diff --git "a/test_math_science_timestamp.json" "b/test_math_science_timestamp.json" new file mode 100644--- /dev/null +++ "b/test_math_science_timestamp.json" @@ -0,0 +1,11797 @@ +[ + { + "Q": "At 7:15,Sal says that PV=k.KE(system).In the last video,he only said that PV=k .So,how come it is k.KE now.I don't get it.Please help.Thanks in advance.", + "A": "Well,I understand your point.I also think of it this way-the units of PV =the units of KE (k is a constant) PV(FV/A)=Nm^3/A=Nm^3/m^2=Nm=kgm^2/s^2 KE(mv^2/2)=kgm^2/s^2 Thus,the units are just the same.The only difference is the constant. Is it because of this that PV=kKE?Am I right?", + "video_name": "x34OTtDE5q8" + }, + { + "Q": "at 7:00 why is Newtons the number of particles?? isnt newton kg*m/s^2\nat 6:15 Sal say its number of molecules. how is that possible if newton is kg*m/s^2?", + "A": "There are no Newtons in this video. N stands for Number, as in Number of molecules. It s a variable, not a unit.", + "video_name": "x34OTtDE5q8" + }, + { + "Q": "Great video, very interesting. When you talk about the Bacteriophages, ( 17:50 ) that inject their DNA though the harder cell walls, how does the DNA then go on to alter the cell if it is just loose genetic material within the cell?", + "A": "Various viruses can do it differently. Sometimes the viral genome comes with proteins that will splice it into the host genome. Sometimes the viral genome is made of RNA that can do the splicing on its own. There are numerous other mechanisms.", + "video_name": "0h5Jd7sgQWY" + }, + { + "Q": "At 17:45, Sal mentions that the bacteria could be far worse for the virus. Could someone explain how the bacteria could potentially harm the virus?", + "A": "I personally think that the bacteria could be more harm to the virus because the virus simply attaches itself to the bacteria, injects everything inside of it, and then it might just kind of sit there and become inactive. I don t believe that things inside of the bacteria can take some of the bacteria s membrane a form a new bacteria. I could be wrong though.", + "video_name": "0h5Jd7sgQWY" + }, + { + "Q": "at13:17, Why isn't there any cure/vaccine for AIDS?", + "A": "The virus mutate itself in no time", + "video_name": "0h5Jd7sgQWY" + }, + { + "Q": "At 19:05, I saw this big red thing on the white blood cell. What was it?", + "A": "This question has been asked several times before, and I ll say what I said before - I m not positive, but I believe that it is a platelet.", + "video_name": "0h5Jd7sgQWY" + }, + { + "Q": "so from 00:01 to 23:17 he talking about the common cold and flu (influenza)? :|", + "A": "He s talking about Viruses in general and not about a specific one. At the beginning he says that because he has a cold that he s going to talk about Viruses. In between those times he covers how a most viruses interact with living cells and also how a retrovirus might.", + "video_name": "0h5Jd7sgQWY" + }, + { + "Q": "At 6:32, is it possible that the ice may slow down due to hydrogen bonding between the molecules?", + "A": "Assume there is no friction, thus now intermolecular bonds between Hs which creates friction", + "video_name": "CQYELiTtUs8" + }, + { + "Q": "At 3:10, the ice has 2 equal forces acting upon it at opposite sides, but wouldn't the ice just go upwards instead of remaining stationary because of friction?", + "A": "No. Friction, in this case, points sideways, so it can t make it go up. The reaction force does point upwards, but it s as big as gravity, so it also can t do that.", + "video_name": "CQYELiTtUs8" + }, + { + "Q": "What I don't understand, is that wouldn't a body not be in a state of rest because of gravity? Sal uses the rock (1:10) as an example, and he says there is no force applied to that rock. Wouldn't gravity be a force on the rock? I mean, wouldn't the rock fly out of the atmosphere from the smallest amount of gravity somewhere else? What I'm thinking is that Earth's gravity would keeping the rock there, but the rock wouldn't be at \"rest.\" So, in this definition there would rarely/never be rest?", + "A": "Force of gravity is balanced by other forces (by restoring force I think but I m not sure), so rock is in state of rest. Many forces are applied to that rock but they balance each other and that s why rock doesn t move.", + "video_name": "CQYELiTtUs8" + }, + { + "Q": "3:23 sal says that while ice sits on ice theres no external force acting upon it but as i understand it the very fact that ice sits there is probabaly because gravity acts on the blocks ,could anyone please explain it to me", + "A": "To get the ice moving, you would need an outside force. As said above, gravity pulls downward, but that is an acceleration. If you want to talk about forces, the weight of the ice is what keeps the ice grounded. The normal force pushes upwards to balance the weight force. Static friction is the reason that is stays still side to side.", + "video_name": "CQYELiTtUs8" + }, + { + "Q": "At 8:12 Sal says \"if gravity disappeared, and you had no air...\". What's the relation between gravity and air?", + "A": "He uses gravity and air as two examples of forces that occur naturally all around us.", + "video_name": "CQYELiTtUs8" + }, + { + "Q": "At around 5:05 Sal says everything will eventually stop, if so, how is the earth constantly orbiting the sun? What is causing the earth to move?", + "A": "The Earth continues to spin upon its axis because there are no outside forces acting to stop its rotation.", + "video_name": "CQYELiTtUs8" + }, + { + "Q": "At 6:20, Sal said that water has a \"lattice structure\". What does that mean?", + "A": "Hi Amol Chavan, Sal refers to a lattice structure or crystal structure is an arrangement of atoms or molecules in a crystalline solid or a liquid. This term is often used to illustrate the bonding of the hydrogen and oxygen atoms in water. Hope that helps! - JK", + "video_name": "CQYELiTtUs8" + }, + { + "Q": "at 6:15 he used H2O as a base can we use the HSO4- from the process where we generate electrophile?", + "A": "HSO\u00e2\u0082\u0084\u00e2\u0081\u00bb can act as a base, but H\u00e2\u0082\u0082O is stronger and it is present in much larger amounts.", + "video_name": "rC165FcI4Yg" + }, + { + "Q": "At 10:30 he says that the Egg gets all the organelles. Does that mean that we get all of the organelles from our mother? (I know about the maternal inheritance of mitochondria.) If so, what happens with the organelles in the sperm cells?", + "A": "No such thing. Organelles are made as instructed by DNA. The part of mitochondrial genome that is still within it is maternally inherited. All others are synthesised using simple molecules, as instructed by maternal and paternal DNA in the nucleus.", + "video_name": "TX7-Kdn6lJQ" + }, + { + "Q": "At 9:30 he talked about the organ of corti that is comprised of both a basilar and tectorial membrane. What is the functionality of the two membranes and where are they located within the organ of corti? Thank you.", + "A": "the basilar membrane is within the cochlea of the ear and is quite stiff . There are two fluid filled tubes that are in the coil and the function of the membrane is to keep these two fluids away from each other as they are very different. the tectorial membrane is a gel with 97% being water. it is parallel to the basilar membrane. its exact function has not yet been found but it is understood that it is essential for normal functioning of the ear.", + "video_name": "6GB_kcdVMQo" + }, + { + "Q": "At 3:21 he mentioned frequency as how close the peaks are, instead that distance between two peaks is called wavelength. Frequency is just the number of waves in a specific time period. Feel free to comment, I am not 100% sure!", + "A": "Yes ,you are correct.", + "video_name": "6GB_kcdVMQo" + }, + { + "Q": "Does the equation at 4:56 imply that there is no magnetic force when a charge isn't moving? If so, how does a paperclip feel a magnetic force towards a magnet when both objects are held stationary?", + "A": "Go to youtube and search for veritasium how do magnets work and watch the pair of videos.", + "video_name": "NnlAI4ZiUrQ" + }, + { + "Q": "what does Q stand for at 5:03", + "A": "The magnitude of the charge.", + "video_name": "NnlAI4ZiUrQ" + }, + { + "Q": "i dont get what a magnetic mono-pole is ( 0:42 - 0:46 ) ?", + "A": "Thanx Matt :)", + "video_name": "NnlAI4ZiUrQ" + }, + { + "Q": "at2:01 why does sal substitute the value of acceleration due to gravity?", + "A": "Because this is equal to the centripetal acceleration at this point as the only force acting on the object at the top of the circle is Fg (draw the free body diagram)", + "video_name": "4SQDybFjhRE" + }, + { + "Q": "at 9:00, you said the cyclobutadiene is antiaromatic, but you didn't really mention this molecule is planar.\nonly at the start when you talk about this molecule, you mentioned the p orbitals may overlap each other.\nbut may doesn't mean definitely", + "A": "If a compound doesn t follow Huckel s rule it can t be aromatic. In fact cyclobutadiene has 4n pi electrons which would make it antiaromatic. And yes it is planar. In fact what happens to avoid this issue: cyclobutadiene will distort into a rectangle with 2 long sides and 2 short sides, this will make more sense if you draw the frost circle for the rectangle. Hopefully that makes sense.", + "video_name": "yg0XJWHPqOA" + }, + { + "Q": "At 0:43 where was the particle before expansion? What were its surroundings?", + "A": "there re no surroundings. The universe is only expanding on the inside because there is no outside. If there were an outside of the universe, it s the same size it s always been.", + "video_name": "eUF59jCFcyQ" + }, + { + "Q": "At 2:40, if the Universe is finite or has no edge then would you be able to get outside or would it be impossible?", + "A": "it would be impossible", + "video_name": "eUF59jCFcyQ" + }, + { + "Q": "At 10:30 , if three points are in the universe , and after some significant amount of time , the universe expands and the three points get separated farther apart. So , is the EARTH getting any farther apart from the SUN and the MOON getting farther apart from EARTH??", + "A": "No, gravitational forces overpower the force of expansion at closer ranges.", + "video_name": "eUF59jCFcyQ" + }, + { + "Q": "in 5:52, If time was the 4th dimension, wouldn't the universe experience a cycle through time?", + "A": "The sphere as a fourth dimension would be infinitely expanding, so even time cannot make it back to the point of origin.", + "video_name": "eUF59jCFcyQ" + }, + { + "Q": "At 10:14 Sal talks about the sphere getting bigger and the points are getting further away from each other. So, if the universe is a sphere and it is continually expanding, Will we (earth) ever possibly get further away from the sun? Will the sun engulf us all before that happens?", + "A": "Earth is held near the sun by gravity, which keeps them together even as the space they are in stretches.", + "video_name": "eUF59jCFcyQ" + }, + { + "Q": "Whats finite at 07:12", + "A": "finite means it has limits unlike infinite", + "video_name": "eUF59jCFcyQ" + }, + { + "Q": "if the percentage of mercury to chlorine is higher, why is there a 1:2 ratio of mercury?", + "A": "An atom of mercury has a lot more mass than an atom of chlorine. Compare the relative atomic masses from the periodic table, mercury is 200.59 while chlorine is only 35.45...so 1 atom of mercury has the mass of about 5.6 chlorine atoms. This is why we need to use moles!!", + "video_name": "NM0WycKCCDU" + }, + { + "Q": "at 6:16 for calculating the ratio, is the bigger number of moles always divided by the smallest number of moles, regardless of the differences in mass percentages?", + "A": "Yes. Always divide all the moles you have calculated by the smallest moles, that gives you the ratio between the atoms which is essentially the empirical formula.", + "video_name": "NM0WycKCCDU" + }, + { + "Q": "at 3:57, I thought that each element had a set number of electrons. So is that a hypothetical question orrr...", + "A": "In a NEUTRAL atom the number of protons is equal to the number of electrons. But this does not always have to be the case. Atoms can and do gain or lose electrons. This is the whole point of the video. An ion is an atom that does not have the same number of electrons and protons, so it has a charge.", + "video_name": "zTUnjPALX_U" + }, + { + "Q": "Hey Sal! at 5:03, you mentioned that there's a 'propyl' functional group on Carbon-3...just to clarify, it's an 'ethyl' group, not propyl (C2H5) :)", + "A": "people with exceptional talent are prone to commit minor mistakes more often - my maths tution teacher", + "video_name": "GFiizJ-jGVw" + }, + { + "Q": "What would the naming be for the last molecule if there were 2 bromines attached to the left hand side carbon in the last molecule (\"3:52\")? Would the E-Z naming apply at all in this case?", + "A": "If there s two then you won t have to convey which bromine is where using the E-Z convention because you have no choice but to draw both in the correct position.", + "video_name": "GFiizJ-jGVw" + }, + { + "Q": "At 4:40 what is Thermogenesis?", + "A": "the production of heat, especially in a human or animal body.", + "video_name": "f_Z1zsR9lFM" + }, + { + "Q": "What does that ATTACK word signifies at 5:16 ?