If you can draw a perfectly horizontal line such that it touches two points on the function, then it is not 1 to 1.", + "video_name": "wSiamij_i_k" + }, + { + "Q": "In 5:00 onwards, why doesn't the -2 turn the whole function into -y/2 +1/2? Shouldn't it invert for both numbers?\n", + "A": "It doesn t invert any of the numbers actually. He had y+1 = -2x, so he divided both sides by -2. Think of it as having to divide both terms on the left side (y and 1) individually by -2. So y divided by -2 is -y/2 and 1 divided by -2 is -1/2. SO you end up with -y/2 - 1/2 = x", + "video_name": "wSiamij_i_k" + }, + { + "Q": "\nat 5:50 he says the slope is -1/2. he moves over in the positive direction on the x axis which i don't quite get and also slope i thought was change in Y over change in X so when he moves down by 1/2 i am at a loss. over by 1 down 1/2 doesn't make sense to me. anybody got another way of explaining by chance?", + "A": "nevermind, i think i got it. i get the same inverse line as Sal if i go down -1 on Y then over 2 on X.", + "video_name": "wSiamij_i_k" + }, + { + "Q": "At 8:50, how can (x+2) be considered positive when -1 still falls in the range of x>-2?\n", + "A": "SG, When x=-1 x+2 = -1+2 = +1 so even though x is not positive, (x+2) is positive. I hope that is of some help.", + "video_name": "ZjeMdXV0QMg" + }, + { + "Q": "At around 00:58: Why is a>0 and b>0 the consequence of a/b>0?\n", + "A": "A/B can only be greater than 0 (in other words, positive) only if A and B are both positive (A>0 and A>0) or A and B are both negative (A<0 and B<0). Any other combination will result in a negative fraction (A/B<0 instead of A/B>0).", + "video_name": "ZjeMdXV0QMg" + }, + { + "Q": "\nAt around 3:40 confused me a lot. He says you can re-write the equation as \"|x - -2|=6\", and then find that the answers are 6 away from -2. While that does appear true, why does it work for that equation, and not the original equation \"|x+2|=6\"? How did Sal know to re-write the \"+2\" as \"- -2\"?", + "A": "The minuses cancel out. Thus, subtracting negative 2 is eqall to adding 2.", + "video_name": "u6zDpUL5RkU" + }, + { + "Q": "\nat 1:40 how did he remove the absolute value portion? Did he just make it into an equation? Can someone please clarify.", + "A": "Sal is solving the absolute value equation of |x-5|=10. To solve this, you have two possible choices (since we have the absolute value there). Either x-5 could be 10 or x-5 could be -10. (because | -10 | = 10. So he is solving the absolute value equation by taking what s inside of it and setting it equal to 10 and -10. x-5=10 and therefore x = 15. x-5=-10 and therefore x= -5. So our two answers are 15 and -5.", + "video_name": "u6zDpUL5RkU" + }, + { + "Q": "6:27 Why isn't it x+3=y or x+3=-y?\n", + "A": "think of what a basic absolute value y = | x | looks like, it is a V shape with the vertex at the origin. Thus for any value of y except 0 (y values are horizontal lines), the value of x would be +y or -y. If y = 1, we would have two points (1,1) and (-1,1), We expand this property into more complicated square roots, so y = x+3 or y = - (x+3)", + "video_name": "u6zDpUL5RkU" + }, + { + "Q": "\nyou lost me at around 1:35 to 2:00. I don't get how 1to the 0 power could equal to 1. isn't the power of powers multiplication? shouldn't 1x0=0?", + "A": "Think of it this way: x\u00c2\u00b3/x\u00c2\u00b2 = x\u00c2\u00b3\u00e2\u0081\u00bb\u00c2\u00b2 = x\u00c2\u00b9 = x Similarly: x\u00c2\u00b3/x\u00c2\u00b3 = x\u00c2\u00b3\u00e2\u0081\u00bb\u00c2\u00b3 = x\u00e2\u0081\u00b0 but, of course, x\u00c2\u00b3/x\u00c2\u00b3 = 1, Thus, x\u00e2\u0081\u00b0=1 Of course, this doesn t work if x=0 , 0\u00e2\u0081\u00b0 is undefined.", + "video_name": "NEaLgGi4Vh4" + }, + { + "Q": "As well as my previous question, at 1:19 sal said that any number to the zeroth power is going to be 1. Does that mean that 8 to the zeroth power will be 1, or that 8 to the zeroth power will be 8?\n", + "A": "It means that 8^0 = 1, even 100^0 = 1, any number to the zero-th power is equal to 1.", + "video_name": "NEaLgGi4Vh4" + }, + { + "Q": "At 0:00 who is the ancient philosopher?\n", + "A": "The video starts out at 0:00 with So you, as the ancient philosopher . So is he you?", + "video_name": "pzQY-9Nmtws" + }, + { + "Q": "\nAt 5:07 Why does he simplify (1/x)(x-1) to (x-1)/x. Could he also have multiplied (1/x) by both halves? so (1/x)(x-1) = (x/x)-(1/x)= -(1/x). I am wondering if these are two different simplifications or if my answer is wrong.", + "A": "You ve made an algebra error where you say (x/x)-(1/x) = -(1/x). The expression (x/x) is equal to 1, so after the equals sign you should have 1 - (1/x), which evaluates to 0 when x = 1.", + "video_name": "MeVFZjT-ABM" + }, + { + "Q": "4:30 Why doesn't the lnx in the numerator cancel with the lnx in the denominator?\n", + "A": "In the denominator, you are adding (+) two things and thus you can not cancel it out with the numerator", + "video_name": "MeVFZjT-ABM" + }, + { + "Q": "\nSo, wait at 5:05 he got rid of a 1? How can he just remove a 1 that he was adding?", + "A": "It was +1 - 1 so he just canceled them out", + "video_name": "MeVFZjT-ABM" + }, + { + "Q": "\nAt 3:49, how is the derivative of x-1 = 1. I thought the derivative of x is 1 so, that 1 minus the 1 should equal 0.", + "A": "You re really taking the derivative of x (which is 1) and the derivative of -1 (which is 0). (1) - (0) = 1. The derivative of -1 is 0 because -1 is a constant. The derivative of any constant is 0. If you imagine a graph with y=-1 (or any constant) the line is horizontal. The tangent line of any point on the graph will also be horizontal, and the slope of a horizontal line is zero.", + "video_name": "MeVFZjT-ABM" + }, + { + "Q": "\nMy memory of math is a bit fuzzy so this might be a stupid question. At 9:00, why did Sal randomly divide the equation 2C1 + 3C1 = 0 by one half?", + "A": "He didn t divide by 1/2, he multiplied by 1/2. He did that to get the same coefficient on the C1 terms in both equations. After that, he can subtract one equation from the other to get rid of C1 altogether. Another possibility would have been to multiply the second equation by 2.", + "video_name": "Alhcv5d_XOs" + }, + { + "Q": "At 3:00 why did you not start writing from a1v1 but rather a2v2?\n", + "A": "It is his way of showing that v1 can be made from a linear combination of the other vectors. If he included v1 in there, then that would be saying that v1 is a linear combination of itself and the other vectors, which is true for all vectors, all the time.", + "video_name": "Alhcv5d_XOs" + }, + { + "Q": "\nI have a question regarding the giveaway problem (around 12:00). Sal says that if there are three two-dimensional vectors in a set, the set will definitely be linearly dependent.\nWhat if:\nv1 = [1,0]\nv2=[2,0]\nv3=[7,8]\nin this case, v1 and v2 are linearly dependent since 2*v1 = v2\nBut there is no way v3 can be represented by the linear combination of v1 and v2, how could this set of these three vectors be linearly dependent?", + "A": "That is an example of a set of three linearly dependent vectors, for the reason you describe. If you understood Sal to mean that a linearly dependent set means that ANY of the vectors is a linear combination of the others, that is incorrect. It is just necessary that at least one of the vectors is a linear combination of the others.", + "video_name": "Alhcv5d_XOs" + }, + { + "Q": "At 0:39, how is this about subtracting formula for a cosine? I am interested in knowing how to solve for cos(u+v)=cos u cos v + sin u sin v\n", + "A": "cos(u + v) is actually cos(u)cos(v) - sin(u)sin(v).", + "video_name": "D_smr0GBPvA" + }, + { + "Q": "At 9:30, was Sal supposed to write a \"t\" after the \"cos^2\"?\n", + "A": "yes he was trying to write cos^2t", + "video_name": "AFF8FXxt5os" + }, + { + "Q": "\nat 08:25, why the equation of normal line is: y-x0^2=-(1/2x0)*(x-x0)?", + "A": "i don t get something here if the y =2x and we want to get a perpendicular line to that one shouldn t it be (-1/2)*x ? as i know the to perpendicular lines have some equations like: m1*m2=-1 so 2*m2=-1 m2 would be -1/2 and then the new line perpendicular to the first one would be just (-1/2)*x please tell me where i am wrong", + "video_name": "viaPc8zDcRI" + }, + { + "Q": "At 2:10 and 4:30, when the questions says the parabola gets smaller and after that starts to increase, isn't it referring to the y values?\n", + "A": "The problem refers to the x coordinates but have the poor use of words and Sal explains what it means by getting smaller and increase . Although, there is a relation as x is getting smaller so is y.", + "video_name": "viaPc8zDcRI" + }, + { + "Q": "\nAt around 11:23: Why do you use the quadratic formula?", + "A": "Sal wants to find the x coordinates of the intersections, and these are the solution of the equation he built by considering the y values of the normaline and the parabola are the same (which happens only at the intersections). But I think he could have factorized the polynomial, because we already know one solution is x0. x\u00c2\u00b2 + (1/(2.x0)).x - ((1/2)+x0\u00c2\u00b2) = (x-x0)(x+(1/(2.x0) + x0) Thus the other solution is -(1/(2.x0) + x0)", + "video_name": "viaPc8zDcRI" + }, + { + "Q": "At 12:36, Sal says \"let's divide everything by 1/2\" shouldn't it be 2, not 1/2?\n", + "A": "You are right, he has a pronunciation error, he should have said either divide everything by 2 or multiply everything by 1/2 . Luckily he did wrote everything correctly.", + "video_name": "viaPc8zDcRI" + }, + { + "Q": "\nAt 7:02 I thought the line perpendicular to y=2x is y=(-1/2)x not y=-1/(2x). I might not be understanding something, but -1/(2x) just doesn't make sense to me.", + "A": "Indeed. I agree entirely. I was under the impression that only the slope was affected, and thus 2x would become -x/2...", + "video_name": "viaPc8zDcRI" + }, + { + "Q": "I find it easier to think of conversion problems in terms of proportions.\nfor example: At 4:36 It make more sense to think of it as 45 degree/ x radii is in proportion to \u00cf\u0080 radii / 180 degrees. So x(180)= 45(\u00cf\u0080), then x=45/180\u00cf\u0080, but that gives 1/4\u00cf\u0080 which is not the answer, how can you solve these with proportions and how would you solve that example from the video using a proportion?\n", + "A": "x/\u00cf\u0080 = 45/180 Is the form I normally use. x is to \u00cf\u0080 as 45 is to 180. 180x = 45\u00cf\u0080 This is the same equation you used, and it works. x = 45\u00cf\u0080/180 x = \u00cf\u0080/4 This is the right answer. 45\u00c2\u00b0 = \u00cf\u0080/4 radians", + "video_name": "z8vj8tUCkxY" + }, + { + "Q": "\nto be included in N, doesn't \u00c2\u00b5(x) also have to be multiplied by y' ?\nAlthough this isn't in this case- at 5:25 Sal is still treating \u00c2\u00b5(x) as part of N. how can he do that?", + "A": "It is actually part of x. \u00c2\u00b5(x) is the factor that needs to be multiplied to M and N to make it integratable not y . If you reason like that, there is no y in M then but you can get dx if you multiply through by dx becayse y = dy/dx. Please vote if that helped.", + "video_name": "j511hg7Hlbg" + }, + { + "Q": "\nAt 5:26 ,shouldn't you take the derivative of (2x+y)? Since he is using the chain rule?", + "A": "At 5:13 Sal mentions that he is using the product rule which states that d/dx[f(x)*g(x)] = d/dx(f(x))*g(x) + f(x)*d/dx(g(x)) in this case f(x)=mu(x) and g(x)=x^2+xy All of that to say that (2x+y) is the derivative of g(x). Notice: To find this derivative with respect to x simply split the function at the + sign and take the derivative of x^2 and xy seperatly to get (2x+y)", + "video_name": "j511hg7Hlbg" + }, + { + "Q": "At 1:31, how does- 3x -(+2x) equal -3x+2x and result in a sum of x?\n", + "A": "The above equation was not solved right. It should be: - 3x - (+2x) = - 3x - 2x = - 5x", + "video_name": "8Wxw9bpKEGQ" + }, + { + "Q": "\nAt 0:52, why did you write x over the 3x? I was taught to write it over the x squared. Sorry, just a little confused.", + "A": "you want to align all like terms wherever possible to keep it organized. if you write x_ over the _x squared , it s more difficult to keep track of your different terms", + "video_name": "8Wxw9bpKEGQ" + }, + { + "Q": "Can a snail live underwater?@12:30pm\n", + "A": "Snails CAN stay underwater for a while but CAN T live underwater.", + "video_name": "gBxeju8dMho" + }, + { + "Q": "at 1:40, hilarious! his pineapple is BLASPHEMY! rotfl\n", + "A": "The pineapple is blasphemy", + "video_name": "gBxeju8dMho" + }, + { + "Q": "why is there a snail wandering around between 0:00 and 1:00\n", + "A": "because she likes it and it is cool, and looks like spongbobs pet garey", + "video_name": "gBxeju8dMho" + }, + { + "Q": "at 0:42, why is the first dot on x axis on zero? It said 1 question = 5 points so shouldn't it be 1 on the x axis and 5 on the y axis?\n", + "A": "no because if you have those points (1,0) and (0,5) the slope would be negative (5-0)/(0-1), and you would quickly go into the negatives for y as x increases. If you get 0 questions right, why would get a 1 point credit? If you get 0 questions correct, you should get 0 points (0,0), if you get 1 question right, 5 points (1,5), 2 questions is 10 points (2,10) etc.", + "video_name": "0eWm-LY23W0" + }, + { + "Q": "Why is 1 over 25/64 equal to 64/25? (at 6:23)? Thank you.\n", + "A": "Ah, that s 1/(25/64) or 1 divided by 25/64 which is the same as 1 * 64/25 or 64/25.", + "video_name": "JnpqlXN9Whw" + }, + { + "Q": "I still don't get the point of the 1 at 0:14. Can someone please help me?\n", + "A": "its just showing that the one doesn t make a difference", + "video_name": "JnpqlXN9Whw" + }, + { + "Q": "i like how at 0:51 it gives that little point out XD\n", + "A": "Me too! it s pretty cool.", + "video_name": "JnpqlXN9Whw" + }, + { + "Q": "\nWhy is at 1:30 the negitave turns into the fraction?", + "A": "The method Sal is using may be confusing, so you may want to solve a negative exponent problem this way: 4 to the negative 3rd power=1*4*4*4(find the reciprocal)> 1/64 Why? Well, we know that 4 to the positive 3rd power is 64, or 64/1, and a negative is the opposite of a positive. Since a negative is the opposite of a positive, we will have to find the opposite, or reciprocal of 64 or 64/1, which is 1/64.", + "video_name": "JnpqlXN9Whw" + }, + { + "Q": "At 0:08 Why does he put the 1. (2^4 = 1 x 2 x 2 x 2 x 2) It does'nt really do anything and it confuses me because I did that on a test and i lost a point so I don't know if it supposed to be like that or not\n", + "A": "he puts the 1 to show you 2^0 still leaves a 1 2^0 = 1 2^1 = 1 * 2 2^2 = 1 * 2 * 2", + "video_name": "JnpqlXN9Whw" + }, + { + "Q": "\nSal said \"negative one\" but meant \"one.\"\n0:54", + "A": "Yes.. The black box pops up and it tells you..", + "video_name": "JnpqlXN9Whw" + }, + { + "Q": "So, at 6:24 Sal says that 5/8^ -2 is 64/25. Isn't that equal to 2 14/25?\n", + "A": "yes, but no use in here by simplifying it", + "video_name": "JnpqlXN9Whw" + }, + { + "Q": "5:25 So, all I have to do to use a negative exponent on a fraction is swap the numerator and denominator on the fraction, and then apply a positive exponent to the faction?\n", + "A": "Yep, that s right!", + "video_name": "JnpqlXN9Whw" + }, + { + "Q": "\nSo the numerator of the fraction will always be 1? At 4:05 I noticed that.", + "A": "Correct, the numerator of the fraction will be one, when a number is raised to a negative exponent.", + "video_name": "JnpqlXN9Whw" + }, + { + "Q": "Isn't scalar only in matrices?? ( 0:40 )\n", + "A": "A scalar is just a number. When you multiply a scalar by a vector or matrix, you will just get a scaled up version of the vector or matrix.", + "video_name": "br7tS1t2SFE" + }, + { + "Q": "\nAt 5:21, he says that you can use the pythagorean theorem to calculate the length of the vector, but wouldn't the length be sqr21, since 3^2+4^2=21?", + "A": "3^2 + 4^2 = 9 + 16 = 25. Where are you getting 21 from?", + "video_name": "br7tS1t2SFE" + }, + { + "Q": "\n0:36 What does \"Scalar\" mean?", + "A": "A scalar is just a real number. This is as opposed to a vector (which is an ordered set of real numbers).", + "video_name": "br7tS1t2SFE" + }, + { + "Q": "\n3:53 Why do you have to substitute the variable into an original equation?", + "A": "So that you can get y.", + "video_name": "vA-55wZtLeE" + }, + { + "Q": "\nAt the time 0:19 9 1/2 ends up being reduced to 3 like you had said. But, what happens to 1/2. Since you are using 3 to divide/reduce you have to use 3 to reduce 1/2 which you can't do. So how does that work. Since 3 is bigger then 1/2 you cant do that because the difference is ginormous like ginormous like absolutely HUGE! Well not that big just 2 1/2 but i mean still please explain.......", + "A": "9 to the exponent 1/2 means principal square root of 9, which is 3 because 3\u00c2\u00b2=9. He didn t divide 9 by 3. Perhaps you need to watch review on exponents from previous videos then come back to this one.", + "video_name": "tn53EdOr6Rw" + }, + { + "Q": "\nAt the minute 1:50 you came out with 1/(-27)^1/3 and you started looking for a number which could be multiplied by itself in order to get -27. So my question is why did not you put the -27 into the radical sign? ( I know that it will lead to imaginary number) But is there any rule to apply when dealing with negative bases?", + "A": "If you have a negative under a 2nd radical, then the answer to the problem is no solution. However, this problem does not need the 2nd radical (square root), but instead the cube root. The cube root can be positive or negative. If your calculator has this button, you can do that, but many simple calculators don t so that s why he was explaining how to find it without a calculator.", + "video_name": "tn53EdOr6Rw" + }, + { + "Q": "Around 5:10-\nIsn't the probability to score 4 out of 10 shots the number of ways you can arrange those 4 scores (namely 10 choose 4) and then multipy by the score probability - 40% to the power equal to the total number of shots. I don't understand why we have to multiply by the probability of a miss too? (He multiplies by (1-P)^n-k I don't understand why this is necessary in order to get the probability of k scores)\n", + "A": "It is necessary to take in to consideration the effect of the missed shots or else you are just finding the probability of making four shots in a row if you hand a probability of making a single shot is 40%. If you don t consider the missed shots its as if you only took four shots all together and not ten. Hope this helps", + "video_name": "SqcxYnNlI3Y" + }, + { + "Q": "At 0:20 where does he get -1?\n", + "A": "the minus before the parenthesis is the same as times -1", + "video_name": "5ZdxnFspyP8" + }, + { + "Q": "At 1:03, if you multiply 3x^2+x-9 by -1, don't you also have to multiply the 16x+14 by -1?\n", + "A": "Don t you have to do the same thing to both sides of the equation?", + "video_name": "5ZdxnFspyP8" + }, + { + "Q": "\nAt 2:06 I did not receive my full points but i watched the whole video and only got 100 points also at 0:25 seconds sal said their was the negative one how did he get that", + "A": "So when you have the problem (4x^2+6x-5)-(2x^2-4x-7) to remove the parenthesis you have to multiply everything after the - sign in the middle by -1 because that is really what the - sign in the middle represents.", + "video_name": "5ZdxnFspyP8" + }, + { + "Q": "1:12 why couldn't a2 be a3:a1?\n", + "A": "Because a^3*a^1 = a^4 the exponents add up.", + "video_name": "c-wtvEdEoVs" + }, + { + "Q": "\nAt 0:30, what if the number isn't a perfect cube?", + "A": "Both methods to do this are likely not in your skill set yet, as they are usually taught in Trig or Calc classes. However, there is the possibility of simplifying the radical down if the number under the radical is a multiple of a perfect cube, such as 16. 16 is 2*2*2*2. As such, you could pull the group of three 2 s out, and leave the last 2 behind under the radical. This would then be 2*(cubic-root 2)", + "video_name": "c-wtvEdEoVs" + }, + { + "Q": "At 04:08 what did you mean about, \"3 is too big\" how does it work?\n", + "A": "3 is too big or too large of a number cuz 3x7=21 but if your trying to find out what equels or what is close to equeling 17...........2 is the right answer cuz 2x7=14 so which is closest.....21 or 14?", + "video_name": "NcADzGz3bSI" + }, + { + "Q": "\nIn this video he explains how to find if a number is divisible by 3 at 6:06 but than because it is changes it at 6:36, the first number when you used his trick added up to 27, the second number it added up to 26, at the end 9:52 the remainder was 2, if you divided 26 by 3 it would be 8 r 2 (same amount remaining as with Sal's problem) so is the method to find if a number is divisible by 3 also a way to find what the remainder would be if it isn't?", + "A": "Pretty much. Good pick up.", + "video_name": "NcADzGz3bSI" + }, + { + "Q": "\nAt 0:32 couldn't he just multiply 21*9=189 and then multiply the same for the other side\n28*6=176 and 189 > 176", + "A": "Not more complicated then what he did", + "video_name": "2dbasvm3iG0" + }, + { + "Q": "In the video you provided \"converting decimals to fractions (ex 1) \" 1:13 I have a question, if there was a number greater than zero in front of the decimal (example 4.0727) would that change the place values to something higher than ten-thousand.\n", + "A": "The number 4.0727 is a mixed number. Any digits to the left of the decimal point are the whole number (the 4). Any digits to the right of the decimal point are the fraction. 4.0727 = 4 727/10,000 The whole number does not change the place value used to create the fraction.", + "video_name": "EGr3KC55sfU" + }, + { + "Q": "\nAt 0:00 why can't you just do this:\n31+50+64+x=180\nx=35", + "A": "Because connecting these two triangles would mean making a bigger triangle and the angle measurements would have to add up to 180\u00c2\u00b0, this would be a way to solve this problem as well. Doing this would allow you to find the missing measurement of other part of the third angle.", + "video_name": "hmj3_zbz2eg" + }, + { + "Q": "\nAt 4:20 why is a+b=WHAT ARE THoSE", + "A": "a and b are variables; they re merely substituting in for a number that we don t know. You technically can use any letter. That s what Sal was using them for -- a demonstration where we didn t know the numbers, just that y = a + b (in the problem he solves at 4:20.)", + "video_name": "hmj3_zbz2eg" + }, + { + "Q": "how can we findout the angles if they r in ratio\nAngles of a triangle are in the ratio 3:5:4 ,the samallest angle of the triangle is ?\n", + "A": "The ratio 3 : 5 : 4 means that if the first angle is 3\u00f0\u009d\u0091\u00a5, then the second angle is 5\u00f0\u009d\u0091\u00a5, and the third angle is 4\u00f0\u009d\u0091\u00a5. The sum of these three angles is 3\u00f0\u009d\u0091\u00a5 + 5\u00f0\u009d\u0091\u00a5 + 4\u00f0\u009d\u0091\u00a5 = 180\u00c2\u00b0 \u00e2\u0087\u0094 \u00f0\u009d\u0091\u00a5 = 180\u00c2\u00b0 \u00e2\u0088\u0095 12 = 15\u00c2\u00b0 So, the first angle is 3 \u00e2\u0088\u0099 15\u00c2\u00b0 = 45\u00c2\u00b0, the second angle is 5 \u00e2\u0088\u0099 15\u00c2\u00b0 = 75\u00c2\u00b0, and the third angle is 4 \u00e2\u0088\u0099 15\u00c2\u00b0 = 60\u00c2\u00b0", + "video_name": "hmj3_zbz2eg" + }, + { + "Q": "\nAt 3:47, do angles a + b equal to y?", + "A": "Yes, actually, that s exactly right :)", + "video_name": "hmj3_zbz2eg" + }, + { + "Q": "\nat 1:51, why did he minus 114 from 114? it would equal to zero anyways!", + "A": "He does this to show that he is subtracting the same amount from both sides, and therefore preserving the equality of the equation. Although it isn t necessary to show, it helps clarify how he is solving the equation.", + "video_name": "hmj3_zbz2eg" + }, + { + "Q": "\n<---- push the up button if i am right, press down if ur a hatr.... My answer is 35.......\nPLZ RESPOND! I paused @ 1:50", + "A": "correct", + "video_name": "hmj3_zbz2eg" + }, + { + "Q": "at 1:50 or so in the video, he says \"one hundred thirty-one thousand, six hundred and seventy-two\"... but isn't 2 to the 17th power 131,072?\n", + "A": "Yes, that was a mistake in the video.", + "video_name": "UCCNoXqCGZQ" + }, + { + "Q": "my bad sorry at 0:13 he says it has 64 squares. But then at 2:07 he says 63 but there is 64 squares.\n", + "A": "He says there are 63 steps. This is measured from the first square. Therefore, the first square had 0 steps, the second square had 1 step, and so on up to the sixty-fourth square, which had 63 steps to get to it.", + "video_name": "UCCNoXqCGZQ" + }, + { + "Q": "\nAt 0:19, Sal says two lines are parallel if they are on the same plane and will never intersect. If two lines are on different planes and never intersect, what is that called?", + "A": "They are called skew!", + "video_name": "aq_XL6FrmGs" + }, + { + "Q": "So whenever (3:01) two lines intersect at a right angle, it's perpendicular? Is there a case where a line is perpendicular to another line without intersecting at a right angle?\n", + "A": "No, you can t have a line that is perpendicular to another line without them intersecting at a right angle, because that is the very definition of perpendicular. The fact that two lines intersect at right angles is what makes them perpendicular. (1:37) And don t forget, right angle just means a 90 degree angle. Also a box indicated at the intersection is what denotes a right angle.", + "video_name": "aq_XL6FrmGs" + }, + { + "Q": "\nAt 3:34, Is the slope of the tangent line constant at any point along the curve?", + "A": "The slope of the tangent line is constant on the tangent line, but only for that tangent line. Each point on the curve has a different tangent line, meaning each point on the curve will have a different slope.", + "video_name": "fqQ6sslzyhY" + }, + { + "Q": "Did Sal mean to say -4/2=-2 instead of 4/2=2 at 4:07?\n", + "A": "No, he s actually right. I ll explain why. At 4:07 of the video, all he does is from y-4=2x, he brings the two from that side over to this side, and divides y-4 by 2. So that way it becomes: y/2 - 4/2 = x. and -4/2 =-2. Hope that helped.", + "video_name": "W84lObmOp8M" + }, + { + "Q": "\nAt 0:58, Sal says you could input any real number into the function. Couldn't you input an imaginary number as well?", + "A": "Yes, it could be a nonreal complex number. However, it is not typical to discuss complex domains and ranges at this level of study. Some teachers might cover that topic, but it is not standard. So, for now, assume that ranges and domains are specifically referring to real numbers unless instructed otherwise.", + "video_name": "W84lObmOp8M" + }, + { + "Q": "@2:45 sal say that inverse of F so does he mean that the inverse is a different function\n", + "A": "Edgar Peixoto thnx a lot :)", + "video_name": "W84lObmOp8M" + }, + { + "Q": "@ 0:05 Sal says that 12 is arbitrary. What does that mean?\n", + "A": "Arbitrary means random, and how he uses it, he means he s picking a random number from his mind, there s really no specific reason he used the number 12. What he was basically saying was: let me just pick a random number, the number 12. instead of, let me just pick an arbitrary number, the number 12. Why does he say arbitrary instead of random ? Well, he s more sophisticated than you and me, and he has a bigger vocabulary than us, so he s probably used to saying arbitrary instead of random . Got it?", + "video_name": "I6TBBzIvgB8" + }, + { + "Q": "\"You'll appreciate this even more when you get into calculus.\"-Sal, 2:53\nWas he referring to how the second derivative of x^2 is 2?\n", + "A": "I believe what he was getting at is that the second derivative of a quadratic equation is always a constant, and because his second step in looking at the change between adjacent numbers did not produce a constant change, the formula can t be quadratic, which is why we go on to determine that it must be a cubic function.", + "video_name": "i7iKLZQ-vCk" + }, + { + "Q": "\nAt 3:19 sal says the sum of 1^2 + 2^2 + ... is equal to An^3 + Bn^2 + Cn + D.\nI understand why he used An^3 + Bn^2 + Cn + D but any chance there's a video which explain that in further details?", + "A": "A^3 Bn^2 +Cn^ + D is just the general form of a cubic equation. if he had determined that the series was quadratic he would have used An^2 + Bn + C .. does that help?", + "video_name": "i7iKLZQ-vCk" + }, + { + "Q": "at 2:18, if your going to do a graph is it easier to do a bar graph?\n", + "A": "It can be, but there are other ways to do it too", + "video_name": "0ZKtsUkrgFQ" + }, + { + "Q": "Hmm... So at 5:08...why doesn't he take the product of 3 *3 ? Both numbers have 3 in common.. Because at 6:15, Sal says that you take the product of both numbers. In that case at 6:15, he multiplies the 3 and the 5... So why doesn't that apply to the situation at 5:08 with the numbers sharing the 3 in common?\n", + "A": "The numbers 21 and 30 have one factor in common: 3 If you tried to use 3*3, you would be saying that 9 is a common factor of 21 and 30. Or, that you can divide both numbers evenly by 9. You can t. The numbers 105 and 30 share 2 common factors: 3 and 5. You can evenly divide both numbers by 3 and 5. Thus, you can also evenly divide both of them by 3*5 = 15. So, the greatest common factor = 15. Do you see the difference? Comment back if you have more questions.", + "video_name": "bLTfBvkrfsM" + }, + { + "Q": "at 4:59, when you say the greatest common divisor is one, that's wrong, it is actually three.\n", + "A": "no, if you go back a couple of seconds it actually says If you see that there s nothing in common here, the GCD or GCF would be 1", + "video_name": "bLTfBvkrfsM" + }, + { + "Q": "\nAt 4:25 Sal says the prime factorisation of 30 is 3*10\n\nBut shouldn't it be 2*15? Aren't you supposed to start with the lowest prime that goes into the number in question, which would make it 2 and not 3?", + "A": "It doesn t matter which prime you start dividing with. The resulting prime factors will always be the same. Method 1: 30 = 3 * 10 -> 2 * 5 prime factors = 3, 2, 5 Method 2: 30 = 2 * 15 -> 3 * 5 prime factors = 2, 3, 5", + "video_name": "bLTfBvkrfsM" + }, + { + "Q": "In 4:28, I don't understand how in the equation b=2(m - 1/2) - 1/2, the 1/2 in brackets becomes -1..... that is the equation becomes b=2m -1 - 1/2\n\nAnd also in 4:44, how does 2m -1 - 1/2 become 2m - 3/2?\n", + "A": "First, everything within the brackets is multiplied by 2, hence b = 2m, -2/2 (2/2 = 1). Second, the same principle applies, 2/2 is the same thing as 1, so -1 (or - 2/2) plus - 1/2 equals -3/2", + "video_name": "cNlwi6lUCEM" + }, + { + "Q": "Why is it that 6- (minus) 1/2 (one half) = 5 1/2 (five and a half) at the time of the video 7:37 ???\n", + "A": "The reason why 6- (minus) 1/2 (one half)= 5 1/2 is because of this: You have 6 units for example this means you have six whole units. Now you want to take away 1/2 of a unit away. What is 1/2? 1/2 is half of a whole unit. So if you have six whole units and then you take away one half of a unit what will you have? 5 1/2. A whole unit is 1, half of that unit is 1/2. I hope this helped.", + "video_name": "cNlwi6lUCEM" + }, + { + "Q": "Where did he get 11 from at 6:42 - when he said 11*300?\n", + "A": "Sal was doing a rough estimate of 3520 divided by 300. 10 *300 = 3000. 11 * 300 = 3300, and 12*300 = 3600.", + "video_name": "AGFO-ROxH_I" + }, + { + "Q": "\nSo how would I write an equation for the example at 2:21 ?", + "A": "Since the sequence is not being summed, then it can t be equated to anything so you can t write an equation (in the strictest sense of the term) for the example. If you are merely trying to notate the sequence then: 5\u00e2\u0080\u00a2(1/7)^n for n = 0 to \u00e2\u0088\u009e", + "video_name": "W2NnNKtquaE" + }, + { + "Q": "In the video at 3:57, Sal made a red number 7 and put a line thru it. But in the video at 4:30, Sal made a green number 7 and didn't put a line thru it. Is the red number 7 a cursive 7?\n", + "A": "Numbers cannot be written in cursive. Some people put a line through their 7s. Neither is right or wrong, and they both mean the same thing", + "video_name": "wx2gI8iwMCA" + }, + { + "Q": "\nHow do you get badges at 1:10 for asking a question.", + "A": "The more questions you ask, the more you ll end up learning, so Khan Academy wants to encourage you to ask questions when you feel stuck.", + "video_name": "wx2gI8iwMCA" + }, + { + "Q": "\nat 0:56 couldnt sal just multiply 2 and 3 and get 6 instead of breaking it down", + "A": "he could have, but I think his objective is not for you to memorize the procedure, but to gain intuition on how he came to the solution.", + "video_name": "Of8ezQj1hRk" + }, + { + "Q": "1:55, why add the two amounts when bees prefer a new solution\n", + "A": "When he added the 2 solutions, that was the new solution.", + "video_name": "JVlfQEhzLMM" + }, + { + "Q": "why at 1:40 did you say you were not going to put x because we might think it was a variable, when we could still mistake the dot for a decimal point? you could have put an asterisk...\n", + "A": "because you put the dot in the middle like this 9 * 34", + "video_name": "JVlfQEhzLMM" + }, + { + "Q": "at 4:35 why did you multiply by 100 but then not put the decimal back in its original place (divide by 100)? Isn't the answer then incorrect?\n", + "A": "If you think about it 4 / 2 = 400 / 200 so there is no reason to adjust the final answer. Since he multiplied both parts of the expression (the divisor and the dividend) they end up cancelling out. This is the same as multiplying the top and bottom of a fraction by the same number when trying to get matching denominators.", + "video_name": "DAikW24_O0A" + }, + { + "Q": "At around 5:21, is it ok to write \"obvious from diagram\" in formal proofs?\n", + "A": "At 5:21, I would say the reason should be the reflexive property since I was taught that was used in this situation.", + "video_name": "fSu1LKnhM5Q" + }, + { + "Q": "at 2:59 how do you get absolute value\n", + "A": "by figuring out how far the number is from 0.", + "video_name": "Oo2vGhVkvDo" + }, + { + "Q": "\nAt 3:25, So, in general, in a equation you must have 2 positive and 1 negative, right?", + "A": "No. An equation has two mathematical expressions that are equal. Those expressions can have any numbers or variables as long as they are equal.", + "video_name": "Oo2vGhVkvDo" + }, + { + "Q": "\n@ 2:00 when he starts making the problem, would it matter if you put the smaller number first rather than the big number?", + "A": "For this particular problem no it wouldn t. You would get the same answer either way.", + "video_name": "Oo2vGhVkvDo" + }, + { + "Q": "\nAt about 0:20, Sal says \"We already know that if all three angle, all three of the corresponding angles are congruent to the corresponding angles of ABC, then we're dealing with congruent triangles\". But actually, we're dealing with similar triangles and NOT congruent triangles, right? Because AAA is not a postulate of congruent triangles.", + "A": "If the angles are congruent then the shapes would be congruent.", + "video_name": "7bO0TmJ6Ba4" + }, + { + "Q": "SOMEONE HELP ME IM CONFUSED D:\nAt the equation on 8:27, why or how did the 1/2 get in front of the log?\nAfter that I got lost...\n", + "A": "The half is the exponent of the log result. Now what I am trying to figure out myself is how did the exponent convert to a coefficient!", + "video_name": "TMmxKZaCqe0" + }, + { + "Q": "At 8:20 why does the base 2 disappear when changing the exponent to the coefficient? He says this is the 3rd rule we learnt but I don't remember seeing this?