\nPlease help. Thank you.", + "A": "Form a bond. The electrons of the O bond to the C.", + "video_name": "Z4F88tTx9-8" + }, + { + "Q": "At 6:17, wouldn't the lack of Hydrogen in the middle Carbon (Carbocation) make it negative instead of positive?", + "A": "No. The middle carbon could be positive, negative, or a radical. It all depends on whether the carbon has lost an H\u00e2\u0081\u00ba, H\u00e2\u0081\u00bb, or H.", + "video_name": "Z4F88tTx9-8" + }, + { + "Q": "At 11:06, What is Molar Concentration?", + "A": "Molar concentration is defined as the number of moles of solute per liter of solvent. For instance, adding 1 mol of NaCl to make a 1 L solution makes a 1 molar solution of NaCl.", + "video_name": "qbCZbP6_j48" + }, + { + "Q": "Where does the term \"spectrophotometry\"come from? 0:04", + "A": "Spectro- meaning to look photo- meaning light -metry- meaning measurement", + "video_name": "qbCZbP6_j48" + }, + { + "Q": "Near 6:40, why does he write twiceT=I2/I0?", + "A": "Because he is mentioning about the second case, but it should be noted in order to not to be confused that it is not twice , it is just a subscript 2 identifying the second case.", + "video_name": "qbCZbP6_j48" + }, + { + "Q": "At 3:12, couldn't you just round the numbers like 1.0079 to just 1.01?", + "A": "No, that is not being done correctly. Unlike what Sal does in many of his videos, you cannot round to whatever amount you find convenient. You MUST respect the number of significant digits you have. Almost any chemistry will mark a problem wrong if you do not round in such a way that your number of significant digits requires. You cannot round less than that, you cannot round more than that.", + "video_name": "UPoXG1Z3sI8" + }, + { + "Q": "02:23 - If you caught the flu between Jan 7th and 10th, why did the symptoms show up only on 11th and not as soon as you caught it ?\n\nI do understand that it takes some time for the virus to start affecting the body, but isnt 3-4 days too long?", + "A": "It takes some time for the tiny amount of virus that you actually pick up to infiltrate cells, reproduce, and infiltrate more cells. Some of the symptoms are from the effects of the virus invading the cells, and some are side effects from your immune system attacking the virus.", + "video_name": "6vy5CX6vK0I" + }, + { + "Q": "Based on the pneumonia videos, pneumonia is the infection of the flu virus in the lungs in the situation described at 10:04, and pneumonitis (inflammation of alveolar walls) is secondary to this infection. At 10:04 when he describes inflammation of the alveolar walls, is that an instance where pneumonitis and pneumonia are interchangeable? Or, should inflammation of alveolar walls always be called pneumonia if it is caused by pneumonia?", + "A": "The disease entity is called pneumonia clinically and usually there is further description such as bacterial pneumonia, viral pneumonia, fungal pneumonia, etc. At the microscopic, pathologic level, the changes seen are called pneumonitis. When there is no infection, sometimes the disease is described based upon the pathologic changes hence things like aspiration pneumonitis.", + "video_name": "6vy5CX6vK0I" + }, + { + "Q": "What would happen if in 1:45 you push on both pistons with the same amount of force? Would the water just displace? What if there is no possibility for the water to displace? Then could you no longer push on the pistons?", + "A": "I think that if you push on both the pistons with the same force, the piston with larger area will displace the liquid as more pressure is applied on it. if there is no possibility for water to displace, then you can no longer push on the pistons.", + "video_name": "lWDtFHDVqqk" + }, + { + "Q": "At around 9:30...how do the -1, 0, 1, relate to the px, py, and pz?", + "A": "This is just a convention that is used. However, the three p orbitals are equivalent to one another and only acquire the x, y and z suffixes based on how the three axes are drawn. Therefore, it is arbitrary which p orbital is linked to -1, 0 and 1 and it would be equally valid to, say, relate -1, 0 and 1 to pz, px and py, or to any other permutation. All you need to know is that if l =1 then this means there are three p orbitals, and that these three p orbitals are along different axes.", + "video_name": "KrXE_SzRoqw" + }, + { + "Q": "At 4:10, if the electron is not found in the sphere of the s orbital, than where else would it be found?", + "A": "That sphere is just the most likely place for an electron to be found, it could be on the other side of the universe but the probability of that is immensely low.", + "video_name": "KrXE_SzRoqw" + }, + { + "Q": "At 5:15, why would you not want to take one of these devices apart? What could be in items like this that you would need to be afraid of?", + "A": "Underneath the bottom cover you find the electric heater and water hoses. This is a dangerous combination (water and electricity). The manufacturer wants to keep you away from the chance of messing up the connections and putting a defective coffeemaker back in service. In this demo video, the coffeemaker takes a one-way trip to full disassembly. It will never make another cup.", + "video_name": "XQTIKNXDAao" + }, + { + "Q": "At 2:50, when Sal started talking about velocity, was he actually meaning instantaneous velocity?", + "A": "Yes, he was meaning instantaneous velocity. There are two kinds of velocity: average velocity and instantaneous velocity. By just saying velocity , we have to think about which one it means through the context.", + "video_name": "ITA1rW5UraU" + }, + { + "Q": "At 12:05, what are some other things that can cause Cardiac Arrest?", + "A": "Many. Among others, Brugada syndrome.", + "video_name": "vYnreB1duro" + }, + { + "Q": "At about 3:00 Sal talks about plaque and how it can damage your heart. So, if you do get plaque in your blood vessel, how do you get rid of it?", + "A": "Presumably exercise, a low fat, healthy diet and stopping smoking if one is doing so already.", + "video_name": "vYnreB1duro" + }, + { + "Q": "at 9:35 why is the carbon cation sp2 hybridized? shouldn't it be sp3?", + "A": "No. A carbocation only has 3 electron domains so it is planar and sp2 hybridized.", + "video_name": "KPh60w6McPI" + }, + { + "Q": "at 08:22 , Sal says that the [ln V] is evaluated over final \"velocity\" to starting \"velocity\". I strongly think it should be replaced with \"volume\".\nPls. correct me if I'm wrong.\n\nthank you.", + "A": "He misspoke. It is volume. After all, the video is on volume...", + "video_name": "ixRtSV3CXPA" + }, + { + "Q": "at 11:16 why is it (Tf/Ts)^2/3(Vf/Vs)=1????\nwhy is it 1???", + "A": "To start with, ln [(Tf/Ts)^3/2(Vf/Vs)]=0. Now, ln (natural log) is logarithm base e (a constant), so log e [(Tf/Ts)^3/2(Vf/Vs)] = 0. From this, and by the property of logarithm, e to the power of 0 (e^0) = [(Tf/Ts)^3/2(Vf/Vs)]. Property of logarithm says whatever number to the 0th power equals 1. So since (e^0) = [(Tf/Ts)^3/2(Vf/Vs)], this whole [(Tf/Ts)^3/2(Vf/Vs)] expression equals 1.", + "video_name": "ixRtSV3CXPA" + }, + { + "Q": "Around 2:00, for the equation for the very first question, why is molarity used instead of the number of moles present?", + "A": "HCl will dissociate completely and form 0.500 moles of H3O+. Molarity is the number of moles present, i.e. the concentration.", + "video_name": "JoGQYSTlOKo" + }, + { + "Q": "At 1:20, shouldn't it be hydroxonium not hydronium?", + "A": "Hydroxonium and hydronium mean the same thing and both terms are in use.", + "video_name": "JoGQYSTlOKo" + }, + { + "Q": "3:55 What sets off that movement/What causes it?\n\nThe other two steps in the molozonide breaking apart make sense, but this first one doesn't.", + "A": "The instability of oxygen-oxygen bonds and electrostatic attraction. The bonds between oxygen are very weak and are prone to breaking. Once that bond breaks, the electrons will be attracted to a positive charge. Since there is a slight partial positive charge on the carbon, the electrons move into carbon s valence shell. However, this violates the octet rule and thus breaks an adjacent C-C bond in order to have only 8 electrons associated with carbon, setting off a chain of bonds breaking/electron movement.", + "video_name": "bFj3HpdC4Uk" + }, + { + "Q": "Why do seismic waves travel faster through denser material (4:45) ?", + "A": "You can think that in a dense material the molecules are very closer together and when a wave hits one molecule it takes less time for it to reach the next one and the wave then travles faster. In air the molecules are far apart and the wave than travles slower.", + "video_name": "yAQSucmHrAk" + }, + { + "Q": "At 2:33 how is the molecule cyclic? Does that mean it can form a ring structure? if so, i'm having trouble picturing how it would do so.", + "A": "The molecule is cyclic because when you follow the bonds from one atom to another, you come back in a loop.to your starting point. The loop is not round like a circle but, because it is a closed loop, it is described as cyclic and as a ring ..", + "video_name": "FaOOx6IZxV8" + }, + { + "Q": "At 6:50, how does the oxygen attach to the tertiary carbocation instead of bromine? Isn't the bromine atom more electronegative than oxygen to hold onto the bond?", + "A": "Water is much more electrophilic than Br\u00e2\u0081\u00bb, and there is much more water available to attack the cyclic bromonium ion.", + "video_name": "FaOOx6IZxV8" + }, + { + "Q": "At 4:27, Jay numbers one of the carbons as Beta Carbon 3. I don't understand why Carbon 3 is a Beta-carbon. It's not connected to the alpha carbon.", + "A": "The \u00ce\u00b1-carbon is the carbon bearing the leaving group (C-2). So the \u00ce\u00b2-carbons are the ones next to it (C-1 and C-3).", + "video_name": "uCW6154hPkc" + }, + { + "Q": "at 9:52, why does he say that because the iso-propyl group is axial can't participate in the mechanism?", + "A": "In order to get elimination of HCl, the Cl onC2 and the \u00ce\u00b2 H must be in a trans diaxial conformation. If the Cl is axial, the isopropyl group on C1 is also axial and the \u00ce\u00b2 H on C1 is equatorial. There is no axial H on C1, because the isopropyl group has replaced it. The axial \u00ce\u00b2 H must therefore come from C3.", + "video_name": "uCW6154hPkc" + }, + { + "Q": "At 1:52 someone mentioned protozoans. What are protozoans", + "A": "In some systems of biological classification, the Protozoa are a diverse group of unicellular eukaryotic organisms. Historically, protozoa were defined as single-celled organisms with animal-like behaviours, such as motility and predation.", + "video_name": "1aJBToJrlvA" + }, + { + "Q": "At 6:17, why is the pz, px, py etc. used and what do the subscripts stand for?", + "A": "In the p subshell there are three p orbitals: the px, py, and pz orbitals. These three orbitals are identical, except that they point in different directions (they are orthogonal to each other). The subscripts distinguish the p orbitals based on their orientation; if you draw an imaginary x-y-z axis with the origin at your atom of interest, then the px orbital points along the x-axis, the py orbital points along the y axis, and the pz orbital points along the z axis.", + "video_name": "FmQoSenbtnU" + }, + { + "Q": "At 1:57, the electron went way far out, how far out can that get?", + "A": "There is no limit, but the probability of being very far away is infinitesimal.", + "video_name": "FmQoSenbtnU" + }, + { + "Q": "In 11:50, he explains about the structure of Nitrogen. It is 1s^2, 2s^2,2p^3. How can there be 3 atoms in p, where it is not possible when its configuration is s?", + "A": "An orbital can have at most 2 electrons. In the s subshell, there is only one orbital, thus an s subshell is full with 2 electrons. In the p subshell, there are three orbitals, each can have at most 2 electrons, for a total maximum of 6 electrons. Similarly, the d subshell has 5 orbitals for a maximum of 10 electrons. The f subshell has 7 orbitals for a maximum of 14 electrons. Thus, in nitrogen each of the three p orbitals in the p subshell has one electron, for a total of 3 electrons in the 2p subshell.", + "video_name": "FmQoSenbtnU" + }, + { + "Q": "When you were in the second period at 8:01 to 8:07 you only count B for boron before making it 2p. Why didnt you count Li lithium and Be Berrilium?", + "A": "The valence electrons of Li and Be occupy the 2s orbital, not the 2p. Thus, they don t have anything to do with the 2p.", + "video_name": "FmQoSenbtnU" + }, + { + "Q": "Around 12:55 it explains silicone and i dont get how you calculate the electron configuration. I find it terrible confusing. how you have added up the numbers. which numbers do i add up to make the electron configuration?", + "A": "Firstly silicon is not the same as silicone (be careful on exams!). For a neutral atom the number of electrons = the number of protons. For silicon that is 14. The fill order is: 1s 2s, 2p 3s, 3p 4s (google orbital fill diagram) An s orbital can take 2 electrons, a p orbital can take 6 electrons. We just keep filling until we get to 14. 