\n", + "A": "At 9:00, he realizes he forgot it and writes it in. As for the third rule, I don t know what you mean.", + "video_name": "TMmxKZaCqe0" + }, + { + "Q": "\nI lost him where he appears to have reduced 1/2log2,32 to 5/2, at 9:51. Help.", + "A": "Dan, log\u00e2\u0082\u0082(32) = 5 because 2*2*2*2*2 = 32 = 2\u00e2\u0081\u00b5 so 1/2 * log\u00e2\u0082\u0082(32) = 1/2 * 5 = 5/2 Also, log\u00e2\u0082\u0082(8) = 3 because 2*2*2 =8 = 2\u00c2\u00b3 so 1/4 * log\u00e2\u0082\u0082(8) = 1/4 * 3 = 3/4 I hope that helps make it click for you.", + "video_name": "TMmxKZaCqe0" + }, + { + "Q": "At 4:35, Sal explains a way that he remembers concave and convex... Is there any other way?\n", + "A": "In Spanish con means with so concave can mean with cave. Another trick to determining concavity is to imagine an elastic band being stretched around the figure, does it touch all sides or does it have to span a gap. If it has to span a gap then the figure must be concave (having a cavity or cave).", + "video_name": "W9B3VYdC5T8" + }, + { + "Q": "\nAt 3:10 Sal said something like clockwise and counterclockwise..\nWhat does he mean by clockwise and counterclockwise ?", + "A": "Clockwise on the clock rotation goes as top-right-down-left. Counterclockwise on the clock rotation goes as top-left-down-right. Most clocks go Clockwise.", + "video_name": "W9B3VYdC5T8" + }, + { + "Q": "At 1:01, you are assuming that the bases of the exponents are the same. How would you solve the expression, if the bases were different numbers? Would you still apply the quotient rule, and add the bases, or what?\n", + "A": "Sadly, you can t solve it the same way if the bases are different. If you really wanted to solve it, then you d have to actually calculate the exponents and then multiply/divide them. An explanation for this is that if you write out the exponents (3^5 * 4^3 = 3*3*3*3*3*4*4*4), you can t tie them together into one exponent, right? So it s not possible to just add the exponents when the bases are different, because a different number is being multiplied.", + "video_name": "tvj42WdKlH4" + }, + { + "Q": "\nAt 4:55 when he was solving a^9-3a^5 .... He got a a4 but it became a^4/3 ??? I kept thinking it would just be 3a^4. How did the a^4 turn into the numerator? and why did 3 stay as the denominator?", + "A": "Divided by", + "video_name": "tvj42WdKlH4" + }, + { + "Q": "\nHow does it work to take away a ten from 10? At 1:27 he takes away one ten from 10, but then has 90.", + "A": "He is not taking a ten away from 10, he is taking a ten away from 10 tens, or 100. 100-10=90", + "video_name": "3lHBgFvr3yE" + }, + { + "Q": "\nI've recently been learning about this at school. I came on here to study and the beginning of the video seemed right to me, but when it got to around 1:40 , I got a bit confused. I was taught to take the total of everything on the first table, which would be 109, and divide 28/109, then 35/109, then 97/109, then 104/109. I'm very confused on how this creates the same answer, though. I'm thoroughly confused, because my teacher does this concept way differently than this video.", + "A": "You re using the same total for both your columns.", + "video_name": "_ETPMszULXc" + }, + { + "Q": "\nAt 14:28, it mentions using function notation for the answer. Would it be counted wrong of you put \"y\"?", + "A": "If you write y without saying what y is, then technically it s not right. At 10:57, Sal defines y=f(x), so after that, it s cool to write y wherever you d write f(x).", + "video_name": "5fkh01mClLU" + }, + { + "Q": "\nI don't get it. At 3:39 is confusing. Why can't we use the slope equation to get the slope and then the slope would be 2 not -2. Am I missing something? He said if it's switch then it would be be negative?", + "A": "OMG that is what I meant! Thank you! I forgot that the number would be negative 6. I can t believe I didn t see it!", + "video_name": "5fkh01mClLU" + }, + { + "Q": "At 8:05 how do you get 5/2. Please explain.\n", + "A": "5/6(3) is the same as diving 6 by 3. 6/3=2 5/2", + "video_name": "5fkh01mClLU" + }, + { + "Q": "\nAt 4:37 Sal says that x goes into 4 zero times. But x is an unknown - how does he know this?", + "A": "because it is a un known so he dosen t know but if it is x and x^2 we know that x goes into x x times.", + "video_name": "FXgV9ySNusc" + }, + { + "Q": "at 3:26, sal puts brackets and says that the equation is in -, how did he know and how did he come to this??\n", + "A": "The subtraction step of long division requires that you subtract the entire binomial: x^2 + x Subtraction of any polynomial requires that you distribute the minus sign across the polynomial being subtracted. To write the problem another way, you are doing: x^2+3x+6 - (x^2+x) = x^2+3x+6 - x^2 -x = 2x + 6 If you don t distribute the minus, you only subtract the x^2 term. The rest gets added. This would be like saying 57 - 32 = 29 (subtract the 3, but add the 2). Hope this helps.", + "video_name": "FXgV9ySNusc" + }, + { + "Q": "At 8:13 Sal removes x+4 as a factor from numerator and denominator. Why isn't a discontinuity marked at x=-4?\n", + "A": "When doing this polynomial division, it is automatically assumed that the denominator is not equal to zero, otherwise you cant divide. Yes you are correct that the expression is undefined at x=-4, but we assume that x is not equal to negative 4 so there is no need to write it.", + "video_name": "FXgV9ySNusc" + }, + { + "Q": "I do not really understand what Sal means by \"factoring the numerator\" at 7:51. Could someone please explain to me what he is doing?\n", + "A": "Sal didn t show all the steps. Option 1: (2x+4)/2 can be changed into 2x/2 + 4/2 -- Reduce each fraction and you get x+2 Option 2: Factor the numerator (factoring out GCF=2) (2x+4)/2 becomes 2(x+2)/2 Cancel the common factor of 2, and you get: (x+2)/1 or x+2 Hope this helps.", + "video_name": "FXgV9ySNusc" + }, + { + "Q": "\nat \"4:10\" Sal mentions anti derivitive. what is that?", + "A": "It s another name for the integral (without any bounds).", + "video_name": "OiNh2DswFt4" + }, + { + "Q": "Why can you assume that s > 0 at 6:36?\n", + "A": "S is representing a frequency as in a per second or 1/second which is why you get 1/s for the Laplace of 1. From a physics perspective there is no such thing as a negative frequency because in reality it is the same thing as the frequency, saying something happens -3 times a second does not make a lot of sense. You can also tell that s cannot equal zero from the 1/s.", + "video_name": "OiNh2DswFt4" + }, + { + "Q": "at 4:02 it really looks hard.\nI don't understand it.\n", + "A": "He is just setting up a histogram. It looks sort of like a bar graph.", + "video_name": "4eLJGG2Ad30" + }, + { + "Q": "At 1:35, does Sal says that he groups them into two groups?\n", + "A": "Yes he does -Andrew", + "video_name": "2nZsIeaiJUo" + }, + { + "Q": "At 6:30, Sal talks about the transversal line. What's that?\n", + "A": "A line that cuts across two or more (usually parallel) lines", + "video_name": "R0EQg9vgbQw" + }, + { + "Q": "\nDid anyone see Vi Hart draw the dolphin at 1:23 above the 42? Anyone get the reference?", + "A": "Vi Hart also makes a reference to Douglas Adams and his book the Hitchhiker s Guide to the Galaxy in another one of her videos at her website, Silly Band Fight .", + "video_name": "a-e8fzqv3CE" + }, + { + "Q": "At 3:28, If you watch what Sal does/says, can you conclude that you can do this:\nthe square root of 60 times the square root of 6 = the square root of 60 times 6??\n", + "A": "Yes, that is correct.", + "video_name": "74iuGIaBgRc" + }, + { + "Q": "\nAt 5:35, Sal says you can put the answer in either way. On the practice, can you put either option? Thanks!", + "A": "It would be better to use the second way, because it is more simple. (8/3) sqrt of (2/3)", + "video_name": "74iuGIaBgRc" + }, + { + "Q": "at 15:03 I was not sure if the answer to that was correct\n", + "A": "it is correct because 9+9+9+9+9+9+9+9=72 or 9x8=72", + "video_name": "xO_1bYgoQvA" + }, + { + "Q": "\nAt around 3:50 to 4:38, Sal constructs matrix A\nHowever he seems to write \"3Rot\"... I'm not too sure what the 3 part of the Rot is. In the previous video, he doesn't write \"2Rot\"... Is the 3 just notation to represent R3? Since intuitively it feels like a multiplication by 3", + "A": "@ around 2:40 he says (roughly): ...let me call it 3Rot(theta) to denote that it s in R^3 .", + "video_name": "gkyuLPzfDV0" + }, + { + "Q": "\nAt 1:37, how did he define f(x) and g(x)?", + "A": "Sal simply splitted the root frunction away from the remaining rest. f(x) is the root function, g(x) is the remaining rest.", + "video_name": "IiBC4ngwH6E" + }, + { + "Q": "At 5:10 would you have to simplify any farther or is that an adequte answer?\n", + "A": "The answer at 5:10 is in its most simplified form. (3x^2 - x)^(-1/2) can t be multiplied with (6x - 1).", + "video_name": "IiBC4ngwH6E" + }, + { + "Q": "At 3:00 I don't understand why f'(x) = 1/2x^-1/2. How and why did we get there from f(x) = x^1/2? What's the rule for moving from f(x) to f'(x)?\n", + "A": "This is a function of the power rule: d/dx( x^n ) \u00e2\u0086\u0092 n\u00e2\u0080\u00a2x^(n - 1) Let: f(x) = sqrt(x) f (x) = d/dx(sqrt(x)) f (x) = d/dx(x^(1/2)) Apply power rule d/dx( x^n ) \u00e2\u0086\u0092 n\u00e2\u0080\u00a2x^(n - 1) where n = 1/2: f (x) = 1/2\u00e2\u0080\u00a2x^(1/2 - 1)\u00e2\u0080\u00a2d/dx(x) f (x) = 1/2\u00e2\u0080\u00a2x^(1/2 - 1)\u00e2\u0080\u00a2dx/dx f (x) = 1/2\u00e2\u0080\u00a2x^(1/2 - 1) f (x) = 1/2\u00e2\u0080\u00a2x^(1/2 - 2/2) f (x) = 1/2\u00e2\u0080\u00a2x^(-1/2) f (x) = 1/(2\u00e2\u0080\u00a2x^(1/2)) f (x) = [1/(2\u00e2\u0080\u00a2sqrt(x))]", + "video_name": "IiBC4ngwH6E" + }, + { + "Q": "\n@3:03 what is does the negative one-half power mean", + "A": "x^(-0.5) = 1/sqrt(x)", + "video_name": "IiBC4ngwH6E" + }, + { + "Q": "In 0:51, did Sal say tenth hundredths or ten hundredths?\n", + "A": "He said ten hundreds.", + "video_name": "o31cLUkS23E" + }, + { + "Q": "\nat 1:54 sal says one people in line", + "A": "He said it twice, probably on purpose.", + "video_name": "BIpsQIJUCC8" + }, + { + "Q": "\ncan we factor something out from a term which is not even present in every subterm...just a little bit confusing because i've heard we can't factor out something which is not present in each term.. sal just did that at 8:35", + "A": "You are right in that it is nonsensical to factor something out that is not present in every term undergoing the factoring. Sal didn t do that. At 8:35, each of the 3 terms had involved c_x (c sub x).", + "video_name": "b7JTVLc_aMk" + }, + { + "Q": "\nQuestion. At 7:03, Sal said \"potential inflection point\" . Just curious, but how could it possibly not be an inflection point if x=0 is a critical number and the second derivative of 0 equals 0.", + "A": "Sometimes critical points are not inflection points. For example take the graph of y=x^3. At zero, we find that the first derivative is zero [y (0)=3(0)^2], indicating a critical point. However if you look at points slightly to the right of zero and slightly to the left of zero, you ll see that the rate of change (first derivative) is positive on both sides. The graph is not changing concavity, even though zero is an inflection point", + "video_name": "hIgnece9ins" + }, + { + "Q": "At 12:50, do you have to be so close to 0? If it was 1 (which is still greater than zero) 3x-2 would be positive. So that value is not negative for all x>0.\n", + "A": "You don t. It just has to be between critical numbers. Let s say you had critical numbers of 1, 5, and 7. You could test 0, 2, 6, and 8 to cover all of your bases. Your test numbers don t have to be so close to your critical numbers.", + "video_name": "hIgnece9ins" + }, + { + "Q": "@ 18:56 for x=0 , if x>0 shouldnt curve be upwards,x<0 be downwards?\n", + "A": "No. The best way to verify this is to graph the original equation. Perhaps a little more detail would help clarify. When x<0 f (x)>0 therefore the original function is concave up. BUT, when 02/3, f (x)>0 again and concave up. Since f has a positive leading coefficient the graph as concave up toward positive and negative infinity.", + "video_name": "hIgnece9ins" + }, + { + "Q": "5:45\u00e3\u0080\u0082\u00e3\u0080\u0082\u00e3\u0080\u0082why derivative zai equals 0...he only proved h(y)=0\n", + "A": "If you remember, the original function was in the form M(x,y)+N(x,y)y = 0. He also assumed u(x)M(x,y) = psi_x and u(x)N(x,y) = psi_y. Using the chain rule for partial derivatives that he showed us that psi = u(x)M(x,y)+u(x)N(x,y)y *. Since *M(x,y)+N(x,y)y = 0 is the same as u(x)M(x,y)+u(x)N(x,y)y = 0, you can say psi = 0.", + "video_name": "0NyeDUhKwBE" + }, + { + "Q": "\nAT 4:30 what happened to the y' how come it did not come down into the new equations, specifically to the right of the equals", + "A": "Because in the method to solving Exact Equations, you consider what is multiplying your y as your function N(x,y) and the rest as your function M(x,y). The original y is used just to separate those 2 parts, it no longer has any involvement in the rest of the solution.", + "video_name": "0NyeDUhKwBE" + }, + { + "Q": "\nHow did you get the negative sixteen to become a positive at 0:51? How is it the same?", + "A": "remember if the problem say is 7- (-9) it makes no sense to solve it. So it s easier if you remember that if there are two minus signs next to each other then change them into a plus sign so there won t have to be any of the minus negative confusion. :) Example: 2+7- (-8)+13 9+15+13 24+13 37", + "video_name": "03yq7XsErqo" + }, + { + "Q": "Why is it 4 becquerel at 3:48 ? Is it because of c=8 and you need to half it because cesium are reduced to half after 30 days?\n", + "A": "Yes, you are right.", + "video_name": "polop-89aIA" + }, + { + "Q": "at 2:20 how the heck does (4x^4-x)/(x^4) simplify to 4 - (1/x^3) ?? I'm missing something, that for sure.\n", + "A": "Recall that in general, (a - b)/c is equivalent to a/c - b/c. So (4x^4-x)/(x^4) = (4x^4)/(x^4) - x/(x^4) = 4 - 1/(x^3). If you are rusty with algebra, you will need to review algebra in order to have a realistic chance of performing well in calculus. Have a blessed, wonderful day!", + "video_name": "uPksX_O9ARo" + }, + { + "Q": "\nat 3:00 how can he go from x^2 right to x?", + "A": "It should be |x| < 1/2.", + "video_name": "6ynr9N-NQ8E" + }, + { + "Q": "\nAt 3:06, can we write the answer as - (m+4)/5\nSince both values have the same denominator, and we can take -1 as a common for the whole numerator, making both m and 4 positive.", + "A": "Yes, the answer could be written that way. It is equivalent to Sal s version.", + "video_name": "rtNuo7R3scY" + }, + { + "Q": "At 1:03 is the expression like this: -5.55 - 8.55c + 4.35c or is it like this: -5.55 + (-8.55c + 4.35c)?\nWhich expression is the right one, or are they the same?\n", + "A": "These expressions are equal to each other due to the associative property of addition and the fact that subtraction is the same as adding a negative. This can be seen more clearly by replacing the terms with easier numbers to visualize. For example, 10 - 5 + 2 = 10 + (-5 + 2). You can play around with the groups and order in addition and even subtraction, as long as you remember that subtraction is adding a negative. Be sure to keep your positive and negative signs with their numbers.", + "video_name": "rtNuo7R3scY" + }, + { + "Q": "\nAt 2:17 in this vid of Extraneous solutions of Rad Eq, Sal goes to Quad Formula. However, at this point aren't we able to factor 4x^2 - 3x -7 = 0 to (4x-7)(x+1) to get one of his answers which is a solution, 7/4, and, -1, which is an extraneous solution.", + "A": "Yes... you can use factoring. It is likely simpler than the quadratic formula.", + "video_name": "m4eiYHL3PP8" + }, + { + "Q": "At 0:42, how does he get 4x^2-4x+1=8-x?\nMore specifically, how does he get the second negative four?\n", + "A": "=(2x-1)^2 =(2x-1)(2x-1) =4x^2-2x-2x+1 =4x^2-4x+1 By using the distributive properties on this perfect square we are able to come up with two 2x and then combine like terms to get -4x.", + "video_name": "m4eiYHL3PP8" + }, + { + "Q": "\nAt 0:21, Sal said that when we've got a limit as x approaches infinity of a compilcated function, we can simplify the function to the most important terms, e.g.:\nlim x->\u00e2\u0088\u009e (5x\u00c2\u00b3+3x\u00c2\u00b2-8)/(x\u00c2\u00b3-60x\u00c2\u00b2+18)\u00e2\u0089\u00885x\u00c2\u00b3 /x\u00c2\u00b3 =5.\nMy question is, what's about x as an exponent? What are the most important terms in a function, where some numbers are in the x-th power, for example:\nlim x->\u00e2\u0088\u009e (5x\u00c2\u00b2 +18pi)/(e^x+5x)?", + "A": "As x goes to infinity, an exponential with a base greater than 1 will eventually outgrow any term with a constant exponent, so the limit in your example is 0 (and it would be 0 even if the first term in the numerator changed to 1000x^1000 and the first term in the denominator changed to 1.001^x). At infinity, exponentials win (unless they re up against something even more powerful, like factorials).", + "video_name": "KcqO1fX9b_I" + }, + { + "Q": "\nwhy at 2:26 did sal say 3x cubed/6x to the fourth is equal to 1/2x?", + "A": "At 2:03. This is plain algebra; the 3 in the numerator and the 6 in the denominator simplify to 1/2. The x^3 in the numerator and the x^4 in the denominator simplifies to 1/x. Perhaps think of the original fraction as 3(x)(x)(x) / 6(x)(x)(x)(x). Can you see three of the x s cancel out leaving 3/6x which is 1/2x ?", + "video_name": "KcqO1fX9b_I" + }, + { + "Q": "When we take limits at infinity we basically look if there is a horizontal asymptote. At 03:57 Sal talks about the case where the limit at infinity is equal to infinity. Wouldn't that look like a vertical rather than a horizontal asymptote?\n", + "A": "If the limit at infinity is infinity, there won t really be an asymptote, it will just look like the line s constantly moving up and to the right.", + "video_name": "KcqO1fX9b_I" + }, + { + "Q": "\nWhy can he take out the constants at 6:35? I'm guessing it won't change the answer, but I don't get how", + "A": "the constant rule states that we can take the constant out because a derivative of a constant is 0", + "video_name": "Xe6YlrCgkIo" + }, + { + "Q": "at 8:27 Saul says \"pi over 12\" but writes 'pi over 2' and carries that mistake through\n", + "A": "yes, yes it is. but he doesn t carry the mistake through. as he fixes it at 10:28", + "video_name": "Xe6YlrCgkIo" + }, + { + "Q": "\nI don't understand how at 6:30 he separates the function to take the derivative and how you know to do so.", + "A": "\u00cf\u0080/12 is a constant, so by definition d/dx [3x^2] is equal to 3*d/dx [x^2]. You might know that the derivative of 3x^2 is equal to 3*2x^2-1, 6x^1 or 6x. Likewise, 3 derivative of x^2 is 3*2x or 6x. Same result. So, d/dt [\u00cf\u0080/12*h^3] is the same of \u00cf\u0080/12*d/dx [h^3]. \u00cf\u0080 is not variable.", + "video_name": "Xe6YlrCgkIo" + }, + { + "Q": "At 11:29 is the rate of change (Dh/dt) cm/s or cm^3/s\n", + "A": "cm/s. The unit of the rate depends on the units of the letters on top and bottom. h(cm)/ t (sec) => cm/s", + "video_name": "Xe6YlrCgkIo" + }, + { + "Q": "\nAt 3:15, if Sal had known that the log10 5 = sqrt(0.5), he would've saved time, but it is tough to calculate the square root of 0.5, because square root of 0.5 is sqrt2 / 2, and the square root of 2 is hard to calculate. Am I right?", + "A": "sqrt(.5)= 0.7071... log 5 = .698... so log 5 =\\= sqrt(.5)", + "video_name": "OkFdDqW9xxM" + }, + { + "Q": "\nWhat are combinatorics, mentioned at 1:51?", + "A": "Combinatorics, often represented by n!, is a field in mathematics dealing with how many ways there are to arrange a certain amount of objects. For example, if I had 4 objects, I could use combinatorics to figure out how many ways I could arrange them. Don t worry about them for now, you will learn about them in later grades.", + "video_name": "RdehfQJ8i_0" + }, + { + "Q": "At 1:51 you said \"do all the COMBINATORICS\". But you never said what it is a combinatoric?\n", + "A": "Combinatoric is just a fancy word for math that has to do with different combinations of something.", + "video_name": "RdehfQJ8i_0" + }, + { + "Q": "So at 1:45 you had to simplify to get 2/3.\n", + "A": "Yeah, you had to", + "video_name": "RdehfQJ8i_0" + }, + { + "Q": "What is that symbol he draws at 1:13?\n", + "A": "greater than or equal to", + "video_name": "RdehfQJ8i_0" + }, + { + "Q": "7:15 - 7;23 you can't simplify 19/20?\n", + "A": "no. there is no number that can go into both 19 and 20.", + "video_name": "bcCLKACsYJ0" + }, + { + "Q": "At 7:25pm, How to rewrite a mixed fraction number into a decimal?\n", + "A": "You turn the mixed number into an improper fraction and the turn it into a decimal. Hope this helps!", + "video_name": "Gn2pdkvdbGQ" + }, + { + "Q": "at 3:00 minutes i got stuck\n", + "A": "ok. you can complain it. that is not a problem. or you have no internet. that is why you are stuck.", + "video_name": "Gn2pdkvdbGQ" + }, + { + "Q": "My calc textbook just told me whenever I see this format of integral that I should just apply a formula. It gave the exact formula Sal achieved at 17:35, and just sub what ever x^2 value I get. IE when it is a a^2-x^2, just sub the x^2 into the formula which is exactly the same as what Sal got at 17:35. Given that this video took 20 mins and the formula takes 2 mins, I don't see any reason why I should disagree.\n", + "A": "Exactly, I have formula for all the problems worked through this chapter. The videos make a nice proof of showing why the formula works but it seems I d never have to do it as Sal does.", + "video_name": "sw2p2tUIFpc" + }, + { + "Q": "i need help on 3:19\n", + "A": "what do you not get?", + "video_name": "x6xtezhuCZ4" + }, + { + "Q": "I can take the derivative of V to find dv:\n[1/\u00cf\u0080 sin \u00cf\u0080x] => (cos \u00cf\u0080x)(\u00cf\u0080) / \u00cf\u0080\nbut (at 11:25) how did Sal find 1/\u00cf\u0080 sin \u00cf\u0080x from cos \u00cf\u0080x to solve for the anti-derivative?\n", + "A": "Yes, I understand now... Thank you for your answer! (cos \u00cf\u0080x) = (cos \u00cf\u0080x)(1) = (cos \u00cf\u0080x)(\u00cf\u0080 / \u00cf\u0080); D[sin \u00cf\u0080x] = \u00cf\u0080 cos \u00cf\u0080x; divide both sides by \u00cf\u0080 which yields: D[(sin \u00cf\u0080x) / \u00cf\u0080] = D[(1/\u00cf\u0080)(sin \u00cf\u0080x)] = (\u00cf\u0080 cos \u00cf\u0080x) / \u00cf\u0080 = cos \u00cf\u0080x", + "video_name": "CZdziIlYIfI" + }, + { + "Q": "I'm thoroughly confused. At 10:06, Sal gives a formula for integration by parts which he says he's gone through many times, but I just watched the integration by parts videos and didn't find it written it in this form? And I really thought I was getting the hang of these du, dv notations :(\n\nCan someone please explain how \u00e2\u0088\u00abf(x)g'(x)dx=\u00e2\u0088\u00abudv? I mean, I get it's some sort of substitution, but can't understand how f, g, and dx can be reduced to u and dv.\n\nAny help is greatly appreciated! :)\n", + "A": "Nvm, I was able to derive it: (uv) =uv +u v d(uv)/dx=u*dv/dx+du/dx*v u*dv/dx=d(uv)/dx-du/dx*v \u00e2\u0088\u00ab(u*dv/dx)dx=\u00e2\u0088\u00abd(uv)/dx*dx-\u00e2\u0088\u00ab(du/dx*v)dx \u00e2\u0088\u00abu*dv=\u00e2\u0088\u00abd(uv)-\u00e2\u0088\u00abdu*v \u00e2\u0088\u00abudv=uv-\u00e2\u0088\u00abvdu", + "video_name": "CZdziIlYIfI" + }, + { + "Q": "1:10\nso there are a infinate number of raidus?\n", + "A": "yes, a circle has infinite radii, as you can keep on changing the angle by a small amount", + "video_name": "04N79tItPEA" + }, + { + "Q": "at 1:34 what dont undertsand bro\n", + "A": "The circumference of a circle is basically the distance around a circle. For example, if you had a park or other outdoor area that was shaped in a perfect circle, and you walked all the way around the edge of it, you would have walked along the circumference of the circle. Basically, you can think of the circumference as the perimeter of a circle.", + "video_name": "04N79tItPEA" + }, + { + "Q": "\nFrom 0:44 to 0:46, Sal says \"then we add 3/4 to -10/6.\" But why add? Should the distributive property apply and we multiply? Vote up if this is a question you have too, please.", + "A": "The distributive property only applies if you re multiplying. Here, you re just adding the three fractions together. It looks confusing because Sal separated two of the fractions and added them together and then he added the third one to those two, but what you re doing to the fractions didn t change -- it s still just three fractions being added.", + "video_name": "9tmtDBpqq9s" + }, + { + "Q": "\nat 2:27 it said negative 9/12 and 20/12 but it forgot to write the plus sign.why is thst", + "A": "Because they are equivalent terms. The rule for subtraction is that you invert/change the sign of the second number and then add. So (-9/12) + (-20/12) is the same as (-9/12) - (20/12). He didn t need to add the plus sign at the end because it didn t change the value of the statement. Hope it helps.", + "video_name": "9tmtDBpqq9s" + }, + { + "Q": "\nln(sinx)/lnx=sinx/x right?so can i omit the step 6:30-11:00?and concluded that limit of ln(sinx)/lnx=1?\nthanks in anvance", + "A": "No, ln (sin x) / ln x DOES NOT equal sin x / x For example, when x = e: ln (sin e) / ln e = ln (sin e) \u00e2\u0089\u0088 -0.8897 but sin (e) / e \u00e2\u0089\u0088 0.15112", + "video_name": "CDf_aE5yg3A" + }, + { + "Q": "At around 10:30 in the video, would it be valid to, instead of splitting up the single limit into two and taking the first derivative of one, just take the second derivative of x*cos(x) / sin(x) to get\ncos(x) + (-x*sin(x)) / cos (x) ? When evaluating it, you still get 1 + 0 / 1, but is that just a coincidence?\n", + "A": "If I followed what you meant correctly, yes, that is a valid way of doing it. You can continue using multiple iterations of l Hopital s provided the derivatives exist AND you continue to have 0/0 or \u00e2\u0088\u009e/\u00e2\u0088\u009e forms. If you have those forms, you do not necessarily have to split up the limit -- though doing so is often easier. Remember that l Hopital s is NOT valid or true if you don t have 0/0 or \u00e2\u0088\u009e/\u00e2\u0088\u009e . So, you must be careful about that.", + "video_name": "CDf_aE5yg3A" + }, + { + "Q": "well actually, at 4:40, there is evidence. both of the triangles that were produced by the parallelogram are the exact same size.\n", + "A": "While the triangles from the parallelogram were congruent, the sides in question were not corresponding sides. DC is congruent to AB Thus, DC/BC equals the cosine, not the sine of \u00e2\u0088\u00a0CBA Thus, none of the options was correct.", + "video_name": "TugWqiUjOU4" + }, + { + "Q": "\nAt 3:13, Sal says that tan(\u00e2\u0088\u00a0ABC) is unequal to AC/EF, right? But what if both the sides are in the same figure, like \u00e2\u0088\u00a0EFG? Does that make tan(\u00e2\u0088\u00a0ABC) = EG/EF?", + "A": "tan(\u00e2\u0088\u00a0ABC) is equal to EG/EF , because triangles ABC and EFG are similar. However, the solution that Sal ruled out said that tan(\u00e2\u0088\u00a0ABC) = AC/EF, which is untrue because there is no way to tell if EG is the same length as AC, because even though the triangles are similar, the size of the triangles can still differ dramatically.", + "video_name": "TugWqiUjOU4" + }, + { + "Q": "at 4:13 why did he put a plus sign and not the minus sign?\n", + "A": "Sal is doing: -2x^2 + 3x^2 -2 + 3 = +1, not -1. If you aren t sure, use the number line. Go left to -2 on the number line. Then, to do +3, move 3 units to the right. You end up on +1. That is why Sal has +x^2 . Hope this helps.", + "video_name": "FNnmseBlvaY" + }, + { + "Q": "At 2:56 why does he put -y instead of -1y?\n", + "A": "-y and -1y are the same thing because -1 times y is -y", + "video_name": "FNnmseBlvaY" + }, + { + "Q": "At around 4:30, it says that by using *(1+1/n)^n* you get e. I understand that, and why, but why do you need the 1 in the beginning? Could you get e just by doing *(1/n)^n* ?\n", + "A": "No, you could not get e without the 1 in the beginning. Since, as n goes to infinity, 1/n approaches 0 and n grows to infinity, (1/n)^n would approach 0^infinity which is definitely 0. Have a blessed, wonderful day!", + "video_name": "oQhp3ndj28Y" + }, + { + "Q": "At 11:40, I'm a little confused as to how Sal simplified the equation on the final step. I get that 1/9 becomes 4/9; but what happened to the exponents that were attached to the integers? It doesn't make sense with the exponent rules that are taught here. What am I missing?\n", + "A": "Because 4 and 1/9 both have the same exponent (1st power) they can be multiplied together.", + "video_name": "64bH_27Ehoc" + }, + { + "Q": "\nAt 2:17 in the video, it is shown how the vector is pointed down in the eastwards direction; then if we are given simple numbers in the form of a column vector, how would we know if the arrow should point westwards or otherwise?", + "A": "If the first number in the column is positive, then it will point partly to the right. If the first number in the column is negative, then it will point partly to the left. If the second number in the column is positive, then it will point partly upward. If the second number in the column is negative, then it will point partly downward.", + "video_name": "8QihetGj3pg" + }, + { + "Q": "\nAt about 1:30 Sal writes a bunch of stuff I don't understand. What is the meaning?I was also wondering why are there braces around the vectors x and y.", + "A": "These are 2 vectors in column (vertical) form, and their sum.", + "video_name": "8QihetGj3pg" + }, + { + "Q": "When Sal is drawing vectors through the video, something came to my mind.\nHow do we know exactly what direction the vectors are going in? Most vectors seem to be drawn going outward from the origin, but couldn't they go inward? Like at 2:09, when he's drawing the purple vector. Couldn't it also be pointing in the opposite direction, but still have the same magnitude?\n\nSorry if the answer is extremely obvious and I just don't see it...\n", + "A": "The numbers in the video represent the vectors he draws. So when he draws a vector from the origin, it will point to the point (a,b). At 2:09, he s drawing the vector [6,-2], so it points from the origin to the right and down because it s positive (right) 6 and negative (down) 2.", + "video_name": "8QihetGj3pg" + }, + { + "Q": "So at 3:36 and a little before that, when Sal says that f(-2) is EQUAL TO g(-1) is that in relation to the translation? Like point \"a\" on g(x) has different coordinates than f(x) but they are still equal because they're both have point \"a\" just one is shifted so that's why it appears different?\n", + "A": "Yes, you are exactly right. This is a big concept in function translation; basically you are trying to find where one function is equal to another, and in this case he means that the function f at -2 is equivalent to function g at -1. Even more specifically, the y-value of x = -2 in f(x) is the same y-value for x= -1 in g(x) (and you can see him drawing horizontal lines across the graphs to illustrate this concept).", + "video_name": "ENFNyNPYfZU" + }, + { + "Q": "\nFrom the exponents of i it looks as if i is a negative number,but a negative number times a negative number equals a positive number.But then no number's square is a negative number.But now Sal says -i at 2:56 and that doesn't support that i is negative. Unless he's actually saying (mathematically )(he doesn't know)that -i is positive i.", + "A": "i is not a negative number, but i^2 is a negative number.....i^2=-1 and i=sqrt. of -1, So -i = -\u00e2\u0088\u009a-1 and hence -i^2=+1", + "video_name": "ysVcAYo7UPI" + }, + { + "Q": "\nThis is simple question: @3:40 how does i x i^3, or i x -i, = (-1)(i)(i) or (-1)(-1)?", + "A": "Do you mean why does i \u00e2\u00a8\u0089 i\u00c2\u00b3 = (-1)(i)(i) = 1? We will use the exponent addition formula for this: i \u00e2\u00a8\u0089 i\u00c2\u00b3 = i\u00e2\u0081\u00b4 = 1. Or we can use this way: i \u00e2\u00a8\u0089 i\u00c2\u00b3 = (-1)(i)(i) = (-1)(-1) = 1 Always remember powers of i: i\u00c2\u00b9 = i, i\u00c2\u00b2 = -1, i\u00c2\u00b3 = -i, i\u00e2\u0081\u00b4 = 1, i\u00e2\u0081\u00b5 = i Hope this helps! \u00e2\u0080\u0094CT-2/002-24", + "video_name": "ysVcAYo7UPI" + }, + { + "Q": "At 0:22 Sal says E. What is that number and can i have a link to it?\n", + "A": "e is a constant that comes up in math and science all the time. It is an irrational and transcendental number the first few digits of which are 2.71828... e is officially defined as: lim h\u00e2\u0086\u00920 (1+h)^(1/h) This same definition can also be expressed as: lim h\u00e2\u0086\u0092 \u00e2\u0088\u009e (1+1/h)^(h)", + "video_name": "ysVcAYo7UPI" + }, + { + "Q": "\non 2:56 why did Sal keep it as -1*i instead of make it -i?{OK i know he corrected it at 3:27}", + "A": "he did that to clarify the the minus is a separate number from i.", + "video_name": "ysVcAYo7UPI" + }, + { + "Q": "at 5:20 Sal said tat i=square root of -1, then how is i=1!\n", + "A": "i = -1 it doesn t equal 1. I don t know if that answered your question...", + "video_name": "ysVcAYo7UPI" + }, + { + "Q": "\nIs there any way to check the problem? Like at 2:32, how is he sure that the answer is 1436.8?", + "A": "He is completely sure since that is the answer the calculator gave him. You can verify by doing the problem again, or if you have a graphing calculator, you can start from the volume and use algebraic manipulation to get back to the radius.", + "video_name": "IelS2vg7JO8" + }, + { + "Q": "1:21 can you explain why the sphere is radius cubed instead of raidus squared\n", + "A": "I think that it is because a sphere is 3 dimensional and a circle is 2 dimensional.", + "video_name": "IelS2vg7JO8" + }, + { + "Q": "At 3:13, why Sal said \"clog\"?\n", + "A": "It was an accident. He means c Log but pronounced it incorrectly.", + "video_name": "yEAxG_D1HDw" + }, + { + "Q": "\nStarting from 6:28, I don't understand what Mr. Khan means when he says that the \"Distance between x and c is less than delta,\" and that the \"distance between f(x) and L is going to be less than epsilon.\" Can someone explain please? Thank you!", + "A": "You feed numbers called x into a function to get numbers called f(x) out. What he is saying is that as the number going in, i.e. x, gets closer and closer to c .. then the output f(x) is getting closer and closer to L. Now delta is just how far away from c a particular input value x is, and epsilon is how far away from L a particular output value f(x) is. The big idea about limits then, is that even if f(x) is not defined when x = c, you can see where it is going as x gets (arbitrarily) close to c.", + "video_name": "w70af5Ou70M" + }, + { + "Q": "\n7:25 side side side? who came up with that name", + "A": "The name refers to the method of finding congruence: it is quite logical. The SSS (or side, side, side) Congruence Postulate states that if all 3 sides of a triangle are congruent to that of another triangle, the two triangles are congruent.", + "video_name": "CJrVOf_3dN0" + }, + { + "Q": "\nAt the beginning of the video this means that the definition of something being congruent would simply be that it has the same size and shape?\nAnd if if at 3:19, this means that if one side is congruent to another side of another triangle, then all 3 sides of both triangles are both congruent to each other?", + "A": "Congruent means to be the same size and shape. However, if one side of a triangle is congruent to another side of a triangle, it would not mean all 3 sides are congruent. You would need another side or angle to be congruent to the other triangle to be sure of that.", + "video_name": "CJrVOf_3dN0" + }, + { + "Q": "\nAt 1:54, why does Sal put 3-1 over 4 instead of just doing the answer of 2 over four?", + "A": "because he s showing you the steps", + "video_name": "0njioQqIxKY" + }, + { + "Q": "at 6:43 coordinates of vertices are 1,23/4. bt we knw that vertex is the point where the conic section and the axis itersect. how is it possible then?\n", + "A": "It is not necessary for the focus to always intersect the axes. The focus can be any point in 2D space. It can also obviously be at the origin.", + "video_name": "w56Vuf9tHfA" + }, + { + "Q": "At 17:30 isn't the 99% confidence interval 0.568 +/- 0.08 actually giving 56% to 57.6% ?\n", + "A": "Because he added the 0 before the . it did seem that way. It got me too :P", + "video_name": "SeQeYVJZ2gE" + }, + { + "Q": "at around 5:00 you said x 10^4 . where did 4 come from? i thought it was 10^5.\n", + "A": "The term 0.3979 * 10^5 is not in scientific notation form. He is converting it to that. Scientific notation is a number with a single non-zero digit in front of the decimal times 10 raised to a power. So he is multiplying the 0.3979 by 10 which removes one of the 10s from the 10^5 turning it into 10^4", + "video_name": "XJBwJjP2_hM" + }, + { + "Q": "1:54 Could we just have calculated both volumes and subtracted the answers together to find the volume of the gold ring\n", + "A": "Well,if you mean taking the volume of the rectangular glass with the ring and subtract the volume of the rectangular glass without the ring, well you are right. Bang on!", + "video_name": "ViFLPsLTO1k" + }, + { + "Q": "\nAt 2:43 he got the sum, but would he have to simplify it? or would that be the absolute answer?", + "A": "OMGGGOMGOMG i knew how do to normal division but when he got the reciprocal out of no where that was confusing!", + "video_name": "Mcm0Q3wGhMo" + }, + { + "Q": "\nWhat would happen if you did the mobius strip - flake that she showed at 3:56? Would you get the pattern, then the pattern reflected, then the pattern again, and then the pattern reflected and so on?", + "A": "Yes, you would. That is called a Frieze pattern.", + "video_name": "8EmhGOQ-DNQ" + }, + { + "Q": "At 5:23 , why does 2y' equal -6e^-3x and not positive 6e^-3x. since you multiply the function 2 times itself and negative times negative becomes positive?\n", + "A": "You actually aren t multiplying the function by itself. The notation is kind of confusing, but 2 is just the coefficient for the first derivative. So 2y = 2 (-3e^-3x) is just -6e^-3x. Because the coefficient (2) is positive, the sign stays the same. I hope this helps.", + "video_name": "6o7b9yyhH7k" + }, + { + "Q": "\nso\ni knew that (\u00e2\u0088\u009a2)^2 =2 and (-\u00e2\u0088\u009a2)^2=2 why did he chose to (\u00e2\u0088\u009a2)^2 =2\nat 0:48", + "A": "\u00e2\u0088\u009a2 is less complicated than -\u00e2\u0088\u009a2 Why complicate things!", + "video_name": "C3QPTCwpIZo" + }, + { + "Q": "\nAt about 5:47, Sal starts talking about how you can't ever add enough 9s onto 4 to get the exact x value of the maximum. But, if you keep putting on more and more 9s to infinity, you get 4.999... on forever. If I'm not mistaken, 0.999... = 1, so wouldn't the maximum be still at x = (4+0.999...) = (4+1) = 5?", + "A": "There is no such number as infinity, so you cannot actually add an infinite number of 9s. So, this is a limit, not an actual finite sum.", + "video_name": "bZYTDst1MOo" + }, + { + "Q": "at 4:10-4:12 minimum happens at A? I'm so confused, I thought minimum was F(c). What are the white lines for?\n", + "A": "The white lines are a completely different function superimposed on the illustration, it is not related at all the original function other than they both share the same domain interval.", + "video_name": "bZYTDst1MOo" + }, + { + "Q": "3:42 is so confusing\n", + "A": "Not really. All that means is this: (6x6x6) TIMES (6x6x6x6x6x6). You have to do the parentheses first and then multiply.", + "video_name": "zM_p7tfWvLU" + }, + { + "Q": "At 3:22 which is the simplest form? (3x)^3 , 3^3 *X^3, or 27x^3\n", + "A": "27x^3 would be simplified.", + "video_name": "zM_p7tfWvLU" + }, + { + "Q": "10:18 what happend to the -1? (-1)^2 = just 1? how?\n", + "A": "A negative times a negative...", + "video_name": "zM_p7tfWvLU" + }, + { + "Q": "\nShouldn't you put a paratheses for the x's on 7:04 of the video.", + "A": "You could, but it s not necessary. Remember our rule for associativity says if we are just multiplying it doesn t matter what order we do it in. This also means that the parentheses aren t necessary.", + "video_name": "zM_p7tfWvLU" + }, + { + "Q": "@10:55, if it doesn't matter the order when you multiple, then what is FOIL?\n\nhe didn't need it for this video, i'm confused on when to use it.\n", + "A": "FOIL is just the standard method of multiplying two binomials (e.g. (a+b)(a-b) ) which you use to make sure you don t miss one of the multiplications necessary (because you need aa, ab, ba and bb) - technically you don t have to do it in that order (because as Sal says the order doesn t matter) but it just helps you make sure you get each of the components.", + "video_name": "zM_p7tfWvLU" + }, + { + "Q": "\nAt 3:40, if Sal did 6^6*6^6 would that equal (6^6)^6", + "A": "6^6*6^6 would equal (6^6)^2 (6^6) gets multiplied two times with it self. (6^6)^6 would equal 6^6 * 6^6 * 6^6 * 6^6 * 6^6 * 6^6", + "video_name": "zM_p7tfWvLU" + }, + { + "Q": "At 9:02 when Sal tells us that the value of (Av) in c(Av) is zero, does that come from 2:57 when he was writing out the set notation for subspace N?\n", + "A": "Yes. You are assuming that the v is in your subspace and you know that Av=0 for all v in your subspace.", + "video_name": "jCwRV1QL_Xs" + }, + { + "Q": "At 1:57, a homogeneous equation is mentioned. What exactly is a homogeneous equation and why is A times vector X =0 a homogeneous equation?\n", + "A": "Being more precise, A x = 0 is a homogeneous system of equations (a set of homogeneous equations). A linear equation is homogeneous when the constant part is zero. For example, ax + by = c is homogeneous only if c is zero. Ax=b is a way to write a system of equations using matrices.", + "video_name": "jCwRV1QL_Xs" + }, + { + "Q": "\nAt 3:34, Sal uses the point (1,2) to find r, but can you use any of the other points? How would you find r by using the next point, (2, 4/3)?", + "A": "You could use any one of the given points. For (2, 4/3) you would substitute the y-value (so 4/3) into g(x) and the x-value ( so 2) into the x to end up with 4/3=3r^2. You then solve that equation to end up with the r. Just be careful because if the x-value is even, you could have two r s so it is more accurate to use a point with an odd x-value when it is available to eliminate any confusion.", + "video_name": "Qst1UVtq8pE" + }, + { + "Q": "At 3:23 minutes, Sal says that the value of |x+10| is going to be greater than or equal to zero. But how can it ever be equal to zero? Shouldn't it just be greater than?\n", + "A": "when x = -10, then |x+10| = 0", + "video_name": "15s6B7K9paA" + }, + { + "Q": "Please can anyone explain how Sal gets from Y/X = -3 to 1/X = -3 x 1/y @ 4:42 and/ or how he gets from X=2/y to 2 x 1/y @ 8:30? Thanks.\n", + "A": "It s okay, I get it now", + "video_name": "92U67CUy9Gc" + }, + { + "Q": "\nat 6:53, why is it called \"inverse?\" is it because the greater \"x\" is, the smaller \"y\" gets?", + "A": "Yes. One variable increases by the same factor that the other decreases. In his example, X multiplies by a factor of 2 while Y divides by a factor of two. If you re graphing the functions, The inverse variation indicates the variables separate from a central point.", + "video_name": "92U67CUy9Gc" + }, + { + "Q": "At 4:40, how did he divide \"y/x\" by \"y\"? I know that multiplying by the inverse is how you divide a fraction; but I don't understand how \"1/y\" times \"y/x\" would equal \"1/x\" unless you cross multiply; but that wouldn't work because \"1/y\" is already inverted, right?\n", + "A": "y/x / y = y/x * 1/y = 1y/xy [Simplify by dividing by y] = 1/x I hope this helps!", + "video_name": "92U67CUy9Gc" + }, + { + "Q": "\ncan someone tell me the mathematical reason as for why Sir Khan multiplied 108 by 139 at 5:09 ?", + "A": "we call also do Cross-Multiplication to get the value of x . which means , multiplying the numerator of LHS with the denominator of RHS and multiplying the numerator of RHS with the denominator of LHS..... provided that there is an equal-to sign between the fractions .", + "video_name": "Z5EnuVJawmY" + }, + { + "Q": "\nat around 5:17 why do we multiply by 108 on all sides? Why wouldn't we multiply by 139, 180, or h?", + "A": "To make h not a fraction, or to remove the 108 from underneath h. Anything else wouldn t have done very well. That is what you need to do to solve for h.", + "video_name": "Z5EnuVJawmY" + }, + { + "Q": "at 3:44, how do we know that the second derivative is less than zero? and how do we even know if this function can have a second derivative? what is needed to, what defines a second derivative? thank you!\n", + "A": "The second derivative is the derivative of the first derivative. e.g. f(x) = x^3 - x^2 f (x) = 3x^2 - 2x f (x) = 6x - 2 So, to know the value of the second derivative at a point (x=c, y=f(c)) you: 1) determine the first and then second derivatives 2) solve for f (c) e.g. for the equation I gave above f (x) = 0 at x = 0, so this is a critical point. f (0) = 6\u00e2\u0080\u00a20 - 2 = -2 Therefore, f(x) is concave downward at x=0 and this critical point is a local maximum. Can you do the same for the other critical point?", + "video_name": "-cW5hCsc9Yc" + }, + { + "Q": "\nat 0:55, wouldn't the notation for the arc be ABC then? how would you specify the major arc if there isn't a point on the circle to differentiate between the two?", + "A": "Hi angela braukman, The notation of the arc would still be two letters because an arc is not a major arc till it is either 180\u00cb\u0099 or more. And to specify it: I would recommend marking your own point if there is no third point. Hope that helps! - Sam", + "video_name": "GOA9XWEo7QI" + }, + { + "Q": "At 1:30, why does Sal give the measure of the minor arc? I thought the question was asking for the major arc on the other side.\n", + "A": "AC by notation is a minor arc, it just happens to have another letter between them, A major arc is designated by three letters always to distinguish it from a minor arc, so you would need an additional point on the left side (D) to be talking about major arc ADC.", + "video_name": "GOA9XWEo7QI" + }, + { + "Q": "At 1:08, Sal says..\"The actual coordinate in R2 on the Cartesian coordinate..\" what does R2 mean?\n", + "A": "It means the x-y coordinate plane. R for the real numbers, and 2 for the number of dimensions (loosely speaking)", + "video_name": "7fYDCUIvZnM" + }, + { + "Q": "at 0:57 Sal introduces a new word to me, degenerate, but doesn't explain it thoroughly. Can someone please help me?\n", + "A": "Imagine a line segment with a point on a side so it s barely a triangle. That s a degenerate triangle in a nutshell", + "video_name": "KlKYvbigBqs" + }, + { + "Q": "What does timesish mean? She says it at 5:06.\n", + "A": "She means taking steps on the number line by multiplying, not adding.", + "video_name": "N-7tcTIrers" + }, + { + "Q": "Maybe he said it and I missed it, but how do we know that the zero vector is the only solution to Rx=0, if he only used the particular solution of c1,c2,0,c4,0 around 3:15?\n", + "A": "It s not, but that s beside the point. We aren t trying to solve c1r1 + c2r2 + c3r3 + c4r4 + c5r5 = 0, only c1r1 + c2r2 + c4r4 = 0. We already know that the other columns are extras .", + "video_name": "BfVjTOjvI30" + }, + { + "Q": "\nAt 6:58, isn't the formula for finding the area of a circle, pi*diameter?", + "A": "NO. The circumference is pi x the diameter. Area is pi x r^2.", + "video_name": "mLE-SlOZToc" + }, + { + "Q": "\nHello! I have a question. In Finding probability example 2 at 9:33 you talk about probability. Why you don't calculated area of the smallest circumference?\nSincerely,Alex.", + "A": "The area of the smaller circle is already calculated as far as we need it to be in order to construct the ratio of areas. It was given as A=16\u00cf\u0080. The larger circles area was not given, so it needed to be calculated from the given circumference.", + "video_name": "mLE-SlOZToc" + }, + { + "Q": "\n6:05\nWhy is there an infinite number of points contained in the circle ?", + "A": "There is an infinite number of points because the distance between two points can always be cut in half, whether it is an arc or a line. If we were standing 64 feet apart and every minute we cut the distance in half, within 6 minutes we will be within one foot, then .5ft, .25.ft, .125ft, .0625ft, .03125ft... in theory, and that is what we are talking about, theory, we would never touch. As it should be...", + "video_name": "mLE-SlOZToc" + }, + { + "Q": "\nAt 0:31-- Why does it ask -2+(-7) when you could do -2-(7)?", + "A": "It is working with negative numbers. This question is showing that adding a negative is the same as subtracting a positive. Either way of writing it is perfectly acceptable.", + "video_name": "3CKpidALDEg" + }, + { + "Q": "\nAt 1:01, how do you round down?", + "A": "you round down if the number is 4 or less", + "video_name": "_MIn3zFkEcc" + }, + { + "Q": "\nAt 6:20 ish, how does Sal say that that function meets all three requirements? if c = 0, the lim as x approaches c of either of the functions neither gives us positive or negitive infinity.", + "A": "Earlier in the video Sal sets up two different ways to meet the requirements for application of l Hospital s rule. One involves the indeterminate form 0/0, and the other involves an indeterminate form with plus or minus infinity in both the numerator and denominator. He s working with an example that meets the first set of conditions, so it doesn t have to meet the other set of conditions.", + "video_name": "PdSzruR5OeE" + }, + { + "Q": "Shouldn't it be lim x->c of f(c)? not f(x)? 2:05\n", + "A": "No. The limit is of the function f(x), not the limit of f(c) because that is already evaluated at a value.", + "video_name": "PdSzruR5OeE" + }, + { + "Q": "Why at 6:35 does Sal considers that 1/cos(theta) =cos(theta)?\n", + "A": "He doesn t \u00e2\u0080\u0093 if you go back and listed from 6:30, he is taking the reciprocal of each element in the inequality \u00e2\u0080\u0093 this is also why he switches the direction of the inequalities.", + "video_name": "5xitzTutKqM" + }, + { + "Q": "\nWhen Theta was divided by sin theta, shouldn't it be theta/sin theta, why it's sin theta/ theta in the video at 6:25 ?", + "A": "He took the reciprocal of all 3 terms, which made \u00ce\u00b8/sin\u00ce\u00b8 into sin\u00ce\u00b8/\u00ce\u00b8.", + "video_name": "5xitzTutKqM" + }, + { + "Q": "At 3:20, why does Sal take only the positive square root of four, and not both negative and positive two? (I get that eventually it will not matter since you will add or subtract it from 6)\n", + "A": "Because he is looking at sqrt(4), which means the principal square root of 4 (the positive value you square to get 4). So that is positive 2 only. You ll notice, however, that in the expression he derives using the quadratic formula, there is a +/- symbol in front of the principal square root sign, so you do get both roots coming into play there. Does that help?", + "video_name": "dnjK4DPqh0k" + }, + { + "Q": "\nWhy did Sal divide (8-6i)/(4) by 2 at 9:17?", + "A": "Because the numerator can easily be divided by 2, and what s left of the denominator will cancel out when multiplied by the 2 outside the parentheses. 2((8 - 6i) / 4) = 2((4 - 3i) / 2) = 2(4 - 3i) / 2 = 4 - 3i You could, of course, do it the other way around: 2((8 - 6i) / 4) = 2(8 - 6i) / 4 = (8 - 6i) / 2 = 4 - 3i", + "video_name": "dnjK4DPqh0k" + }, + { + "Q": "At 1:43, Sal takes -6 squared to be positive 36 but if you press -6^2 on a calculator, you get -36. I remember working out a question wrong on Khan Academy. I had at some point in the problem work out g= -1^2 +4. I got 5 as an answer to be wrong. Khan Academy took -1^2 to be -1 and the correct answer was 3. Can somebody please explain?\n", + "A": "You wrote it like -6\u00c2\u00b2, but you need to write it like (-6)\u00c2\u00b2", + "video_name": "dnjK4DPqh0k" + }, + { + "Q": "\nAt 5:45 how 9 + 6i is resulted from 2(3+i/2)^2 ? I did the distributive property and came out with (36 + i^4) / 2\nWhy did Sal multiply \"3\" and \"i\" while there is a plus sign between them at 5:35?", + "A": "You have some errors... To square a binomial, use FOIL. It looks like you only squared the end values. and I have no idea how i became i^4 in your version as i*i = i^2 = -1. It also looks like you never squared the denominator. [(3+i)/2]^2 = (3+i)(3+i)/[2*2] = [9 + 3i + 3i + i^2]/4 = [9 + 6i -1]/4 = [8 + 6i]/4 Multiply it by 2 and it becomes: [8 + 6i]/2 The fraction can then be reduced: 8/2 + 6i/2 = 4 + 3i Hope this helps.", + "video_name": "dnjK4DPqh0k" + }, + { + "Q": "At 8:24 how does Sal get (-i)^2=-1?\n", + "A": "(-i)^2 = i^2, just like (-2)^2 = 2^2, because when you multiply negative by negative you get positive. i^2 = -1, because that s the definition of i.", + "video_name": "dnjK4DPqh0k" + }, + { + "Q": "I don't get why it is 1/a (3:11)? Why not -a?\n", + "A": "hmm.. let s suppose a was 2 2^4=16 2^3=8 2^2=4 2^1=2 2^0=1 at each step, we re dividing by 2 (that is, a) therefore, 2^-1 should be 1 divided by 2 2^-1= 1/2 replace 2 by a and you get a^-1= 1/a (if you have a question comment below)", + "video_name": "Tqpcku0hrPU" + }, + { + "Q": "At 3:33, Sal says \"when you take 1/a and divide by a you get 1/a^2\". Why is this?\n", + "A": "Walk it thru using the rules to divide fractions. 1/a divided by a/1 = 1/a * 1/a = 1/a^2 Hope this helps.", + "video_name": "Tqpcku0hrPU" + }, + { + "Q": "at 4:30pm, how do you write a percentage as a fraction or mix number in simplest form? for ex: 146.8 into a fraction or mixed number in simplest form\n", + "A": "Since the 8 is in the tenths place you create a fraction with 1468 in the numerator and 10 (for the tenths place) in the denominator. This gives you the fraction 1468/10. Now you reduce the fraction by dividing numerator and denominator by 2. This gives you 734/5 as an improper fraction. If you want a mixed number you leave the 146 as is and create a fraction using the 8. This gives you 146 8/10 which reduces to 146 4/5.", + "video_name": "-gB1y-PMWfs" + }, + { + "Q": "At 0:57 why do you devide 36 and 100 by 4?\n", + "A": "Dividing 36 and 100 by 4 is just simplifying it to its simplest form, which is 9/20.", + "video_name": "OS1g4PDdNdM" + }, + { + "Q": "at 5:31 how is the moon larger enough to block the sun? Isn't it WAY bigger?\n", + "A": "The sun is bigger! But the Moon is closer to us, so when the Moon is in line with the Earth and Sun, the Sun appears to be blocked out because the Moon is right in it s way. If something is super far away, but you can still see it, it appears really small. But as it moves closer to you, it gets bigger. So because the Moon is closer to us than the Sun, it appears as if the Moon is just as big as the Sun.", + "video_name": "s8_14yxp1lQ" + }, + { + "Q": "\nAt 0:09, what does Sal mean by \" one term\"?", + "A": "a term is anything in a equation for example: x is a term x + 3 are 2 terms remember, terms are only separated by addition and subtraction signs", + "video_name": "p_61XhXdlxI" + }, + { + "Q": "At 6:30\n\nCould you also find the vertex by using the -b/2a that Sal used in the previous video?\n", + "A": "Yes, but I m pretty sure that you use -b/2a only to find the x-value of the vertex. Well, I guess you do end up finding the vertex, because you could just then plug the x-value into the quadratic to find the y-value of the vertex.", + "video_name": "FksgVpM_iXs" + }, + { + "Q": "at2:15-2:45 i am confused\n", + "A": "It s easy, just multiply the numerator by the numerator and the denominator by the denominator, but first convert the mixed number to an improper fraction if neccesary", + "video_name": "XaJQse2u5TQ" + }, + { + "Q": "Why, at 5:30, did Sal use the word \"Dimension?\" It makes it sound like the rectangle's some sort of galactic unknown universe where extra-terrestial life lurks unseen! Shouln't it be \"Area?\"\n", + "A": "Dimension is the width, length, or height of an object. At 5:30 he was referring to the width of the square, saying that it s eight units", + "video_name": "FKJjqEdfB9Y" + }, + { + "Q": "where does 0 and 1 come from in 2:01? Is this a formula or rule? Why do we use 0 and 1 in this example and can other numbers be substituted?\n", + "A": "Sal just plucked them out the air. Any 2 numbers would do, which could be substituted in to the formula to workout what y should equal. I m guessing he chose small numbers so the graph he had to draw wouldn t be to big, but any 2 numbers would do 5, 7, 100 or 1000000 as long as the value of x can be used to calculate the corresponding value of y", + "video_name": "SSNA9gaAOVc" + }, + { + "Q": "\nAt 1:44, why cannot the answer be -1 to both equations. It should be simple right?", + "A": "Hey Asish, Sal is trying to demonstrated the fact that one of them must be equal to zero. -1 is not even somewhat related to making the equations zero. I will demonstrate in the equation he is using. (2x - 1) = 0 substitute -` (2 * -1 - 1) = 0 (-2 - 1) = 0 -3 = 0 This is not true, so -1 does not work in the first part. (x + 4) = 0 substitute -1 (-1 + 4) = 0 (3) = 0 3 = 0 That is not possible, so -1 does not work in this part too. Hope that helps! - JK #YouCanLearnAnything", + "video_name": "-lWVpoPaPBc" + }, + { + "Q": "At 10:39, you take the square root of both sides - yet keep the less than/equal sign unchanged.\nCouldn't it be that there might be a case which \"less than\" should turn into \"greater than\" ? In case ||x+y|| <0 ?\n", + "A": "|x+y| is never < 0.", + "video_name": "PsNidCBr5II" + }, + { + "Q": "\nAt 1:34, Sal multiplied both numerator and denominator by 10, however he did not multiplied the left hand side of the equation by 10 too! And so, how is the equality still maintained?", + "A": "When he multiplies the top and bottom by 10, it is equivalent to multiplying by 1, so you don t need to multiply the left hand side to maintain equality. Take a really simple example: 5 = 10/2 I can multiply the RHS by 10/10 to give: 5= 100/20 (which still holds) But I cannot multiply the LHS by just 10, ie: 50 = 100/20 which is the wrong answer But I can do this: 50/10 = 100/20 The key here is as long as you re multiplying by what is essentially 1, you don t need to multiply the other side by anything.", + "video_name": "a3acutLstF8" + }, + { + "Q": "At 2:21 my answer was 0.5 instead of 1/2 because I chose to divide the decimals. Since that's equivalent would it still be correct to write it in decimal form?\n", + "A": "I think that it would be fine if you got 0.5 instead of 1/2 because they are equivalent.", + "video_name": "a3acutLstF8" + }, + { + "Q": "2:07 How can you cross both of those lines when they are not equal to each other and call them parallel?\n", + "A": "I am not sure what you mean by not equal to each other. Lines, while he does not show it with arrows on the end, go forever.", + "video_name": "V0xounKGEXs" + }, + { + "Q": "\nat 1:00 doesn't the numbers in A add by itself too?", + "A": "In the example, the pattern of the numbers in A is a doubling one, that is (1, 2, 4, 8, 16, 32). This means that the increase is one of multiplication (each interval is 2 times larger than the previous one) rather than one of simple addition.", + "video_name": "Muba9-W2FOQ" + }, + { + "Q": "At 1:17, Sal said something about a \"negative squared is just going to be a 1\". I can't wrap my head around how this actually happened in that particular equation (y= -sqrt(x-3)). Anyone who can clarify this one?\n", + "A": "What he s talking about is the assumed coefficient in front of the radical. Writing -sqrt(x-3) is the same thing as writing -1 * sqrt(x-3). So if you square -1, you get a positive 1.", + "video_name": "QWLcNxQ3KvQ" + }, + { + "Q": "\nAt 5:44, where did the three came from?", + "A": "There was three chairs", + "video_name": "DROZVHObeko" + }, + { + "Q": "\nAt 4:51, when Sal writes 5!/2!, couldn't he just write (5/2)! ?", + "A": "No, Sal could not do this. Factorial does not distribute over division. Example: 4!/2! = (1*2*3*4)/(1*2) = 12, but (4/2)! = 2! = 2*1 = 2. In this particular situation, 5!/2! = (1*2*3*4*5)/(1*2) = 60, but (5/2)! = 2.5! which turns out be approximately 3.32 from using a calculator (the definition of fractional factorials is much more complex than the definition of integer factorials). Have a blessed, wonderful day!", + "video_name": "DROZVHObeko" + }, + { + "Q": "At 2:10 , what does Sal mean by \"0 degree terms?\"\n", + "A": "Basically, the degree refers to the power of the term s variable. So 2x is a 1-degree term and 3x^2 is a second degree term. 0-degree terms simply are constant terms, like the 5 in 4x + 5. They are 0-degree because you can think of the 5 as 5x^0, which is just 5*1.", + "video_name": "n34dqyVCXs4" + }, + { + "Q": "At 1:10, how did you determine the number range for the buckets?\n", + "A": "Looking that the time you referenced, do you mean the ranges of ages that Sal put in the t-chart? If so, the reason why is that is it is really easy to group everything in tens. There is no right way to determine the number range. It is just a matter of preference.", + "video_name": "gSEYtAjuZ-Y" + }, + { + "Q": "\nIsn't it enough to just stop at 4:35, the part where you claim a is a multiple of an integer k times p. Since a/b is said to be 2 integers with no factors in common in the beginning of the video wouldn't a=kp be impossible, since p is prime then this claims p=a/k, and a prime cannot be defined as a integer divided by an integer?", + "A": "Any prime p can be represented as p/1, both of which are integers.", + "video_name": "W-Nio466Ek4" + }, + { + "Q": "i didn't understand how b\u00c2\u00b2=k\u00c2\u00b2p in 5:45\n", + "A": "If you understand why a = kp, then it s just simple algebra from the video, starting around 5:14. If you don t know why a = kp, ask about that.", + "video_name": "W-Nio466Ek4" + }, + { + "Q": "Just noticed that in this vid about 9:13, when simplifying and rearranging, the \"b\" term was dropped. Just so everyone watching does not get too lost.\nThanks for the vids tho. Actually beginning to understand why I did this the first time.\n", + "A": "I saw that too, good that you pointed it out.", + "video_name": "9kW6zFK5E5c" + }, + { + "Q": "\naround 1:54, could you be more specific when you say NO X Value is equal to -14", + "A": "The question was 24x + 80 = 24x - 14 What he is saying is that it doesn t matter what value you give to 24x, there is no value that you could give to the x and then multiply that number by 24 so that 24x would then make 80 = -14", + "video_name": "zKotuhQWIRg" + }, + { + "Q": "\nIs there a proper name for the operation Sal calls a \"slash\" at 4:19?", + "A": "Not like. That is a backslash. Pretty simple character. There can t really be any misinterpreting it, though there could always be additional names for it like anything.", + "video_name": "2B4EBvVvf9w" + }, + { + "Q": "At 6:05 the symbol for a null set is written as a 0 with a slash going through it. The slash is with the top to the right ( / ). Can it also be written with the top on the left ( \\ ) ?\n", + "A": "It s better to donate null set as { } or {0}. However, both slash thing is also correct.", + "video_name": "2B4EBvVvf9w" + }, + { + "Q": "At 3:35, he uses (f(c - h), f(c + h)) to symbolize getting near f(c). However, wouldn't it be more accurate to write:\nlimit as h approaches c of f(h) < f(c) For maximum\nlimit as h approaches c of f(h) > f(c) For minimum\n", + "A": "I agree with the strictly less than/greater than, otherwise f(c) could be equal to surrounding f(x) values (as implied by the or equal to notation on the inequalities)", + "video_name": "Hoyv3-BMAGc" + }, + { + "Q": "\nAt 2:46 the lines are not parallel because they have different slope.\nJust find the slope for both lines.", + "A": "No, they have the same slope - it is 4 for both.", + "video_name": "BNHLzEv6Mjg" + }, + { + "Q": "At 0:48, Sal divides it by 8 but why does he multiply it by 8 also?\n", + "A": "He is just factoring out the 8; it is still the same answer. -> 8+4+2 is the same as 2(4+2+1).", + "video_name": "GMoqg_s4Dl4" + }, + { + "Q": "\nAre the charts mentioned at the 9:00 marker something that is given or would I have to fill it in myself while solving the problem. If so, how would i go about doing that?", + "A": "You do not memorize the values. If you are doing homework/classwork, the tables are provided at the end of the book. On a test, the table should be attached to the test or the teacher should allow you to look up the critical value for a specified level of significance and degrees of freedom using the text. I hope this helps.", + "video_name": "2QeDRsxSF9M" + }, + { + "Q": "\nAt 5:31, Sal decides to use the line as a transversal. If the point of this video is to prove that a line has a constant slope, wouldn't it be bad science to use an assumption of a line's constant slope to prove it has a constant slope?", + "A": "Using the line as a transversal is making no assumptions about the slope. All he is doing here is using the fact that if you have a line that crosses two parallel lines (in other words, if you have a transversal) that the corresponding angles are congruent. This is something we know from geometry. From here he is able to prove that the triangles are similar and thus the equation for the slope is the same for both segments.", + "video_name": "24WMbh1BBKc" + }, + { + "Q": "at 4:30 why does Sal move 4,-1 clock wise for the rotation example? Is negative clockwise and positive counter?\n\nThanks\n", + "A": "Just to answer your question, when you rotate it counter-clockwise it is positive. when it is rotated clockwise it is negative. I hope this answers your question :)", + "video_name": "_eAWDuLYVfg" + }, + { + "Q": "\nIn 1:15, why can't it be a translation? I didn't understand.", + "A": "Because one point would have to move 6 to the right and 4 down. While the other would move 12 to the right and 8 down. In a translation, all points should be moved the same distance.", + "video_name": "_eAWDuLYVfg" + }, + { + "Q": "\nI got lost at around 6:00\nCan someone please help me?", + "A": "Do you have a more specific question? I can help if I know how : )", + "video_name": "dvoHB9djouc" + }, + { + "Q": "\nAround 6:10 he's talking about the 20 being the squared distance away from the population mean - is there a time when you would take the square root?", + "A": "Yep. The square root of the variance is called the standard deviation, which will be another crucial concept that you ll get to pretty soon.", + "video_name": "dvoHB9djouc" + }, + { + "Q": "At 3:20, how did Sal go from cos(2*theta) to cos^2(theta) - sin^2(theta)? I didn't get that part, can someone please help me? Thanks!\n", + "A": "That s a double angle formula. It s a known trig identity.", + "video_name": "lXShNH1G6Pk" + }, + { + "Q": "At 10:05, why is f(x) continuous at a when a = -\u00cf\u0080/4? Isn't f(-\u00cf\u0080/4) undefined?\n", + "A": "Sal is just making a general statement about limit equality between functions. E.g if f(x)=a for all x, and g(x)=a for all x!=10 and g(10)=1234 then g(x) -> 4 when x -> 10. The functions have exactly the same limits, regardless of x-value.", + "video_name": "lXShNH1G6Pk" + }, + { + "Q": "\nAt 1:21 what does it mean by past the . that the numbers are smaller than the 1's?", + "A": "The numbers to the right of the decimal point represent fractions, anything less than 1. For instance, 0.1 is one tenth and is the same as 1/10.", + "video_name": "BItpeFXC4vA" + }, + { + "Q": "at 2:51 it says multiply both by 2/3 cant you just divide both by 3 and then multiply them by 2?\n", + "A": "Yes you can but that s the same thing as multiplying both sides by 2/3. Because 2*1/3 = 2 divided 3 = 2/3", + "video_name": "wo7DSaPP8hQ" + }, + { + "Q": "\nI don't know if this is a mistake, but at 3:23 in the video, Sal says Maple Farms lost 2/3 of their farm, not 1/3.Is this a mistake, or did i miss something?", + "A": "At 2.22, Sal explains why it is 2/3 : 1/3 less than an amount x is x-1/3x which equals 2/3x. Hope this helps! :)", + "video_name": "wo7DSaPP8hQ" + }, + { + "Q": "At 1:07 to 2:59, couldn't he find the area and then multiply it by 3/4 and you get an answer?\n", + "A": "Sure, if what you needed was the area. But the exercise is asking for the arc length which is part of the circumference and not the area. Just remember that arc length, and circumference for that matter, is a measurement of length as the name implies while area is not.", + "video_name": "YjWCDdNlXxc" + }, + { + "Q": "At 2:03 to 2:13, I wish he would have wrote out the 10^5-10^7 to show what he did in his head.\n", + "A": "That would certainly be helpful!", + "video_name": "497oIjqRPco" + }, + { + "Q": "\nAt 1:40 Sal says that (7 * 10^5) / (5 * 10^7) = (7 / 5) * (10^5 / 10^7). Why can we detach 7 / 5 like this? Shouldn't we get a different answer? I'm sure Sal says the right thing, I just don't get why it works.", + "A": "How many sides does your polygon have?", + "video_name": "497oIjqRPco" + }, + { + "Q": "\nAround 2:25 he mentions \"f of x\", this mightt sound like a stupid question but what does this mean? Function?", + "A": "yup yup yups!", + "video_name": "W0VWO4asgmk" + }, + { + "Q": "So around the time 4:43 in the video, he is talking about simplifying your answer. The answer I got that I think I need to simplify is -3x+9y=-6. My question is would it be possible to divide the positive 9 by a negative 3 or the only way you would be able to divide that positive is by a positive vice versa.\n", + "A": "Yes it would be possible. I would divide it by -3. So you would have -3x/-3=x and 9y/-3=-3y and -6/-3=2 . The simplified version would be x+3y+2 :)", + "video_name": "XOIhNVeLfWs" + }, + { + "Q": "At 2:44 , SAl said the slope is 7. How is it 7 ? is he assuming ?\n", + "A": "In the video there s a graphic clip with given information: Let f be a differentiable function for all x. If f(-2) = 3 and f (x) \u00e2\u0089\u00a4 7 for all x, then what is the largest possible value of f(10). f (x) is the slope of f(x).", + "video_name": "EXLVMGSDQbI" + }, + { + "Q": "at 3:30 sal multiplies vector a with a 'scalar quantity'-1.....but how come -1 is scalar....1 represents magnitude and the negative sign represents direction so it has to be a vector. and if it is a vector how do we plot it on a graph\n", + "A": "That s creative! But not exactly how that works. You could think of the number 2 as having a + in front of it, that we just don t write. The negative symbol is a part of the number. It says we are going negative one in some direction, it does not say whether we are going negative 1 up, or left or right or down or diagonally, just that we are going negative 1. Does that make sense?", + "video_name": "ZN7YaSbY3-w" + }, + { + "Q": "\nAt 4:03 Sal said the magnitude didn't change. But he added, essentially, 1 more of the original vector in the negative direction. Am Imissing something?", + "A": "The magnitude remained the same only for the -1 scalar.", + "video_name": "ZN7YaSbY3-w" + }, + { + "Q": "\n10:50 what are pictograms?", + "A": "Pictograms are the pictures/symbols themselves. A pictograph is the entire graph.", + "video_name": "qrVvpYt3Vl0" + }, + { + "Q": "\nWhy at 1:58 is 8x-7x= to x ?", + "A": "8-7=1. 1x is the same thing as x. It is easier to say x than 1x, but you could actually say 1x, and it wouldn t be wrong.", + "video_name": "E0TNh9uWesw" + }, + { + "Q": "At 1:57 in the video, he says that 8x - 7x = x, which I think I understand. But what if my number was larger than just x? What would I do from there, divide both sides?\n\nThanks\n", + "A": "Yes, you would. It s nice that you can know (or take a good guess at) what to do.", + "video_name": "E0TNh9uWesw" + }, + { + "Q": "\nAround 2:00, 8x - 7x = x? I assume the missing 1 is just a place holder?", + "A": "Yeah, if there is no coefficient in front of a variable, that means that there is a coefficient of 1: 1x = x", + "video_name": "E0TNh9uWesw" + }, + { + "Q": "On that last one (5:31) shouldn't we have multiplied 2/1 by three to get the denominators to be the same before we multiplied it... to get our final answer?