1s2 (12 left), 2s2 (10 left), 2p6 (4 left), 3s2 (2 left), 3p2 (none left). Sorry can t do the superscripts here.", + "video_name": "FmQoSenbtnU" + }, + { + "Q": "at 05:38 it shows wierd looking things, what are those?", + "A": "Those weird looking things are orbitals, the s, p, d and f orbitals. These orbitals are the mathematical functions of the regions of space about the nucleus in which the electrons can be found, maximum of 2 electrons per orbital.", + "video_name": "FmQoSenbtnU" + }, + { + "Q": "What are the diagrams at 04:49 , I don't know them even though Sal mentioned them.", + "A": "These diagrams show the spacial geometry of atomic orbitals. The s orbitals (first column) are actually spheres, but they are shown here as cross-sections to show their nodes (places where the probability of finding an electron is 0). The red shows where the formula describing the orbital (called a wavefunction, from quantum mechanics) has a positive value, and the blue is where it has a negative value.", + "video_name": "FmQoSenbtnU" + }, + { + "Q": "At 11:17, why is Be 2s one when Li is 1s two? They are right beside each other.", + "A": "He was only doing lithium. The complete electron configuration of Li is 1s2 2s1. The electron configuration of Be is 1s2 2s2.", + "video_name": "FmQoSenbtnU" + }, + { + "Q": "In 4:50, does the red and blue represent + 1/2 and -1/2 spin?", + "A": "No, the different colours do not represent the spin as if you look at the 4 lobes of the d orbital (for example the dxz sub-shell), there are two red and two blue sections, but at most it will only contain 2 electrons, which can be found in any of the 4 lobes and not one in each section or even pair of sections.", + "video_name": "FmQoSenbtnU" + }, + { + "Q": "how can we place helium[inert gas]in the second group \"10:20\"?", + "A": "becouse it has two electrons in its outer shell just like the other elements of the second group. the rest of the noblegasses have 8 electrons in their outer shell", + "video_name": "FmQoSenbtnU" + }, + { + "Q": "I dont get how to use the chart at 4:46?", + "A": "The chart show the shapes of each of the orbitals in a given energy level. For example, for n = 4, the chart shows in turn the shapes of the orbitals: 4s, 4px, 4py, 4pz, the five 4d orbitals, and some of the 4f orbitals.Except for levels 1 to 3, you do not have to memorize the shapes. It is more of a reference tool when you want to know what the shapes look like.", + "video_name": "FmQoSenbtnU" + }, + { + "Q": "great vid Sal. But wouldn't @11:11 Lithium be 2s^1 then 2s^2?", + "A": "You would have to fill up the lowest orbital, which means the electron configuration always starts with 1s^1, 1s^2 and so forth. When writing it s like taking the electron configuration of the rightmost element immediately above the period of that element and then writing out the next configuration of the period it is in.", + "video_name": "FmQoSenbtnU" + }, + { + "Q": "configuration of berilium is 2s1 or 2s2 at 11:30", + "A": "Beryllium has four electrons, so its configuration is 1s\u00c2\u00b22s\u00c2\u00b2.", + "video_name": "FmQoSenbtnU" + }, + { + "Q": "At 00:42 Sal says that the reaction is \"spontaneous\", but I don't exactly understand what that means. How did he figure that out?", + "A": "Spontaneous means that somethings starting energy is higher than its ending, it comes from something called Gibbs free energy. This means it releases energy and doesn t need energy to proceed.", + "video_name": "-KE7jTXwNYs" + }, + { + "Q": "At 2:06 NH4Cl is called an acid, but isn't it a salt?", + "A": "It is a salt, but NH4+ is ammonium, which is the conjugate acid of ammonia (NH3).", + "video_name": "lsHq5aqz4uQ" + }, + { + "Q": "how can i identify that solution is buffer solution ? And at 4:35 how does he know that whole of the NH4Cl is going to dissociate into 0.20M of NH4+", + "A": "You need to identify the conjugate acids and bases, and I presume that comes with practice. The same way you know that HCl dissolves to form H+ and Cl-, or H2SO4 form 2H+ and (SO4)2-. In this example with NH4Cl, the conjugate acids and bases are NH4+ and Cl-. Notice how also the way the formula is written will help you identify the conjugate acids and bases (acids come first on the left, bases on the right)", + "video_name": "lsHq5aqz4uQ" + }, + { + "Q": "At 8:48, why is it that you first have to react HCL with H2O to get H3O, and in turn, react the with NH3 instead of directly reacting HCL with HN3 as you did (with NH4 and NaOH) in the first example? I would like to know, for future examples, what instances I would have to utilize this method instead of the first method.", + "A": "The HCl exists in water almost exclusively as H\u00e2\u0082\u0083O\u00e2\u0081\u00ba and Cl\u00e2\u0081\u00bb. So it is more correct chemically to write the reaction using H\u00e2\u0082\u0083O\u00e2\u0081\u00ba. In practice, you can do it either way. What matters is the concentration of NH\u00e2\u0082\u0084\u00e2\u0081\u00ba, not the equations you use to produce it.", + "video_name": "lsHq5aqz4uQ" + }, + { + "Q": "At 3:52 what life could survive without nitrogen?", + "A": "Nothing. Nitrogen is one of the building blocks of protein. As all living things need protein, all life would die - plants and animals.", + "video_name": "6rwoktPmqpY" + }, + { + "Q": "I have a problem with how we include friction in this problem. If the entire premise of the easy style of doing these problems is to treat the system as a single object, shouldn't we use 20 kg for the friction component, and not 12?\n\nIt makes sense to me that the box is being pressed down on the table by the additional force, and the normal force pressing back upwards would also be 20 kg * 9.8, rather than 12 kg *9.8.\n\nThis occurs at 4:40", + "A": "How is the box pressing down with 20 * 9.8 N of force? The force from the 3 and 5 kg blocks on the 12 kg block comes from the ropes that are going over the pulleys so it is horizontal and not not down so it doesn t add to the normal force.", + "video_name": "ibdidr-bEvI" + }, + { + "Q": "At 0:13 Sal uses a sign to represent the angle of the launch. I wanted to know what that sign means? Thanks.", + "A": "It s the Greek letter theta, which stands for angle (it s often used in place of an unknown angle). Hope this helps!", + "video_name": "RhUdv0jjfcE" + }, + { + "Q": "at 3:23 shouldn't the hypothesis be in an if, then statement?", + "A": "You can set up a hypothesis as an if/then statement, but it isn t always required. Hope that helps!", + "video_name": "N6IAzlugWw0" + }, + { + "Q": "oxygen and carbon are having a triple bond at 6:17 the valency of oxygen is 2 how is it possible?", + "A": "I think this is because the new third bond is a dative covalent bond , when both electrons of electron pair shared to form a bond is from ONE atom (in this case, oxygen) only. It can be wrong so plz look it up :)", + "video_name": "vFfriC55fFw" + }, + { + "Q": "at 2:59, what is a photon?", + "A": "Its the basic unit of light. Its the smallest amount of light that you can play around(create, reflect, refract) with.", + "video_name": "y55tzg_jW9I" + }, + { + "Q": "At 6:30, don't you need to take the inverse of that expression to get the equivalent resistance of the 2 resistors in parallel?", + "A": "There are two formulas for computing 2 parallel resistors. The one I used is Rp = (R1 R2)/(R1+R2). The other formula is the one with all the reciprocals. That s the one you are thinking of: 1/Rp = 1/R1 + 1/R2. Both give the same answer.", + "video_name": "j-iR7puLj6M" + }, + { + "Q": "at 7:30,what are microtubules?", + "A": "mi\u00c2\u00b7cro\u00c2\u00b7tu\u00c2\u00b7bule A microscopic tubular structure present in numbers in the cytoplasm of cells, sometimes aggregating to form more complex structures", + "video_name": "X1bmedVziGw" + }, + { + "Q": "At 9:07 does mol mean molecule or is that what it is called.", + "A": "mol means mole (which is Avagadro s number of an atom or molecule).", + "video_name": "-QpkmwIoMaY" + }, + { + "Q": "At 13:26 I don't understand why Sal multiplied the H2O g with the density of water that's stated in the question above. I would love an explanation.", + "A": "Density is mass per volume of a substance. So Density=Mass/Volume (which is why the unit is grams/mL). We have the mass for water = 980grams and density of water (at the same temp) as 0.997g/ml. so substituting the value we can get the volume of water as 980g/0.997g/mL which gives us the volume in mL.", + "video_name": "-QpkmwIoMaY" + }, + { + "Q": "At 8:30, why is the volume of the room used instead of the volume of water?", + "A": "As the liquid water sits in the container, it releases water vapour which spreads throughout the room until it is at an equilibrium with the liquid water. There will be equal amounts of water vapour in every spot of the room and Sal wants to know how many total molecules of vapour there are. So, he takes the entire volume of the room and not just that of the liquid water.", + "video_name": "-QpkmwIoMaY" + }, + { + "Q": "10:50 \"You could treat a Covalent Bond like an Ionic Bond\", this confuses me. Does an electron actually move into the other atoms shell in an Ionic Bond ? or is the Ionic Bond just a Covelant Bond, where the probability of finding the shared electron is much higher around the more Electroniegative atom ?", + "A": "It s somewhere in between. In a completely ionic bond, the electron would move into the other atom s shell and not be shared at all. In most, if not all, actual ionic bonds, the probability of not finding the shared electron in an orbital around the more electronegative atom is very low, so we just say that the electron moved to the more electronegative atom.", + "video_name": "126N4hox9YA" + }, + { + "Q": "At 3:58 he says that carbon and hydrogen have an electromagnetism difference of 0.4 and that still is considered a non polar covalent bond. At what difference would it be considered a polar covalent bond? 0.5, 0.8, 1?", + "A": "You must have meant electronegativity difference The auto-correct changes that to electromagnetism :) generally 0.5 works. Some textbooks say other values, so I don t believe there is a standard value.", + "video_name": "126N4hox9YA" + }, + { + "Q": "i dont understand 1.7 means what at 9:53", + "A": "If the difference in electronegativities of the two atoms is greater than 1.7, the bond between them is considered to be ionic.", + "video_name": "126N4hox9YA" + }, + { + "Q": "at 10:44, carbon forms an ionic bond with lithium. But as we have seen earlier carbon ALWAYS FORMS COVALENT BONDS. So how come it is forming an ionic bond with lithium?", + "A": "Bonds vary all the way from 100 % ionic to 100 % covalent. The C-Li bond is about 43 % ionic and 57 % covalent. The bond is highly polar covalent. It behaves in many reactions as if it were ionic.", + "video_name": "126N4hox9YA" + }, + { + "Q": "At 4:19, Sal started listing momentums and positions for the atoms. But doesn't that violate the Heisenberg Uncertainty Principle?", + "A": "Yes, it does. He can t be certain of both at the same time, however, his point was not to show the momentums and positions but rather to demonstrate the difference between micro and macrostates.", + "video_name": "5EU-y1VF7g4" + }, + { + "Q": "At 9:03 Sal says that it all takes place in space . So if it takes place in space how would the rock move downwards . I mean there is no gravitational force there acting vertically downwards .", + "A": "By space, he meant vacuum. He didn t mean the space where there is no gravity", + "video_name": "5EU-y1VF7g4" + }, + { + "Q": "At 10:01, if you're doing this in space, the rock on top would not be able to offset the pressure inside of the cylinder, right? Since there's no gravity, it would render the rock weightless. I guess I'm being nit-picky, haha.", + "A": "That bothered me a little too. I believe it s in space so that there s no extra air pressure acting on the system from outside, or anything like that, but he may have forgotten about that when he talked about the rock. In the right setup, you could still experience enough gravity in space to make this work. I settled for, It s on the moon, as my explanation. EDIT: And it seems other possibilities are covered in other people s questions and answers!", + "video_name": "5EU-y1VF7g4" + }, + { + "Q": "As at 1:38 minutes it is said that this emission spectrum is unique to hydrogen atom , which means we have different emission spectrum's for different atoms , so does that in turn mean that we have different energies for same energy levels in different atoms ?", + "A": "Yes. Some even swap places.", + "video_name": "Kv-hRvEOjuA" + }, + { + "Q": "He explains the process of the oxidation of water (at about 15:26) but where does the energy for this oxidation come from?", + "A": "From the sun, every process in photosynthesis is fueled indirectly through light. During the light reaction ATP (energy) and NADPH2 (reduction power) is produced which can be later used for reducing CO2 to sugar. The NADPH2 contains the electrons which were taken from the water oxidation.", + "video_name": "GR2GA7chA_c" + }, + { + "Q": "at 10:04 sal says 'hydrogen protons,what is the difference between an hydrogen proton and a simple proton?", + "A": "protons are protons. He s just explaining how they came to be there.", + "video_name": "GR2GA7chA_c" + }, + { + "Q": "At 15:30, Sal explains that water is hydrolyzed to resupply photosystem II with electrons it transferred to photosystem I. I always learned this reaction was carried out by a photoactive enzyme on the phospholipid bilayer but Sal seems to indicate its actually carried out by the photosystem. Any ideas?", + "A": "The reaction is carried out by a poorly understood Oxygen Evolving Complex (OEC) which is very integrally attached to the photosystem II and its working is strongly coupled with the working of PSII and therefore it is actually considered to be single complex.", + "video_name": "GR2GA7chA_c" + }, + { + "Q": "Why is photosystem II before photosystem I? 9:10", + "A": "Photosystem I was discovered before photosystem II, even though photosystem I is the one that comes first. So they re named a bit counterintuitively, but that s only because of the order they were discovered in.", + "video_name": "GR2GA7chA_c" + }, + { + "Q": "At 12:00, is the ATP synthase drawn backwards? Shouldn't the rotor be on bottom if it is pumping the electrons from the lumen to the stroma and producing ATP?", + "A": "Sal drew the ATP synthase the correct way round - upside down relative to in a mitochondrion. In the thylakoid, protons go from inside (the lumen) to outside (the stroma), and ATP is generated in the stroma. In a mitochondrion, protons go from outside to the inside, and generate ATP within the mitochondrion. In some bacteria, the ATP synthase is used in reverse, so ATP is hydrolysed to pump protons out of the cell, but this is not what s happening here.", + "video_name": "GR2GA7chA_c" + }, + { + "Q": "At 1:26 it says that the red light reflected of the rose enters our eye and falls on one of the red colored cones, we can see that the rose is red. What would happen if this ray of light falls on a blue or green cone, is this situation even possible?", + "A": "Different receptors are built to respond to different stimuli. The other cones would not respond to the light of a different frequency. Think about sound, people lose their high range because these specific receptors are damaged and die. Think about the skin, some receptors respond to touch, different ones respond to heat. It is amazing.", + "video_name": "0ugcw7wOZBg" + }, + { + "Q": "At 9:28 why exactly does he write 3d6 when he should be writing 4d6?", + "A": "He writes 3d\u00e2\u0081\u00b6 because the 3d subshell id filled after the 4s subshell.", + "video_name": "NYtPw0WiUCo" + }, + { + "Q": "At 5:34, why does carbon have 4 valence electrons instead of 2 when the 2s2 shell is filled already?", + "A": "To expand on Just Keith s answer and clarify a bit more, only the level 1 shell is filled in carbon. The 2s sublevel is filled, but the electrons in it are still much closer in energy to the 2p sublevel than they are to those in the filled level 1.", + "video_name": "NYtPw0WiUCo" + }, + { + "Q": "At 5:00, why am I not supposed to write the electron confu-thingy as Be 2p2?\nIts confusing.", + "A": "Be is not a noble gas, the square bracket notation is only used with noble gasses", + "video_name": "NYtPw0WiUCo" + }, + { + "Q": "At 9:38 when Sal says, \"the 4th energy subshell,\" is subshell interchangeable with energy level? I thought the subshell related to the shape of the orbital.", + "A": "He should have said the 4s subshell. Energy levels can split into subshells which are composed of orbitals that correspond with the type of subshell. The way we name these are a bit confusing, because there is a difference between say the 2p subshell and a 2p orbital. It is very easy to use the wrong word when describing this stuff.", + "video_name": "NYtPw0WiUCo" + }, + { + "Q": "9:28 Why is it 3d^2 and not 4d^2? Why is it written [Ne] when he's talking about iron (Fe)?", + "A": "Because it is? The 4s and 3d orbitals are similar in energy so they are filled around the same time, but the 4d orbitals are quite a bit higher than those two. Why is what written [Ne]? That element in square brackets notation represents the electron configuration of the noble gas from the row above, it saves time when you get to much heavier elements by removing redundant information. Argon is the noble gas in the row above iron so you use [Ar] to represent the following: 1s^2 2s^2 2p^6 3s^2 3p^6", + "video_name": "NYtPw0WiUCo" + }, + { + "Q": "At 5:20, is the esophagus a part of the lower or upper respiratory tract, or is it not included because it is meant for food and water?", + "A": "It is not included because it is meant for food and water, it is part of the digestive tract.", + "video_name": "Z-yv3Yq4Aw4" + }, + { + "Q": "At 11:05, Rishi said respiratory bronchials, did he mean respiratory bronchides?", + "A": "I think so since there s alveoli on bottom.", + "video_name": "Z-yv3Yq4Aw4" + }, + { + "Q": "I'm pretty sure at 2:17 the C has only 2 methyl groups on it; the third one on the right is supposed to be the bond that was connected to X, right?", + "A": "Don t they have to be hydrogens? SN2 can t occur with a tertiary carbon, or occurs so little to be negligible.", + "video_name": "X9ypryY7hrQ" + }, + { + "Q": "At about 6:28, Sal says that he should only have 3 spots to the right of the decimal, but shouldn't he actually end up expressing his answer as 18.0149 because that still has the same amount of significant figures as the 15.999 because the 0 to the right of the decimal point before the other digits in 18.0149 should not be considered significant.", + "A": "That 0 is significant", + "video_name": "_WXndBGQnyI" + }, + { + "Q": "9:13, when did the first oceans come from , how did they form", + "A": "We re not sure, but water is fairly common in the solar system. The water on earth might have come mostly from comets striking the earth.", + "video_name": "nYFuxTXDj90" + }, + { + "Q": "what does it mean for the orbit to go outward at 1:40 ?", + "A": "They got further away from the Sun.", + "video_name": "nYFuxTXDj90" + }, + { + "Q": "At 2:17, if Earth had life only for part of its history (starting in ~3.8 - 4 Ga), then does that mean that other planets might have had life at one point in their histories?", + "A": "Sure, that s possible. There are some tantalizing hints that Mars may have had bacteria-like life at one point, but we don t know.", + "video_name": "nYFuxTXDj90" + }, + { + "Q": "What do the arrows below the reaction arrow represent? (At 3:18)", + "A": "They are just lines connecting the Br\u00c3\u00b8nsted acids to their conjugate bases, and the Br\u00c3\u00b8nsted bases to their conjugate a", + "video_name": "jIL333CKE9A" + }, + { + "Q": "At 6:32 why did the empirical formula was H2SO4 and why not H2O4S", + "A": "The sulfate anion is just more formally written as SO\u00e2\u0082\u0084 rather than as O\u00e2\u0082\u0084S. Many other elements form similar ions, and they re also written with the general formula of YO\u00e2\u0082\u0093.", + "video_name": "sXOIIEZh6qg" + }, + { + "Q": "0:34: Isn't 2.04% + 65.3% +32.65% = 99.99% and not 100% so wouldn't that statement be incorrect?", + "A": "he rounded a tiny bit, that .01% is not enough to make the statement incorrect", + "video_name": "sXOIIEZh6qg" + }, + { + "Q": "at 6:31, can I write H2O4S instead of H2SO4 like Sal?", + "A": "yes most people go alphabetically when arranging molecular formulas.", + "video_name": "sXOIIEZh6qg" + }, + { + "Q": "At 6:35, Sal writes the empirical formula as H2 S O4. Is there usually a specific order we need to write empirical or molecular formulas?", + "A": "In H2SO4 H2 is the positively charged ion while the SO4 is negatively charged. While writing the molecular formula, the most electropositive element is written first. Hope this helps :)", + "video_name": "sXOIIEZh6qg" + }, + { + "Q": "Shouldn't a mole of different gases have different volumes not all the same of 22.4 at 11:50? Is it because in ideal gases we disregard the gas's volume?", + "A": "Most gases approximate ideal gas behavior as long as the pressure is not to high and the temperature is not too low.", + "video_name": "GwoX_BemwHs" + }, + { + "Q": "At 4:59, there's a model of a molecular structure. What kind of molecule is it modeling?", + "A": "That is nitroglycerin. The black balls represent carbons, white is hydrogen, blue is nitrogen and red is oxygen.", + "video_name": "Rd4a1X3B61w" + }, + { + "Q": "At 5:26 why did it become 16? and where do 4 come from? why is it plus not minus not like the other example?", + "A": "CO2 C has 4 valence electrons, O has 6 valence electrons 4 + 6 + 6 = 16 valence electrons", + "video_name": "97POZGcfoY8" + }, + { + "Q": "At 1:56 how come we don't put 2 more lone pairs of electrons on Be?", + "A": "Total number of electrons in BeCL2 = 16 Which are all used up. ( 6 each to Cl + 4 electrons as bonds)", + "video_name": "97POZGcfoY8" + }, + { + "Q": "At 6:45 Sal says that the base must have the same number of moles as the weak acid. Doesn't that statement assume the acid is monoprotic (donates 1 H+)? How would the calculation change for a diprotic acid (donates 2 H+)? The moles for the acid would just be doubled, right?", + "A": "You re right, so the normality of the base must equal the normality of the acid. Therefore, for diprotic molecules you would need twice as much base.", + "video_name": "BBIGR0RAMtY" + }, + { + "Q": "A magnetic field creates a force on a moving charge and a moving charge creates a magnetic field which would then create a force on a moving charge..., right? How does stationary charge create its own static electric charge like Sal is talking about at 9:01? Did I misunderstand him? I am trying to grasp how electricity and magnetism are the same. Thanks for your help! :-)", + "A": "Electric fields originate from any charge (moving or not) and changing magnetic fields. Magnetic fields originate from moving charge (ie. current) and changing electric fields. A charge will not interact with the field it generates itself.", + "video_name": "Ri557hvwhcM" + }, + { + "Q": "Why does the acid and base stay liquid and turn pink but not form H20 (water) and NaCl (Salt) as the formula stated at about 1:40 in the video?", + "A": "It turns pink because you add an indicator, which has a pink colour in basic solutions. And they reaction has produced water en NaCl, but the salt stays dissolved in the solution. (NaCl is easily soluble).", + "video_name": "d1XTOsnNlgg" + }, + { + "Q": "At 4:53, how do you know that there's a 1-1 mole ratio? And what does he mean by that?", + "A": "From the balanced equation; the unwritten (1) before the element/compound is the balance. (1)NaOH+(1)HCl==>(1)NaCl+(1)H2O", + "video_name": "d1XTOsnNlgg" + }, + { + "Q": "At around 3:45, David said that the momentums were positive 5 and negative 10. Could you choose that moving to the left was instead positive and moving to the right was negative? Making the equation: (0.2kg)(-5m/s) - (0.2kg)(10m/s)?", + "A": "Try it and see what happens. Good way to learn.", + "video_name": "uMYAc04D0ak" + }, + { + "Q": "how does bacteria get its energy 1:40", + "A": "Bacteria obtain energy by either ingesting other organisms and organic compounds or by producing their own food. The bacteria that produce their own food are called autotrophs. Bacteria that must consume other organic molecules for energy are called heterotrophs.", + "video_name": "dQCsA2cCdvA" + }, + { + "Q": "2:07\nhow much DNA do we have?", + "A": "Humans have 46 chromosomes that contain all of the genetic information, and there are over 25,000 genes in the human genome. Genes are composed of DNA, and it is predicted that there are over 3 billion base pairs in the human genome. Humans have approximately 10 trillion cells, so if you were to line all of the DNA found in every cell of a human body it would stretch from the earth to the sun 100 times!", + "video_name": "dQCsA2cCdvA" + }, + { + "Q": "At 11:20:\n\nWhat did 12 ever do?