\n", + "A": "if you add 2/1 to -(1/3), then yes. But this is a multiplication problem. So just multiply the numerators and multiply the denominators respectively.", + "video_name": "a_Wi-6SRBTc" + }, + { + "Q": "\nx < -1 (-infinity,-1) since the -1 is in the parenthesis, shouldn't it be less than or equal to? @1:29", + "A": "The parentheses mean only less than . To have x <= -1, the interval would be written as (-infinity, -1] The square bracket indicates that x can also be equal to -1.", + "video_name": "xOxvyeSl0uA" + }, + { + "Q": "\nat 5:40, why do you subtract -8x instead of adding 12x to both sides or adding 5 or 7 to both first. Is there a reason you pick 8x to subtract first?", + "A": "That is what I would have advised my students to do so that the coefficient of the variable stays positive. There is no reason for subtracting 8 except to possibly remind us of the need to flip the inequality sign when dividing by a negative. You should have gotten the same answer.", + "video_name": "xOxvyeSl0uA" + }, + { + "Q": "\nwhy do you flip the sign at 2:35???", + "A": "oh ok thank you for explaining this to me", + "video_name": "xOxvyeSl0uA" + }, + { + "Q": "\nAt 4:00, while setting up the problem, verbally \"8x minus 5\", then at 4:24 while simplifying the inequality, verbally says \"distribute the negative 5\".\nWhile trying to respect the order of operations, this interchangeable \"subtraction\" and \"negative\" concept is very confusing. Any help would be appreciated, thank you in advance!", + "A": "Do you already know that subtraction is adding the opposite? For example, having $10 and then spending $4 could be written 10 - 4 (ten take away four) or it could be written 10 + -4 (having ten and then losing 4). Think of that for this distribution problem: 8x - 5(4x + 1) could be written 8x + -5(4x + 1). Now can you see how it is a negative 5 that needs to be distributed?", + "video_name": "xOxvyeSl0uA" + }, + { + "Q": "At 1:13, I thought that multiplying or dividing in an inequality you were supposed to flip the sign?\n", + "A": "For an inequality, you only flip the sign if you re multiplying or dividing by a negative number. At that point in the video, he s dividing by positive 4, so there s no need to flip the inequality sign.", + "video_name": "xOxvyeSl0uA" + }, + { + "Q": "At 4:34 Sal calculates the probability of small to be (1/26-1/2600). Why isn't this probability equal to (9/10*9/10*1/26)?\nSince, Probability of losing number = 9/10 and Probability of winning alphabet = 1/26.\n", + "A": "I did the problem like you say. Once you buy a ticket, the expected values are as follows: Expected Value of $5 payout = probability*value = 1 * (-$5) EV(grand prize) = P(x)*x = (1/10*1/10*1/26) * (10405) = 4.0019 EV(small prize) = (1/10*9/10*1/26) * 100 + (9/10*1/10*1/26) * 100 + (9/10*9/10*1/26) * 100 [ there are 2 ways to get 1 number, 1 way to get no numbers] = 0.34615 + 0.34615 + 3.1154 Total is 7.81 - 5 = 2.81", + "video_name": "6vlBOHckmzU" + }, + { + "Q": "at 1-1:20, how did you choose the bounds? The upper limit can be anything right? I was confused because 3 is the value you get when you plug X= -2 into the y=x^2-1 formula. I thought it had extra significance. As for the lower bound, I understand y= -1 is the minimum of the parabola. Is that the reason for it being the bound? Thank you.\n", + "A": "Since the only part of the function that is being rotated is the one for positive x values, it is a mere coincidence that 3 is the intersection of the whole function and x = -2. The part of the function for negative x values was never considered and the number 3 was chosen at random.", + "video_name": "jxf7XqvZWWg" + }, + { + "Q": "At 7:57, Sal mentions that dA is used as a shorthand. Isn't it also used to generalize dxdy so that the order of integration (and the coordinate system) is not specified? I feel like this would make it more applicable in proofs and theorems and such.\n", + "A": "dA is often used to indicate integration over an area without specifying how the integration will be performed. dA can even indicate integration over a curved surface in 3-D.", + "video_name": "twT-WZChfZ8" + }, + { + "Q": "\nAt 8:52 Sal says we can do this in polar coordinates. Can someone explain to me how this would work?", + "A": "3D polar could be either with an extra angle coordinate or another radius coordinate , spherical or cylindrical respectively. You might try 2D polar first, I would go back and watch integration videos in 2D and do a parallel situation in polar. But basically, the idea is to split the area into sectors of a circle where dTHETA becomes infinitely small. The area of a sector is 1/2*pi*r^2. Be mindful of your endpoints - integrating from pi/4 to 3pi/2 is much different than -pi/4 to pi/4. Hope this helps.", + "video_name": "twT-WZChfZ8" + }, + { + "Q": "at 0:10, Why did you call the space \"blank\"?\n", + "A": "Blank represents any unknown or missing value. It is commonly used in language and math lessons. The goal is to find the/an answer that fits in the blank and completes the sentence or problem.", + "video_name": "OPpmp-kAuE4" + }, + { + "Q": "shouldnt the x+5 over 100 @ 16:12 be a 10 because of ([x--5]/10)^2 ?!\n", + "A": "Yes, in the exponential term of the yellow integral either the denominator should be 10 or the square should be limited to the numerator", + "video_name": "hgtMWR3TFnY" + }, + { + "Q": "why is the middle one horizontal at 1:35 in the video?\n", + "A": "As Sal explain from 1:36 onward, the reason it was initially horizontal, is to remind us, how we have to put the numbers vertically, with the ones aligned, and the tens aligned. It s just a reminder that an addition might be presented in a test in this (horizontal) notation, and that we have to arrange them in the specific way to carry out the addition procedure.", + "video_name": "9hM32lsQ4aI" + }, + { + "Q": "At 2:00 what if it remained as dt? Could we still do it with respect to another variable, like in differentiation?\n", + "A": "Yes! You can still do the problem but treating all the other variables as constants. So you re answer would be: (e^a + 1/a)t + c Everything within the parenthesis can be thought of as a single constant. So the problem would be the same as say integral(3) = 3t + c Hope that helps!", + "video_name": "hXg-6YgAARk" + }, + { + "Q": "\nAt 3:45 couldn't the indefinite integral of (1/a) also be ln(a)+c or does the (a) part have to be its absolute value like Sal put it, ln(IaI)+c?\nThanks in advance", + "A": "Sometimes people don t bother with the absolute value for this integral, but in that case you re stating the integral only for positive values of x, because ln(x) is undefined for x<=0. When you include the absolute value, you state the integral for all x in the domain of 1/x (that is, all x except 0).", + "video_name": "hXg-6YgAARk" + }, + { + "Q": "At 5:57 Vi mentions an equilateral right triangle. How can an equilateral triangle also be a right triangle? Doesn't each angle have to be 60 degrees?\n", + "A": "Whenever Vi says equilateral right triangle, she means isosceles right triangle. She actually makes that mistake a lot.", + "video_name": "Oc8sWN_jNF4" + }, + { + "Q": "\nAt 2:50what would be an example of what he's explaining?", + "A": "Sal is saying that given two functions, if each is substituted into the other, different answers will (usually) result. Say we had f(x) = x - 3 and g(x) = - 4x + 7. Substituting f(x) into g will give us - 4 ( x - 3 ) +7 which simplifies to - 4x +19. But substituting g(x) into f will give us ( - 4x + 7 ) - 3 which simplifies to - 4x +4. Hope this helps!", + "video_name": "_b-2rZpX5z4" + }, + { + "Q": "\nAt 2:35, can you cancel out the square root of x - 1 in the numerator and the denominator? What would the answer be if you could?", + "A": "First, it is sqrt(x^2-1), not x-1 in both numerator & denominator. Second, you can t cancel them out because the sqrt(x^2-1) in the denominator is being added to 1. You can only cancel items being multiplied (factors), not terms (items being added/subtracted).", + "video_name": "_b-2rZpX5z4" + }, + { + "Q": "\nat 11:20, I dont understand, like why does the y axis have to have the price, and the x axis is months why cant the y axis be months, and x axis be price ?", + "A": "X is usually used for representing an independent variable. Y is usually for dependent variables. Since time is independent (time goes on no matter what) the months are put on the X axis. I don t expect text books to do it the other way around.", + "video_name": "36v2EXZRzUE" + }, + { + "Q": "\nAt 5:19, Why didn't he use positive 4 instead of \"I minus x\"? which is from what I can understand here is, 1 minus 4? And how did he get the answer 4 instead?", + "A": "Using the lower value of the domain, -3. 1-(-3) = 4", + "video_name": "rpI-X9Gn5a4" + }, + { + "Q": "When Salman does range past 3:00, why are x values inputted?\n", + "A": "Since this is a piecewise function, you have to figure out the range for each piece . And, each piece is used depending upon the value of X. So, if you are looking for the range of the 1st piece, you look at the X-values that would use that piece and what they create for output values. Hope this helps.", + "video_name": "rpI-X9Gn5a4" + }, + { + "Q": "\nat 1:55, you crossed out the 9 and made it a 3, and you made the 3 into a 1. when you did the simplified equation, instead of writing 3/100+1/1*, you wrote 3/100+1/3* shown at 2:22. when i did the problem 3/100+1/1, the answer was 103/100. when you did the problem you answered 109/300.\ndid you make a mistake? or did i miss something in a previous video?", + "A": "Why do you have the extra * at the end of two numbers? Sal simplified 1/3 + 9/100 * 1/3 into 1/3 + 3/100 * 1/1. Because *1/1 is the same as *1 and doesn t change anything, he wrote it as 1/3 + 3/100 instead, leaving out the *1/1.", + "video_name": "MZpULgKhaEU" + }, + { + "Q": "\nhow can the temperature be same on a particular day every year. At 2:37 you can observe Sal saying in future January 7 also you will have the highest average temperature as 29C .", + "A": "It isn t the same on a particular day every year, but if you averaged all of the temperatures that it had previously been on that day of the year, it would be the temperature that Sal used. Therefore, the temperature could really have been 30C or 26C, but it is most likely to be 29C.", + "video_name": "mVlCXkht6hg" + }, + { + "Q": "At 2:48, why did he take 25^2 and not -25^2 like he did with the -b part of the abc formula?\n", + "A": "He made a mistake saying it, it is supposed to be (-25)\u00c2\u00b2 but because when you square a number or its negative, it will be the same thing, so he got away with it. Good job spotting it. You should report so they can add an annotation to youtube that he meant (-25)\u00c2\u00b2 to clear the confusion for others.", + "video_name": "711pdW8TbbY" + }, + { + "Q": "1:27 is really confusing. Need some clarification\n", + "A": "He expanded (2x-6)^2, making it now 4x^2-24x+36. When you have the square of a binomial, you take square of the first monomial=4x^2; multiply (2)(the first)(the second): (2)(2x)(-6): -24x. Then you square the second=36. 4x^-24x+36. If you didn t get that you can multiply (2x-6)(2x-6). You will get the same.", + "video_name": "711pdW8TbbY" + }, + { + "Q": "at 2:17 after he subtracted x from both sides why did he right -25x when in the equation above it he had written -24x, and where did he subtract the x on the right hand side from\n", + "A": "becuz hes subtracting a -24 by a -x and the x on the right hand side hes combining with the -24. so a -24 minus -x=-25", + "video_name": "711pdW8TbbY" + }, + { + "Q": "\nAt 0:55, isn't PEMDAS the same as Please Excuse My Dear Aunt Sally?", + "A": "Yes. It is the same thing. :) some people find it easier to remember PEMDAS, others say GEMDAS (where G stands for Grouping symbols), and yet others memorize the mnemonic Please Excuse My Dear Aunt Sally. Another version of it is Please Excuse My Dear Aunt Sally, she limps from left to right. This helps the student remember which direction do do these symbols in. :) Hope this helps! Sylvia.", + "video_name": "0uCslW40VHQ" + }, + { + "Q": "\nIn the video on calculating the square footage of a house, at 2:50 how did you get the width of the green rectangle to be 25ft? Shouldn't it be 26ft, the same as the width of the blue one?", + "A": "It isn t drawn to scale.", + "video_name": "xo4VpX2IIMk" + }, + { + "Q": "At 1:00, couldn't there be another line that bisects angle BCA starting from point C and ending at a point that is between A and B?\n", + "A": "Yes. There could be another line.", + "video_name": "21vbBiCVijE" + }, + { + "Q": "ok, be sure to watch all the way to the end ! sal makes an important correction after minute 5:26. for a minute there i thought i still didn't get how to simplify fractions! whew... :))\n", + "A": "This is a duplicate - see the question above", + "video_name": "CLrImGKeuEI" + }, + { + "Q": "\nAt 2:06 how did he get the four in the equation? (8^2 -4 (-1)(-1)...", + "A": "It is part of the quadratic formula: x = [-B +/= sqrt(B^2 - 4AC)] / 2A", + "video_name": "CLrImGKeuEI" + }, + { + "Q": "\nAt 0:35 what would be the way to solve for x?", + "A": "3x + 5 = 17 To solve for x, we need to be on one side of the equation by itself. To do this we could first subtract 5 from both sides of the equation so that we would get 3x = 12. Then we can divide both sides of the equation by 3 so that the equation then becomes x = 4 Did that help?", + "video_name": "XoEn1LfVoTo" + }, + { + "Q": "\nAt 0:34 Arnt you supposed to do minus 3 on both sides? 3x=17 im new to this thing", + "A": "For 3x=17, we need to divide by 3 because x is being multiplied by 3 and the opposite of multiplication is division, not subtraction. Does that make sense?", + "video_name": "XoEn1LfVoTo" + }, + { + "Q": "\nAt 8:21 can you make the fraction -8/7 a decimal?", + "A": "Yes! It is also equal to -(8/7). So you can make it a negative mixed number -(1 and 1/7). You ignore the 1 for a moment, and you do 1 divided by 7, which is 0.14285714285, and 0.14285714285 plus the ignored 1 is equal to 1.14285714285.", + "video_name": "XoEn1LfVoTo" + }, + { + "Q": "xD is that all you simplify it to!? seems like you alreddy got the awnser at 8:21\n", + "A": "yes you want to make sure u simplify everything if u want it to be correct", + "video_name": "XoEn1LfVoTo" + }, + { + "Q": "At 1:58 What if the outcomes werent all equally likely? How would I solve it?\n", + "A": "As long as the other holly wands have a probability not all zero, the answer would be the same. This is because the probability of a set of events happening must be greater than the probability of a proper subset of them happening.", + "video_name": "0uHhk7P9SNo" + }, + { + "Q": "\nAt 1:34, why did he switched around y-x=5 to y=5+x?", + "A": "if you add x to both sides of the equal sign, then you can eliminate the negative x on the left side, and add a positive x on the right side (-x + x = 0, and 0 + x = x)", + "video_name": "0BgUKHTW37E" + }, + { + "Q": "\nat 1:30 of the video why do we need to subtract 5 or add -5 to the problem 3 times.", + "A": "Because 3x has an x in it, and x is a variable meaning it can change. so if: x=2 3x = 6 there are too many possibilites, so we would call that another term But -5 is just -5! So it would not change. That is why we do that. Hope that helped!", + "video_name": "cvB8b4AACyE" + }, + { + "Q": "\nAt 7:41 Sal says that an ellipse is the locus of all points. What does Sal mean when he says locus?", + "A": "No, he does not mean focus. A locus can be defined as a set of points satisfying a given condition. Sal defines a locus as a set of points which are such that the sum of the distance between the point and two fixed points (f1 and f2) is constant.", + "video_name": "QR2vxfwiHAU" + }, + { + "Q": "\nhow can it be reduced to a scalar multiple of the first vector?\n2:18", + "A": "the first vector is 2 3 and second vector 4 6 let C1 be the scalar multiple of first vector and C2 be the scalar multiple of second vector but, second vector = [4 6] = 2 [2 3] = 2 first vector therefore, Linear combination = (C1 + 2C2) [2 3] by substituting *(C1 + 2C2)* as C3, C3 becomes a new scalar multiple for the first vector", + "video_name": "CrV1xCWdY-g" + }, + { + "Q": "at 5:23, whats place values?\n", + "A": "Place values are which place a specific digit is in a number. It goes ones, tens, hundreds, thousands, hundred thousands, and so on. So, for a number 7,932, the 2 is in the ones place, the 3 is in the tens place, the 9 is in the hundreds place, and the 7 is in the thousands place.", + "video_name": "UzXoxglkr98" + }, + { + "Q": "\nAt 1:15, why does Sal say \"this is the probability of 5 coin flips, NOT of the outcomes of X\"? I thought X was defined as the outcome of 5 coin flips.\nPlease answer ASAP and thanks in advance.", + "A": "He isn t finding the probability of X at that moment. He says that he needs to FIRST find out what the probability is of 5 coin flips is so that LATER he can find the probability of X. X is defined as the # of heads out of five flips.", + "video_name": "WWv0RUxDfbs" + }, + { + "Q": "why At 2:27, Sal puts +10 below the 15 when the 15 is positive? shouldn't have been negative the 10?\n", + "A": "Sal wanted to eliminate the - 10 from the left-hand side of the equation so that only the variable term would remain there. That s why he added + 10 to both sides of the equation.", + "video_name": "Z7C69xP08d8" + }, + { + "Q": "At 4:30 he just \"sees\", that \u00ce\u00bb\u00c2\u00b2-4\u00ce\u00bb-5 is equal to (\u00ce\u00bb-5)(\u00ce\u00bb+1). How does one just see something like this? Did I miss something?\n", + "A": "-5 and 1 are two factors of -5 that sum to -4", + "video_name": "pZ6mMVEE89g" + }, + { + "Q": "\nWhat does the symbol that Sal draws at 2:34 mean?", + "A": "If you are referring to the \u00e2\u0088\u00a9 symbol, that means intersection. For instance, let A and B be to possible events. If we want to talk about the probability of event A taking place, we would write P(A), and similarly P(B) for B. What if we want to talk about the probability of both A and B happening at the same time? We would write that as P(A \u00e2\u0088\u00a9 B) - the probability of A and B. C = A \u00e2\u0088\u00a9 B is a new set containing all the elements common to both sets A and B - the intersection of the two.", + "video_name": "VjLEoo3hIoM" + }, + { + "Q": "at 6:30 , why did Sal write the \"0.30*$1=0.30\"??\n", + "A": "Because he had just worked out that you had a 30% chance of winning the game which when multiplied by what your prize will give you your average gain (30 cents as opposed to playing 35 cents to play the game).", + "video_name": "VjLEoo3hIoM" + }, + { + "Q": "What does the upside down U symbol at 2:32-2:35 mean?\n", + "A": "In this example, Sal is asking what is the probability of both the first AND second being green . The upside down U symbol in this case stands for the AND. The symbol typically stands for intersection and is used in set theory to refer to common numbers or letters in sets. For example, the intersection of {1, 3, 5, 7} and {4, 5, 6, 7} is {5, 7} because those are the numbers that you can find in both sets.", + "video_name": "VjLEoo3hIoM" + }, + { + "Q": "\nAt 0:40, does it matter what kind of brackets to draw? Or can any be used?", + "A": "Set notation traditionally uses the curly brackets { }", + "video_name": "KRFiAlo7t1E" + }, + { + "Q": "Why did he add the K-1 thing at about 3:11\n", + "A": "Around 3:11 Sal put in the k - 1 in to show the term before K. hope it helps", + "video_name": "KRFiAlo7t1E" + }, + { + "Q": "at 4:28 Sal writes {a sub k} k = 1, is it correct for him to write that k = 1 because if you look at the sequence then you can see that (a sub 1) is 3?\n", + "A": "Be careful here. k is the number of the term (first term, second term, third term, fourth term), not the value of the term ( 1, 4, 7, and 10). In Sal s first example, k went from 1 to 4 because there are 4 terms in the sequence., but the values of those terms were 1 , 4, 7, and 10. The number of the first term ( 1 ) just happened to be the same as the value of the first term ( 1 ).", + "video_name": "KRFiAlo7t1E" + }, + { + "Q": "\nAt 3:09, why does he put \"k-1\" into that function?", + "A": "Starting on the first term, we need to move (\u00f0\u009d\u0091\u0098 \u00e2\u0088\u0092 1) spaces in the sequence in order to get to the \u00f0\u009d\u0091\u0098:th term. (Moving 1 space gets us to the 2nd term, moving 2 spaces gets us to the 3rd term, and so on...) And each time we move a space, we add 3, so by the time we get to the \u00f0\u009d\u0091\u0098:th term we have added 3(\u00f0\u009d\u0091\u0098 \u00e2\u0088\u0092 1).", + "video_name": "KRFiAlo7t1E" + }, + { + "Q": "at time 3:42, why the radius of the surface is radical 2?\n", + "A": "The radius isn t set at the square root of 2: it is the square root of y. The radius is variable as the function increases in either direction, and is equal to the distance between the y axis and f(x). The radius is only the square root of 2 when f(x) is 2.", + "video_name": "43AS7bPUORc" + }, + { + "Q": "did he graph it in a wrong way at 6:03\n", + "A": "He did not. Since 1/2x was there, he started the grAph at (0, -6) , before going down by 1/2 from there.", + "video_name": "unSBFwK881s" + }, + { + "Q": "\ni'm confused,at1:25 do you graph the whole equation", + "A": "You do graph the line just as you would if you were given the equality: y = 4x + 3 Once you have graphed the line, you look at the inequality to see if you should shade the area above the line or below it. For y > 4x + 3, you would shade above, and make the line a dotted line For y >= 4x+3, you would shade above, and make the line a solid line For y < 4x + 3, you would shade below, and make the line a dotted line For y <= 4x+3, you would shade below, and make the line a solid line", + "video_name": "unSBFwK881s" + }, + { + "Q": "@ around 4:15 Sal talks about:\n\n\"...the set of all of the positions or all of the position vectors that specify the triangle that is essentially formed by connecting these dots.\"\n\nI'm thinking that yes, the \"...set of all of the positions...\"; but not \"...all of the position vectors...\" which seem to span the interior of the (transformed or untransformed) triangle (if their tails are at the origin). Anyone disagree?\n", + "A": "When it comes to vectors in standard position (starting at the origin) (i.e. position vectors), we only care about the position of the head. The line which composes the body of the vector is immaterial, merely a graphical representation which is not preserved in the numerical representation.", + "video_name": "qkfODKmZ-x4" + }, + { + "Q": "\n3:25 Isn't this essentially another logarithmic property?", + "A": "Yes. \u00f0\u009d\u0091\u008f^(log[\u00f0\u009d\u0091\u008f] (4)) = 4. 4^(log[4] (\u00f0\u009d\u0091\u008f)) = \u00f0\u009d\u0091\u008f \u00e2\u0087\u0094 4 = \u00f0\u009d\u0091\u008f^(1/(log[4] (\u00f0\u009d\u0091\u008f))). Thereby log[\u00f0\u009d\u0091\u008f] (4) = 1/(log[4] (\u00f0\u009d\u0091\u008f))", + "video_name": "qtsMgdZ98Yg" + }, + { + "Q": "At 0:58, Sal mentions \"mu\". Is that the symbol for the arithmetic mean?\n", + "A": "In the context of statistics, the letter mu (\u00ce\u00bc) often indeed refers to the arithmetic mean. In mathematics in general, it is used for many things in mathematics - sometimes even just as a variable (much like n for a natural number). The context should make it clear which \u00ce\u00bc is meant.", + "video_name": "PWiWkqHmum0" + }, + { + "Q": "How is \u00cf\u0086 - 1 = 1/\u00cf\u0086 ? How is \u00cf\u0086 ^2-\u00cf\u0086 -1=0?? (At 1:38) and (4:17)\n", + "A": "\u00cf\u0086 = 1 + (1/ \u00cf\u0086) He subtracts 1 from both sides. \u00cf\u0086 - 1 = 1 + (1/ \u00cf\u0086) - 1. On the right side, 1 - 1 is just 0. You are left with \u00cf\u0086 - 1 = 1/ \u00cf\u0086 \u00cf\u0086 = 1 + (1/ \u00cf\u0086) He multiplies both sides by \u00cf\u0086, like this: (\u00cf\u0086)\u00cf\u0086 = (1 + 1/\u00cf\u0086) (\u00cf\u0086). You get \u00cf\u0086^2 = \u00cf\u0086 + 1 To make a quadratic equation, subtract \u00cf\u0086 and 1 from the right side. You get \u00cf\u0086^2 - \u00cf\u0086 - 1 = 0", + "video_name": "5zosU6XTgSY" + }, + { + "Q": "At 11:30 Sal says b/(a-b) = 1/((a-b)/b)\nHe says that he took the reciprocal, I guess I don't understand the mechanics behind taking reciprocals of fractures? Can someone explain?\n", + "A": "Reciprocals are basically when you divided 1 by a certain fraction. What this does is it swaps both the top and the bottom parts of the fraction. So, the reciprocal of, to use this example, b/(a-b) is 1/b/(a-b), or (a-b)/b. However, you might note that the two are not equal. Therefore, in order to use it in an equation, you need to have 1/(a-b)/b, which is equal to the original fraction.", + "video_name": "5zosU6XTgSY" + }, + { + "Q": "\n@ 4:57, how come a is = to it's coefficient, and b = to it's coefficient?", + "A": "He is using the quadratic formula to solve this quadratic equation (if you changed it to x s to make it more clear: x^2 - x - 1 = 0 The letters in the video are phi s, but it really makes no difference.", + "video_name": "5zosU6XTgSY" + }, + { + "Q": "\nHow does Phi=1+1/Phi = Phi^2=Phi+1\nDoes 1/(x^2)=x\n(3:14)", + "A": "If 1 + 1/phi = phi then you can multiply both sides by phi: phi(1 + 1/phi) = phi x phi (now use the distributive property on the left side: phi + 1 = phi^2 I hope my answer is clear enough", + "video_name": "5zosU6XTgSY" + }, + { + "Q": "Hey Guys, and Khan, I just have one question at aaround 3:10 3:09, just say that you times both side by \u00c3\u0098 (\u00c3\u0098=phi) , but I don't understand how u get \u00c3\u0098^2= \u00c3\u0098+1, because the origional equation is \u00c3\u0098= 1+1/\u00c3\u0098, and then when you times both side by \u00c3\u0098, \u00c3\u0098^2= 1+ 1/\u00c3\u0098*\u00c3\u0098 = \u00c3\u0098^2 = 1+1, because 1/\u00c3\u0098*\u00c3\u0098 = 1/1 ... or have I got a brain malfunction ??...\n", + "A": "I believe you re missing one step here. You are forgetting to fully distribute phi on the right side of the equation, (1+ 1/phi), for I don t believe you are multiplying the constant 1 by phi. If you multiply the whole equation by phi , then you ll first have (phi = 1 + 1/phi) * phi; then after distribution (phi * phi) = (1 * phi) + (phi * 1/phi), which of course leads to the equation phi^2 = phi +1. I this still isn t making sense I would suggest watching some of Sal s Algebra videos. Cheers!", + "video_name": "5zosU6XTgSY" + }, + { + "Q": "At 1:33 is that the only symbol for phi?\n", + "A": "yes like this:\u00cf\u0086", + "video_name": "5zosU6XTgSY" + }, + { + "Q": "\nAt about 11:35 Sal determines that the reciprocal of b/a-b= 1/a-b/b. Why isn't it just a-b/b?", + "A": "b/(a-b)=1/((a-b)/b) This is equivalent to b/(a-b). The second expression is the reciprocal of the reciprocal, not just the reciprocal, of b/(a-b), so it is equivalent to it. I hope this helps!", + "video_name": "5zosU6XTgSY" + }, + { + "Q": "at 1:41, when would we use the golden ratio?\n", + "A": "Music, art, and nature according to Sal. Check out the pics on the end!", + "video_name": "5zosU6XTgSY" + }, + { + "Q": "At 1:50, sal said 8-24-3= negative 19. 8-24 is 16, not 22.\n", + "A": "just listen to the guy", + "video_name": "-rxUip6Ulnw" + }, + { + "Q": "\nat 0:18 why do we put a sqwiggle under (8-3)", + "A": "That means we will solve that part first. (8-3) Also, you have to solve that part first, because it is in parentheses.", + "video_name": "-rxUip6Ulnw" + }, + { + "Q": "At 4:30 Sal says that all bi's should be members of R3. Shouldn't be all bi's members of R4 as B has 4 column components ? Or my understanding is wrong ?\n", + "A": "How many components do B s column vectors have? What vector space are they in? How many components do B s row vectors have? What vector space are they in? (3, R3. 4, R4.) (Rn is defined as the set of all the vectors with n real number components.) This matrix B itself is 4x3 , and it s not an Rn or an Rm vector - although parts of it (e.g., its rows and columns) are. An mx1 matrix is an Rm column vector. A 1xn matrix is an Rn row vector.", + "video_name": "x1z0hOyjapU" + }, + { + "Q": "\ni did not clearly understand how Sal undistributed s(s+5) -7(s+5)=0\nat 2:15 .. could someone help me out please ?", + "A": "so simple see that video once again seeit was s^2 +5s -7s -35 then he (s^2 +5s)_ _ _ _ _ _ (i) -(7s +35) _ _ _ _ _ _(ii) in (i) s is common so, s(s+5) in (ii) -7 is common so, -7(s+5) done this is the easiest way", + "video_name": "2ZzuZvz33X0" + }, + { + "Q": "\nDo you come out with two answers when you do these kinds of equations? If S=S is a true statement, how could it be possible that S could equal both -5 or 7 as shown at 4:00? I'm so confused! HELP! :-O", + "A": "S can t equal both values at the same time. But, both values (-5 and 7) will make the equation be true. This means each value on its own is a valid solution to the equation. Hope this helps.", + "video_name": "2ZzuZvz33X0" + }, + { + "Q": "\nAt 2:39 isn't -2*8 equals -16?", + "A": "-2*8 is -16 but he added the -2, making it -18", + "video_name": "jlID_mIJXi4" + }, + { + "Q": "At 8:20 when x=1, why is that y is incremented by 'half' of dy/dx( 1.5 ) and not 1.5 itself?\n", + "A": "Because our \u00ce\u0094x = 0.5, so we only advance half a unit. dy/dx = 1.5 means that an increment of 1 in x would carry an increment of 1.5 in y, but since we are only incrementing x by 0.5, we only increment y by 0.75.", + "video_name": "q87L9R9v274" + }, + { + "Q": "\nAt 8:29, how did Sal get y=2.5 when x=1? I thought it would be 1+(1.5*.5)", + "A": "Sal got y=2.25 when x=1. 1.5 + (1.5*.5) =2.25", + "video_name": "q87L9R9v274" + }, + { + "Q": "\nat 3:35, how does he know that it's x squared and not anything else", + "A": "Okay, well he knows that he has to find the greatest common factor (GCF) among x^2, x^3, and x^4. So what terms can he evenly divide each of the above terms by, so that there is no remainder? First of all, there s x. Another option would be x-squared (x^2). x^2 divided by x^2 = 1 x^3 divided by x^2 = x x^4 divided by x^2 = x^2 But nothing larger than x^2 can fit evenly into x-squared. The only options are x and x^2. x^2 is the GREATEST, so that is what he will use to factor out of all the numbers.", + "video_name": "tYknkDjp-bQ" + }, + { + "Q": "At 1:50 why bother multiplying by 1/2? You could have multiplied the right by 2; it wouldn't have been easier than adding the extra step?\n", + "A": "They are not a bother. Both ways are correct.", + "video_name": "STcsaKuW-24" + }, + { + "Q": "At 1:06, why wouldn't it be 30^2 instead of 30 since they directions tell you that area equals 30in^2?\n", + "A": "in^2 is a term for telling you the area of something. That is virtually all it is, just like you would use My room has 50 feet of flooring you could easily say My room s floor is 50 ft^2 and it would mean the same thing. You only have to worry about the in^2 thing when you get into physics and such. I hope that helps!", + "video_name": "STcsaKuW-24" + }, + { + "Q": "This question has been asked before, I think but it hasn't been answered yet so I'll just bring it up again. At 3:42 Sal mentions that he'll explain why he's picking the numbers he's picking. My question is that could you have made the height of the rectangle any fraction with the tau in the denominator as long as the limit to it went to infinity? Are we trying to force the area to 1 perhaps?\n", + "A": "Yes, we are trying to get the area to be 1, so that it will approach the dirac delta function as \u00cf\u0084 approaches 0.", + "video_name": "4qfdCwys2ew" + }, + { + "Q": "\nwhat is an abaquabapattern 2:05", + "A": "It s abacaba or abacabadabacaba. You can learn about it in Vi s other video, Fractal Fractions. Hope this helps :)", + "video_name": "pjrI91J6jOw" + }, + { + "Q": "\nAt 3:54, it shows the egg with the whites still surrounding the yolk. How did she get it to stay together instead of all smushing around? Did she leave it inside of the shells? If so, then how do you eat it?", + "A": "They were hard-boiled and peeled.", + "video_name": "pjrI91J6jOw" + }, + { + "Q": "At 3:07, when she sows the turkey to hold everything, I wondered if she was actually going to eat that, considering the fact that there is now string somewhere in there. Or will she just take the string out when she gets to it?\n", + "A": "She probably took the string out once it was cooked.", + "video_name": "pjrI91J6jOw" + }, + { + "Q": "\nI am extremely confused as to how he got s=1.04 at time 1:52... He says that s=sqrt(sum(x-xbar)^2/(n-1)), however, when I do this, I get s=2.8074. I've tried looking at other sites and they say the same thing about the formula that I wrote above. I've used the formula many times, and I still don't understand how he gets 1.04. Any help?", + "A": "I m getting 1.04 the same as Sal. In Excel it would be: =SQRT(((1.5-2.34)^2+(2.9-2.34)^2+(0.9-2.34)^2+(3.9-2.34)^2+(3.2-2.34)^2+(2.1-2.34)^2+(1.9-2.34)^2)/6) and this gives you 1.042209", + "video_name": "K4KDLWENXm0" + }, + { + "Q": "\n@3:32 why are we movie 1 step toward x and 7 towards y?? or 1 step back towards negative x and 7 steps towards positive y??", + "A": "There are 2 different ways to write the slope 7, you can just say 7, or you can say 7/1 because they are the same thing, so when you move 7 up you move 1 to the right, the reason you can move 1 to the left and 7 down is because the line will be in the same spot either way.", + "video_name": "MxiqyE2uMCo" + }, + { + "Q": "\nAt 5:19, he says ' x - -3, is the same thing as x + 3, I don't understand... I always have problems trying to simplify the point-slope form...", + "A": "First you must understand that the opposite of the opposite of 3 is 3. Think of it this way: First you find the opposite of 3 (-3) and then find the opposite of that (3). I hope that answers your question.", + "video_name": "-6Fu2T_RSGM" + }, + { + "Q": "Do you have to do what Sal does at about 7:39? He simplified the fraction. Is this necessary?\n", + "A": "Doesn t seem necessary", + "video_name": "-6Fu2T_RSGM" + }, + { + "Q": "At 0:08 what does the line over the letter stand 4?\n", + "A": "That line indicates that you are talking about a segment defined by the points A and B. Those are the two ends of the line you are talking about. You may also see other similar forms of notation, like a small triangle next to the letters ABC describing triangle ABC, or something that looks like a small angle next to some letters indicating that the angle is defined by whatever is after it, like XYZ.", + "video_name": "bJF9R8_-0O0" + }, + { + "Q": "At 1:12, why is the derivative of sqrt(3)x^2/36 = root 3x/18? I tried using chain rule and quotient rule on that term and I ended up getting 4 root 3x as my final answer. Was there an easier way to do that, or a correct way rather?\n", + "A": "No need for the chain rule or the quotient rule here. All you have is x^2 times a constant (which happens to be sqrt(3)/36). The derivative of x^2 is 2x, and you multiply that by the constant to get the result indicated.", + "video_name": "eS-_ZFzHjYA" + }, + { + "Q": "\nStarting at 1:05, why did you just divide by 2 to get the derivative?", + "A": "There s 2 things going on here. First, to get from sqrt(3)x/36 to sqrt(3)x/18, you multiply by 2, not divide. He does this due to the Power Rule for derivatives. Suppose that you have a function a*x^n, where a and n are both constants. The derivative of this function is (a*n)*x^(n-1). You multiply the constant by the exponent and then reduce the exponent by 1. As you see in the video, we go from having an x^2 to an x^1. There s a video on this website that describes this rule in more detail.", + "video_name": "eS-_ZFzHjYA" + }, + { + "Q": "At 3:42, the second missing number that you were explaining with the help of the number line.