\nHow was it activated?", + "A": "Factor 12 is the first factor that is activated in the intrinsic pathway. It is activated by a called Kallikrein. Factor 12 then simply becomes a catalyst to convert 11 from its inactive form to its active form.", + "video_name": "FNVvQ788wzk" + }, + { + "Q": "At 4:08 why would it be an SN2 if that is a tertiary carbon and SN2 rxn only happens in primary and secondary carbons?", + "A": "its not a tertiary carbon, its given at the start that its a secondary or primary carbon", + "video_name": "LccmkSz-Y-w" + }, + { + "Q": "Hey, at 5:40, is there any reason we use PBr3 instead of H-Br? Thanks.", + "A": "The phosphate ester that is made when you use PBr3 provides a better leaving group than OH on its own. Jay makes this point in the video.", + "video_name": "LccmkSz-Y-w" + }, + { + "Q": "at 1:35 you said that a bullet goes as fast as a jet. how fast does a jet go in miles?", + "A": "Legally around 300MPH for the big commercial jets, Regular Jets can go around 600MPH legally, but when we talking Illegally were talking 1000MPH+", + "video_name": "GZx3U0dbASg" + }, + { + "Q": "At 6:15, when you begin to talk about AUs, the measurement is about equal to the distance between the earth and the sun. Was this done on purpose?", + "A": "yes, that s the definition of the AU", + "video_name": "GZx3U0dbASg" + }, + { + "Q": "At 3:32, how do you know the speed of a bullet.", + "A": "The muzzle velocity of standard rounds for guns are well known. The manufacturing is well controlled so that they will have predictable trajectories when fired.", + "video_name": "GZx3U0dbASg" + }, + { + "Q": "At around 1:21, Sal mentions that the Earth is approximately 40,000 km. About how many miles is that?", + "A": "To convert to miles just divide by 1.6; so 25,000", + "video_name": "GZx3U0dbASg" + }, + { + "Q": "in 6:10 why does sal multiply both sides of the equation by 2?", + "A": "to remove the 2 times acceleration which is in the denominator in the RHS of the equation.", + "video_name": "2ZgBJxT9pbU" + }, + { + "Q": "At 9:48, wouldn't it be more accurate to express Vf as Vf = - |sqrt(19.6h)| m/s?", + "A": "Yes, but by convention when we use the square root sign we mean the positive root of the value.", + "video_name": "2ZgBJxT9pbU" + }, + { + "Q": "At 4:00, how does he get (final velocity + initial velocity) / 2 ?", + "A": "That s how you calculate an average of two numbers. You add them up and divide by 2.", + "video_name": "2ZgBJxT9pbU" + }, + { + "Q": "At 9:13 when both sides are square rooted, how come the 19.6 doesnt become 4.42?", + "A": "It is true that you could write 4.42 instead of \u00e2\u0088\u009a19.6, but you would lose the accuracy of the number. 19.6 is not equal to 4.42, rather 4.4271887242357310647984509622058. And yet, though it is more accurate, it is still not. If you get an irrational number, just keep it in the \u00e2\u0088\u009a form.", + "video_name": "2ZgBJxT9pbU" + }, + { + "Q": "at 3:34 how come it is called the swimmers view?", + "A": "Because one arm is raised up by the patient s head as if they were swimming the freestyle stroke.", + "video_name": "cbkTTluHaTw" + }, + { + "Q": "3:40 why did carbon have 'too many bonds' isnt it perfectly stable with 4 bonds and 0 formal charge?", + "A": "You re forgetting the implied hydrogen on each carbon, benzene has the formula C6H6, each carbon is bonded to 2 other carbons and 1 hydrogen", + "video_name": "oxf0LMJTklg" + }, + { + "Q": "at 8:38 aren't the both of the products same molecule flipped around ?", + "A": "I don t know which way you want to flip, but the answer is No . They are different molecules. You can flip them any way you want, and you will not be able to make all the bonds coincide with each other.", + "video_name": "fSk1Crn3R2E" + }, + { + "Q": "At 9:32, are we supposed to just know that charcoal (C) is needed with our metal (Pd), or is there some rule being followed?", + "A": "This is just something to know. When the Pd is spread over carbon, it greatly increases the available surface area, and thus the efficiency, of the catalyst. Thus, practically, a palladium hydrogenation is usually palladium on carbon (written as Pd/C).", + "video_name": "fSk1Crn3R2E" + }, + { + "Q": "ok, wait. for statement two, or 3:30, an unbalanced force doesn't necessarily mean tethering the moving object. what if the object hit a wall? then it would slow down, right? or if it rubbed against a surface, it might change direction, but it would also change speed. how is statement 2 wrong?", + "A": "hitting a wall and rubbing against a surface are unbalanced forces and they change the motion of the object", + "video_name": "D1NubiWCpQg" + }, + { + "Q": "At 3:58,Sal said that the satellite changes its direction but not its speed.So if that same planet is moving around the sun, shouldn't the speed of the satellite vary if it has to go around the planet?", + "A": "I think when the satellite is in the geo stationary orbit its velocity is constant other wise the satellite velocity changes like a planet around the sun", + "video_name": "D1NubiWCpQg" + }, + { + "Q": "at 2:56, it says \"and they could hold on to the rope, and as long as they hold on to the rope, they'll keep going in circles. wound't they eventually stop from the friction on the ice?", + "A": "yes but he is imagining ice that is so slippery that it has no friction, so that we can get the idea of what it means for an object to have no net force on it", + "video_name": "D1NubiWCpQg" + }, + { + "Q": "At 1:10, why the first statement is true?", + "A": "Why wouldn t it be true? All the statement is doing is rephrasing Newton s First Law.", + "video_name": "D1NubiWCpQg" + }, + { + "Q": "Once Sal has simplified the equation (12:51) to be 3PV=mv^2 N he divides the equation by two. This takes on the form 3/2PV=(mv^2/2 N). Why doesn't the number of molecules in the system also get divided by two when he divides the two halves of the equation by two? It seems to be exempt from his division of two on both sides of the equation. Shouldn't the equation look like 3/2PV=(mv^2 N)/2?", + "A": "If you remember order of operations, division and multiplication can be done in either order. He wrote it as (mv^2)/2 *N so that you could see that 1/2 * mv^2 is kinetic energy", + "video_name": "qSFY7GKhSRs" + }, + { + "Q": "At 2:35, it is said that experimental studies have shown that the structure of the amide is planar, which means the molecule's sp2 hybridized resonance structure contributes more towards the resonance hybrid. But the stability of the first structure (with sp3 hybrid N) is greater due to zero formal charge. Why is that the stable structure does not contribute more to the resonance hybrid?", + "A": "Although the first structure does not have any formal charges, the electronegativity of the oxygen atom does give it a partial negative charge. The resonance on the second structure is a stabilizing factor, and its sp2 hybridization is more stable than the sp3 hybridization of the first structure. (Covered later in the section on acid-base chemistry.)", + "video_name": "kQCS1AhAnMI" + }, + { + "Q": "What is the proper usage of the spelling (5:35), blastocoele vs. blastocoel? My textbook says blastocoele, and I am just curious. Thanks!", + "A": "both are right", + "video_name": "-yCIMk1x0Pk" + }, + { + "Q": "At 6:00 what is the difference between MORULA and BLASTOCYST??", + "A": "A morula is a special kind of blastocyst, it has 16 cells assembled in a solid block of cells and looks like a mulberry/ Latin: morula. A proper blastocyst is a few days older, has more cell and forms a hollow sphere.", + "video_name": "-yCIMk1x0Pk" + }, + { + "Q": "at around 3:56 , does this mean that oxygen can have an oxidation state of 1+ when bonded with any other element in it's group ?", + "A": "No, oxygen is more electronegative than the other elements in its group so it will be -2 with all of them.", + "video_name": "R2EtXOoIU-E" + }, + { + "Q": "At 6:33, Sal says vector v is the sum of is the sum the other two component vector and he has even proved it in his previous video. But, doesn't that break down the traditional Pythagorean Theorem?\nEven the result at the end of the video doesn't sum up to 10(value of vector v) but when we use the Pythagorean Theorem, the equation does satisfy. Anyone please explain .", + "A": "When you use the Pythagoras theorem, you find the magnitude of the vector. But, in this video, Sal was talking about the vectors, not just their magnitude. Hope this helps :)", + "video_name": "2QjdcVTgTTA" + }, + { + "Q": "At 2:15 Sal mentions an \" important caveat \" , what exactly is that ?", + "A": "A caveat often means an exeption or a problem, ex. It is fun to ride a bike but there s a caveat, you might fall over and hurt yourself", + "video_name": "zA0fvwtvgvA" + }, + { + "Q": "6:35 Isn't the inaccuracy in finding the work in each measured area coming from the fact that you are only measured the area of the rectangle instead of including the triangle above it as well? Assuming that the pressure changes form a straight line, in order to get an accurate value, couldn't you get the area of the rectangle, then use an equation to find the area of a right triangle to find the area above, then add both to find the correct area?", + "A": "I suggest that you watch the calculus videos, it will help to make sense of finding the areas under curves. You are right, when dV is not infinitely small, then it is not exactly a perfect rectangle. But using calculus, we can make it so that we are adding up all the rectangles where dV is so infinitely small that the little triangle at the top doesn t exist. I m sure Sal can explain this a lot better than me, in his Calculus videos :)", + "video_name": "M5uOIy-JTmo" + }, + { + "Q": "At 13:54 the amount of work needed for the system to reach from state 1 to state 2 is larger than the amount of the whole cycle. Is it because when the system was returning from state 2 to state 1 it was doing work?", + "A": "You have it in reverse. From state 1 to state 2, the system is doing work on the surroundings. (Volume is increasing (work of expansion)). From state 2 to state 1, the surroundings are doing work on the system. (Volume is decreasing (work of compression)). Because the area under 1 to 2, is greater than the area under 2 to 1, the net effect is more work being done on the surroundings than is being done on the system.", + "video_name": "M5uOIy-JTmo" + }, + { + "Q": "At 8:22 how does thermal radiation interact with our skin and transfer energy?Is it the magnetic and electric field that interacts or the photon of light that transfers heat?", + "A": "I was confused about this as well, seeing as the apparent cold air still exists between you and the fire as you are warming up. I m not sure that is true once the fire is active. You are correct in assuming that the photon transfers the heat. Photons can carry heat energy, even though they have no mass. This phenomenon also explains how you warm up when you step into the sunlight on a chilly day :)", + "video_name": "8GQvMt-ow4w" + }, + { + "Q": "At 3:20 why 7 times?", + "A": "Just an arbitrary amount of times, he could have done it more or less. The amount of windings would effect the current produced.", + "video_name": "jabo8iTesqQ" + }, + { + "Q": "0:30 How do you know that Co2 is going to be your cation? Sorry, I'm a bit behind. (And confused)", + "A": "In the formula of an ionic compound (at least in one that only has 2 different elements) the first element is the cation and the second is the anion.", + "video_name": "vVTwzjvWySs" + }, + { + "Q": "Around 9:30, Sal is trying to find the legs of the right triangle. Why does he use \"soh\" and \"cah\"? How do either of those relate to the length of the side?\nAt 9:55, he says \"5 sine, of 36.899, is equal to...\" What is \"sine\" and \"cosine\"? And how are they used here?\nThanks in advance.", + "A": "soh, cah and toa are mnemonics (look it up) for Sine = Opposite side / Hypotenuse ==> SOH Cosine = Adjacent side / Hypotenuse ==> CAH Tangent = Opposite side / Adjacent side ==> TOA", + "video_name": "xp6ibuI8UuQ" + }, + { + "Q": "In 6:25, Sal writes ||a||. What do the double lines mean?", + "A": "Those lines indicate that we are taking the magnitude of the vector between them. They are sort of like a vector version of the absolute value sign in math.", + "video_name": "xp6ibuI8UuQ" + }, + { + "Q": "at 12:30 What does he mean by saying making this a 2 component velocity", + "A": "Sal said: break that down into two component velocities . These velocities are horizontal and vertical components of the given velocity.", + "video_name": "xp6ibuI8UuQ" + }, + { + "Q": "At 3:41, what is a nuetron", + "A": "A nuetron is a sub-atomic particle that is inisde an atom. In a nuclues (which is in an atom) there are two sub-atomic particles - protons and neutrons. Neutrons have a mass of 1 (relative to the mass of a proton) and a charge of 0.", + "video_name": "i-NNWI8Ccas" + }, + { + "Q": "at 5:00,it is said that hydrogen will turn to deuterium and then to helium , why cant deuterium change to TRITIUM and then to helium ?", + "A": "You start with a bunch of Hydrogen-1, which is basically free protons. Some of the protons fuse, and immediately decay to form deuterium. Where do the free neutrons, which only have a 15 minute half life, come from to then fuse to form tritium?", + "video_name": "i-NNWI8Ccas" + }, + { + "Q": "I was reading that a neutron is heavier than a proton. Then how could a proton and a neutron have a smaller mass than 2 protons (as Sal mentioned at around 4:00)? To convert a proton into a neutron, one would have to add the mass difference in the form of energy. Then how would the reaction be exothermic?", + "A": "The Deuteron D is a stable particle composed of a proton p and a neutron n. To separate D into its components you have to provide energy in order to overcome the strong binding forces. This energy you have to add corresponds to a mass according to Einsteins formula E=mc^2 Therefore the products (p+n) are heavier than the particle D you startet from.", + "video_name": "i-NNWI8Ccas" + }, + { + "Q": "As far as i know a neutron is composed of one proton and one electron but Sal at 3:53 said that when two protons come very very close to each other, a proton degrades into a neutron.