\nI am someone who gets very confused with Math, and the second 'number line' explanation, got me very confused. Rather I'd like to get this clarified.\nWhen trying to find a missing number i.e. ___ -(-2) = -7, as mentioned above. If minus of (minus some number) is nothing but a positive number, can we start with +2 on the number line and find out how much is needed to get to -7?\n", + "A": "Yes, -(-2) becomes +2 and you can start with +2 on the number line to get to -7. Hopefully, I didn t confuse you any further.", + "video_name": "KNGa11O2uLE" + }, + { + "Q": "what is si in 0:25 and deta in 2:04\n", + "A": "Psi and theta are Greek letters. Greek letters are often used to denote angles.", + "video_name": "MyzGVbCHh5M" + }, + { + "Q": "\nAt 0:25, is there a special meaning si has? Oh, and theta too. (2:01.)", + "A": "psi and theta are just like using x in algebra they are just variables", + "video_name": "MyzGVbCHh5M" + }, + { + "Q": "how does sal gets 1/2 at 5:50 - 5:56\n", + "A": "He divided both sides of the equation by 2. i.e. if 2 pens are worth 1 dollar, then 1 pen is worth 1/2 a dollar.", + "video_name": "MyzGVbCHh5M" + }, + { + "Q": "At 3:56, what does base angle mean?\n", + "A": "Let s back up for a second. Sal has a triangle with an unknown side (a chord) and two radii. Because the two radii are congruent, then we know the triangle is isosceles. A base angle in an isosceles triangle is one of the two angles formed by the base (non congruent side) and one congruent side. A vertex angle is the angle formed by the two congruent sides of the triangle, in this case two radii.", + "video_name": "MyzGVbCHh5M" + }, + { + "Q": "\nat 1: 40 ish what's an alternate interior angle it means whats in alternate interior angle it said it at around 1:40 in the video", + "A": "An Alternate interior angle are angles that are on opposite sides of the transversal, and are between the lines cut by the ttransversal", + "video_name": "LhrGS4-Dd9I" + }, + { + "Q": "\nWhy do we have to go down by one and a half ?\nduring 3:45", + "A": "To make a right triangle between point N and the line of reflection", + "video_name": "kj3ZfOQGKdE" + }, + { + "Q": "At about 1:40 Sal shows that you can multiply the numerator by the reciprocal (8 x 36/8, or simplified which is 8 x 9/2) to get the denominator. But why? I mean how does he know he can do that? Where does this idea come from? I feel like there's something that I am missing here.\n", + "A": "they have top find out what to multiply the next ratio by so you flip the numerator and the denominator (pardon my spelling) which you can sliplify to 9/2 . WHich means you multiply thenext ratio by 9 over 2 that is how they know this.", + "video_name": "GO5ajwbFqVQ" + }, + { + "Q": "\nCouldn't Sal have just converted 5/4 into 1.25 instead of going through all the motions at 0:60?", + "A": "I like the other ways because it gives me more than one POV and more ways to solve it.", + "video_name": "GO5ajwbFqVQ" + }, + { + "Q": "\nI'm doing proportions right now, and I'm trying the first method that he used at 0:25 , but when I use the method on the problem, 9/8 = 11/r, and I try to divide 11 by 9 to see what times 9 is equal to 11, I'm getting a repeating decimal! What should I do? Thanks.", + "A": "Thanks this is super helpful!", + "video_name": "GO5ajwbFqVQ" + }, + { + "Q": "At 4:55, I'm not sure where Sal gets the extra ten. Is it one of the two 10s left over from the beginning?\n", + "A": "He got an extra ten at that time because Sal rewrote 29.12 into 2.912. Since 29.12 equals 2.912 x 10.", + "video_name": "xxAFh-qHPPA" + }, + { + "Q": "at 1:23, he said the oval had no sides, but doesnt it have 1?\n", + "A": "it has infinite tangents, but no sides, just like a circle.", + "video_name": "8xbIS2UkQxI" + }, + { + "Q": "\nAt the end of the video he messed up. It was around 3:34. It confused me", + "A": "he said so all the side are not the same length when ther are 2 small and 2 long sides", + "video_name": "8xbIS2UkQxI" + }, + { + "Q": "\nCan a circle or an oval be considered to have 1 side? At 1:32 Sal said, \"Or at least the way that I am thinking about it.\" It makes me wonder if there is a rule about this.", + "A": "no because it must have a starting and ending point to be a side but if we flatten the perimete of the circle (for example put a thread around a circle then measure the length ) to be a side then that s what we call a circumference", + "video_name": "8xbIS2UkQxI" + }, + { + "Q": "What does Sal mean when he says \"we can take the scalar out\" at 2:49? What does a scalar mean in this case? Thank you!\n", + "A": "coefficient on the h", + "video_name": "t4GfuftHH5c" + }, + { + "Q": "Am I the only one who was blown away at how quickly Sal calculated the height of the container in his head at 12:22 when he said, \"5 divided by 1.65 squared ... is going to be roughly a little under 2 meters tall\" ? (actual answer is h=1.84 meters). Once again, Sal is AMAZING !\n", + "A": "It was kind of easy to estimate that. 5/(1.65)^2 is approximately 5/(2)^2. 5/(2)^2=5/4=1.25 Since we made the denominator bigger, our answer is smaller than the actual, so it was probably more around (1.75, 2). This wasn t meant to insult or downgrade Sal s awesomeness, though. smile", + "video_name": "tSMuKcN-RKM" + }, + { + "Q": "At 3:47 can someone explain why he set the radian measurement sin(theta+pi/2) as the y coordinate?\n", + "A": "He s comparing cos(theta) with sin(theta+pi/2). For example, what s sin(pi/6)? What s cos(pi/6+pi/2)?", + "video_name": "h-TPSylHrvE" + }, + { + "Q": "does anyone else sees a realistic calculator at 3:43 to 4:27?\n", + "A": "No I think that you are the only one.", + "video_name": "ZElOxG7_m3c" + }, + { + "Q": "\nstarting at 0:17 seconds within the video....\n\nThere are situations where two sides are known but there are no labels for which side is side a or b or c. Should I always assume the largest-looking side is side c?", + "A": "The side that says a = ? is the A side, the side that says b = 12 is the B side, and the side that says c = 9 is the C side. If you are trying to solve a side on a triangle that is not labeled for use of the law of cosines, then A is automatically the side you are trying to solve, and B and C are the other sides. It doesn t matter which side is B and which side is C, as they are interchangeable. I hope this helps!", + "video_name": "ZElOxG7_m3c" + }, + { + "Q": "At 7:25, he says \"X sub i-1.\" What does \"sub\" mean?\n", + "A": "Sub just means that it is in the subscript, the smaller text following the bottom half of the X.", + "video_name": "ViqrHGae7FA" + }, + { + "Q": "\nIn the Video at mark 2:36 I do not understand how it is true when f(x) when x=0 is equal to 0. wouldn't f(x) be equal to 0?", + "A": "No, he does not say that f(x) is equal to 0, when x=0. The question was, what is the limit as x--->0- (coming from the left of 0), which is 1. This is why he says it is true. lim x--->0- f(x) = 1 => True.", + "video_name": "_WOr9-_HbAM" + }, + { + "Q": "6:45 Sal's referring to HL (Hypotenuse-Leg) postulate right?\n", + "A": "He doesn t mention that at 6:45", + "video_name": "f8svAm237xM" + }, + { + "Q": "\nAt 0:45, Mr. Sal has gotten me confused.\nHe says \" twenty per hundred.\"\nTwenty WHAT?", + "A": "What he means when he said that: -cent means hundred . He was explaining what percent means per and cent = per and hundred. Get what I m saying? what s he s basically saying is twenty per-cent. Hope this cleared it up for you!", + "video_name": "Lvr2YsxG10o" + }, + { + "Q": "\nCouldn't you have substituted 180 = pi into -pi/3 at 2:39?", + "A": "Yes. And that is essentially what Sal did. He multiplied by 180 and divided by pi; thus, he cancelled out the pi, and put in a 180, so he basically just substituted it. But your way is a nice shortcut; so if you can do it that way in your head, feel free to.", + "video_name": "z0-1gBy1ykE" + }, + { + "Q": "At 3:09, why is the answer -60? I thought degree measurements could not be negative, like length measurements.\n", + "A": "Angle measurement can be negative. Starting on the positive x-axis, it is negative when you draw it clockwise, and positive when you draw it counter-clockwise.", + "video_name": "z0-1gBy1ykE" + }, + { + "Q": "\nFor the formula [Sn=a/(1-r)], the beginning value doesn't have to necessarily be k=1, for example at 5:02? Does that imply that any value for \"k\" can be used, such as starting at 2 or 1000?", + "A": "That formula only works for k=0 to infinity.", + "video_name": "2BgWWsypzLA" + }, + { + "Q": "\nAt 6:05, Sal said that the equation of a circle is x^2 + y^2 = r^2, but I remember in the previous lessons that the standard form is (x \u00e2\u0080\u0093 a)^2 + (y \u00e2\u0080\u0093 b)^2 = r^2. Can someone please clarify the differences?", + "A": "a and b (a,b) are used to determine the center of the circle. In the equation x^2 + y^2 = r^2, we have a and b equal to zero, so the center of the circle would be (0,0). If the equation of the circle were to be (x-3)^2 + (y-4)^2 = r^2, the center of the circle would be (3,4). So basically, the 2 equations that Sal gave mean the same thing, but the a and b are used to define the center of the circle. Comment if you have any further questions.", + "video_name": "lvAYFUIEpFI" + }, + { + "Q": "at 9:15 Sal says that. if we add 2 to any function then we shift it down by two. but in reality that is not true.\nwe should subtract 2 in function to shift it down.\n", + "A": "I would usually make the same mistake. You see, what helped me was writing the equation like this, for the standard form: (x-(h))^2/a^2 + (y-(k))^2/b^2.... So if either h or k is negative, it would then be a double negative, which in turn makes it positive, like so: (x-(-h))/a^2 + (y-(-k))/b^2=1 or: (x+h)^2/a^2 + (y+k)^2/b^2. Really hope this helps you like it did me!!", + "video_name": "lvAYFUIEpFI" + }, + { + "Q": "So when Sal says at 1:49 that the area is 1/2 b\u00c2\u00b7h it is the answer of b\u00c2\u00b7h cut in half?\n", + "A": "You can think of it as half of a rectangle", + "video_name": "YTRimTJ5nX4" + }, + { + "Q": "At 2:40, you begin to explain that you want to change dy / dx = 1 / cos y into something in terms of x by using the Pythagorean Identity and setting that (the Pythagorean Identity) equal to cos y . Could you just have inserted your original definition of y (y = sin^-1 x) instead? You would end up with:\n\ndy / dx = 1 / (cos (sin^-1 x)).\n\nDoes that work ? tried it with a few arbitrary numbers for x and was getting the same answer for both equations, but wasn't sure if it technically was correct.\n", + "A": "Yes. If you want to visualize, try to type cos(arcsin(x)) and sqrt(1-x^2) into Google or is cos(arcsin(x)) equal to sqrt(1-x^2) into WolframAlpha.", + "video_name": "yIQUhXa-n-M" + }, + { + "Q": "I'm confused...\n\n1) In the last 2 videos \"Proof: product of rational & irrational is irrational\" and \"Proof: sum of rational and irrational is irrational\" state in the title that the sum or product of rational and irrational is irrational.\n\n2) BUT, @5:31 in this video Sal says, \"You don't know whether the product is going to be rational or irrational unless someone tells you the specific numbers\".\n\nSo which is correct, 1 or 2?\n", + "A": "There is no conflict. The last 2 videos were about sum/products of a rational and an irrational number. At 5:31, Sal is talking about the product of 2 irrational numbers. So, this is a whole different scenario. Hope this helps.", + "video_name": "16-GZWi66CI" + }, + { + "Q": "\nI don' understand what happened at 6:57 - 7:42. I tried to follow by reading what you said, and I couldn't follow", + "A": "He said: -2+2*1=0, 4+2(-2)=0, and -10+2(5)=0. This came from the row operation: 2R2+R3 replace R3.", + "video_name": "L0CmbneYETs" + }, + { + "Q": "\nAt 4:21, why is Khan allowed to subtract the second row from the first row and put it in the second row? I thought he could only do that vice versa: subtracting first row from the second row and making that the new second row.", + "A": "I agree with you and I do it the way you thought is correct, because it s less confusing for me; however: Both operations are equivalent, because if you multiply both sides of row 1 - row 2 by -1, you get row 2 - row 1 (try it), and these are just scalar multiples of each other. a-c = b-d <=> c-a = d-b", + "video_name": "L0CmbneYETs" + }, + { + "Q": "Where did Sal get x2 = 0 1 0 and x4= 0 0 1 at 14:30?\n", + "A": "I m still a little confused about this also. As far as I can tell the solution is correct with or without x2 and x4 components.", + "video_name": "L0CmbneYETs" + }, + { + "Q": "At 2:58, Sal mentions \"previous videos where I was trying to figure out whether things were linearly independent or not.\" Where are these videos?\n", + "A": "Videos about linear independence within, I suspect, the linear algebra subjects.", + "video_name": "L0CmbneYETs" + }, + { + "Q": "What determines the row you will use to minus with another row to replace a particular row? for example at 3:00 you replaced row 1 with (1st row - 2nd row)...why didn't you use the (3rd row - 2 times 1st row)? since it will still give you the same answer...?\n", + "A": "You can replace any row with: 1) its multiple 2) its difference from any other row or from any multiple of a row.", + "video_name": "L0CmbneYETs" + }, + { + "Q": "\nWhy did Sal say 1 minus minus 1 at 4:37?", + "A": "It s just another way of saying 1 minus negative 1. Or 1 - (-1). He s subtracting row 2 from row 1. The 4th column in row 1 is 1, the 4th column in row to is -1. So 1 - (-1) = 2.", + "video_name": "L0CmbneYETs" + }, + { + "Q": "At 11:16, can't you solve for the free variables if you switch the order of the variables and make them your pivot variables by changing how you change the matrix?\n", + "A": "If you use the matrix method in this video, you have to swap entire column vectors (but not the last, constant one) with each other. It seems to me that then the equations are the same, and the variables remain in their own columns, and the result should be equivalent, but as you suggest expressed as x2 and x4 in terms of x1 and x3. I put the column vectors in the order x2, x4, x1, x3 , and got: x2 = 19/4 - (x1)/2 - 3(x3)/4, x4 = -5/2 + (x3)/2. What do you get?", + "video_name": "L0CmbneYETs" + }, + { + "Q": "\nAt 2:25, why is the exponent on 7 zero? Wouldn't it be one? I know that everything to the first power is just itself, but why does that x^0 have to go there instead of 7^1?", + "A": "He writes it to show you that there is an x with a degree on the 7, even though we usually don t write it.", + "video_name": "REiDXCN0lGU" + }, + { + "Q": "\nAround the 1:45 mark, it's mentioned that the 7 is a coefficient of the x^0. I've always understood that the lonely number at the end is a constant, not a coefficient. Which is it and why?", + "A": "x^0 = 1 and anything multiplied by 1 is itself. Therefore, it s perfectly logical to say that the constant is the coefficient of x^0 power. It helps in solving certain problems as you go further in your mathematical career. For now, you should just understand the logic behind it and why it makes sense.", + "video_name": "REiDXCN0lGU" + }, + { + "Q": "At 1:05, can we say that the exponent on x always counts as part of x, and has nothing to do with the coefficient?\n", + "A": "Yes, exactly.", + "video_name": "REiDXCN0lGU" + }, + { + "Q": "at 2:56 he adds an h(y). I don't understand his explanation\n", + "A": "If you were taking the indefinite anti-derivative of some function, you would add a +C on the end, to account for any constants that may have been lost. In this case, we took the indefinite anti-derivative of a partial function. So we add the h(y) on the end to account for any function of y that may have been lost. If you think about it backwards, if you took the partial derivative of Psi with respect to x, the function of y goes to zero.", + "video_name": "eu_GFuU7tLI" + }, + { + "Q": "At 0:56, I'm confused about the form. Some places I see have the from M(x,y)dx + N(x,y)dy = 0, while others (I have the same textbook as Khan) have the form like he has it, M(x,y) +N(x,y)dy/dx. Anyone know which way is correct? I've been using the dx and dy at the end to figure out which function is M and which function is N too. How do you pick your Ms and Ns without it?\n", + "A": "M(x,y)dx + N(x,y)dy = 0 divide by dx, and you get: M(x,y) +N(x,y)dy/dx = 0.", + "video_name": "eu_GFuU7tLI" + }, + { + "Q": "\nHow can you understand this at 6:38 with out more help?", + "A": "i am asuming you mean at 1:38 becasue the video is less than 2 minutes long. At that time he is placing the 4.1 on the number line and you would find 4 and then realise that youneed to go .1 positive (to the right) from that point.", + "video_name": "uC09taczvOo" + }, + { + "Q": "\nWhy do we want x and y values that give zero in perfect squares? #3:35\nThanks for help.", + "A": "Technically, we could have the x and y values be anything, and that would probably give us a random point along the circle we graph. However, the zeroes of a graph are generally a good place to start as they tend to be easier to find than any other point.", + "video_name": "XyDMsotfJhE" + }, + { + "Q": "At 1:00, Sal says that it has to be plus y squared minus 4y, but isn't the y squared a minus?\n", + "A": "The original problem has a + y^2. It s only when Sal circles it that the upstroke on the + disappears so that it looks like it s a minus sign.", + "video_name": "XyDMsotfJhE" + }, + { + "Q": "\n3:15, how did he know that it 6.5 equals to 3.5 and 3?", + "A": "Because, 3.5 plus 3 equals 6.5.", + "video_name": "loAA3TCNAvU" + }, + { + "Q": "\nAt 3:39,why sai said because of SAS so those triangles are similar?isn't SAS is for congruent?", + "A": "SAS applies both to similarity and congruence. In this case, Sal was using SAS to show similarity.", + "video_name": "Ly86lwq_2gc" + }, + { + "Q": "\nAt 5:47, why is it written as a square root, it makes no sense. is it representing a long line of decimals. Someone tell me if I'm having a stupid moment.", + "A": "The square root is used because it s more accurate and easier to write than a list of decimals.", + "video_name": "Ly86lwq_2gc" + }, + { + "Q": "At 0:57, what is mx?\n", + "A": "mx is the slope of the line, or the steepness (is that a word??)", + "video_name": "YBYu5aZPLeg" + }, + { + "Q": "\nAt 2:50 why is it x- -3 as oppose to just x-3?", + "A": "Because in the standard formula of a circle, it should be like the following: (x - h)^2 + (y - k)^2 = r^2 And the problem gives you (x + 3)........................................ Mr. Khan just likes to rewrite it in the subtraction like in the standard formula: (x - -3) Let me write this way, it be clearer to you: (x - (-3)). Now, you can see -3 is the x component of the center of the circle in the problem. For the y , you don t need to rewrite, because it is already in the format of subtraction (y - 4).", + "video_name": "JvDpYlyKkNU" + }, + { + "Q": "@ 09:02 he multiplies by 15 but shouldn't it be 15/64 ?\nI think he made a typo\n", + "A": "The 1/64 comes from flipping a fair coin (1/2 chance of heads or tails each time) 6 times, because (1/2)^6 = 1/64. At 9:02, he s talking about the unfair coin (4/5 chance of heads & 1/5 chance of tails each time,) so instead of (1/2)^6, he uses (4/5)^4 * (1/5)^2. That number (~1.64%) represents the chance of a particular permutation e.g. HTHHTH, but since we don t care about the order of the flips, he multiplies by 15 because there are 15 ways to arrange the 4 heads within the 6 flips.", + "video_name": "xw6utjoyMi4" + }, + { + "Q": "\nAt 5:22, he switches from \"-2cos2x\" to \"+4sin2x\". Where exactly did he get the \"4\" from?", + "A": "It came from the derivative of the inner function, 2x. d/dx -2 cos 2x = 2 * 2 sin 2x = 4 sin 2x", + "video_name": "BiVOC3WocXs" + }, + { + "Q": "\n@4:48 why is the right side of the numerator 4sin2x?\nwhy I use chain rule i get -4sin(2cos)?\n\nf'(x) = g'(x).h'(g(x))\nso\ng(x)= 2cos and h(x)=2x\n\nthen\n-2sin*2(2cos) is the same as -4sin(2cos)\n\nIf some replies, could you workout the steps.", + "A": "Hello excuse me for butting- I see what you ve done but could you explain this in more mathematical terms? Ideally Sal could explain this. I know how to use the chain rule but it seems the usage is different in this case. Maybe I m missing something about trigonometry? Chain Rule: f(x)=h[g(x)] -> f (x)=g (x) * h [g(x)] I am quite confused.", + "video_name": "BiVOC3WocXs" + }, + { + "Q": "\nat 5:37 are you allowed to cancel out the sin(x) to make it -2+4(2)/1 which is -2+8 which also equals 6 to find your answer?", + "A": "No, because they are not all sines of the same value. Two of them are sin(x) the other is sin(2x).", + "video_name": "BiVOC3WocXs" + }, + { + "Q": "Hi!\n\nAround 12:12, Sal starts transforming 0.5 to 5. Why can't we just leave the 0.5 as is, given that, once multiplied by 10 to the 17th power, we will get the same answer? I mean, isn't 0.5 times 10 to the 17th power just as correct as 5 times 10 to the 16th power?\n\nCheers!\n", + "A": "Scientific notation requires that the mantissa (the first bit!) is greater than or equal to 1, and less than 10. So if you put 0.5 x 10^17, that is not valid scientific notation because 0.5 is not greater than or equal to 1. You are correct that 0.5 x 10^17 is equal to 5 x 10^16, but one is valid scientific notation and the other is not.", + "video_name": "0Dd-y_apbRw" + }, + { + "Q": "At 12:00 I thought you had to multiply or divide equaly on both sides of the equation. Here you multiply on one side and divide on the other.\n", + "A": "He is making two changes to the same side of the equation. The only way that is legal is when the changes cancel each other.", + "video_name": "0Dd-y_apbRw" + }, + { + "Q": "At 2:27, at the top left says 10^-3. Since the number is getting larger due to the decimal moving to the right, why is the exponent a negative?\n", + "A": "0.00852 = 8.52* 10^(-3) the exponent -3 is negative because the number 8.52 is 1000 times larger than 0.00852 . The negative exponent -3 means you divide by 1000 and is equal to the multiplication with 1/1000 some examples: 8.52* 10^(-3) = 8.52 * 1/1000 = 8.52 / 1000 = 0.00852 hope this will help you", + "video_name": "0Dd-y_apbRw" + }, + { + "Q": "At at 6:14, why would x^2\u00c2\u00b72 = 4x? Wouldn't it be 2x^2?\n", + "A": "x^(2) * 2 is equal to 2x^(2). However, in this case we are also taking \u00e2\u0088\u0082/\u00e2\u0088\u0082x(x^(2) * 2) which is equal to 4x. \u00e2\u0088\u0082/\u00e2\u0088\u0082x(x^(2) * 2) = \u00e2\u0088\u0082/\u00e2\u0088\u0082x(2x^(2)) = 4x", + "video_name": "AXqhWeUEtQU" + }, + { + "Q": "at 1:41, how do you divide 1/6 by side and dividing both side also with 6 can someone explain.\n", + "A": "He says multiply both sides by 1/6, or another way you could think about it is we re dividing both sides by 6.", + "video_name": "u5dPUHjagSI" + }, + { + "Q": "At 1:53, how can we figure out what number to multiply by the equation? Every equation isnt this simple, Khan should do one easy equation and one really hard equation to show that its possible.\n", + "A": "multiplying everything by 1/6 is the same as dividing it all by 6. The equation was 6x-6y=24. 6 goes into all the numbers equally therefore we are able to divide it by 6. The end product is x-y=4", + "video_name": "u5dPUHjagSI" + }, + { + "Q": "\nAt 0:08 why was a dot there insted of a X?", + "A": "Because some people use dots for multiplication instead of an X!", + "video_name": "0WUXQNjdRvM" + }, + { + "Q": "At about 1:44 Sal said when we move to the tens place we put a zero under the quitiont. But can you also put an X?\n", + "A": "Yes. Both are correct and valid strategies. Some people use a 0 and some use an X, both are meant to help you not to mix up which column to put your current step s number in - otherwise known as a placeholder. I learned the 0 method, but if you re comfortable with X, or that s what your teacher/tutor/coach expects, then that s fine, too.", + "video_name": "0WUXQNjdRvM" + }, + { + "Q": "At 2:13 how can you just split the triangle into two right triangles? Are you allowed to do that for a equilateral triangle too?\n", + "A": "You can do it for any triangle. To do it, pick a side of the triangle. Obviously, we can draw perpendiculars to that side wherever we like. And surely one of those perpendiculars will go through the opposite vertex. This divides the triangle into two right triangles.", + "video_name": "pGaDcOMdw48" + }, + { + "Q": "\nAt 4:40, how does Sal know to solve for m (the magenta line) in terms of b and theta? For example, we can also say that tan theta = m/c, no?", + "A": "maybe because tan theta = m/d actually, and that would introduce another variable that he doesn t want. He wants to relate the existing variables to keep it simple. Also possibly because he knows sin and cos functions are complimentary and so hopes they will cancel or simplify easier down the track in the math..", + "video_name": "pGaDcOMdw48" + }, + { + "Q": "\nI was able to follow his process up until 6:24 when he wrote Csquared-2cbcos(theta). Where did he get that part of the equation from? To me it looked like he pulled it out of nowhere.", + "A": "He simply FOILed the (c-bcos(theta))^2, i.e. multipled out the (c-bcos(theta))^2, which is just (c-bcos(theta))(c-bcos(theta)). That multiples out to c^2-cbcos(theta)-cbcos(theta)+(bcos(theta))^2, and there are two -cbccos(theta), so it simplifies to c^2-2bcos(theta)+(bcos(theta)^2.", + "video_name": "pGaDcOMdw48" + }, + { + "Q": "What happens to the -1 = 15 at 8:37? He glances his cursor towards the direction -1=15 and utters the number 16 but he loses me at that point.\n", + "A": "He adds 1 to both sides, resulting in 16 for the right hand side, and then subtracts 8 from both sides, which yields 8 for the right hand side. He could have subtracted 1 from 8 for the left hand side and then subtracted 7 from both sides. Same result.", + "video_name": "A52fEdPn9lg" + }, + { + "Q": "\nWhy is it (x-2)^2? It should be 2(x-2)! If (x-2)^2=(x-2)(x-2). 2(x-2)=(x-2)+(x-2). (at 00:56):D", + "A": "(x-2)^2 = (x-2)*(x-2) = x^2-4x+4 what you wrote is: 2(x-2) = 2x-4 (x-2)+(x-2) = 2x-4 these are completely different polynomials from the one in the problem.", + "video_name": "A52fEdPn9lg" + }, + { + "Q": "\nconfused at 0:55 NEED HELP!", + "A": "If you re really having difficulty, please try to stay on topic (refrain from gratuitous woodchuck references in the future). Are you having trouble understanding why b -48 4\u00e2\u0080\u00a2y > -48 - 8 4\u00e2\u0080\u00a2y > -56 4\u00e2\u0080\u00a2y/4 > -56/4 y > -14", + "video_name": "d2cnQ5ahHgE" + }, + { + "Q": "\nAt 0:58 Sal talks about \"when x is 0, y is 3 - that's our y intercept\" and then talks about how the slope goes down from there. I've been following everything I can on geometry but I seemed to have missed exactly how these slopes work. Is there another unit I can look at that describes how the whole y = 3 - x thing works?", + "A": "I would suggest looking up equations of a line and slope-intercept form on the KA search bar.", + "video_name": "-nufZ41Kg5c" + }, + { + "Q": "Isn't the remainder 21 instead of 31 at 7:12?\n", + "A": "It is 31, 31 + 291 = 322", + "video_name": "omFelSZvaJc" + }, + { + "Q": "\nAt 6:55: isn't that shape an octagon instead of a decagon? Isn't Sal supposed to connect the far right purple line with the far right yellow line? (And do the same with the left?)", + "A": "It s just, if you drew a square with the top first and the bottom next, you wouldn t say you have a 6 sided figure.", + "video_name": "qG3HnRccrQU" + }, + { + "Q": "at 4:46 the hexagon looks like cone! : )\n", + "A": "Hexagons can be in any form as long as it has the right amount of sides and is connected", + "video_name": "qG3HnRccrQU" + }, + { + "Q": "where did the 4 come from in the s-4 @ 8:07?\n", + "A": "He states that the first 4 sides of the shapes will produce 2 triangles, then after the 4 sides, every side will add an additional triangle, So he adds two in the beginning (my two triangles) then the 5th side would add one (5-4), a 6th side would add two (6-4), etc. The s-4 just shows the first four sides creating the 2 triangles.", + "video_name": "qG3HnRccrQU" + }, + { + "Q": "At about 5:20 Sal says \"Mu of X\", this makes it sound like Mu is some function of X, which may or may not end up being true, he should be saying \"Mu times X\". Sal makes this mistake twice when verbalizing the equation.\n", + "A": "You are right, it s a slight mistake when verbalizing the equations.", + "video_name": "jJyRrIZ595c" + }, + { + "Q": "Why \"dv\" at 8:30?\n", + "A": "because you re summing very small bits of volume. (v for volume)", + "video_name": "XyiQ2dwJHXE" + }, + { + "Q": "At 6:46 Sal says -45/45 = 1. Is -45/45=-1?\n", + "A": "Listen more carefully to what he says. He says you divide 45/45 and you get 1 and you are left with -1 ... When you are doing operations, it is easier to think about the signs and numbers separate from each other and then combine them in the answer which is what he did", + "video_name": "O3jvUZ8wvZs" + }, + { + "Q": "At 6:20, why does Salman call X and B vectors?\n", + "A": "ya why does it call it that.... is it just to confuse us all", + "video_name": "EC2mgUZyzoA" + }, + { + "Q": "I don't understand why Khan wrote at 05:34 wrote 3*(7/16) after 55/16, would someone please explain it?\n", + "A": "Sal just converted the improper fraction 55/16 into the mixed number 3 plus 7/16 . If that process is confusing to you, try looking up the videos and exercise about improper fractions and mixed numbers.", + "video_name": "pPnxPrhf6Ww" + }, + { + "Q": "\nDid you (Khan) mean to say the median is the middle number at 6:24? It's hard to tell what you meant, because the mode is the same as the median: 3. But it seems odd to call the mode the middle number.", + "A": "Median is the middle number, and the mode is the most commonly occurring number. (Occurs the most in a data set) The mode can be the same as the median if the middle number is also the most commonly occurring number. Does this clear things up?", + "video_name": "pPnxPrhf6Ww" + }, + { + "Q": "in 3:20-4:05 in the video, why is 6 and 7 not with a decimal because 2 had a . which is the amount behind it so why not 6 or 7? Is there a reason for it or is it just because the number has only one dot?\n", + "A": "There isn t any decimal points, those dots are multiplication as a different symbol.", + "video_name": "pPnxPrhf6Ww" + }, + { + "Q": "\nWhy does he have to multiply from 1:04 to 1:36?", + "A": "at those points, multiple people ate the same number of fruit. so he was calculating each person s contribution to the arithmetic mean.", + "video_name": "pPnxPrhf6Ww" + }, + { + "Q": "At 1:01 how does he know whether to subtract or add the terms? Would you use the sign in front of or behind the term?\n", + "A": "Yes you use the sign in front of the term. In the example Sal uses 5x^2 + 2x^2 it results in 7x^2 however later in the question we get a +8x, -7x, +13x using the signs 8x-7x = x, x+13x = 14x hope that helps :)", + "video_name": "ahdKdxsTj8E" + }, + { + "Q": "At 0:41 he says that he would have to distribute the negative; what is the process/operation for doing that?\n", + "A": "Multiply the polynomial by -1. This is what he is talking about, I think. :)", + "video_name": "ahdKdxsTj8E" + }, + { + "Q": "\ndo yo know about the math error starting at about 1:11 in the video?", + "A": "There is no error at that point in the video. Sal briefly makes an error later on at about 1:28 when he writes 15x, but he quickly corrects it to 14x. Other than that, there are no errors in the video. What do you think is in error? Maybe I can help clarify.", + "video_name": "ahdKdxsTj8E" + }, + { + "Q": "\nAt 6:42, why did Sal put a negative sign for cosine but not sine, aren't the ratios the same?", + "A": "In the second and third quadrant, cosine values are always negative. When sine is being taken in the third and fourth quadrant, the sine values will be negative. Does this help?", + "video_name": "tzQ7arA917E" + }, + { + "Q": "At 2:43, you said, 'this angle right over here is theta'. I don't understand why, shouldn't it be negative theta? Thank you for the video anyway; it was really informative!\n", + "A": "It s going down, and it s below the x axis, but notice that it s still going counterclockwise, so it is positive. On the unit circle, the angle is not x or y in the xy plane. It s just stuck in there and goes around. It has its own relationships to x and y. It s not graphed in the xy plane like the circle is.", + "video_name": "tzQ7arA917E" + }, + { + "Q": "at 4:35 how can the angle in yellow be equal to cos(pie minus theta),sin( pie minus theta)\nand how can it be equal to sin of theta and cos of theta at 6:09\n", + "A": "Be careful. Sal isn t saying that the angle equals cos or sine. Sal is labelling the x and y co-ordinates for points where the terminal ray of the angle in question intersects the unit circle. So, for the yellow angle of ( \u00cf\u0080 - theta ), its x co-ordinate is cos ( \u00cf\u0080 - theta) and its x co-ordinate is sin ( \u00cf\u0080 - theta. Likewise for the green angle of theta. Its x co-ordinate is cos (theta) and its y co-ordinate is sin (theta).", + "video_name": "tzQ7arA917E" + }, + { + "Q": "\nAt 0:33 , a constant , '9' ,has been used .Can we use a variable for the value of 'c'\nEx: what will be the value of 'c' when using the quadratic equation to solve the equation\nx^2 - x - 12 = 0", + "A": "What exactly do you mean by a variable for c? In your example, a=1, b= - 1, and c= - 12. To use the quadratic formula, all of a, b, and c have to be numbers (a and b are coefficients, and c is the constant). c can equal 0 such as x^2 + 2x, but then it is easier to factor x(x+2) so solutions are 0 and -2 than it is to use the quadratic formula. No, none of a, b or c can be a variable.", + "video_name": "iulx0z1lz8M" + }, + { + "Q": "\nAt 4:00, hwy did he put + instead of - ? Was there a certain reason? Also, thanks for the video! :-) Oh, nevermind! XD", + "A": "with the \u00c2\u00b1 sign, the logical way of doing it is to do the + first since it is on top, then do the - second, but it really does not matter. \u00c2\u00b1 reads as plus or minus and is two separate operations", + "video_name": "iulx0z1lz8M" + }, + { + "Q": "at 2:01 i dont get it\n", + "A": "Simple division. 42/3 is 14", + "video_name": "DqeMQHomwAU" + }, + { + "Q": "From 0:56 to 1:40 you explain the whole process but, wouldn't it be easier if we just multiplied 14 times 3 and done?? Can someone respond to this because doing the whole process seems sorta like unnecessary in a way.\n", + "A": "The whole point of the video isn t just to intuit the entire process, but to break the process, and, as contrary as it seems, to analyse your intuition. That s why 0:50 to 1:40 exists.", + "video_name": "DqeMQHomwAU" + }, + { + "Q": "\nWhen Sal used the variables A (1:27-1:49) and X (3:39-4:19). Sal says that the two variables are the same. What if (for example) we had 3exp-3 * 2exp-3. Then would we multiply the base and then add the exponents?", + "A": "The rules for exponents only work if you have a common base. In your expression: 3^(-3) * 2^(-3) you have different bases (the 3 and 2). You can only add exponents if you are multiplying with a common base. Since the exponents match, you can do: (3*2)^(-3) = 6^(-3) This only works because the exponents match. If the exponents were different, you would be required to follow PEMDAS rules and complete the exponents before doing any multiplication. Hope this helps.", + "video_name": "CZ5ne_mX5_I" + }, + { + "Q": "\nWhy does the division problem at 2:40 become a multiplication problem when he's finished with it?", + "A": "12^(-5) can be converted to have a positive exponent if you use its reciprocal. 