\nSo, how is it possible for the creation of a neutron without a proton?", + "A": "A neutron is not composed of a proton and electron. A proton decays into a neutron when one of its constituent up quarks decays into a down quark. A neutron can also decay into a proton via the reverse process.", + "video_name": "i-NNWI8Ccas" + }, + { + "Q": "During the video on the birth of stars, Sal said at about 0:17 that gravity would bring the hydrogen atoms together. But excluding the clouds of hydrogen, there is really nothing in space. Why won't the hydrogen atoms just diffuse and get evenly distributed in the universe?", + "A": "Even individual atoms have a tiny tiny bit of gravitational force that attracts them into forming clouds. If a certain cluster of hydrogen atoms form a dense enough cloud, they attract even more hydrogen atoms until eventually you get the kind of mass associated with stars.", + "video_name": "i-NNWI8Ccas" + }, + { + "Q": "In the beginning Sal starts with hydrogen atoms...\nQ1.Were did that hydrogen come from in the first place?\nQ2.How did it become a cloud 0:03? (Why were the hydrogen atoms slightly close in the beginning)", + "A": "The hydrogen came from the big bang (supposedly), just like all of the other matter. It became a cloud because the atoms were and are attracted to each other, and they like to form together.", + "video_name": "i-NNWI8Ccas" + }, + { + "Q": "0:30 wouldn't the hydrogen atoms accelerate since the gravatational force begins acting over a shorter and shorter distance therefore becoming stronger", + "A": "I would imagine that since as they move in more, they heat up more, and so the gas would also try to expand, creating a counter force that would balance it out.", + "video_name": "i-NNWI8Ccas" + }, + { + "Q": "What's a nuclei? {2:48}", + "A": "More than one nucleus.", + "video_name": "i-NNWI8Ccas" + }, + { + "Q": "7:10- What does he say?", + "A": "At 7:10, he says, ...there s a huge step temperature...", + "video_name": "i-NNWI8Ccas" + }, + { + "Q": "So at 7:16 he mentioned that Jupiter was a example of not fusing into a star. If there was enough mass, could Juipter become a star?", + "A": "Jupiter would have to engulf all of the other planets in the solar system 20 times over in order to be massive enough to star fusing its hydrogen.", + "video_name": "i-NNWI8Ccas" + }, + { + "Q": "at 0:30, Sal says that the gravity interacts with \"atoms\" in a huuge distance, Doesn't gravity has a limitation? Sorry for my english.", + "A": "No, as far as we understand it, gravity has unlimited range, although the strength of the field declines with the square of the distance from the mass that generates the field.", + "video_name": "i-NNWI8Ccas" + }, + { + "Q": "At 0:33 , why sal took theta between 0 and 90 degrees ?\nPlease explain .\nThank you .", + "A": "At 0 or 90 degrees, the given equation for distance (d=(2s^2/g)*cosX*sinX) is 0 (sin 90=0, cos 0=0). This can be seen in the graph at 1:26, where 0 and 90 are x-axis intercepts. Since we re looking for optimal distance, these values can be immediately discarded. This makes sense in a real world way, because the horizontal distance traveled if the projectile is shot straight up or straight into the surface will be 0.", + "video_name": "snw0BrCBQYQ" + }, + { + "Q": "At 5:30, in reference to the formula, how can one tell what the graph will look like?", + "A": "Calculate a few points on it, and make a sketch", + "video_name": "2GQTfpDE9DQ" + }, + { + "Q": "At 3:03 how does the OH molecule gets 1+ve formal charge? I'm not able to understand......", + "A": "The O atom in the oxonium ion has two electrons in a lone pair, plus one electron from each of the \u00cf\u0083 bonds (5 valence electrons). That\u00e2\u0080\u0099s one less valence electron than in an isolated O atom. \u00e2\u0088\u00b4 Formal charge = 6 - 5 = +1.", + "video_name": "wCspf85eQQo" + }, + { + "Q": "At 4:32 It says that only one cell will be a successful sex cell while the other three are polar bodies- what do these polar bodies do?", + "A": "In humans, they really don t do anything. However, in plants, they also become sex cells.,", + "video_name": "IQJ4DBkCnco" + }, + { + "Q": "at 0:19, what is a diploid number?", + "A": "Diploid number means the number of chromosomes in the body cells of a diploid organism. In humans, 46 is the diploid number (body cells) and 23 is the haploid number (egg and sperm). Note: A diploid organism has paired sets of chromosomes in a cell. In humans, there are 23 homologous pairs of chromosomes where one set is inherited from each parent. Hope it helps.", + "video_name": "IQJ4DBkCnco" + }, + { + "Q": "4:37 If Meiosis is occurring in the respective reproductive organs than why does he speak about mixing our parents dna, I know that DNA get's passed on, but how does the whole \"mixing process\" occur in our own bodies? And to what extent?", + "A": "During sexual reproduction, the male and female gametes (The sperm and the egg) fuse, leading to the formation of a zygote. The zygote s DNA is a mixture of both the parents DNA, which comes from the respective gametes.", + "video_name": "IQJ4DBkCnco" + }, + { + "Q": "Sorry if this seems like an awfully basic question, but why does O get a negative charge at 4:01?", + "A": "Well oxygen is a very electronegative atom hence it can remain stable holding an additional electron/negative charge.", + "video_name": "nv2kfBFkv4s" + }, + { + "Q": "at 0:44, Sal describes the first law of thermodynamics. however, isn't it the law of conservation of energy?", + "A": "Indeed the first law of thermodynamics is a version of the law of conservation of energy.", + "video_name": "Xb05CaG7TsQ" + }, + { + "Q": "heat isn't a form of energy is it? @ 7:28 I thought heat was the process or transfer of energy from system to surroundings?", + "A": "Heat is a form of thermal energy.", + "video_name": "Xb05CaG7TsQ" + }, + { + "Q": "At 11:06, Sal used the full decimal for the atomic weight of Chlorine, but rounded for the atomic weight of Phosphorus. Won't this throw off some of his data?", + "A": "He will have to round his final answer to the same number of sig figs as his chlorine number.", + "video_name": "jFv6k2OV7IU" + }, + { + "Q": "8:00 , how do we know what ratio goes on top or bottom", + "A": "The compound you have goes on the bottom, the one you want goes on top. In that example he needs to convert moles P4 to moles Cl2 so in the ratio moles P4 goes in the denominator so it will cancel, and moles Cl2 goes in the numerator.", + "video_name": "jFv6k2OV7IU" + }, + { + "Q": "at 4:05 is there a difference between \"mole\" and \"mol\" ?", + "A": "Using mol for mole is like using m for meter", + "video_name": "jFv6k2OV7IU" + }, + { + "Q": "i thought at 3:10 ~ 3:20 sal said atomic weight but ment atomic mass unit\nwhat is a atomic weight? or is this a typo?", + "A": "Atomic weight is an outdated term that we no longer use, as we once did, to refer to atomic mass.", + "video_name": "jFv6k2OV7IU" + }, + { + "Q": "why did sal used 1.45g p4 at time 4:47?", + "A": "If you go back to 00:00 you ll see it s given in the question", + "video_name": "jFv6k2OV7IU" + }, + { + "Q": "At 7:04, why 6 moles multiplied in the conversion equation instead of 12 moles?", + "A": "See the balanced equation,in that 6 is the stoichiometric coefficient of cl2 . this meant 6 moles of cl2 . this was why 6 was multiplied.", + "video_name": "jFv6k2OV7IU" + }, + { + "Q": "at 9:20, why did he use 35.453 instead of rounding up to 36 or down to 35 like he would have in the other videos?", + "A": "Because Chlorine exists as three different isotopes with atomic weights of 35, 36 and 37, precision chemistry uses an average atomic weight based on the proportion of the isotopes in nature. Early chemistry just uses the Cl 35 for simplicity as it is the most abundant.", + "video_name": "jFv6k2OV7IU" + }, + { + "Q": "At 4:24, does the unit like grams or moles effect the problem?", + "A": "Is it different to have 2 kg of socks instead of 2 socks? Yes, right? A mole is a number. Gram is a measure of mass. Not interchangeable.", + "video_name": "jFv6k2OV7IU" + }, + { + "Q": "at 3:59 you wrote mol. do you mean mole?", + "A": "mol is the standard abbreviation for mole.", + "video_name": "jFv6k2OV7IU" + }, + { + "Q": "At around 9:20, why did Sal not round the atomic weight of chlorine to 35? You can't have a chlorine atom that has 18.453 neutrons right?", + "A": "No but you can have trillions and trillions of atoms that average out to that weight.", + "video_name": "jFv6k2OV7IU" + }, + { + "Q": "About 2:40, when he's describing the configuration for nickel, if the 3d8 is at the end then it's organized by energy state, right? And if the 4s2 is last with the 3d8 behind it then it's organized by distance from the nucleus?", + "A": "yes", + "video_name": "YURReI6OJsg" + }, + { + "Q": "is D orbitals always like the chart that khan made in 5:53", + "A": "Yes the d orbitals have more energy, but backfill previous shells.", + "video_name": "YURReI6OJsg" + }, + { + "Q": "at 7:23, where are noble gases on the periodic table and what are they?", + "A": "They are all the way over on the right side, and they are gases that generally will not engage in chemical reactions. They are inert.", + "video_name": "YURReI6OJsg" + }, + { + "Q": "2:30 , why is isn't 4D 8 , why do we subtract 1 from the D block", + "A": "there is a trend with the respective D and S orbitals once you are referring to Copper and Chromium. The trend is that when 4s orbitals have a lower energy than the 3d orbitals so they give off an electron and have only one electron on its orbital instead of the required electron pair. When referring to 4D and 5s orbitals its the same trend.", + "video_name": "YURReI6OJsg" + }, + { + "Q": "At 02:43, shouldn't the 3d8 come before the 4s2?", + "A": "4s comes before 3d because, before the orbitals are filled, the 4s is lower in energy than the 3d so is occupied first.", + "video_name": "YURReI6OJsg" + }, + { + "Q": "In the first video in this series on 'Orbitals' Sal instructed us to visualize that those electrons furthest away from the nucleus posses the greatest potential energy; they are in the highest energy state. On this logic, how is it that at around 3:20 in this video Sal lets us know that within Nickel [Ni] the 3D8 electrons are higher energy than the 4S2; how can this be when the 4S2 electrons are further away from the nucleus than 3D8?", + "A": "The 3d electrons in Ni have to fit in between the negative charges of all of the 3s and 3p electrons. The 4s shell doesn t have as much repulsion, so it takes less energy for an e- to live in a 4s orbital than in a 3d orbital.", + "video_name": "YURReI6OJsg" + }, + { + "Q": "At 00:21 Sir said that helium belongs to 's' block but all noble gases belong to 'p' block. This can disturb the configuration of electrons in Ni atom. Why is 'He' considered to be in 's' block?", + "A": "He has no p orbitals at all. It just has a completely full 1s\u00c2\u00b2 orbital and that is all.", + "video_name": "YURReI6OJsg" + }, + { + "Q": "At 1:35, are there more than one type of current if there is electron current? I thought that the only thing moving was the electrons moving from atom to atom, or are the atoms actually moving, because protons can't move on their own.", + "A": "Current is a general concept of moving charge. There are two types of charge, but we don t divide that into two types of current. One + charge moving to the left is the same current as one - charge moving to the right.", + "video_name": "17EhKw2tsu4" + }, + { + "Q": "9:50 When you said 1c=6.24x10^18, can you show me step by step to convert it to electrons? how did you get 1.6x10^-19?", + "A": "1 C = 6.24E18 electrons. Divide both sides bye 6.24E18 and you will have coulombs per electron.", + "video_name": "IDQYakHRAG8" + }, + { + "Q": "At 6:55, Sal says that your hair is attracted to the balloon because the negative charge of the balloon has repelled the electrons in your hair, leaving a disproportionate number of protons. But wouldn't it also be the case (and simpler to explain) that you hair is positively charged simply because it's missing the electrons that were \"stolen\" by the balloon?", + "A": "But the balloon attracts hair that it did not rub. How does it do that?", + "video_name": "IDQYakHRAG8" + }, + { + "Q": "At 6:16, why does the balloon grab electrons only? Why not protons?", + "A": "Protons are very heavy and are tightly bound in the nucleus of the atoms. Electrons are light and are loosely bound to their atoms", + "video_name": "IDQYakHRAG8" + }, + { + "Q": "6:19\nThis might be an arbitrary detail, but why is the balloon grabbing electrons from your hair and not protons? Is there a reason for this?