12^(-5) = 1/12^5 Divide: 12^(-7) / 1/12^5 = 12^(-7) * 12^5/1 Hope this helps.", + "video_name": "CZ5ne_mX5_I" + }, + { + "Q": "At 1:18 of the video why did Sal say that he figured out the sum of 35 and another number? He multiplied 7 by 5 to get part of the answer. Isn't the answer to a multiplication problem known as a product?\n", + "A": "Yes, however........ He multiplied 7 x 5 to get the product. Then 7 x 11 to get that product. Then he added the SUM of those products. 35+77", + "video_name": "xC-fQ0KEzsM" + }, + { + "Q": "For question 35 can't you use the side ratios for 30:60:90 triangles?\n", + "A": "yes, you can.", + "video_name": "BJSk1joCQsM" + }, + { + "Q": "At 0:55, what does it mean when it says 8 liters per fish?\n", + "A": "It is saying how many liters there are for one fish. They are trying to find the unit rate.", + "video_name": "jOZ98FDyl2E" + }, + { + "Q": "\nDid anyone notice that at 2:54 Sal accidentally put greatest on the middle number?", + "A": "Yeah, but the video explained for him", + "video_name": "jOZ98FDyl2E" + }, + { + "Q": "\nWhy (at 4:58) is (x-4)\u00c2\u00b2 \u00e2\u0089\u00a5 0?? Then why, when you multiply it by -3 is it \u00e2\u0089\u00a4 0? Am I missing something?", + "A": "Squares are always positive or equal to 0. Hence, (x-4)\u00c2\u00b2 \u00e2\u0089\u00a5 0. Yes, when you multiply by -3, it becomes \u00e2\u0089\u00a4 0 as +ve * -ve = -ve. But, there is also 0. Anything *0 = 0.", + "video_name": "IbI-l7mbKO4" + }, + { + "Q": "\nI don't get how he got 16 around 2:10", + "A": "You have to think about how to achieve a perfect square. In this case, he looked at the coefficient of the second term (-8), divided it by 2 (which equals -4), and then squared it to get 16. You can also double check afterwards to make sure you have correctly calculated a perfect square. Is (x-4)*(x-4) equal to x2 -8x +16? It is, so you re good to move forward with the next steps of simplification.", + "video_name": "IbI-l7mbKO4" + }, + { + "Q": "\nAt 2:09, Sal completes the square by adding and subtracting 16. Could he have also done this by adding 27 to both sides and finding the perfect square?", + "A": "Your thinking is correct, but your method is not as good. Since we are looking to get in vertex form, moving the 27 to the other side serves no purpose since we would have to move it back later on. However (this is what you are getting at), leaving the -27 outside of the perfect square is acceptable and how a lot of math thinkers would do it. The answer would end up the same.", + "video_name": "IbI-l7mbKO4" + }, + { + "Q": "\nAt 1:50 Sal has broken down the expression 2 * 4/3 to 1/3+1/3+1/3+1/3+1/3+1/3+1/3+1/3. I am learning the process of thinking of it in this way for more difficult problems?\n\nI can do the mental math to know that 2 * 4/3 = 8/3 = 2 2/3. What is the importance of the process of breaking it down to 1/3+1/3+1/3+1/3+1/3+1/3+1/3+1/3 that I am not understanding?", + "A": "yah me too i never thought of it as this way", + "video_name": "ZlhrXO1-osA" + }, + { + "Q": "there is a extra decimal at 0:01 the question has a extra decimal\n", + "A": "no,actually that is just the period at the end of the sentence . :)", + "video_name": "Eq4mVCd-yyo" + }, + { + "Q": "At 3:15 - How do you get y=0? Did you divide or multiply 5/2 ? Why?\n", + "A": "He got y=0 by substituting x=4 into our function rule. y=10-(5/2)x x=4. y=10-(5/2)(4) We multiply 4 by 5/2 because that s how our rule works. (5/2)(4)=10. y=10-10 10-10=0. y=0 I hope this explains what Sal did and why!", + "video_name": "86NwKBcOlow" + }, + { + "Q": "Why did he change the 4 to a 2 3:40\n", + "A": "I don t entirely understand your question, but at 3:40, he was simplifying his multiplication", + "video_name": "86NwKBcOlow" + }, + { + "Q": "\nlike at 3:16, those x in the table could be replace with numbers -2,-1, 0, 1, 2 in this kind of order can we solve this given equation? Our teacher said that we can only use this numbers to have a uniform answers in our problem.", + "A": "Linear equations have an infinite number of possible values for X. You can use any value of X to calculate Y and create a point on the line. Your teacher likely wants everyone finding the same points so there is consistency in the way the class is approaching the problem.", + "video_name": "86NwKBcOlow" + }, + { + "Q": "\nAt 1:08 could Sal have simplified y = 10 - 5/2x even more?\n\ny = 5- 5x (cross reducing the numerator 10 and the denominator 2)", + "A": "Cross cancelling only works when the fractions are being multiplied. In this case, the problem is subtracting not multiplication. So, you can t do it.", + "video_name": "86NwKBcOlow" + }, + { + "Q": "\nat 1:17 he takes 8 away from 9 and calls it 10/10 what dos that mean?", + "A": "10/10 is equal to 1 because 10 10 s is", + "video_name": "lDXaju6JoQ0" + }, + { + "Q": "\nin 0:40... he said nothingness... what does nothingness mean??", + "A": "Basically nothingness is the equivalent of the word nothing . Hope this helps!", + "video_name": "lDXaju6JoQ0" + }, + { + "Q": "\nAt 1:02 it says meth why would she say that?", + "A": "She said math, not meth. --Blue Leaf", + "video_name": "WkmPDOq2WfA" + }, + { + "Q": "At 1:23 how come 6 times 1/6 cancels?\n", + "A": "6 multiplied by 1/6 is the same thing as 6 divided by 6, which is equal to 1. You will learn how to do this in later classes. I hope this helps.", + "video_name": "CJyVct57-9s" + }, + { + "Q": "At 2:51, he says that there's no way to simplify that. Why doesn't he use mixed numbers like 12 1/4?\n", + "A": "In algebra, it is easier to use improper fractions.", + "video_name": "CJyVct57-9s" + }, + { + "Q": "\nHes making no sense when he wrote down the exponent why did he bring down the numbers? can u just right down (2x2x2)x(2x2x2x2x2)? then solve? but do you HAVE to put parenthese?at 0:37", + "A": "You can do it that way but that was just a simplified example. It may be as complex as 2^67 x 2^89. Exponents make it easier. The parenthesis is needed if the number is negatice or if you need to find the opposite of the answer ex: -(x)^2 or if multiplying with another exponent", + "video_name": "kITJ6qH7jS0" + }, + { + "Q": "At 1:58, why is it 2^8 and not 2^15?\n", + "A": "Because you add 3+5 and not multiply 3x5.", + "video_name": "kITJ6qH7jS0" + }, + { + "Q": "\nat 7:16 why does this work", + "A": "Because it is the rule ofcancellation. x^200/x^50 if you wrote all these x s out and then cancelled them out, you d be able the cancel off 50 from each from before being left with no more x s on the bottom. So you d be left with x^150 as 50x s from the top would leave 150 x s.", + "video_name": "kITJ6qH7jS0" + }, + { + "Q": "I don't understand at 8:08 how the 7^-5 can change into 7^5...?\nThanks!\n", + "A": "when you have a negative exponent in the denominator of the fraction you have to move the exponent and its base to the numerator and the exponent is now positive. If that doesn t help then try to watch a video on negative exponents. its complicated", + "video_name": "kITJ6qH7jS0" + }, + { + "Q": "At 6:11 he says 2^9/2^10 is the same as 2^9*1/2^10 . Could someone explain how this works?\n", + "A": "Anything times one is going to be that number. 9*1 = 9. 54*1 = 54. That means that 2^9*1 = 2^9, so you might as well not have the *1 there.", + "video_name": "kITJ6qH7jS0" + }, + { + "Q": "How in the world does he do that at 6:21 ?!!!?\n", + "A": "One of the earlier videos explains it, but i cant remember which one... 1/2^10 is the same as 2 to the 10th root, which can be written as 2^-10", + "video_name": "kITJ6qH7jS0" + }, + { + "Q": "\nAt 1:22 he says \"the easiest way to split this whole into tenths is to take each of those fifths and turn them into 2 tenths.\" What's the other way to do it? (Even if it's not the easiest.)", + "A": "Not really, because the only way to turn fifths to tenths is to multiply 5 by 2. Hope this helps!", + "video_name": "XHLgY7Z3cb8" + }, + { + "Q": "At the end of the video: 5:25 Sal says \"converges to zero\"\n\nWhat makes this epsilon proof valid?\n\nWould not we be forced to count all the possibilities to prove this to be right??\nAnd as there are infinitely many cases for epsilon it seems to be impossible.\n\nWhat is the axiom behind this limit proof or\nin what is this epsilon limit proof based on??\nCommon sense??\n", + "A": "Yeah, but as we know for example that infinity +1 = infinity, one could ask then that if epsilon is infinitesimally small, would not then |an-L|= roughly epsilon and not strictly smaller than (0, there IS a positive M such that if n>M then |a (sub)n-L|right triangles>special right triangles.", + "video_name": "UKQ65tiIQ6o" + }, + { + "Q": "At 5:48 , how does Sal know that the intersecting point is exactly at pi/4? You cannot just assume that since the intersecting point is in between two points, that it is located in the middle. Can someone please help clarify this for me. Thank you.\n", + "A": "You can get an exact result: sin(x) = cos(x) sin^2(x) + cos^2(x) = 1 sin^2(x) = 1 - cos^2(x) sin(x) = sqrt(1 - cos^2(x)) sqrt(1 - cos^2(x)) = cos(x) sqrt(1 - cos^2(x))^2 = cos^2(x) 1 - cos^2(x) = cos^2(x) 1 = 2\u00e2\u0080\u00a2cos^2(x) 1/2 = cos^2(x) sqrt(1/2) = cos(x) sqrt(1)/sqrt(2) = cos(x) sqrt(2)/2 = cos(x) arccos(sqrt(2)/2) = x pi/4 = x", + "video_name": "fp9DZYmiSC4" + }, + { + "Q": "At 5:17 Sal found that the graphs of y=sin(theta) and y=cos(theta) intersect at two points in the given interval. So couldn\u00e2\u0080\u0099t the answer to the question asked (which is 2) be given then and there without doing anything else?\n", + "A": "yes, the answer could have been found easily but he is trying to explain why it is", + "video_name": "fp9DZYmiSC4" + }, + { + "Q": "\nSo basically in the whole row I can make any changes which would be equivalent in standard equation? (At 1:25 is mentioned the addition)", + "A": "Yes, it s like solving a system of linear equations using the elimination method. Same operations.", + "video_name": "obts_JDS6_Q" + }, + { + "Q": "\nAt 0:08, why does Sal convert to an improper fraction, instead of just adding the 2/3 to the 8 1/3 to get 9. Wouldn't that be much easier? I just think it's a waste of time.", + "A": "becauseit s easier to multiply and divide with it, and he can convert at the end.", + "video_name": "y7QLay8wrW8" + }, + { + "Q": "At 2:10\nCould you add +12y to both sides and subtract 2 you would get\n12y > -27\n= y > -27/12\n= y > -9/4\n", + "A": "That is correct. You could certainly do it that way.", + "video_name": "y7QLay8wrW8" + }, + { + "Q": "\nAt 0:56, do you have to multiply by 3, or can you add 25/3 to both sides? Thanks!!", + "A": "If Sal had added 25/3 on both sides, he would still be left with a fraction (getting him no where, just moving the number) multiplying by 3 gets rid of the denominator of 3.", + "video_name": "y7QLay8wrW8" + }, + { + "Q": "\nat 1:38 Sal says '3 times negative 25 over 3 is just negative 25'. I don't remember it ever being -25. Did Sal just say it wrong, or I'm I missing something?", + "A": "The equation starts out with -25/3. The minus in front of the fraction makes that fraction negative. -25/3 *3/1 = -25 Hope this helps.", + "video_name": "y7QLay8wrW8" + }, + { + "Q": "can you explain it briefly? I couldn't understand from 2:31 to 4:04. pl. explain it again in a theoretical way.\n", + "A": "the third point is the right answer because the limit of f(x) when x approaches k from the negative direction = to the limit of f(x) when x approaches k from the positive direction.", + "video_name": "_bBAiZhfH_4" + }, + { + "Q": "\nTo make sure x=4 is a minimum value (at 4:22) can you also use the first derivative test and test around the point x=4?\nIf the derivative goes from decreasing to increasing at x=4 it would indicate a minimum at that point.", + "A": "Correct. I prefer your technique too.", + "video_name": "1TK8V_qmqrk" + }, + { + "Q": "Sal in 7:34 86-30=56,and you said it is 50.That does not make any sense\n", + "A": "Yes, he did, and you are correct, but if you continue to watch, you will realize that he catches his mistake.", + "video_name": "ko-cYG3d6ec" + }, + { + "Q": "\nAt 7:17, Sal said X=50' but probably meant X=56'.", + "A": "he fixed it around 7:20 there is a little note that pops up", + "video_name": "ko-cYG3d6ec" + }, + { + "Q": "\nAt 2:25 Sal mentions that factorial shows up in other topics of math. What might these other topics be?", + "A": "Some of the things where factorial comes up is really advanced math, but it does appear in what are known as Taylor Polynomials.", + "video_name": "HGoZfzz6dU0" + }, + { + "Q": "Can, at 1:30, this be done if the coefficient in front is a negative one? If not, would we just use long division?\n", + "A": "It can be done just negative will become positive and same procedure applies.", + "video_name": "1byR9UEQJN0" + }, + { + "Q": "\nAround 2:24 in the video u mentioned turning the 4 in the denominator in -4. So what if the number in the denominator is already negative. would you keep it or change it positive.", + "A": "If you had x-4 in the denominator, you use +4. The X and the minus are ignored. Hope this helps.", + "video_name": "1byR9UEQJN0" + }, + { + "Q": "\nAt 1:48, why did Sal add 9 to each number and then cross out the 9's?", + "A": "This is because 9-9 equals 0. Crossing it out is another way to show that it is 0.", + "video_name": "qzsR7cChujg" + }, + { + "Q": "at 5:24 why does vi wear the hilbert curve\n", + "A": "1. Because she SO rocks it. 2. I m not sure.", + "video_name": "ik2CZqsAw28" + }, + { + "Q": "\nIs there any design other than the one at 4:19 (The one that that person made?) Also, is Vi her real name, or is it Violet?", + "A": "There are uncountably infinitely many space-filling curves. Her name is Victoria. She prefers to be called Vi.", + "video_name": "ik2CZqsAw28" + }, + { + "Q": "At 1:26, when he divides -5 times the cubed root of y by -5, why can the fives cancel and you are left with the cubed root of y when -5 times the cubed root of y divided by five is equal to -5/-5 times the cubed root of y/-5?\n", + "A": "[ 1/(-5) ] * [ (-5)*cbrt(y) ] = [ [ 1/(-5) ] * (-5) ] * cbrt(y) (associative law) = 1*cbrt(y).", + "video_name": "b6WtwQddAcY" + }, + { + "Q": "At 2:43, the third and fourth probability terms are identical. Sal says the fourth term correctly but writes it incorrectly. Am I correct?\n", + "A": "just saw that myself. it has to be a typo/writo(so). it should read ttth, not ttht.", + "video_name": "8TIben0bJpU" + }, + { + "Q": "I'm confused at 1:15, because I thought that (4x^2)/5 was equivalent to 4/5 and (x^2)/5. However, Sal sets it up as 4/5x^2 where x^2 is not being divided by 5. Any reasons why this is so?\n", + "A": "It s the difference between addition and multiplication. (\u00f0\u009d\u0091\u008e + \u00f0\u009d\u0091\u008f) \u00e2\u0088\u0095 \u00f0\u009d\u0091\u0090 = \u00f0\u009d\u0091\u008e \u00e2\u0088\u0095 \u00f0\u009d\u0091\u0090 + \u00f0\u009d\u0091\u008f \u00e2\u0088\u0095 \u00f0\u009d\u0091\u0090 (\u00f0\u009d\u0091\u008e \u00e2\u0088\u0099 \u00f0\u009d\u0091\u008f) \u00e2\u0088\u0095 \u00f0\u009d\u0091\u0090 = (\u00f0\u009d\u0091\u008e \u00e2\u0088\u0095 \u00f0\u009d\u0091\u0090)\u00f0\u009d\u0091\u008f", + "video_name": "6nALFmvvgds" + }, + { + "Q": "\nAt 1:56, Sal writes that the limit of g(x) as x approaches 6 from the negative direction = \"not exist\". Is there an actual notation for it not existing? Maybe something like the zero with a slash through it would do it? A preemptive thanks to anyone who may have an answer to my question.", + "A": "it s kind of common to write DNE", + "video_name": "5f1-Rg3MmKs" + }, + { + "Q": "\nAt 0:58, what is a p/2-gon?", + "A": "She said that wrong. She meant 2p-gon....I think. I think this because if you have two of the same Polygons (as in p) and overlap them. you have twice as many sides as the first polygons", + "video_name": "CfJzrmS9UfY" + }, + { + "Q": "\nAt 4:24 how is -9 times 1 = -8. Doesn't he mean -9 + 1?", + "A": "He multiplied (10^1)*(10^-9). When you multiply numbers that are the same base to an exponent, you can add the exponents. Because of that, while he s multiplying 10^1 with 10^-9 to get 10^-8, he s adding 1 with -9 to get -8. I hope this helps!", + "video_name": "67jn5Zv-myg" + }, + { + "Q": "\nHi at 3:16 in the video he had the value (40.1534x10^-9) I was wondering why you cant simply move the decimal one to the left and add a -1 to the exponent. Is it because moving the decimal to the left and adding the negative exponent to the ten would change the true value of the numer by a tenth?", + "A": "He does move the decimal over and add a -1 to the exponent. First, he multiplied the numbers 1.45, 9.2 and 3.01. That s where he got the 40.1534. Then he multiplied the 10s. So then he had (40.1534x10^-9). Finally, he puts it into scientific notation in the way you described.", + "video_name": "67jn5Zv-myg" + }, + { + "Q": "\nAt 3:13, what does Sal mean when he says this:\n\"When arithmetic is a noun, we call it arithmetic. When arithmetic is an adjective like this, we call it arithmetic, arithmetic mean.\"\n?", + "A": "He is telling you how to pronounce the word, arithmetic, as in an arithmetic mean. Listen carefully to how he says the two words differently. The word has two different pronounciations, depending on their meaning. He puts the emphasis on a different syllable so that we know which way he is using the word.", + "video_name": "h8EYEJ32oQ8" + }, + { + "Q": "At 5:40, Sal says you have to repeat the one since it is repeated. Why? Why can't you just put one 1?\n", + "A": "In the example that Khan is doing, the numbers are 431617. There are two ones in this sequence so the first 1 is repeated. If I was trying to find the average of 58972, I wouldn t have to repeat any number because every number in that sequence was different. Hope this helps!", + "video_name": "h8EYEJ32oQ8" + }, + { + "Q": "\nat 7:55pm est...what is the shape, center, and mean in statistics?", + "A": "It is the number that is the answer when 2-3 or more are put together in an equation?", + "video_name": "h8EYEJ32oQ8" + }, + { + "Q": "At 2:11 I don't get how you move the x+1 over to the numerator. What happens to the denominator? Does the numerator become x+2 times x+1? Thanks.\n", + "A": "how do you know which one the denominator is?", + "video_name": "9IUEk9fn2Vs" + }, + { + "Q": "At 4:58 why is it Kt and not K^2/2?\n", + "A": "It s because K is a constant and we re integrating *with respect to t - the dt bit in \u00e2\u0088\u00ab K dt If we were integrating with respect to (a variable) K, then we d have \u00e2\u0088\u00ab K dK and you d be right, the integral would be K\u00c2\u00b2/2", + "video_name": "IYFkXWlgC_w" + }, + { + "Q": "0:08 you said they skipped 7 and 8 why did they skip them are their no tricks for 7 or 8\n", + "A": "sorry I did t read below", + "video_name": "2G_Jr_XpnY4" + }, + { + "Q": "\nAt 3:19, why can we simply assume that cos(theta) is positive?", + "A": "Sal has explained this in one of the past videos, we have assumed x=asin(theta) and we have no problem with that, now based on this assumption sin(theta)=x/a now apply the arcsine function, theta= arcsine(x/a), the range of arcsine function is (-pi/2, pi/2) therefore based on our first assumption theta is between -pi/2 and pi/2, in this domain cos function has a positive value, thus cos(theta) is always positive, hope this helped", + "video_name": "nMrJ6nbOQhQ" + }, + { + "Q": "at 2:42 in the video, he is able to rule out cos and pick sin because he says one of them evaluates to 0. What does that mean, its very confusing.\n", + "A": "sin(kx) = 0 if x is 0. cos(kx) = 1 if x is 0. So where the function crosses the y-axis, the function will be at the midline for sine and the maximum for cosine. Since it s at the midline, we can eliminate cosine.", + "video_name": "yHo0CcDVHsk" + }, + { + "Q": "At 0:17 what does Sal mean by when he says the midline and the amplitude are not just the plain vanilla function?\n", + "A": "In the plain versions of the sine and cosine functions, the midline would be at y = 0, and the amplitude would be 1. Since this is not the case in the given example, these considerations will come into play.", + "video_name": "yHo0CcDVHsk" + }, + { + "Q": "Sal begins explaining which function to choose @ about 2:00 .\nI'm still not sure why Cos(0) = 1 and Sin(0) = 0\nIs it because in the unit circle when an angle is 0 Cos = the x value, would still be one, but Sin = the y value which would be 0?\n", + "A": "That s exactly why, yes. For any angle you can refer to the unit circle definition of sine and cosine.", + "video_name": "yHo0CcDVHsk" + }, + { + "Q": "\nat 3:01 how is it 625 i am getting confused", + "A": "It s 625 because it s 5^4 (he says 5 x 5 x 5 x 5) 5 x 5 (5 squared) =25 25 x 5 (5 cubed) =125 125 x 5 (5^4) = 625", + "video_name": "XZRQhkii0h0" + }, + { + "Q": "\n2:03 , Is there a simple way to do exponents?", + "A": "Well, think of the exponent like this: the raised number is how many times you multiply the the other number. For example, 2 to the power of 3 is just 2x2x2.", + "video_name": "XZRQhkii0h0" + }, + { + "Q": "At 2:46 we multipy 25 times 5 then 5 again?\n", + "A": "YES!! It is 5 x 5 = 25 25 x 5 = 125 125 x 5 = 625", + "video_name": "XZRQhkii0h0" + }, + { + "Q": "at 7:12. when sal was copy pasting the diagram in the middle, what about the two right triangles sticking out. aren't those a part of the diagram too?\n", + "A": "Sal only used those triangles to show that the heights of the parallelograms are equal to \u00f0\u009d\u0091\u008e and \u00f0\u009d\u0091\u008f respectively, thereby showing that their respective areas are definitely equal to \u00f0\u009d\u0091\u008e\u00c2\u00b2 and \u00f0\u009d\u0091\u008f\u00c2\u00b2, which is of course imperative to the proof. After that the triangles can be discarded because they are no longer needed for the rest of the proof.", + "video_name": "rcBaqkGp7CA" + }, + { + "Q": "\nIn around 0:02, Sal mentions \"hypotenuse\". What douse that mean?", + "A": "also the equation being A squared + B squared = C squared", + "video_name": "rcBaqkGp7CA" + }, + { + "Q": "Why x-c at an approximate 6:30???\n", + "A": "Do you remember how a parabola f(x) = x^2 can be translated? f(x) = x^2 is a parabola opening up, centered at 0 . A new function g(x) = (x - 2)^2 is just like f(x) = x^2, just moved over 2 units to the right on the x-axis. The same idea can be applied to this video. Instead of approximating the function at 0 , we approximate the function at a new point x = c. Hope that helps.", + "video_name": "1LxhXqD3_CE" + }, + { + "Q": "\nSal Uses The F.O.I.L Method at 1:11 right? Just Making Sure!", + "A": "Yes! He is using the F.O.I.L Method!", + "video_name": "eF6zYNzlZKQ" + }, + { + "Q": "\ndoes it matter which variable is which number? for example, in 2:57, he says that a could equal 1, and b could equal 9. So, my question is, could he have said a=9 and b=1 and have the equation come out to be the same? (other than switching the values of a and b of course)", + "A": "Yes, he could have said it that way. The order of factors does not matter.", + "video_name": "eF6zYNzlZKQ" + }, + { + "Q": "3:11- can the the number be 5 and 5 instead of 1 and 9\n", + "A": "5 and 5 would not work because the numbers have to fit two things. They have to add to be 10 and they have to multiply to be 9. 5+5 = 10 is okay but 5*5 = 25 which is not 9. Notice that 1+9 = 10 okay; and 1*9 = 9 okay as well. Good luck with your factoring.", + "video_name": "eF6zYNzlZKQ" + }, + { + "Q": "At 15:10, why can't a * b be taken directly as (-1)(-72) ? Is that a wrong method?\n", + "A": "a and b also have to sum to -(-18) = 18. They don t, so they re wrong.", + "video_name": "eF6zYNzlZKQ" + }, + { + "Q": "is 2x the same thing as x squared? for example, around 1:30 when we use the foil method to do (x+a) (x+b) and we do x times x, does it become 2x or x squared?\n", + "A": "2x = x + x x^2 = x * x. So, you want x^2", + "video_name": "eF6zYNzlZKQ" + }, + { + "Q": "\nat 15:30 can't we do this without factoring out negative 1?", + "A": "Most likely, but factoring out the -1 is easy, and the tools we have for factoring are known to work on positive x-squared s. In the real world all behavior that is not specifically forbidden is allowed... in mathematics all that is not specifically allowed is forbidden. So I would first have to verify that the factoring procedure I was using was certain to work with negative leading coefficients.", + "video_name": "eF6zYNzlZKQ" + }, + { + "Q": "\nI have a question at 6:11 min in the video. I would like to know if the answers for x1 and x2 are negative or positive? I ask because I see that clearly they are -3 and -8 in the binomial answer (x-3)(x-8) but all the online Quadratic Equation Solvers show that the answers are positive numbers i.e. x1=3 and x2=8. thx", + "A": "They would be positive, because you want x-3 or x-8 to be equal to zero, so the right side is equal to zero. 3-3=0 and 8-8=0, so your answers would be positive.", + "video_name": "eF6zYNzlZKQ" + }, + { + "Q": "\nAt 0:45, where did you get the (x+a)(x+b) from?", + "A": "He was just showing you the general method, it wasn t directly part of the main problem.", + "video_name": "eF6zYNzlZKQ" + }, + { + "Q": "\nat 0:01 til 4:14 way do we need to emphasise this point in short way do i need this video !", + "A": "One real life situation that this is used for is exchanging money or making change. Because many people have not studied this idea, they get very nervous when exchanging money. They don t feel confident that Ten $20 bills is the same as Two $100 bills. Similarly they don t feel confident that 35 dimes is the same as 3 $1 bills and 10 nickles.", + "video_name": "3szFVS5p_7A" + }, + { + "Q": "At 8:05, Can anybody say please what means \"slope=6\"? What means that value?\n", + "A": "Slope is: (change in y)/(change in x) In linear notation: y = m\u00e2\u0080\u00a2x + b m is the slope derived from: (y(2) - y(1))/(x(2) - x(1)) b is the y intercept: b = y - m\u00e2\u0080\u00a2x Slope = 6 means that for every \u00c2\u00b11 in x, results in a \u00c2\u00b16 in y.", + "video_name": "IePCHjMeFkE" + }, + { + "Q": "\nHow did he get 6 delta x as part of the y coordinate at 4:13?", + "A": "He foiled the (3 + delta X)^2. 3 * 3 + 3 * delta X + delta X * 3 + delta X * delta X = 9 + 3deltaX + 3deltaX + deltaX^2 = 9 + 6deltaX + deltaX^2", + "video_name": "IePCHjMeFkE" + }, + { + "Q": "\nAt 6:33 how does it equal 6+deltax and not 6+deltax^2?", + "A": "Immediately before that point we ve determined that the slope is equal to (6\u00ce\u0094x + (\u00ce\u0094x)\u00c2\u00b2)/\u00ce\u0094x. Divide 6\u00ce\u0094x by \u00ce\u0094x to get 6 and divide (\u00ce\u0094x)\u00c2\u00b2 by \u00ce\u0094x to get \u00ce\u0094x.", + "video_name": "IePCHjMeFkE" + }, + { + "Q": "1:58 You can solve the quadratic equation without using the quadratic formula like this:\n4r^2 - 8t + 3 = 0 |Divide by four:\nr^2 - (8/4)r + 3/4 = 0 |Multiply both numerator and denominator of 3/4 by four:\nr^2 - (8/4)r + 12/16 = 0 |Figure out two numbers a,b that satisfy a + b = -8 and ab = 12:\na = -2, b = -6 |Substitute a,b into (r + a/4) (r + b/4) = 0:\n(r - 2/4) (r - 6/4) = 0\n(r - 1/2) (r - 3/2) = 0\nr = 1/2 or r = 3/2\n", + "A": "It seems easier to just -> (2r - 1)(2r - 3)", + "video_name": "3uO_uPb9H8w" + }, + { + "Q": "\nAt 6:04 is multiplying only top equation right? It seems intuitive, but doesn't that affect the solution?", + "A": "No, that one of the most common ways to save a system of equations. Since you are multiplying the whole equation (both sides of the equal sign), you are not modifying the equation at all.", + "video_name": "3uO_uPb9H8w" + }, + { + "Q": "\nWhat is the \"a\" he is talking about in 5:00?", + "A": "Sal is just using a as an arbitrary critical point. It can mean any critical point, and it s analogous to using letters such as x or \u00ce\u00b2 to represent any given quantity.", + "video_name": "lFQ4kMcODzU" + }, + { + "Q": "\nIn 2:12 how did you change 5/5 into a whole?", + "A": "5/5 is equal to 1. (A whole) Imagine a pie cut into 5 pieces. If all five pieces are there, then the pie is whole.", + "video_name": "U44my48zgFE" + }, + { + "Q": "at (0:30), where did the 5t come from? I watched the last video and was it because the car is going 5 m/s?\n", + "A": "Yes. He is simply putting the base information from the previous video so that we can continue with the same problem.", + "video_name": "wToSIQJ2o_8" + }, + { + "Q": "\nI assume that at 4:34 he meant to say \"1.5\" rather than 1.25?", + "A": "Yeah, but I think he did it correctly, so...", + "video_name": "dEAk0BHBYCM" + }, + { + "Q": "\nAt 4:58, shouldn't Sal put a comma instead of a addition sign?", + "A": "Good question! The complex plane isn t the same as the usual x, y plane because you plot complex numbers on it like 3 + 4i (3 in the x direction and 4 in the imaginary direction) while on the x, y plane you plot an ordered pair like (4,5) (4 in the x direction and 5 in the y). So no there shouldn t be a comma because it is one complex number rather than two real numbers. A complex number has a real part and an imaginary part so you plot them separately on the complex plane. I hope that answers your question :)", + "video_name": "Efoeqb6tC88" + }, + { + "Q": "\nAt 3:07 Sal says that A, B, and D are non-collinear. I get that part. But how are they not coplanar? Or am I seeing this wrong? If A and B exist on all plains, shouldn't they be exist on the same plane as D?", + "A": "They are coplanar because any three non-collinear points create a plane, but they are not coplanar on plane S in the diagram.", + "video_name": "J2Qz-7ZWDAE" + }, + { + "Q": "\n1:47 What does sufficient mean?", + "A": "Sufficient = enough to fulfill one s needs. It s not sufficient (/it s not enough) to say that three points define a plane, because we also need the points to be non-collinear.", + "video_name": "J2Qz-7ZWDAE" + }, + { + "Q": "\nAt 0:18 sal said that the plane is something that is not curved goes off in every direction infinitely. He said that it is two dimensional and exists in three dimensions. How can it not have round edges if it goes off infinitely in every direction? Wouldn't it eventually become round, once it reaches infinity?", + "A": "Infinity does not have curves. The negative space the curves create are not everything and thus infinity is a square. Think of it like this: If you had a sandbox and wanted to cover all of it, and the sandbox went on forever, there would be no edge for curves to exist on.", + "video_name": "J2Qz-7ZWDAE" + }, + { + "Q": "\nAt about 1:05 Sal said lumber line\nWhen he meant to say number line", + "A": "Yes, Sal ( the man speaking in the video ) was meant to say number line.", + "video_name": "LpLnmuAyNWg" + }, + { + "Q": "At 0:17, the answer is 11! just kidding.... but isn't this basically a common sense video?\n", + "A": "Well, it s introducing you to the idea of adding variables to simple equations.", + "video_name": "P6_sK8hRWCA" + }, + { + "Q": "At 4:15, how did he make the expression -8 - 5a into the expression 8 + 5a, I don't understand how it is possible to do that, I thought that you can only make that kind of equation into -8 + (-5a)?\n", + "A": "He stated that he multiplies both sides of the equation by -1. so he changed the signs of all the terms on both sides of the equation which is valid", + "video_name": "adPgapI-h3g" + }, + { + "Q": "at 2:30, Khan said something called Algebraic Manipulations. What does that mean?\n", + "A": "Algebraic Manipulation. The key to solving simple algebraic equations containing a single unknown (e.g. x + 6 = 10) is to realize that the equation is an equality.", + "video_name": "2REbsY4-S70" + }, + { + "Q": "\nSo the angle with a smaller area can have more degrees as long as they equal 180? (as noted at 1:54 in parallel lines 2)", + "A": "no, I think he just had it backwards, he switched the 60 and 120, I think he meant to do it the other way around", + "video_name": "0eDwckZOffc" + }, + { + "Q": "at1:54 can you explain what in the world he's talking?\n", + "A": "He s saying that both of those angles are equal to 180 degrees. We already know one of them is 60, so to figure out what the other one is you just subtract 60 from 180. And that will leave you with 120. So that mystery angle is 120.", + "video_name": "0eDwckZOffc" + }, + { + "Q": "\nHow did you get those angles for 1:26 ? I'm confused", + "A": "He made up those angles.", + "video_name": "0eDwckZOffc" + }, + { + "Q": "at 2:30,sal said 3,6,12,24's pattern is*2,but itcould be+3,+6,+9,+12...\n", + "A": "I did changer the pattern", + "video_name": "l-6uEtTBH7g" + }, + { + "Q": "3:16, what if you put x instead of nothing for the -8x+8x? Will it still be right?\n", + "A": "No, that would be incorrect as -8 + 8 does not = 1; it equals zero. If you make -8x + 8x = x, the x has a coefficient of 1. Hope this helps.", + "video_name": "vN0aL-_vIKM" + }, + { + "Q": "\nAt around 2:30 Sal says that he used the commutative property of 'addition and subtraction' to change the order, but is there even a 'commutative property of subtraction'? (I understand that one use the commutative property of addition to add both positive and negative numbers in any order).", + "A": "That is what he meant. Treat subtraction as the addition of a negative and it becomes commutative. a - b = a + (-b) = -b + a", + "video_name": "vN0aL-_vIKM" + }, + { + "Q": "At 2:52, when Sal was subtracting the terms, does it mean the term without the numerical coefficient is equal to one?\n", + "A": "The term of -x^2 has a coefficient of -1. Whenever the coefficient is not shown, it s understood to be 1 or -1, depending on its sign.", + "video_name": "vN0aL-_vIKM" + }, + { + "Q": "may someone explain to me what he is starting to do at 0:30 in the video. do I have to do that simplifying in all my problems.\nthanks in advanced.\n", + "A": "thanks again that helped", + "video_name": "vN0aL-_vIKM" + }, + { + "Q": "\nAt 1:47 how did you know the slope equaled 1?", + "A": "When Rise=Run (delta x = delta y), The slope is one", + "video_name": "EQoNfxToez0" + }, + { + "Q": "How did you get Negative 4 at 3:22? You are not starting from 0 you are starting from 1 to go down. wouldn't it be -5?\n", + "A": "Yes, the distance is -5, as Sal goes on to say. The confusion arises because in finding that distance, Sal subtracted the y-values, the first y-value being at -4, the second point lying at +1, So that subtraction gave him ( -4 ) - ( +1 ) = -5.", + "video_name": "iX5UgArMyiI" + }, + { + "Q": "at 7:42 I do not understand why it is our lower bound sqrt of y, from were we concluded that that's the funtion of our curved? thanks\n", + "A": "The curved shape that we are integrating at that moment of the video is bounded by x = 1 on the upper end and by the curve formed by y = x\u00c2\u00b2 at the lower end. As Sal says, we don t know what point we would chose, so we need a value of x . We need to put the bounds in terms of x so the next step is to find the inverse of y = x\u00c2\u00b2 . We can do that by taking the square root of both side of y = x\u00c2\u00b2 which gives \u00e2\u0088\u009ay = x", + "video_name": "hrIPO8mQqtw" + }, + { + "Q": "At 1:57, doesn't 5/2 = 2.5 instead of 2.4?\n", + "A": "Yes, well caught.", + "video_name": "LoKEPEPaNm4" + }, + { + "Q": "\nFor the second triangle at 2:30, when he writes that the two base angles are 3x+5 and x+6, does that mean that 3x+5 is equal to x+6, therefore x= 0.5?", + "A": "When he calculates the second triangle at 3:30, he writes that the base angles are 3x+5 and x+16. This means the value of x = 11/2, or 5.5: 3x+5 = x+16 2x+5 = 16 2x = 11 x = 11/2", + "video_name": "ceDV0QBpcMA" + }, + { + "Q": "\nAt 1:51, I still don't understand how you're able to express the integral in terms of \"n\" or \"m\"... could someone explain/refer me to a link? Otherwise, if I were to do practice problems where I convert the improper integral into a definite integral, I'll only have a slight idea of how to do so.", + "A": "A definite integral from a to b measures the area under a curve from x = a to x = b. If we have an indefinite integral, say from 0 to infinity, we are saying a = 0 and trying to figure out what the area is when b gets VERY LARGE. So in the context of the video, in the red integral he is setting the upper bound of the integral as a variable m, so we are measuring the area under the curve from 0 to m, and taking the limit as m goes to infinity to see what happens when the upper bound becomes infinitely large.", + "video_name": "9JX2s90_RNQ" + }, + { + "Q": "At 03:28: What is the archtangent?\n", + "A": "It s the inverse of the tangent function. For example, tangent(Pi/4 + kPi) = 1. So arctangent(1)=Pi/4 + kPi. Where k is a whole number.", + "video_name": "9JX2s90_RNQ" + }, + { + "Q": "Near 2:52 7/9 does not equal 2/9 + 3/9 x 2/9\n", + "A": "The second sign is an addition sign. You were mistaken. 2/9 + 3/9 + 2/9 = 7/9.", + "video_name": "_E9fG8BYcBo" + }, + { + "Q": "at 8:03, why substitute t=b\u0002a?\n", + "A": "So that by 11:06 we would have a form similar to that we were looking for in the first place. Remember that the inequality was valid for any t, so Sal used one that he knew would lead to a simplification.", + "video_name": "r2PogGDl8_U" + }, + { + "Q": "\nFrom 0:40 onwards, I notice that whenever Sal has to find a derivative of a log with an arbitrary base, he always chooses to represent the log (via change of base formula) as a base-e log and not a base-10 log. Is that how you should always interpret a log with an arbitrary base when finding its derivative?", + "A": "It is not about interpreting (what ever you meant by that). The only reason, we transform to base-e is simply that we know its derivative. There is (as far as I know) no other way to do it.", + "video_name": "ssz6TElXEOM" + }, + { + "Q": "At 2:55 , what is meant by derivative of something \" with respect to\" something else?\n", + "A": "It means that the variable on top of the derivative symbol is changing due to changes in variable on the bottom (the independent variable). For instance, a lot of calculus in physics uses dt as the bottom, meaning with respect to time. So dV/dt describes how volume changes in response to passing time.", + "video_name": "ssz6TElXEOM" + }, + { + "Q": "\nAt 3:56, sal says 25 goes into zero 0 times. How does that work? That number was 60....", + "A": "You could think it this way... You have no candy, and 25 people want some from you. How are you going to give them candy? So 25 goes into 0, ZERO times!", + "video_name": "TvSKeTFsaj4" + }, + { + "Q": "\n2:10 I still don't understand why it would be x--5, how did he get that from x+5?", + "A": "x - (-5) is the same as x + 5. The general formula for a circle with center (a, b) and radius r is (x-a)^2 + (y-b)^2 = r^2 for a center at (-5, 7) and a radius of 3, the equation is (x- -5)^2 + (y - 7)^2 = 3^2 or (x+5)^2 + (y - 7)^2 = 9", + "video_name": "thDrJvWNI8M" + }, + { + "Q": "At 0:26, why tan of a number is equal to sin of the number divided by the cosine of the number?\n", + "A": "(It s tangent of an a n g l e). Sketch an angle on the unit circle in the 1st quadrant, and include x, y, and r. (y/r)/(x/r) = sin/cos = y/x = tan. Do it for the other 3 quadrants.", + "video_name": "k_wJsio68D4" + }, + { + "Q": "Are there any other videos covering the area of equilateral triangles, like why the perpendicular bisector at 2:40 is equal to (\u00e2\u0088\u009a3*s)/2 ?\n", + "A": "Well you find the area of the circle than find the area of the square than subtract both of them together, in this case if the square is in the circle than the square would be smaller than the circle so you would subtract the area of the square from the area of the circle.", + "video_name": "QVxqgxVtKbs" + }, + { + "Q": "\nAt 03:15, why is the denominator 4 instead of 2? I am still confused here.", + "A": "He is calculating the area of the entire equilateral triangle at this point. The formula for the area of an equilateral triangle is 1/2(base x height) He has calculated the height as being the square root of 3 divided by 2. Therefore, Area = 1/2(S x sqr(3)/2), so multiply out the denominators to get (S x sqr(3)) / 4", + "video_name": "QVxqgxVtKbs" + }, + { + "Q": "\nAt 2:12, Sal mentions that the 1st quartile begins at 14 instead of assuming it would begin at 14 as originally mentioned in the video. Does that mean, that every quartile ends at the end of each one?", + "A": "In this problem box plot is given, Sal isn\u00e2\u0080\u0099t assuming 14. This data shows age of 100 trees. About 25 trees have the age between 8-14 years. Another 25 have the age between 14-21. You should not see gap between two quartiles(For e.g. Q1 and Q2) in box plots. Hope this helps.", + "video_name": "b2C9I8HuCe4" + }, + { + "Q": "\nWhen he starts grouping @ 2:59 and he switches @ 3:33 and starts to factor out 3f does that mean we can do it both ways and still come out with the correct answer?", + "A": "Yes. You can do math in quite a few ways, but still end up with the same answers. :) Hope this helps! :)", + "video_name": "d-2Lcp0QKfI" + }, + { + "Q": "\nAT 3:00 he said that 2-2= 1 but that is not true right ?", + "A": "It was a mistake", + "video_name": "uCBm8iDyg1s" + }, + { + "Q": "At 7:30, in this case we are talking about a Normal Distribution, but what if the coin is an unfair coin? Would we get something completely different? or just something displaced to one of the two sides?\n\nIn other words, what kind of distribution we get when the possible outcomes are not equally likely?\n", + "A": "Even if the possible outcomes are not equally likely, it will still be a binomial distribution because there are only two possible outcomes from each flip. It doesn t matter what the actual probabilities are of each outcome as long as they sum up to 1.", + "video_name": "NF0lrkqXIkQ" + }, + { + "Q": "\nAround 8:30, is a normal distribution by definition continuous? How does a very large discrete (binomial?) distribution (flip a coin 5 trillion times) differ from a normal distribution?", + "A": "It doesn t differ significantly beyond the fact that you have discrete results (which can be easily accounted for using a continuity correction). This is the premise of the Central Limit Theorem which states that the mean of many random variables independently drawn from the same distribution is distributed approximately normally, irrespective of the form of the original distribution (wikipedia.org)", + "video_name": "NF0lrkqXIkQ" + }, + { + "Q": "At 0:37, what is the meaning of arbitrary point?\n", + "A": "An arbitrary point is a point of your choosing. You could pick any point on that line and Sal s proof would still work.", + "video_name": "KXZ6w91DioU" + }, + { + "Q": "\nAt 2:48 equidistant means equal to right?", + "A": "Equidistant means equal distance", + "video_name": "KXZ6w91DioU" + }, + { + "Q": "\nAt 3:10, Sal says that that proof covers all the points C, but what if C is on segment AB?", + "A": "If C is on segment AB, then triangle CAM and triangle CBM would be degenerate triangles (triangles with the measure 0,0, 180) and will technically be congruent.", + "video_name": "KXZ6w91DioU" + }, + { + "Q": "\nAt 0:52 why did he use the word (Concerned?)", + "A": "I guess because he was concerned about something", + "video_name": "ory05j2jgBM" + }, + { + "Q": "at 0:17,what is a tape graph?!\n", + "A": "its to help you compare fractions.", + "video_name": "ory05j2jgBM" + }, + { + "Q": "Re: 04:06. Is Sal saying that all (emphasis) 3 points cannot be on the same line to have a triangle, though it is true that there will always be 2 of the 3 points which are on the same line.\n", + "A": "Any two points, no matter how far apart or weirdly placed (even in 3D, if the two points were at any depth), will always form a line. But if you get three points on the same line, all it would form is a line, and not a triangle, which is a polygon and not a line. To better explain, if you had three points that fell on a same line, you couldn t make a triangle out of them, consequently preventing you from taking a circumcenter (because you don t have a triangle), and finally not letting you make a circle.", + "video_name": "4_xhiP6g2ow" + }, + { + "Q": "At 1:30, why does using the fraction 9/13 work? I think I understand, but sometimes having other people's thoughts make my own clearer.\n", + "A": "The fraction 9/13 works because there are 13 integers between 36 and 49 (the closest square numbers). 45 is 9 integers greater than 36, so that gives you 9/13. In other words, you want to find out the relationship of the number you have with the close square numbers you can find nearby.", + "video_name": "EFVrAk61xjE" + }, + { + "Q": "At 0:50 what does he mean when he says \"the principle root of 49 is 7?\" What is a principle root? Why not just say root?\n", + "A": "A principal (square) root is a unique, positive square root. 49 has two square roots: 7 & -7, but only has one principal root: 7.", + "video_name": "EFVrAk61xjE" + }, + { + "Q": "\nWhat if you are doing a problem with an octagon, could it be used the same way? Question starting from 3:24", + "A": "Yes", + "video_name": "ZqzAOZ9pP9Q" + }, + { + "Q": "At 13:26, shouldn't it have been sqrt(b2-a2)? He added them, but I thought that was for finding the foci of an ellipse.\n", + "A": "For finding the foci of hyperbolas, the equation is like the Pythagorean theorum, sqrt(a2+b2) For an ellipse, its sqrt(a2-b2)", + "video_name": "S0Fd2Tg2v7M" + }, + { + "Q": "\nI understand the difference between a leading coefficient and coefficient. In the expression at 4:40 wouldn't the leading coefficient be 1 since the x^2 is being multipled by 1.", + "A": "It appears you didn t quite understand it. Leading coefficient means the coefficient of the term with the highest exponent. It is usually the first term, but not necessarily always the case. As you see in the video, 7x\u00e2\u0081\u00b5 was not in the first order. If you were to rewrite them in order as Khan did, you d see it be in the first order. Just remember that the leading is the highest power, not the necessarily the one standing in first order.", + "video_name": "ZgFXL6SEUiI" + }, + { + "Q": "at 1:42 Sal said x have to be raised to a non negative power or positive so that means 1/2 power or positive or principal square root should be acceptable as polynomial?\n", + "A": "The definition of a polynomial is a rational expression in which no variable occurs as a denominator. Perhaps Sal should have been more explicit stating that the powers a variable is raised to is limited to whole numbers which excludes negative numbers and fractional numbers. True that 4/2 is a rational and whole number but it is not allowed when writing a polynomial.", + "video_name": "ZgFXL6SEUiI" + }, + { + "Q": "\nAt 6:16 on the video, what would you do if you were in a situation where 2 of the numbers had no exponents?", + "A": "Most likely that will not happen and if so just add the two numbers in each term", + "video_name": "ZgFXL6SEUiI" + }, + { + "Q": "At 1:19 why did Sal say \"negative and FRACTIONAL exponent\", isn't it supposed to be RATIONAL exponent? Just need a clarification.\n\nThanks,\nAnkit Thumma\n", + "A": "No. A rational exponent is anything that does NOT have a square root in it. A fractional exponent is any fraction. When exponents are fractions, they have a square root portion. For example, x^(1/2)= \u00e2\u0088\u009ax You will most likely learn more about this later.", + "video_name": "ZgFXL6SEUiI" + }, + { + "Q": "\nat 14:00 it doesnt seem very mathematically sound after working out this whole proof to just assume that (f^2-a^2) = b^2 is there no other way to connect the two without saying that looks like that other thing so lets assume this part of the equation equals that other part?", + "A": "How do we know f = a + b?", + "video_name": "HPRFmu7JsKU" + }, + { + "Q": "I don't understand how this proof can apply for an ellipse. I've tried the same proof, while naturally adding both d's instead of subtracting one from the other.\nUp until 9:07 the proof works fine, and in the ellipse's case fx and a^2 switch places. But once we raise the equation to the power of two, (fx-a^2)^2 is the exact same thing as (a^2-fx)^2 - and from that point on we can prove that the ellipse is - a hyperbola?!\n", + "A": "after you factor out a -1 from the denominator of the y term and simplify you get + y^2/(a^2-f^2). With an ellipse f^2 = a^2-b^2. or b^2=a^2-f^2. So y^2/b^2 = y^2/(a^2-f^2). It works. I did the entire proof only to end up with the same equation too. I was also confused about how the same equation could be both an ellipse and a hyperbola but it s the value of f that ultimately determines which one. If f > a, then it s a hyperbola.", + "video_name": "HPRFmu7JsKU" + }, + { + "Q": "\nAt 3:02 he devides both sides of the equation by nine, but doesn`t he only have to devide once on the left side of the equation in stead of deviding all numbers?", + "A": "Since the equation has an equals sign (=), the equation must be kept equal at all times. Multiply the left by 11, you have to multiply the right by 11. If not, then the equation will be false since both sides are no longer equal. However, if you set 1 side equal to 0, you can divide or multiply both sides and still have the 0 side set to 0 since 0 times/divided by anything is 0.", + "video_name": "vl9o9XEfXtw" + }, + { + "Q": "at 9:27 what would the answer be if he had done 1000 instead of 100 what would it be?\n", + "A": "0.00865556 is the answer if sal had done it right. I used a calculator so that may be an abreviated version but that s what I got.", + "video_name": "ScvuRb6vsz4" + }, + { + "Q": "\nNot sure what to do with this. \"The 1st unit of PRBCs 250mL was started by the nurse at 7:30PM to be infused at 120 mL/hr in the first 15 minutes; then increased to 225mL/hr after the first 15 minutes. How long will the entire infusion take? (Provide answer in hours and minutes) \"", + "A": "you need to know the volume of the unit of blood. Typically it s written on the bag. In the equation they should have provided the volume in the unit (usually for an adult) between 280 and a bit over 300ml/unit of blood", + "video_name": "ScvuRb6vsz4" + }, + { + "Q": "Do you mean 1000 times .9 @9:28?\n", + "A": "yes A do bleave that is true!", + "video_name": "ScvuRb6vsz4" + }, + { + "Q": "at the point 0:38, how are we expected to know which is concave and which is not?\n", + "A": "All curves are concave. The question is if they are upward or downward.", + "video_name": "UK2shgCXALo" + }, + { + "Q": "At 3:09 you described each of a function and an equation what would an example be of something that falls into both a function and an equation category?\n", + "A": "Here are some examples: y=f(x)=x\u00c2\u00b2 y=f(x)=x+1 y=f(x)=2 y=f(x)=cos(x) y=f(x)=sin(x) and so on. These equations are functions because they assign each real number x to ONE real number f(x).", + "video_name": "l3iXON1xEC4" + }, + { + "Q": "Is that suppose to be a '=' instead of a minus sign at 6:00 ?\n", + "A": "Yes, it s intended to be a =, not a -.", + "video_name": "4PCktDZJH8E" + }, + { + "Q": "\nAt 4:59 he says \"you can always construct a faster-expanding function.\" Is that really true? What if you had a function that was only defined for the domain consisting of two x-values: 0, 1. And f(0) was defined to be negative infinity, and f(1) was defined to be infinity. How could you construct a faster-expanding function than that?", + "A": "Sal is specifically talking about real-valued functions. Since infinity is not defined in the context of real numbers, it would not make sense to define a function to have an infinite value. Infinites only make sense as a limiting value, not a functional value.", + "video_name": "6WMZ7J0wwMI" + }, + { + "Q": "\nAt 4:28 Sal says \"were getting getting number closer and closer to 0, without actually ever approaching 0.\", yet the function does approach 0 when counting towards the negative direction of x.", + "A": "Poor choice of words on Sal s part. But, a box does pop up at 4:33 in the video and tells you that Sal meant without ever reaching 0 .", + "video_name": "6WMZ7J0wwMI" + }, + { + "Q": "at 5:51: Why can f'(a) also be undefined?\n", + "A": "He is saying that it can either be 0 or undefined. Not 0 and also undefined. At any no endpoint max or min, the derivative has to be either 0 or undefined. This is part of the definition of a non endpoint max/min.", + "video_name": "lDY9JcFaRd4" + }, + { + "Q": "\nAt 0:46, what does he mean by x0? Does he mean x to the 0th power?", + "A": "The subscript appended x_0 signifies a specific value of x. If we are trying to talk about specific values of x, we will just use the subscripts to differentiate them (x_0, x_1, x_2...). This is much easier and makes much more sense than assigning new variables/letters to these values of x.", + "video_name": "lDY9JcFaRd4" + }, + { + "Q": "On 5:17, Sal said that there aren't any other solutions. Can't the values for a and b switch around? So what I am basically asking is that instead of 3 solutions, aren't there supposed to be 6 solutions because a and b will switch their values and be a repeat?\n", + "A": "He s assuming that such things are accounted for (i.e. order is irrelevant, because multiplication and addition are commutative).", + "video_name": "JPQ8cfOsYxo" + }, + { + "Q": "\nAt around 0:06, if Consistent solution #1 is independent, Consistent solution #2 is dependent, then what is an INconistent solution?", + "A": "He draws an inconsistent system at 1:20 - it s 2 parallel lines.", + "video_name": "WSpF5uvApLA" + }, + { + "Q": "\nat 3:06, when 7 doesn't go into 5, why doesn't he write 0, and instead he immediately uses \"51\"?", + "A": "This is a stylistic preference. Placing a zero to the left of a number will not change its value, so you are free to place a zero there if you like. However, when reporting your final answer, I would not include superfluous digits, so you would have to change it again.", + "video_name": "cfr-yZxTH8Y" + }, + { + "Q": "At 2:57,why was it 1/2 of the whole triangle?\n", + "A": "The 1/2 is not based on the triangle, it is based on a triangle being exactly 1/2 of the rectangle that it is enclosed within. In the case that he is using, he is actually showing 1/2 of the parallelogram, not the triangle.", + "video_name": "rRTXKQpblEc" + }, + { + "Q": "What was that thing that popped up at 2:08?\n\n(It seems to be something called ArtRage. . .)\n", + "A": "I agree because it said ART, and the person was drawing", + "video_name": "rRTXKQpblEc" + }, + { + "Q": "\nAt 2:18, why is there -B on the right side?", + "A": "It is the same thing as saying: A=50-B It also equals: A=50+-B", + "video_name": "3mimxluSVBo" + }, + { + "Q": "\nAt 3:47 Sal said factor but didn't he mean simplify?", + "A": "Hi Knight of Stone / Ninjormon (Mormon ninja), Sal did say factor, but meant simplify. They have added the correction to the video in the box which shows up at 3:45. Hope that helps! - JK", + "video_name": "f-wz_ZzSDdg" + }, + { + "Q": "at 2:10, to think of it as 4/8 is that the easiest way to think about 1/2?\n", + "A": "Yes, 4/8 is equal to 1/2, because 4 is half of 8 and 1 is half of 2. 1/2 is the lowest simplified form of 4/8.", + "video_name": "erZe85NrsK0" + }, + { + "Q": "\nWhy did Sal take anti derivative at 8:25?", + "A": "Because derivative of arctan(2x) = f(x) at 2:46 So, antiderivative of f(x) = arctan(2x) at 8:25", + "video_name": "NgYrsqoKXpM" + }, + { + "Q": "\nDear Sal, I think you made a mistake at 1:20 - 1:21 when you said that the third term is ar to the third power. Didn't you write ar^2/ar squared? I am slightly confused there. It might've been a careless mistake.", + "A": "yeah it was just a careless mistake", + "video_name": "dIGLhLMsy2U" + }, + { + "Q": "\nAt 3:47, what was that other sequence that wasn't geometric, and how do you solve it/put it into explicit form? For instance, my sequence is 1, 3, 6, 10, 15, and 21. How could I solve to find the 100th term?\nSide note just found out this is a triangular sequence. no idea wat that means...", + "A": "In general, there s no easy way to do this. But for a lot of cases, taking the sequence of differences or the sequence of quotients is a good way to approach this. In your case, the sequence of differences is 2,3,4,5,6,... From there we can say that a\u00e2\u0082\u0099 = a\u00e2\u0082\u0099\u00e2\u0082\u008b\u00e2\u0082\u0081 + n+1 and a\u00e2\u0082\u0081 = 1 so a\u00e2\u0082\u0099 = 1+2+3+4+...+n+(n+1) = n(n+1)/2.", + "video_name": "dIGLhLMsy2U" + }, + { + "Q": "\ni dont get what you sal said at 5:36", + "A": "because he is smart", + "video_name": "t8m0NalQtEk" + }, + { + "Q": "At 1:39 Sal says that -10 and -4 will work for both 40 and -14. Would it matter if you used 8 and 5 too?\n", + "A": "It matters... The 2 numbers you pick must add to -14 AND multiply to 40. While 8 and 5 multiply to 40, they do not add to -14. 8+5 = +13. So, the 8 and 5 will not work. Hope this helps.", + "video_name": "1kfq0aR3ASs" + }, + { + "Q": "\nI Don't Get what he said at 2:03.", + "A": "He is writing the remainder part as a single fraction instead of two separate fractions.", + "video_name": "WqNc6My1aNU" + }, + { + "Q": "\nAt 2:11 You factor the 15x and not the 8 but at 4:45 you factor the 16 and 10x. Why was the 8 not a factor in the first part?", + "A": "In the first part we need two numbers such that their product is 16(8*2)(coefficient of x^2 and constant term) and their sum is 15(coefficient of x). The nos. are 16 and -1 Similarly, in the 2nd part. But, we factor out only 16 as coefficient of x^2 over there is just 1.", + "video_name": "u9v_bakOIcU" + }, + { + "Q": "\nAt 3:35, how did Sal get 2x(x+8) from 2x^2 + 16x?", + "A": "Sal is distributing the 2x and multiplying with the x and the 8. To get a better visualization, learn about the distributive property.", + "video_name": "u9v_bakOIcU" + }, + { + "Q": "\nwhat is Sal doing, @ 2:28?", + "A": "He is trying to factor out f(x).", + "video_name": "u9v_bakOIcU" + }, + { + "Q": "Hey at 4:24, does the perpendicular sign have to be turned upside-down?\n", + "A": "no it is written correctly", + "video_name": "BTnAlNSgNsY" + }, + { + "Q": "\nat 1:19 ,do adjacent angles have to add up to 90 degrees?", + "A": "No. They can, but they don t have to. Adjacent angles can sum up to any valid angle.", + "video_name": "BTnAlNSgNsY" + }, + { + "Q": "\nWhy at 0:21 did Sal change the angle name from DAB to DBA? Does it matter because the subtitles don't change from DBA when he changes it in the first place?", + "A": "There is a difference: angle DAB is the angle made by lines DA and AB. The angle itself is at point (or vertex , see my answer to your other question) A. Angle DBA on the other hand is the angle made by lines DB and BA, and the vertex is at point B. Sal changed his mind and drew line DB (not line DA as he first intended), so DBA is the correct name for that angle. One side note: angle DBA is the same as angle ABD; the order doesn t matter as long as the point where the angle is remains in the middle.", + "video_name": "BTnAlNSgNsY" + }, + { + "Q": "\nstarting at 0:34, there is an lowercase 'm' in front of all of the angles. What is it for, and why is it there?", + "A": "That means measure of . For example: m\u00e2\u0088\u00a0ABC = 50\u00cb\u009a That means the measure of angle ABC is 50 degrees.", + "video_name": "BTnAlNSgNsY" + }, + { + "Q": "during 2:31 are complementary angles only made up of 2 different types angles?\n", + "A": "Yes. They only consist of two types of angles.", + "video_name": "BTnAlNSgNsY" + }, + { + "Q": "\nAt 1:45, Sal begins to talk about Unit Vectors using the variables 'i' and 'j' with what he describes as 'little hats' on top. Could someone please explain the importance or relevance of these symbols? Can one only use letters i and j? Or does it matter?", + "A": "That notation means that those vectors are unit vectors , (the meaning is that does vectors have direction but their lengh is alwayes equal to 1 ). Any letter can be used to represent a vecor .", + "video_name": "9ylUcCOTH8Y" + }, + { + "Q": "At 3:31, could x be zero? Or would the square root of zero be a non-real number?\n", + "A": "Yes... you can do sqrt(0), it just = 0 because 0^2 = 0.", + "video_name": "qFFhdLlX220" + }, + { + "Q": "\nAround 2:18 of the video Sal mentions the absolute value of | x | which he got from the x^2 under the radical. if he were to use the absolute value for the x^2 why would he not use the absolute value of the lone | x | under the radical?", + "A": "Because the lone x was not a perfect square, he could not simplify the radical. Only if you are taking the principle root and you are SIMPLIFYING the radical can you put in the absolute value. If he would have put the absolute value sign for the x under the radical it would ve become: sqrt(|x|) = +/- (x^1/2) Which still gives you the negative root which is extraneous for principle roots. Therefore putting the absolute value under the radical is never done when taking the principle root as it yields unwanted answers.", + "video_name": "qFFhdLlX220" + }, + { + "Q": "is there a mathematical pattern for 1:46 or is that just random?\n", + "A": "There is no pattern because it s the digits of tau, which like pi is transcendental (which is just a fancy term meaning that not only is it irrational, but you can t even have it as a solution for a polynomial).", + "video_name": "FtxmFlMLYRI" + }, + { + "Q": "At 1:20, why does she start talking about the forth dimension?\n", + "A": "It s to show that the third dimension isn t the highest we can go.", + "video_name": "FtxmFlMLYRI" + }, + { + "Q": "At around 1:30, you can see how (ab)^4 is the same as (a^4) * (b^4). Why is it that when you add different terms and square them, you need to use FOIL, but when multiplying you can simply do that? I mean, sure, it works on paper but a textbook explanation would be nice to think about. They just look so similar.\n", + "A": "Expanding (ab)^2, for example, yields (ab)(ab), which is (a^2)(b^2). Expanding (a+b)^2, however gives you (a+b)(a+b), which is aa+ab+ba+bb, or a^2+2ab+b^2", + "video_name": "SwqOrUWzDY8" + }, + { + "Q": "At 10:59, why is Sal dividing 7:7 instead of multiplying (35*1)/(4*7) = (35/28) and then dividing the whole fraction by 7?\n", + "A": "its kinda late but hat 11:00 when he said you divide 7 by 7. 35/4 * 1/7 = 35/28. simplify it by dividing 7. sames as 5/4 so yeah.", + "video_name": "wYrxKGt_bLg" + }, + { + "Q": "\nHow do you know which number to multiply it by at 2:20", + "A": "Because we can t see a clear variable to eliminate right away, we want to find the lowest common multiple of 5 and 7, in order to eliminate x. lcm(5, 7) = 5 x 7 = 35 Therefore, in order to get to 35x and -35x (one can be negative to cancel out when added together), we need to multiply the top equation by 7 and the bottom equation by -5. 7(5x+7) = 7(15) -5(7x-3y) = -5(5)", + "video_name": "wYrxKGt_bLg" + }, + { + "Q": "\nat about 3:20, he wrote 15, but it is supposed to be five. Just so you all know.", + "A": "Please review the video again. That did not happen. The video starts with the following system. . . . 5x - 10y = 15 3x - 2y = 3 Sal chooses to isolate the x term by multiplying the -2y in equation two by -5, so that the 10y produced, cancels with the -10y in equation one. Naturally, you need to keep the system balanced by multiplying both sides of equation two by -5 -5(3x - 2y) = (-5)3 and that gives -15x + 10y = -15 Everything is correct as he did it.", + "video_name": "wYrxKGt_bLg" + }, + { + "Q": "Sal makes a mistake at 3:21\n", + "A": "At 3:27: 5x + (-15x) = -10x - this is correct -10y + 10y = 0 - this is correct 15 + (-15) = 0 - this is also correct. No errors there.", + "video_name": "wYrxKGt_bLg" + }, + { + "Q": "\nAt 10:31 you said 7x = 20/4 + 15/4 but I thought we got rid of the 15/4 when we added it to both sides of the equation 7x - 15/4 = 5. It would look like this 7x-15/4+15/4 = 5+15/4. The 15/4's on the left side cancel out. 5+15/4 on the right side becomes 20/4. Why do you then add 15/4 to the 20/4?", + "A": "To add a whole number and a fraction, you have to get a common denominator, so 5 \u00e2\u0080\u00a2 4/4 = 20/4. What you are trying to do is (5+15)/4 which is incorrect order of operations. If switched to decimals, it would be 5 + 3.75 which is 8.75 or 35/4.", + "video_name": "wYrxKGt_bLg" + }, + { + "Q": "\nWhat does Sal mean at 0:08 when he says \"Massage the Equation\"?", + "A": "Sal meant that to solve the systems of equations, you first must manipulate or change the equations. Once this is done, it will be much easier to solve the system.", + "video_name": "wYrxKGt_bLg" + }, + { + "Q": "at 2:50 sal talks about a \"zero matrix\" what does he mean by it?\n", + "A": "A zero matrix is a matrix all of whose entries are zero.", + "video_name": "OjF765iVuF8" + }, + { + "Q": "\nAt 1:00 why is it +4 and not *4? I don't understand above it was y^2/4. So wouldn't you multiply both sides by 4? And instead of getting (4/9)x^2 + 4 wouldn't it be (4/36)4x^2?\nI'm not doing to well in this chapter, so someone please explain this!", + "A": "Sal isn t showing the multiplication on each side. He is taking each term times 4. y^2/4 * 4 = y^2; x^2/9 * 4 = 4/9 x^2; 1 * 4 = 4. The +4 comes from taking the +1 times 4.", + "video_name": "hl58vTCqVIY" + }, + { + "Q": "1:55 The +4 disappears just because it \"becomes irrelevant\" compared to the other term?\n", + "A": "The +4 is reverent to the equation, Its what makes the asymptotes that are the basis of the hyperbolas shape but when finding the asymptotes we want to find the line it get increasingly closer to. Since the +4 is what separates the function from the asymptotes if you remove the +4 you get the asymptotes", + "video_name": "hl58vTCqVIY" + }, + { + "Q": "\n3:43 Inverse sin? Is there a video explaining raising trig functions to exponents?", + "A": "Inverse sine and sine to the power of -1 are different things. Sine Inverse: sin(x) = y arcsin(y) = x (the inverse function is commonly notated with arcsin) Sine to an exponent: sin^n(x) = [sin(x)]^n", + "video_name": "IJySBMtFlnQ" + }, + { + "Q": "\ni don't understand why did he use inverse sine to solve for it\nat around 4:15", + "A": "Inverse sin basically negates sin. Think of it like this: sin(90)=1 so arcsin(1)=90. It takes the output and gives the input. So in order to solve for sin(x)=(4/3)(sin(40), you have to take the inverse sin of both sides to get rid of the sin(x) and solve for x. Remember, (4/3)sin(40) is simply just a number.", + "video_name": "IJySBMtFlnQ" + }, + { + "Q": "\ncan someone please elaborate on why Sal took the inverse sine instead of just dividing both side of the equation by sine to isolate theta at 3:50? Thank you!", + "A": "sine is a function, not a variable", + "video_name": "IJySBMtFlnQ" + }, + { + "Q": "\nin 0:44 - 0:46 Sal says \"law of cosines \" twice (Though the second time the captions say \"sines\") does anyone know why?? I'm not sure if he just made a mistake or if I am hearing incorrectly.", + "A": "In this case, all Sal was trying to do was say that you could use EITHER the law of cosines or the law of sines for the problem shown above, but for the purpose of the video, he decided to use the law of sines. But, the second time he said the law of cosines was a mistake and it was corrected.", + "video_name": "IJySBMtFlnQ" + }, + { + "Q": "\nWhat is the troll he's talking about in 0:02?", + "A": "Watch the 2 previous videos Sal has made in that catagory. Hope that helps!", + "video_name": "VhH2nEDCd68" + }, + { + "Q": "\n1:05 you were counting, why , I dont understand where you were counting?", + "A": "The slope of the equation was 7/5. Therefore, for every increase of 7 in y there s an increase of 5 in x. Sal counted the 7/5 slope and adjusted the line to follow it.", + "video_name": "VhH2nEDCd68" + }, + { + "Q": "\nDoesn't \"constant\" begin with a c, so why do we use K? (0:17) I really do not get it.", + "A": "It does not matter what number you use. Unless you are dealing with a problem that has specific words like baseball, or cookies then you would probably want to use what ever letter it starts with. At least thats what I have always been told and I have an A in math.", + "video_name": "lkP-E2LUnjA" + }, + { + "Q": "At 5:01, Sal uses three numbers for his example, do you NEED to have three numbers?\n", + "A": "Yes, in the scope of standard multivariable calculus, you can only use the cross product if you have vectors with three components.", + "video_name": "pJzmiywagfY" + }, + { + "Q": "\nAt 0:33 how does she do that? Can anyone help me I really want to try it?!", + "A": "Yeah, I don t know but it is so cool. I am afraid you will have to explore it yourself.... I wish I knew.", + "video_name": "VIVIegSt81k" + }, + { + "Q": "\nAt 1:17, why didn't he take the (-) sign? Is there a reason?", + "A": "It s the definition: If (x - a) is a factor, f(a) = 0. Otherwise if (x + a) is a factor, you have to check wether f(-a) = 0. You have to revert the sign.", + "video_name": "JAdNNJynWM4" + }, + { + "Q": "at 0:37, I am a bit confused on how that worked. How is X 2 and Y 5? How do we assign solution numbers to the variables? How do we know which ones to assign? Couldn't it be X 5 and Y 2? Checking the inequalities is really difficult for me.\n", + "A": "The question is asking to check for an x,y coordinate. I think the video assumes the watcher to understand the typical structure of a coordinate point: (x, y). So x = 2 and y = 5. Not the other way around. And after that, simply substitute the values into the inequalities.", + "video_name": "XzYNh2wpO0A" + }, + { + "Q": "At 5:13, why doesn't he take the reciprocal of (2^-70) and make the exponent positive?\n\nHope that makes sense.\n", + "A": "I would agree that his final answer should have a positive exponent as that is the preferred form. He did leave his final answer as 2^(-98). This should have been changed to 1 / 2^98. However, while he is simplifying the expression, he can work with negative exponents.", + "video_name": "dC1ojsMi1yU" + }, + { + "Q": "\nAt 6:43 Sal says that (3^-8*7^3) is equivalent to (7^3/3^8). Shouldn't it be (7^3/3^-8)?", + "A": "No. The negative exponent tells you to use the reciprocal to change it to a positive exponent. So: 3^(-8) = 1/3^8. Multiply that with 7^3, and you get: 7^3/3^8 Hope this helps.", + "video_name": "dC1ojsMi1yU" + }, + { + "Q": "At 10:11, why does 1/2i become the square root of 1/4?\n", + "A": "because as we square 1/2, the numerator 1^2= 1 and denominator 2^2=4 and take the square root of 1/4, this is base on Pythagorean Theorem.", + "video_name": "FwuPXchH2rA" + }, + { + "Q": "\nat 8:55 why is i squared +1 or 4/4? shouldn't it be minus 1?", + "A": "Sal is looking for a and b, which are the amplitude of the real and imaginary parts. b is the amplitude of the imaginary part by definition, so you remove the i before you square the coefficient. I m sure Sal could explain it better, but I hope that makes some sense to you.", + "video_name": "FwuPXchH2rA" + }, + { + "Q": "at 0:56 you mentioned the principal root what does that mean\n", + "A": "This means ignoring the negative when you take a square root. That is, the number 4 has two square roots; 2 and -2. Principal means you only take the positive one. Cheers", + "video_name": "P1DJxuG7U9A" + }, + { + "Q": "At 1:11, shouldn't the unknown angle be 180-90-theta? Just for the sake of clarity.?\n", + "A": "that just makes it more confusing, we see the 90 degree angle. so the other two add to 90. so one is theta and one is 90-theta.", + "video_name": "QuZMXVJNLCo" + }, + { + "Q": "At 6:55, is he saying that sine, cosine, and tangent are all equal to each other?