\nThanks.", + "A": "Atoms have electrons on the outside, and nuclei on the inside. The electrons are very small compared to the nucleus.", + "video_name": "IDQYakHRAG8" + }, + { + "Q": "10:03 i thought coulombs were only for electrons/positrons", + "A": "Coulomb is the unit of charge. Whatever has charge, the charge can be measured in coulombs.", + "video_name": "IDQYakHRAG8" + }, + { + "Q": "At 10:40 Why does he say -19 not -18?", + "A": "As when we divide 1 by 6.24x10 to the power 18,then we get a value 0.1609x10 to the power -18,and shifting one decimal backwards,th value becomes 1.609x 10 to the power -19.", + "video_name": "IDQYakHRAG8" + }, + { + "Q": "Starting with 7:45, Sal multiplied the number of the mole( ~6 * 10 ^ 23 molecules / mole) with the 1 * 10 ^ -7 moles / liter.\nI know what the term \"mole\" is.\nHowever, I just don't get the part why would you multiply the mole on the already made(shown) [H3O]?", + "A": "I didn t watch the video, but he must have wanted to know how many molecules there are per liter (molecules / mole) * (moles / liter ) = molecules / liter", + "video_name": "NUyYlRxMtcs" + }, + { + "Q": "4:05, what are ions?", + "A": "Ions are atoms that have either lost or gained an electron, giving them an overall charge since they have an unequal number of protons (positive charge) and electrons (negative charge).", + "video_name": "NUyYlRxMtcs" + }, + { + "Q": "How can that one Hydrogen at 3:37 take 2 electrons if it only has one proton (+1) charge?", + "A": "No hydrogens took any electrons at any point here Both the electrons that once were in an oxygen-hydrogen bond on the right water molecule have become a third lone pair of electrons on that right product (hydroxide)", + "video_name": "NUyYlRxMtcs" + }, + { + "Q": "at 11:13, how are you getting 116 J? what is the conversion?", + "A": "1/2 * 0.145 kg * (40 m/s)\u00c2\u00b2 = 116 kg*m\u00c2\u00b2/s\u00c2\u00b2 = 116 J", + "video_name": "o7_zmuBweHI" + }, + { + "Q": "5:57 When we are numbering the \"shortest path\" as stated in the video, i.e. the carbons between the bridge carbons, do we automatically number away from carbon number 1? So if there were 2 carbons between bridge carbons 1 and 4, how would we number them?", + "A": "If it s symmetrical then it doesn t really matter If it was subsituted then you would number the carbon with the functional group first", + "video_name": "cM-SFbffb7k" + }, + { + "Q": "9:43. Looking at the bicyclo on the left...why couldn't you start from the bridge carbon and then go left and make the 6th carbon into the second? I'm guessing Counting on the longest carbon chain takes precedence over having the methyl on a lower carbon?", + "A": "Correct. Counting on the longest carbon chain takes precedence over having the methyl on a lower numbered carbon. But if the 6-methyl had been on C-7, the name would still be 6,8-dimethylbicyclo[3.2.1]octane. We would still start numbering by going around the largest bridge, but we would use the numbering in the crossed-out structure in order to get the lowest numbers.", + "video_name": "cM-SFbffb7k" + }, + { + "Q": "At 1:48, how is the OH coming out at us in space", + "A": "That picture of the model with black carbons and a red oxygen is showing how the model looks in 3D. If you put the carbon backbone in the same plane, then the groups coming off the carbon are either coming towards you or going away. It may help if you get your hands on a molecular modelling kit.", + "video_name": "ZAgQH2azx3w" + }, + { + "Q": "7:13 - 7:20 | Is there not also some Carbon-13 and Carbon-11?", + "A": "Most carbon is carbon-12, followed by a small about of carbon-13. All other isotopes of carbon are radioactive and only exist in insignificant trace amounts. However, carbon-11 is important for medical purposes.", + "video_name": "NG-rrorZcM8" + }, + { + "Q": "At 6:50 Sal says \"one proton or one neutron is very close to 1 amu\". He had said before that the electron has really small mass. Does that mean that 1 amu is essentially the combined mass of 1 proton or neutron plus 1 electron?", + "A": "No. An individual proton is 1.007276466812 u. An individual neutron is 1.00866491600 u. And an individual electron is 0.00054857990946 u. The amu is defined as 1/12th the mass of Carbon-12, which includes 6 protons, neutrons, electrons. It also has binding energy, which converts some of the mass into energy to hold the nucleus together.", + "video_name": "NG-rrorZcM8" + }, + { + "Q": "At 3:10, can't we write HOH as H2O?", + "A": "You can, but HOH is more commonly used in university or higher level organic chemistry when you deal with reaction mechanism.", + "video_name": "XEPdMvZqCHQ" + }, + { + "Q": "At 5:07 (CH)3COCH3, Is the Centered Carbon primary,secondary or tertiary?", + "A": "Given that the definitions for primary through quaternary carbons are based on how many other carbon atoms are attached - what do you think the answer is? Look at the Lewis structure 6:09, there are three bonds to the carbons of CH3 groups and one to oxygen. That means the central carbon is a tertiary carbon. Note that the condensed structure is actually (CH3)3COCH3.", + "video_name": "XEPdMvZqCHQ" + }, + { + "Q": "At 1:25, instead of having two double bonds in the sulphuric acid shouldn't have two dative bonds?", + "A": "As far as I know, either way, it should mean the same thing.", + "video_name": "dbdVMThH1n8" + }, + { + "Q": "I am actually looking at an updated organic textbook right now and I believe 13:53 should be be two different steps. Deprotanation occurs after the leaving group leaves hope that helps all you guys understand the mechanism better but thanks Kahn for doing most of it right!", + "A": "No. Actually you are mistaken. You are a step premature....there must be a proton transfer between OH and OR before the leaving group leaves. He has the correct mechanism...I have no idea what you re specifically referring to.", + "video_name": "dbdVMThH1n8" + }, + { + "Q": "At 3:36, can you give me an example of a good mutation?", + "A": "Bacterial flagella, antibiotic resistance, and the ability to metabolize many sugars for food. hope that helps :)", + "video_name": "tzqZsPjHFVQ" + }, + { + "Q": "around 3:02 John talks about sexual selection choosing a mate. I thought it was endorphins in the brain that caused this. Correct me if i am wrong", + "A": "Half to half. Yes, sexual selection does help choose a mate, but endorphins help.", + "video_name": "tzqZsPjHFVQ" + }, + { + "Q": "On 6:30, what does he mean by \"to nab on to a hydrogen proton\"?", + "A": "To nab on to a hydrogen proton basically means that the oxygen can bond to a hydrogen proton.", + "video_name": "L677-Fl0joY" + }, + { + "Q": "At about 7:40 what is hydronium?", + "A": "Hydronium is H30. A water molecule is H20. When some molecular structure release a hydrogen ion (hydroxide), the water molecule, being electronegative (hoging electrons), take the hydroxide, thus forming Hydronium, with three Hydrogen molecules and one Oxygen molecule.", + "video_name": "L677-Fl0joY" + }, + { + "Q": "At 7:37 Sal says the Hydrogen might have lost an electron. How does that happen?", + "A": "Atoms lose electrons in chemical reactions or when they come in contact with other atoms whether of the same element or another. So when the hydrogen atom comes in contact with another atom, it may lose or also gain electrons (from its outermost shell). Thus an Hydrogen ion is formed.", + "video_name": "TStjgUmL1RQ" + }, + { + "Q": "Around 6:50, what is meant by 'imbalance of electrons or protons'? How does this imbalance occur?", + "A": "Imbalance of protons and electrons means that it will either have more electrons (and less protons) or more protons (and less electrons). This imbalance causes it to have a positive or negative charge.", + "video_name": "TStjgUmL1RQ" + }, + { + "Q": "At 6:55 Sal talks about a positive \"+\" Hydrogen ion.\nWouldn't that just be a proton, as Hydrogen has only 1 electron and 1 proton as an atom?", + "A": "Yes a hydrogen ion is a proton.", + "video_name": "TStjgUmL1RQ" + }, + { + "Q": "At 3:51 Sal says the atoms are bouncing around and have a lot of energy,but where does that energy come from", + "A": "Energy comes from the universe. Just like matter, energy can not be created or destroyed, only transferred. Sometimes energy is transferred through heat, or it could be seen as movement. Energy comes from the atoms surroundings, and it will in turn release energy to the surroundings, depending on whether or not the reaction is exothermic or endothermic.", + "video_name": "TStjgUmL1RQ" + }, + { + "Q": "Around 3:20, Sal mentions that the formation of water produces a lot of energy, but how can a chemical reaction lead to the production of energy. Doesn't it violates the law of Conservation of Energy?", + "A": "no. Potential energy gets converted to another form (thermal, or KE)", + "video_name": "TStjgUmL1RQ" + }, + { + "Q": "are the two products that were formed(b1 and b2) at 7:00 exactly the same or are they enantiomers?", + "A": "They are identical, there are no chiral centers on the molecule, and the double bond is in the same spot", + "video_name": "MDh_5n0OO2M" + }, + { + "Q": "at 7:33 could these three (two) molecules be considered isoprenes? Does the location of the double bond matter in an isoprene?", + "A": "Isoprene is 2-methylbuta-1,3-diene. These molecules are not isoprenes, although they have an isoprene skeleton (C atoms joined as in 2-methylbutane). When we say that molecules contain isoprene units, we mean that they consist of 5-carbon isoprene units joined together. The location of any double bonds doesn t matter.", + "video_name": "MDh_5n0OO2M" + }, + { + "Q": "At 3:26 and 3:42, how does he know that both the products are either trisusbtitual or disubstitual?", + "A": "You count the number of C atoms that are directly attached to the alkene carbons. In 1-methylcyclohexene, the alkene carbons are C1 and C2. The carbon atoms directly attached to C1 are C6 and the methyl carbon. The carbon atom directly attached to C2 is C3. This makes a total of three carbons, so the alkene is trisubstituted. In 3-methylcyclohexene, the carbon atom directly attached to C1 is C6. The carbon atom directly attached to C2 is C3. This makes a total of two carbons, so the alkene is disubstituted.", + "video_name": "MDh_5n0OO2M" + }, + { + "Q": "At 5:49 you named the molecule Cyclohexane Carbaldehyde but you did not explain why that particular compound is called a Carbaldehyde.", + "A": "A carbaldehyde is an aldehyde that is attached to another entity which is often a ring system.", + "video_name": "JMsqu236bZo" + }, + { + "Q": "From 6:56-7:08, is there an example that would make what was said about the relationship about mass and acceleration easier to understand? At 7:08, what do you mean by \"the harder it is to change it's constant velocity?\"", + "A": "the harder it is to change it s constant velocity A velocity is changed by accelerating or decelarating. Sal is saying that if you apply the same force to an object with a larger mass, it will accelerate less than an object with lower mass. This happens when you strike a tennis ball and a bowling ball with the same amount of force. The tennis ball will accelerate more than the bowling ball, because the mass of a tennis ball is lower than a bowling ball.", + "video_name": "ou9YMWlJgkE" + }, + { + "Q": "at 1:10 Sal says that Force equals mass times acceleration. Isn't \"net force\" equals mass times acceleration?", + "A": "Yes it is, but f=ma is just an easy-to-understand, basic version of the equation. The real equation is: The sum of the forces on an object equals the mass of the object times its acceleration \u00ce\u00a3F = m * a", + "video_name": "ou9YMWlJgkE" + }, + { + "Q": "In 5:07 why do we divide both sides by 2kg?", + "A": "We divide both sides by 2kg so that the mass gets neutralized on one side so that we can find the acceleration.", + "video_name": "ou9YMWlJgkE" + }, + { + "Q": "At 1:16, Sal said something about a vector quantity. Um, what is a vector quantity?", + "A": "A quantity which has magnitude and direction both", + "video_name": "ou9YMWlJgkE" + }, + { + "Q": "At 0:39, Sal says methanol is a protic solvent and releases H+ ions into the solution, but at 7:05, he says that methanol is a weak base. If methanol releases H+, it should be an acid but here it also acts like a base...so which one is it?", + "A": "Methanol is like water. It can act as either an acid or a base.", + "video_name": "MtwvLru62Qw" + }, + { + "Q": "At 7:53 he says 'a meagenta electron has been donated to the carbocation', what is a 'magenta electron'?", + "A": "He is simply referring to the colour of the dot that he uses on the screen to make it clear which is the moving electron. All the other dots in the structure of methanol on the screen are blue. There is no such thing as a magenta or a blue electron. Electrons are too small to have any colour.", + "video_name": "MtwvLru62Qw" + }, + { + "Q": "At 4:00, Sal talks about friction between the 'piston' and the 'wall' of the cylinder. Now my question is more of an observation. Sal doesn't seem to mention anything about the friction generated from the molecules within the cylinder, assuming they have KE during this process. Therefore, wouldn't the heat generated from this also influence the result in this video? Like I said, just an observation and wondered whether there might be a reason for sal not saying anything about it.", + "A": "Ideal gases have no friction between molecules. Most of the