\n", + "A": "Actually, Sal is saying that the ratio of the lengths of two sides of one triangle is equal to the ratio of the corresponding sides of a similar triangle. He is certainly not implying that the sine, cosine and tangent are equivalent.", + "video_name": "QuZMXVJNLCo" + }, + { + "Q": "\nAt 5:43,why is angle 1 a supplement of angle 2?", + "A": "The angle 1 and the angle that Sal put a magenta arc on are corresponding angles therefore they are equal. Since they are equal then you know that \u00e2\u0088\u00a01 + \u00e2\u0088\u00a02 = 180\u00c2\u00b0 since the magenta arc and \u00e2\u0088\u00a02 form a straight line.", + "video_name": "h0FFEBHBufo" + }, + { + "Q": "\nAt 0:37, doesn't 5*3=3*3*3*3*3? I know it's the same thing, but I was wondering which one was the right way.", + "A": "5*3 is either 5+5+5 or 3+3+3+3+3. 5*3 = 3*5 because of the commutative property of multiplication. The commutative property of multiplication states that rearranging the order of the factors will not affect the product. Because of that, 5+5+5 = 3+3+3+3+3. They are both correct, but what you are asking is different. In your question, you multiplied 3 by itself 5 times. That would make it 3^5 and not 5*3. 5^3 = 5*5*5 = 125 is very different from 3^5 = 3*3*3*3*3 = 243.", + "video_name": "5qfOViJda_g" + }, + { + "Q": "\nIs the cochlea able to tune out any sound besides the frequency that is coming into the ear? 10:22 Confused me and made me wonder if the cochlea could do such a thing.", + "A": "Compare this to when you are watching a video, but an air conditioner is running in the background. You will subconsciously tune it out in order to focus on the video. The cochlea translates all frequencies into sounds, but the brain is where they are chosen to be ignored or not.", + "video_name": "i_0DXxNeaQ0" + }, + { + "Q": "\nI think that Sal should't make up a word called \"furgle\" at 2:14~3:43\nbecause,then many people would find it very confusing weather or\nnot \"furgle is a real word.", + "A": "When you think about, someone, long ago, made up the words mile , inch , and pound . Sal is trying to explain an idea. He used a made up word so students wouldn t think the idea only worked with inches or centimeters or whatever real word he could have used instead.", + "video_name": "O1R4H3Ca82E" + }, + { + "Q": "\nAt 2:51, when he was talking about 30 x 40, how did the 4 change to 40?", + "A": "It didn t. 30*4 is 120. If it was 40, his answer would ve been 1200.", + "video_name": "8bK-xfh8-rY" + }, + { + "Q": "\nCan the expression at 3:40 also be expressed as 5n+1 ?", + "A": "It was expressed as 5n + 1 when Sal simplified 6 + 5(n - 1) then he observed that 5n + 1 was equal to 1 + 5n. I prefer 5n + 1 because it can be used to visualize the pattern without resorting to a 0 term. 5n toothpicks can be used to almost construct n houses. Almost, because 1 more toothpick is needed for the right wall on the rightmost house.", + "video_name": "GvbrtnEYRpY" + }, + { + "Q": "There is no longer a clarification for Sal's mistake at 2:20.\nHow do we fix this? This could really confuse a kid.\n", + "A": "Request a change, that might work", + "video_name": "muZmOiiukQE" + }, + { + "Q": "at 0:43, why did you use x instead of t for tiles\n", + "A": "variables represent values that you are solving for, often times the letter used to represent the unknown is arbitrary. he certainly could have used t, but most likely elected to avoid t because it is often used to represent time", + "video_name": "FZ2APP6-grU" + }, + { + "Q": "@1:00, Sal writes 3x<1000. Can we also write 3x-1000? Is that communicating the same thing.?- Thank You\n", + "A": "Adriene, If you have 3x<1000 you could subtract 1000 from both sides and then you would have 3x-1000<0", + "video_name": "FZ2APP6-grU" + }, + { + "Q": "\nat 1:44, you said ' if we subtract these 2 guy's', then said '90 plus 90 is 180'. it is, but weren't you going to subtract?", + "A": "I believe he said If we subtract... so these two guys.. not If we subtract these two guys . He was talking about subtracting theta from 180, not subtracting 90.", + "video_name": "iqeGTtyzQ1I" + }, + { + "Q": "At 2:20 he integrated g'(x)=1 to get g(x)=x, but shouldn't the integral of g'(x)=1 be g(x)=x+c?\n", + "A": "That is correct if that is where you were going to end your problem, but since there will be further integrals down the road, you can just add a +C at the end of the problem to encompass all the +C you would have had to put in.", + "video_name": "iw5eLJV0Sj4" + }, + { + "Q": "at 12:22 and earlier, could we have constructed the triangle to have the right angle at the tip of a? ..and would this have any other effect besides flipping the projection from a\u00e2\u0086\u0092b to b\u00e2\u0086\u0092a?\n", + "A": "a\u00c2\u00b7b and b\u00c2\u00b7a yield the same result, so switching the vectors is fine as long as you evaluate them consistently. For simplicity, I would call the shorter vector a so I m doing most of my work with smaller values. Sal was also unclear on what happens when the projection of a is shorter than the length of b. I doubt it would be an issue but am having trouble visualizing the area in that situation.", + "video_name": "tdwFdzVqito" + }, + { + "Q": "At about 5:10, wouldn't the \"- x\" (minus x) in \"-y * (x - x)\" be changed to \"-x\" (negative x)?\n", + "A": "No because the expression is -y * (x-x) which in words would read, negative y times x minus x. Since any number subtracted by itself is zero then your final product will equal zero.", + "video_name": "hmtJV49AWio" + }, + { + "Q": "In 3:45 (or so) he says that the derivative of ln2 = ln2. How is this possible, if the derivative of lnx=1/x? shouldn't then the derivative of ln2 = 1/2?\n", + "A": "Gotcha, so you re saying there s a big difference in whether or not an x is involved with the ln. derivative of lnx=1/x therefore derivative of lncx (where c is a constant) = 1/cx. And then derivative of lnc=lnc, because its a number, without a variable. Is that right? (This is a response to Tysaki, not another answer)", + "video_name": "Mci8Cuik_Gw" + }, + { + "Q": "\nAt 3:12, when we get our final answer, why did we integrate just sinx and not 1? Shouldn't it be in the end \"xsinx + xcosx + c\" or x (sinx +cosx) + c?", + "A": "Yes yes! Thankyou :) I was terribly confused.", + "video_name": "bZ8YAHDTFJ8" + }, + { + "Q": "At 1:48, why does g(x) = sinx. Why is it not g(x) = sinx + c?\n", + "A": "He is just noting what g (x) and g(x) are. The actual integration happens in the problem. When he does the integration the integral sign and dx disappear and that is your signal to add the +c to your answer before you put the little box around it. If the problem had more than one integral you would not put +c every time you did an integration. Only when the last integral disappears would you add a +c which represents all the arbitrary constants from all the integrations that happened.", + "video_name": "bZ8YAHDTFJ8" + }, + { + "Q": "\nat 2:33 I don't understand, why does he write expected value as m rather than E(X). Is it the same thing or not?", + "A": "he wrote mu, it just looked liked M", + "video_name": "ry81_iSHt6E" + }, + { + "Q": "how did Sal get 3/3 when there is only one three present? @2:05 in the video.\n", + "A": "The average change is calculated using (y1-y1)/(x2-x1), or the slope, right? Here y is a function of f, that means we have (f(x2) - f(x1))/(x2 - x1) We are told that x1=2 and x2=5 We are told that f(x) = x\u00c2\u00b2 - 6x + 8. That means f(x2) = f(5) = 5\u00c2\u00b2 - (6)(5) + 8 = 25 - 30 + 8 = 3 And that f(x1) = f(2) = 2\u00c2\u00b2 - (6)(2) + 8 = 4 - 12 + 8 = 0. THEREFORE (y1-y1)/(x2-x1) = (f(x2) - f(x1))/(x2 - x1) = (3 - 0)/(5 - 2) = 3/3.", + "video_name": "S_YIUXy-WFM" + }, + { + "Q": "At 3:01 shouldn't it be:\n2a^2-4a\n----------\n(a+2)(a+2)\n", + "A": "No, if you multiply it out using FOIL, you ll see (a+2)(a-2) = a^2 - 2a + 2a - 4. The a terms cancel out and you are left with a^2 - 4.", + "video_name": "IKsi-DQU2zo" + }, + { + "Q": "At 1:17, isn't it supposed to be 150/1000 instead of 150/100? Or is it just for the decimals?\n", + "A": "Sal is starting with 150%. A percent by definition is a ratio that has a denominator of 100. So, it is 150/100. Hope this helps.", + "video_name": "xEDnwEOOf7Y" + }, + { + "Q": "\nAt 0:57, what is the difference between a zig and a zag?", + "A": "The direction.", + "video_name": "EdyociU35u8" + }, + { + "Q": "In 6:52, why does the paper's edge stay the same instead of shrinking just like the infinitely small paper is?\n", + "A": "because of how she folded it. if she folded it alternating sides the edge would shrink", + "video_name": "EdyociU35u8" + }, + { + "Q": "\nAt 2:24 she mentions e. What is e?", + "A": "e is a mathematical constant that show up in many areas of mathematics.", + "video_name": "5iUh_CSjaSw" + }, + { + "Q": "\nin 2:18, can you make it until 'z' with using all the alphabets in a row?", + "A": "Sure you can! Neat stuff!", + "video_name": "a5z-OEIfw3s" + }, + { + "Q": "At 1:44, why do we use binary trees for situations like this in math? We can use some other, like just figuring out what kinds of parts and adding them.\n", + "A": "Binary trees are powerful tools for solving search space problems, but in the video at 1:44, Vi is pointing out the resemblence of the expressions to binary trees.", + "video_name": "a5z-OEIfw3s" + }, + { + "Q": "\nIn 2:29 Sal made delta= f(epsilon) but I think it should be epsilon=f(delta), shouldn't it ?", + "A": "In this kind of proof delta is a function of epsilon, even though epsilon refers to the y-axis. In his game, Sal has someone pick an epsilon first. Then he finds the delta to go with it. Thus, epsilon is the independent variable, not delta.", + "video_name": "0sCttufU-jQ" + }, + { + "Q": "At 6:46, why isn't delta divided by 2? He says that it is delta/2 but also multiplied by 2 so the 2s will cancel, but I don't see where the 2 that is multiplied is coming from.\n", + "A": "This is taken from the function. We want to show that |x-5|<\u00e2\u0088\u0082 in the form of |f(x)-L|<\u00ce\u00b5. That is to show that \u00e2\u0088\u0082 is a function of \u00ce\u00b5 .", + "video_name": "0sCttufU-jQ" + }, + { + "Q": "\nAt 4:17, when the calculator is shown in the video, is it correct to say that the symbol n! is like the one that can facilitate the factorial multiplication? Do all scientific calculators have it?", + "A": "Yes, that s correct. n! represents the factorial as long as n is non-negative integer. It is more than just like it. It IS it. I would assume that all scientific calculators have a factorial function, but I wouldn t rule out the possibility of the existence of a calculator deemed scientific to exclude it.", + "video_name": "SbpoyXTpC84" + }, + { + "Q": "Why is there a blank space on 2:12\n", + "A": "the pie was eaten 5 + 3 slices. and the pie initially have 9 slices. so, 8/9. (left 1 blank space). hope that help", + "video_name": "u2hLYcmI5y4" + }, + { + "Q": "\nat 2:08, when he was rewriting the expressions, how come he did 6(2^2) instead of 6(2)^2?", + "A": "They mean the same thing. So, either form is acceptable.", + "video_name": "I9eLKDbc8og" + }, + { + "Q": "At 1:27 am pacific time, what does it mean to evaluate an expression?\n", + "A": "make all the appropriate calculations to obtain the final result of the expression", + "video_name": "I9eLKDbc8og" + }, + { + "Q": "\nat 7:57, why do the sun and moon travel across the sky?", + "A": "because it needs its orbit 24 hours and the moon goes down the sun comes up and when the sun goes down the moon comes up", + "video_name": "I9eLKDbc8og" + }, + { + "Q": "\nat 0:30, Sal said the first one is irrational. but 8/2 is four and square of 4 is 2 which is rational.", + "A": "it was sqrt of 8 by 2 not 8/2", + "video_name": "d9pO2z2qvXU" + }, + { + "Q": "At 0:18 Sal states that if you take the square root of a non-perfect square you will always end up with an irrational number. My question is this... 'What is a non-perfect square?'\n", + "A": "A perfect square is created when you multiply a number with itself. For example: 3 * 3 = 9. So, 9 is a perfect square. A number that does not have matching factors would be a non-perfect square. Hope this helps.", + "video_name": "d9pO2z2qvXU" + }, + { + "Q": "\nAt 8:17, how is cos 1/3 x zero? Is it because the y-value is zero which makes the cos zero? And when you multiply -2.5 you get zero?\n\nThanks for the help!", + "A": "Yes, cos[(1/3)x] is 0 at that point because the y-value is 0. Also, yes, when you multiply that value, 0, by -2.5, you still get zero.", + "video_name": "uBVhtGL9y88" + }, + { + "Q": "in 5:31 you said the M was negitive 800 why\n", + "A": "The negative 800 is paired with the W, not the M.", + "video_name": "VuJEidLhY1E" + }, + { + "Q": "At 1:43, wouldn't the logicians know if their forehead was painted? They would obviously feel that somebody painted/was painting their forehead.\n", + "A": "Yes, I agree. They would feel it, wouldn t they? Maybe the paint is special or something :)", + "video_name": "rBaCDC52NOY" + }, + { + "Q": "\n3:45 - 3:58 Can you think of a formula to help me with all this information you just gave me? I think it would really help me during school.", + "A": "What he is describing is the variance of a population, which he goes over in a video with the same title.", + "video_name": "iHXdzfF7UEs" + }, + { + "Q": "\nat 9:32, Why didn't Sal write it as sqrt((a+b+c/2)*(a-b+c/2))", + "A": "because the second (a+b+c)/2 is a part of (a+b+c)/2 - 2b/2. for multiplying how you said he would have had to multiply (a+b+c)/2 with -2b/2 .", + "video_name": "nZu7IZLhJRI" + }, + { + "Q": "I have noticed that when talking about Vectors Sal generally denotes them as a column matrix like he did at 3:00 when describing vector x?\nIS there a reason to do so or could your represent them as a row vector also?\n", + "A": "You could use a row vector without changing any meaning. It only becomes significant when mixing vectors with matrices, where a row and column are very different and in that context one or the other is used as appropriate.", + "video_name": "gAbadNuQEjI" + }, + { + "Q": "\nAt 1:16 Sal says that in order to have a vertical asymptote \"it cannot be defined there. \" What does he mean by this? What is he referring to as it? Why can \"it\" not be defined?", + "A": "It means that at that particular x value, the equation doesn t work so the y value is undefined. For example if the function is a fraction and at a particular x value the bottom of the fraction is equal to 0, then the output would be undefined since we can t divide by 0, so there would be an asymptote on the graph.", + "video_name": "onmNaDrxwmo" + }, + { + "Q": "\nAround 3:53, why does 10 to the power of both sides cancel out the base 10 and the log_10 exponent?", + "A": "Since that s how logarithms work; exponentiation and logarithms are inverse operations to each other. Since log(10) a is whatever 10 needs to be raised in to get a, 10^(log(10) a) = a.", + "video_name": "Kv2iHde7Xgw" + }, + { + "Q": "\nI'm getting confused at 3:42, when he offers an alternate way of solving the equation. Can someone theoretically explain to me how raising both sides of the equation to the log's base solves the problem?\nI understand the lesson up until that part.", + "A": "logarithms are just inverse functions of exponential functions so that the base and the exponents cancel and equal 1 .try this logany base (withthat number)=1 as well exponets leading coeffitient with raised with any logsame numbe =1 let say 10^x(power)=100 by logarithm rules it inverse it intern of x log(10_base)(100)=x so that x=2 log( 10^x(power))=log(100) this simplifies to x=log 100 or 2", + "video_name": "Kv2iHde7Xgw" + }, + { + "Q": "\nat 1:24 is 3-4 the same as 4-3", + "A": "3-4 is not the same as 4-3 because in subtracting, there is no Commutative Property. 3-4 would be -1, while 4-3 would be positive 1.", + "video_name": "AO9bHbUdg-M" + }, + { + "Q": "At 12:46, how did he factor a -x out of +17x^2??\n", + "A": "Sal divided 17x^2 by -x. Another way to think about this is to say what does -x have to be multiplied by in order to get +17x^2.", + "video_name": "X7B_tH4O-_s" + }, + { + "Q": "\nAt 9:36, you put fhx instead of fhx^2 when you multiplied fx and hx, why?", + "A": "Sal just made a mistake. It has been corrected already if you watch the video again.", + "video_name": "X7B_tH4O-_s" + }, + { + "Q": "I am confused why at about 7:40, the 6x needed to come before the 1x. Why couldn't it have been the other way around??\n", + "A": "The 6x did not need to come first. You can absolutely write out the new polynomial as: 6x^2 + 1x + 6x + 1. If you finish the factoring process, you will get the same 2 binomial factors as Sal has in the video. Your intermediate steps will look a little different, but the end result will be the same. Hope this helps.", + "video_name": "X7B_tH4O-_s" + }, + { + "Q": "At, 1:55, if it is a*b, won't it be 4*25, instead of 4*-21?\n", + "A": "In this case a and b are not from the classical form a x\u00c2\u00b2 + b x + c, but rather two independent variables to use the method. You could call them p and q if thats easier for you. Or in short: For a x\u00c2\u00b2 + b x + c you search p and q such as p * q = a * c and p + q = b As Sal didn t use the a, b, c in the equation, he just chose them as variables.", + "video_name": "X7B_tH4O-_s" + }, + { + "Q": "\nSal mentions the Z-Score table at 12:56. How were the values on this table calculated - where did they come from?", + "A": "What could have been made more clear is that Sal is looking for the probability for X to be between 0 and up to 2+(2.02*0.099)=2.19998 liters of water. Since we know that it is a normal distribution we can write: X is N(2 , 0.099) and we look for P(0X and f from X-->Y shouldn't the composition of these functions be a mapping from Y-->Y?\n", + "A": "gof = g(f) maps from the domain of f (= X) to the codomain of f (= Y), and g maps from Y back to X (first you do f, then g - right to left ).", + "video_name": "-eAzhBZgq28" + }, + { + "Q": "At 6:33 what is a codomain?\n", + "A": "If the range of f (the set of all the y such that y = f(x)) is a subset of the real numbers, then the real numbers might be a codomain.", + "video_name": "-eAzhBZgq28" + }, + { + "Q": "At 2:40 he gives the number 0.714141414\nI fully understand the answer that he gives to solve this problem.\nBut it seems to me that the repeating section is 14, not 41.\nWhy doesn't 100x - x work?\n", + "A": "it depends whether you want to use the repeating section 14 or 41 because the repeating period or cycle is just every two digits. Some numbers like 1/23, 1/4093 or 1/8779 have repeating cycles of 22 digits", + "video_name": "Ihws0d-WLzU" + }, + { + "Q": "At 5:05 can you just multiply by 10 every time your numerator is a decimal?\n", + "A": "Yes, but only if the decimal stops at the tenths place...if it goes to the hundredths place, multiply by 100. If it goes to the thousandths place, multiply by 1000, and so on...", + "video_name": "Ihws0d-WLzU" + }, + { + "Q": "\nAt 4:25 I was confused on why it was changed to p^2-17p+4 why is it plus 4?", + "A": "This is Algebra II. The process of going from equation 1 to equation involves multiplying by 4. This is one of the most common operations in Algebra. If the process confuses you, consider reviewing the courses of Algebra that involve solving quadratic equations.", + "video_name": "GDppV18XDCs" + }, + { + "Q": "\nI don't understand the braiding thing Vi does at 1:33. Someone please help!", + "A": "All she does is put 2 like an 8, and weaves the other, whoch she cut in half, into the others.", + "video_name": "4tsjCND2ZfM" + }, + { + "Q": "who's she cooking with at 0:11?\n", + "A": "Marc ten Bosch, the 4 dimensional Frenchman who invented the Borromean Onion Rings.", + "video_name": "4tsjCND2ZfM" + }, + { + "Q": "\nat 1:01 , i do not get why it is 20-6, when it is 200-60", + "A": "because you can take away a 0 from the end of the numbers, the you can add a zero to the answer i.e. 200-6 20-6 = 14 which becomes 140", + "video_name": "iivtjjdSu9I" + }, + { + "Q": "\nat 2:37, why did Sal use the phrase \"Not to beat a dead horse\"? Is it a simile, metaphor, or WHAT? Also, i like horses. I am very much offended.", + "A": "It means not to belabor the point. Yes, it is a figurative phrase.", + "video_name": "AuD2TX-90Cc" + }, + { + "Q": "What does beat a dead horse mean? Because at 2:36, Sal said, \"Not to beat a dead horse...\"\n", + "A": "Beat a dead horse means, Keep doing what we have done enough of. , or Waste energy doing something that useless.", + "video_name": "AuD2TX-90Cc" + }, + { + "Q": "what does Sal mean at 2:35 \"not to beat a dead horse\"?\n", + "A": "The phrase means to keep doing or saying something over and over even after it has become pointless .", + "video_name": "AuD2TX-90Cc" + }, + { + "Q": "I might be asking a question explained in another video, but at 0:47, he said that, \"We have two angles (angle CDE and angle ABC) that are congruent.\" Why is that?\n\n(I am young in learning this)\n", + "A": "In geometry, the alternate interior angle rule says that those angles are congruent. Try searching for that rule.", + "video_name": "R-6CAr_zEEk" + }, + { + "Q": "\nat 4:26, wouldn't Aij be the determinate of the submatrix, not the submatrix itself?", + "A": "No, Sal defined Aij to be the submatrix itself.", + "video_name": "H9BWRYJNIv4" + }, + { + "Q": "At 6:26, we get the same answer by treating the question as ratios. That is, 0.6:0.7 as 0.5:x. Is the reasoning sound?\n", + "A": "Yup, because ratios are just fractions, so in the end everything will work out; your reasoning is sound.", + "video_name": "6xPkG2pA-TU" + }, + { + "Q": "\nAt 1:30 , Sal wrote down cos 58 with no parentheses. Usually he uses parentheses when he has a degree measure. What is the correct way to do it?", + "A": "It s better to write it using parentheses,", + "video_name": "yiH6GoscimY" + }, + { + "Q": "at 5:04 it confuses me that the two sides of a seemingly isosceles triangle to have different angles at both acute sides is that impossible or am i mistaken\n", + "A": "it may look like an isosceles triangle, but it is not. If the 2 seemingly equal sides were in fact of equal length, the 2 angles would have each been 30\u00c2\u00b0, instead of 25\u00c2\u00b0 and 35\u00c2\u00b0.", + "video_name": "D5lZ3thuEeA" + }, + { + "Q": "At 3:13 you are multiplying the results by -1.....where did the \"-1\" come from?\n", + "A": "Sal multiplied both sides of the equation by -1 because it was in the form -p = -17. We are trying to solve for p not for negative p. The fastest way to transform one side of an equation from negative to positive or vice versa is to multiply both sides by -1 because only the sign changes and not the value.", + "video_name": "bRwJ-QCz9XU" + }, + { + "Q": "At 1:15, why does Sal write a 16 instead of a 6?\n", + "A": "That s bracket start (6 months) .", + "video_name": "BKGx8GMVu88" + }, + { + "Q": "\nat 3:00 ,why does the square root of 2 times the square root of 6 equals the square root of 12 ?", + "A": "Because if you multiply 2 and 6, you get 12. You wouldn t be able to combine/simplify them if you were adding, but since you are multiply, it s ok.", + "video_name": "yAH3722GrP8" + }, + { + "Q": "2:10, if |r| > 1, the number will become massively huge. How can we come up with the formula \u00ce\u00a3 = a / (1 - r) if |r| > 1? Please notice that I fully understand \u00ce\u00a3 = a / (1 - r) if 0 < |r| < 1. Did I miss something there?\n", + "A": "You re right--the formula \u00ce\u00a3 = a / (1 - r) does not apply if |r| > 1. So our formula for the sum of a geometric series only applies if |r| < 1, which Sal begins to address around 2:30.", + "video_name": "b-7kCymoUpg" + }, + { + "Q": "At 0:13 Sal talks about a vertical cut. What is a vertical cut?\n", + "A": "It means you re cutting up and down. A horizontal cut would be cutting from side to side.", + "video_name": "hoa1RBk4dTo" + }, + { + "Q": "\n9:00 Does that mean, for instance, that the range of ground movement in 2011 Japan was 100 times greater than in 1989 Loma Prieta?", + "A": "Yes; you re moving from 7.0 to 9.0, a difference of 2. On the logarithmic scale we use, that s 10^2 or 100.", + "video_name": "RFn-IGlayAg" + }, + { + "Q": "At 2:41 Sal says 1 -3= -1\nIs that a mistake or am I just not understanding something?\n", + "A": "It said in the corner that Sal meant -2, but accidentally said -1. He just made a mistake.", + "video_name": "s4cLM0l1gd4" + }, + { + "Q": "\nat 4:13 in the video when he talks about periods, does the point have to reach zero in order to determine the period, or can you start from anywhere, like start from 4, 6 or anywhere on the graph?", + "A": "Period can be derived from any two points in the domain of the function that have the exact same y value and have identical slopes.", + "video_name": "s4cLM0l1gd4" + }, + { + "Q": "At 4:21, why is the period not 2pi over two (simplifies to pi)? Why is it two?\n", + "A": "Why would it be 2\u00f0\u009d\u009c\u008b/2 = \u00f0\u009d\u009c\u008b? Nothing in the problem suggests that it is! The period of a function is the smallest \u00f0\u009d\u0091\u009d > 0 such that \u00f0\u009d\u0091\u0093(\u00f0\u009d\u0091\u00a5) = \u00f0\u009d\u0091\u0093(\u00f0\u009d\u0091\u00a5 + \u00f0\u009d\u0091\u009d) for all \u00f0\u009d\u0091\u00a5 \u00e2\u0088\u0088 Dom \u00f0\u009d\u0091\u0093. In this case, the function repeats every 2 units away from the point being considered, hence by definition, the period of the function is 2.", + "video_name": "s4cLM0l1gd4" + }, + { + "Q": "How can you derive an already derived function (0:13) ?\nI mean, given that f(x)=2x^2, it's derivative would be f '(x)=4x.\nSo, if i understood correctly, to get the antiderivative, i would have to derive f ' (x), which is F(x)=4\nbut... thats not equal to f(x).\nI'm confused.\n", + "A": "So, if i understood correctly You didnt. If you do a deriavative of a derivative you get the sencond derivative. f(x)=2x^2 f (x)=4x f (x)=4 To get the antiderivative, you have to find a function such that its derivative is your original function. F(x) = 2/3 x^3 Do the derivative and you get back to: F (x) = f(x) = 2 x^2", + "video_name": "61ecnr8m04U" + }, + { + "Q": "at 0:43 sal says there is a positive trend between them, i do not see any?\n", + "A": "The scores appear to be getting generally higher as study time is increased, a trend that teachers expect to happen. (positive trend is as independent increases, dependent also increases). Lowest scores are on the left and highest scores are on the right (even though the max score is not with max study time). What do you see that thinks it is not positive?", + "video_name": "Jpbm5YgciqI" + }, + { + "Q": "\nat 0:36 what is a parabola?", + "A": "the graph of the quadratic function. This ------> y = x^2 is just an example of the parent quadratic function. it could be something as broad as y = 456x^2+567x. The parent parabolic graph is an even graph because it is symmetric over the y-axis.", + "video_name": "0A7RR0oy2ho" + }, + { + "Q": "At 12:10 Sal says that if he has time then he would make a video so I was wondering If he can make a video seeing as to that there are no exercises to make sure that I have learned the material. Where would I go to ask the site staff or Sal to ask him to make a video as a continuation to Parametric equations?\n", + "A": "If you click on ask a question... look on the right side. there is an option to request a feature, rather than post a question.", + "video_name": "IReD6c_njOY" + }, + { + "Q": "\nAt 9:00 Sal says that making both negative will make the path reverse. Wouldn't it only reverse if one was negative and one positive?", + "A": "cos -t = cos t so the only thing that really matters is changing the sign of sin t", + "video_name": "IReD6c_njOY" + }, + { + "Q": "At 0:12 are the numbers on the line tenths or wholes\n", + "A": "The blue lines are whole numbers and the little black lines are tenths.", + "video_name": "qb0QSP7Sfz4" + }, + { + "Q": "\nAt 3:24, Sal is just dividing both the sides by tan... Am I right? Thanks in advance :)", + "A": "Yes...you could think about it that way.", + "video_name": "aHzd-u35LuA" + }, + { + "Q": "At 3:56, you change the calculator to degree mode. For CC Geometry, should you keep the calculator at degree mode?\n", + "A": "It depends on the question, if its asked to write the answer in Radians, there is no other way!", + "video_name": "aHzd-u35LuA" + }, + { + "Q": "At 1:41 what does he mean by transitive, communicative and commutative?\n", + "A": "The Commutative Laws say we can swap numbers over and still get the same answer ... a+b = b+a Hope it helps :D Have a great day/night :) :)", + "video_name": "d8lP5tR2R3Q" + }, + { + "Q": "\nWho is saying this? 0:00", + "A": "sal is doing this.", + "video_name": "d8lP5tR2R3Q" + }, + { + "Q": "At around 6:30, Sal starts to talk about how the overlap is only supposed to be counted once. But why would it be counted even once if the question is the P (yellow OR cube?) anyways? Doesn't this question not want the area where we can get both outcomes? If that is the case, then is the addition rule really necessary? Couldn't you just simply add together the P(only Yellow), which would be 7, and P(only Cube), which would be 8?\n", + "A": "P(yellow or cube) includes yellow cubes because you re looking for the probability of either. Since yellow cubes have both traits, they automatically have either and are therefore part of the outcome we re looking for. The rule exists so that they re counted, but not double-counted.", + "video_name": "QE2uR6Z-NcU" + }, + { + "Q": "\nAt 1:37, why do we take half of -6?", + "A": "We are working with completing the square. It starts from the concept that (x + b) ^2 = x(x+b)+b(x+b) = x^2 + bx + bx + b^2 or x^2 + 2bx + b^2. Since the middle has to come from two middle terms, we divide by two. In the specific problem, we have to say that 2b = - 6, thus when we divide both sides, we get b = -3 and b^2 = (-3)^2 = 9.", + "video_name": "4Bx06GFyhUA" + }, + { + "Q": "\nOkay I'm having troubles at 2:30.\nI don't understand where you got the 4 from, when I multiply 3x -2^2 I get 12 not 4?", + "A": "He got twelve, but then subtracted it.", + "video_name": "za0QJRZ-yQ4" + }, + { + "Q": "At 2:33, did Sal just choose -2 randomly? If it wasn't random, why did he choose -2?\n", + "A": "He picked -2 because that is a place that he normally starts his tables and graphs on, it is just habit, there is no specific reason.", + "video_name": "za0QJRZ-yQ4" + }, + { + "Q": "I Am SOOOO Lost?\nCan Anyone Help Me\n0:00 - 4:17\n", + "A": "ask a question and i think someone will come along.in the meantime watch the math videos and play them more than once if you miss what the person is saying", + "video_name": "tVDslyeLefU" + }, + { + "Q": "why would you divide 8:20 to 2:5 when 20 can divide by more then just 5?\n", + "A": "8 : 20 is the ratio and when you simplify a ratio you need to take BOTH values into consideration. If you watch some Algebra/ Pre-Algebra concepts you will see that what you do to one side needs to be done to the other to balance it out. 8 : 20 can be simplified no lower than 2 : 5 because the greatest divisor of 8 and 20 is 4 so it ends up as 2 :5. I hope this helped.", + "video_name": "UK-_qEDtvYo" + }, + { + "Q": "\nHow are fractions and ratios the same? How are they different? Is 2:5 the same as 2/5?", + "A": "Yes, they are the same exact thing.", + "video_name": "UK-_qEDtvYo" + }, + { + "Q": "So the first ratio number goes on top of the fraction so 4:6 is 4 over 6?\n", + "A": "Yes, that is correct.", + "video_name": "UK-_qEDtvYo" + }, + { + "Q": "\nSo can 2:3 become 2/3? I'm taking notes...", + "A": "The bottom number does not (nor should it ever) refer to the whole group. The first and second items (example 2:3) added together will sum to the whole group. Instructions for mixing chemicals are given in this notation.", + "video_name": "UK-_qEDtvYo" + }, + { + "Q": "So for example does 8 to 8 equal to 8:8 and 8/8?\n", + "A": "Yes... and if you reduce it, the ratio is 1 to 1", + "video_name": "UK-_qEDtvYo" + }, + { + "Q": "\nIs 2:3, 4:6, and 8:12 equivalent", + "A": "Yes, they are equivalent.", + "video_name": "UK-_qEDtvYo" + }, + { + "Q": "\nHow can you get 30:39 equal?", + "A": "If you mean how do you simplify 30:39, then you just divide by three. 30 divided by 3 is 10 and 39 divided by 3 is 13. Your final simplified ratio is 10 to 13. Both 10 to 13 and 30 to 39 are equal though. Hope this helps! :)", + "video_name": "UK-_qEDtvYo" + }, + { + "Q": "\nAt 7:43 in the video, isn't A really A transpose? And what Sal calls r1T, r2T aren't they really the transpose of Column 1 Column2, so maybe they should be labelled c1T, c2T? Because the r1T suggests the transpose of a row to a column.", + "A": "@Jonh I believe you right. r1T is in reality c1T, but as siddhantsabo said, the notation used was to point you re dealing now with rows instead of columns.", + "video_name": "QOTjdgmNqlg" + }, + { + "Q": "At 1:36, how did you get the side length of 10?\n", + "A": "It s indicated on the diagram along the bottom edge.", + "video_name": "mtMNvnm71Z0" + }, + { + "Q": "\nAt 3:50, is (350/50)=(350/10)/(50/10)=35/5=7 correct?", + "A": "That is right. When you get rid of the zeroes, it is the same as 35/7.", + "video_name": "ccS5Fy5yLjk" + }, + { + "Q": "\nSal, at 0:42, how do you know that a-sub2 is equal to -8/5, why is it not a-sub1? Why did you start with 2 instead of 1?", + "A": "Because i = 2 in the Sigma statement.", + "video_name": "yvddTWa9ptU" + }, + { + "Q": "\nSee 1:47 into the video. Referring to the denominator, why is it 0-(-a) and not (-a)-0. Thanks ;)", + "A": "You could do that, but the answer would be the same. For example, if the 2 points were (9,2) and (7,5), 5-2/7-9 would equal 3/-2, which equals -(3/2.) If you switched the order, it would be 2-5/9-7, which is -3/2. The answers are the same. It does not matter which you put first, as long as when you put the y value of it first, then that point s x value has to be in front too.", + "video_name": "H6ZNLD1AeM8" + }, + { + "Q": "\nIn the example at 5:50 wouldn't the 2a affect the actual slope of the line because it is not a quadratic?", + "A": "I m not quite sure what you mean, but we are only comparing the slope of the secant lines, not the actual slope of the curve. The slope of the secant line is \u00ce\u0094y/\u00ce\u0094x", + "video_name": "H6ZNLD1AeM8" + }, + { + "Q": "At 2:59 min, why is the \"divided by 2\" switched with \"times 1/2\"?\n", + "A": "1/2 and divided by 2 are both 0.5 A Half can be written... As a fraction: 1/2 As a decimal: 0.5 As a percentage: 50%", + "video_name": "GwycEivqYYI" + }, + { + "Q": "\nAt 0:36 Sal starts to extend the number. Do I need to do that all the time?", + "A": "No, that s only to help you understand the concept. If you get it, that s great. =) You may have to do this when asked to expand the number.", + "video_name": "jxA8MffVmPs" + }, + { + "Q": "At 3:40 , i didn't understand why sal used that formula ? May i know which video can i look upon for the formula ?\n", + "A": "Finding the sum of n squares part 1/ part 2", + "video_name": "LwhJVURumAA" + }, + { + "Q": "at 1:15 you say that the domain is 6. but when you substitute x as 6 in the numerator as well you get\n6^2 - 36/6 - 6\n=36 - 36/6 - 6\n=0/0 = 0\n", + "A": "The domain is not 6. In fact, the domain is all real numbers EXCEPT 6, because 6 doesn t work in the expression (leads to division by zero). In the simplification you just did, at the end, 0/0 = undefined or indeterminate, 0/0 does not equal 0.", + "video_name": "ey_b3aPsRl8" + }, + { + "Q": "At 1:52 how would you solve the equation if you left in the 75?\n", + "A": "You would factor the expression. You need to find two numbers that add up to 10 and multiply to equal -75. Those two numbers are 15 and -5. Thus, x^2+10x -75 = (x+15)(x-5). Now, solving either bracket for x gives you x = -15 and x = 5.", + "video_name": "TV5kDqiJ1Os" + }, + { + "Q": "\nAt 3:40, why did he color in 8/15 instead of 10/15 because there is still 2/15 remaining on the side.?", + "A": "He wasn t dealing with the whole 15/15 but rather 4/5 of it = 12/15 2/3 x 4/5 = 8/15", + "video_name": "hr_mTd-oJ-M" + } +] \ No newline at end of file