time when we are doing introductory level thermo we are assuming an ideal gas, which is not a bad assumption because many gases behave close to ideal as long as the pressure is not too high and the temperature is not too low", + "video_name": "PFcGiMLwjeY" + }, + { + "Q": "At 0:03, Sal said \"nucleuses\". Is it nuclei?", + "A": "Yes, the plural of nucleus is nuclei.", + "video_name": "lJX8DxoPRfk" + }, + { + "Q": "I have a question at 10:44, when Sal starts to draw the pi bonds - those p-Orbitals overlap two times, so in total the C Atoms would have 3 bonds, two pi bonds and including the sigma bond, right? Shouldn't it be only one overlap of the p-Orbitals, as each C Atom has only one more electron to share in the p-Orbital? Or is it irrelevant, how many times this p-Orbital overlaps, because it only has one more electron inside?", + "A": "While the drawing shows two overlaps, of the pi bond it is actually a theoretical drawing of the possibilities of where the electrons can be. The electron can not be in two places at one time, so though it appears to overlap two times, you are correct to think that it is irrelevant how many times it overlaps because there is only one electron inside. Short answer, though the drawing overlaps two times, it is only representing one bond.", + "video_name": "lJX8DxoPRfk" + }, + { + "Q": "This might be a stupid question, but at 11:00 Sal divided the products over the reactants, and this is really the equiiibrium constant formula. But what difference would it make if we took the reactants and divided by the products? (Ok, we would get the inverse value, but what difference would it make?)", + "A": "As long as the inverse of the equilibrium constant is used, there is no difference. It is normally just easier to use the products divided by the reactants because then the inverse is not needed.", + "video_name": "ONBJo7dXJm8" + }, + { + "Q": "At 2:30, it's being said that energy of photon =E3 - E1\nBut in reality we always do final energy shell - initial energy shell so over here also it should be E1 - E3....?na..??", + "A": "Which way you write it depends on whether you are referring to the excitation of the electron from E1 to E3, or the dropping back down of the electron from E3 to E1. The magnitude of the two will be the same.", + "video_name": "AznXSVx2xX0" + }, + { + "Q": "At about 4:46, he says that the back panel was injection molded. What exactly does it mean if something is injection molded?", + "A": "It means that a material with a high melting point (usually metal) is used to make a mold in which molten plastic or polypropylene or other materials can be injected. After the material cools off, the mold is opened and the object can be taken out. Injection molding is usually used because it s quite cheap", + "video_name": "qLMsZKx_a8s" + }, + { + "Q": "At 4:06, why doesn't the ethylene glycol react with the carboxylic acid as well as the ketone?", + "A": "It could, but I believe the reaction with the ketone is faster because there is less steric hindrance. Therefore, this will be your major product.", + "video_name": "fY_ejjMRYg0" + }, + { + "Q": "At 2:37 isn't the angle supposed to be 60degrees? Because if there's a right angled triangle, then the right angle would be 90degrees and theta would be 30 so 180-90-30=60, no?", + "A": "Since the is an interior angle alternate to the angle theta, it is 30 degrees. Sal does a great job of explaining this in the previous video, Inclined Plane Force Components, starting at about 4:24.", + "video_name": "Mz2nDXElcoM" + }, + { + "Q": "At 1:15, Sal says that the force is 98 Newtons. Because it is downward, wouldn't it be -98?", + "A": "Sal is probably referring to the magnitude of the force, but yes, if you define up to be positive direction, then down would be negative.", + "video_name": "Mz2nDXElcoM" + }, + { + "Q": "You found out force acting parallel to the plane is 49N while force acting perpendicular to the plane if 49*(1.732) [49root3]. Therefore force along vertical is more than horizontal. Therefore the body should not move. But the body will move with acceleration 4.9m/s^2 as mentioned in 10:05. Why ?", + "A": "Why do you think the body should not move? There is a force of 49 N pushing it down the plane. Why would that force not cause acceleration? I think maybe you should watch the video again. You might need to also watch some of the earlier videos about Newton s laws", + "video_name": "Mz2nDXElcoM" + }, + { + "Q": "At 1:05, you talked of the asteroid that wiped off the dinosaurs. What is the name of this asteroid? And what are the other theories of the beginning of the universe except the big bang?", + "A": "The asteroid impact crater linked to the end of the age of dinosaurs is found at Chicxulub, Mexico. The big bang theory is the only currently successful scientific theory for a aging universe. It replaced the solid state theory after the discovery, by Erwin Hubble, of the universe s expansion.", + "video_name": "DRtLXagrMHw" + }, + { + "Q": "9:51 wouldn't the line be more of a curve?", + "A": "Hi, The line would be straight because in this we assume the velocity is constant.", + "video_name": "T0zpF_j7Mvo" + }, + { + "Q": "At 08:10, you state that for the molecule, you couldn't get a tertiary carbocation, and I was wondering why not. Couldn't you move one of the hydrogens from the second carbon?", + "A": "You could, but then the second carbon would still be secondary, not tertiary.", + "video_name": "iEKA0jUstPs" + }, + { + "Q": "At 6:26, I don't understand why that tertiary carbon has a positive charge.. Didn't it lose a proton? Therefore shouldn't it be negatively charged?", + "A": "No it lost a hydride, the H took both electrons that were in the C-H bond. That carbon now has 3 bonds and 0 lone pairs Formal charge = valence electrons - lone pair electrons - bonds 4 - 0 - 3 = +1", + "video_name": "iEKA0jUstPs" + }, + { + "Q": "At 5:52, Isn't it 2-methylbutyl? Shouldn't the methyl get the lowest possible number(Count Carbons from the right)? Oh, maybe when counting the carbons in a substituent, I have to count from the carbon ATTACHED to the main chain? Am I right?", + "A": "Yes when you re numbering something like this you number from where the group attaches to the main chain.", + "video_name": "joQd0qVnX4M" + }, + { + "Q": "At 6:50, NeoPentyl can also be IsoPentyl, because the C is touching only one other C, am I right?", + "A": "No. Neopentyl has two methyl groups on C2 of a three-carbon chain. Isopentyl has one methyl group on C3 of a four-carbon chain. They are two completely different things.", + "video_name": "joQd0qVnX4M" + }, + { + "Q": "At 1:00 when 1-methylethyl is being named, why is the longest carbon chain ethyl which has two carbons rather than propyl which would be a three carbon chain?", + "A": "This is because you need to be clear which carbon the group of connected by. You CAN call it a butyl group, but you still must specify which carbon the group is attached to, in this case, it is a sec-butyl.", + "video_name": "joQd0qVnX4M" + }, + { + "Q": "At 8:16, why is the carbon compound called 1-methylpropylcyclobutane but not butylcyclobutane?", + "A": "A butyl group consists of a consists of a chain of four carbon atoms. The longest chain (starting from the ring attachment!) is only three carbon atoms long, so it cannot be named butyl, even though it has four carbon atoms in total.", + "video_name": "joQd0qVnX4M" + }, + { + "Q": "At 6:25, where do you get the Oxaloacetic Acid from?", + "A": "At the end of krebs cycle oxalo acetate is formed from malate in the presence of the enzyme malate dehydrogenase. the same oxalo acetic acid is used to combine with Acetyl Co enzyme-A The whole thing s a cycle", + "video_name": "juM2ROSLWfw" + }, + { + "Q": "@12:27 its shows that 10 NADH molecules are formed from one glucose molecule, however at the end of the video we count 8NADH molecules. Which one is correct?", + "A": "You should have 10NADH at the very end of cellular respiration. 2 from glycolysis, 2 from bridging reaction and 6 from TCA/Kreb/Citric acid cycle.", + "video_name": "juM2ROSLWfw" + }, + { + "Q": "At 2:35 a correction appears saying he meant to say glycolysis occurs in the cytosol not the cytoplasm. I learned in my class it does occur in the cytoplasm, what's the difference between these two terms?", + "A": "Cytosol is a part of cytoplasm. It is the part containing all the water and organic molecules. Cytoplasm consist of the cytosol and the organelles suspended in it.", + "video_name": "juM2ROSLWfw" + }, + { + "Q": "at 5:23, sal was trying to find out the work required to move the charger a distance of 5 meter closer. shoudnt he have multiplied the force by the distance before integrating?", + "A": "well he already did that when he multiplied it by dr. And he also mentioned it at about 5:50 that it is the work done in moving the particle by a distance dr and he is going to sum up the work done by using integration. She already has multiplied the force by the infinitiesmally small distance and then adding them up using integral.", + "video_name": "CqsYCIjSm9A" + }, + { + "Q": "At 7:00 , could anyone do a brief explanation of why integration is important of it works applying it in this case?", + "A": "integration here is important as the electric field is not uniform. it keeps changing with every point, so by applying the formula we do not get a clear idea of the work done throughout, so we do integration of small distance", + "video_name": "CqsYCIjSm9A" + }, + { + "Q": "in 3:37, Sal says that the arteries are blue. Is that true, because I thought the veins were blue?", + "A": "Sal might have said that arteries are blue but may be it meant pulmonary arteries are blue.", + "video_name": "QhiVnFvshZg" + }, + { + "Q": "At 9:28, Sal said that Veins carry deoxygenated blood but before it he labeled that veins carry oxygenated blood.", + "A": "The one Sal labelled before, so he was talking about the pulmonary vein. And where he labelled on 9:28 that was not dealing with lungs, thus it was labelled a vein that caries deoxygenated blood. Remember, when one is talking about pulmonary , it refers to that one which which is dealing with the lungs. The lungs have an opposite effect as compared to the other body; the veins carry oxygenated while the arteries carry deoxygenated blood.", + "video_name": "QhiVnFvshZg" + }, + { + "Q": "At 10:18 sal says that the blood from the pulmonary artery goes to the heart but shouldn't it be going to the lungs?", + "A": "Yes, it should go to the lungs. \u00f0\u009f\u0098\u008a", + "video_name": "QhiVnFvshZg" + }, + { + "Q": "At 8:52, he mentions something about a hydronium ion being produced. Does this ion affect the solution or organism such that it causes harm to them?", + "A": "The hydronium ion is just a water molecule that has been protonated. Water is H2O and the hydronium ion is H3O+ (ie, water with an extra H, giving rise to a positive charge). It occurs naturally in water, even at neutral pH, and is present at increasingly higher concentrations as the pH of water is reduced by adding acid. It is only harmful if the pH of the solution is very low although bear in mind that the pH of stomach acid is very low (pH 1.5 to 3.5).", + "video_name": "-Aj5BTnz-v0" + }, + { + "Q": "When Sal talks about the atoms 'ionizing' (1:30), where do the electrons that were knocked off go? Could there be He-, like there is He+?", + "A": "The electrons just jump off into the space around the atom, but they are no longer orbiting it. Sort of like the nucleus was swinging them around on a string; then the string broke. Another atom might pick up the electron or it could just float around between atoms. And He- can exist but it s not very happy so that extra electron tends to not stick around for very long.", + "video_name": "X_3QAB3o4Vw" + }, + { + "Q": "At 2:03, why the voltage drop is +10 V and voltage rise is -10V?\nshouldn't be in a opposite way?", + "A": "Hello Moon, It s a play on words. To drop an object is to give it a negative rise. Same thing in each case. Regards, APD", + "video_name": "Bt6V7D5av9A" + }, + { + "Q": "0:47 Why is it weak?\nIs it weak because both oxygens have the same electronegitivity?", + "A": "Not because of the electronegativity but because of how alcohols are more stable than cyclic peroxides and can easily form from a reaction with water.", + "video_name": "KfTosrMs5W0" + }, + { + "Q": "around 7:25 - why would the H2O nucleophilic attack the partially positive carbons when the oxygen in the epoxide has a formal positive charge?", + "A": "Formal charge is not necessarily the same thing as the actual charge. In this case much of the actual positive charge is on the carbons. Also, the result of that interaction would be a peroxide with a highly unstable (high energy) bond between two oxygens.", + "video_name": "KfTosrMs5W0" + }, + { + "Q": "6:58 Where does the water come from?", + "A": "The H2O is deprotentated (minus 1 hydrogen) H3O.", + "video_name": "KfTosrMs5W0" + }, + { + "Q": "so at 9:44 the picture has two purple dun bell shaped p orbtials are they individual or is it just one long p orbital for C2H4", + "A": "At 2:30 he shows the shape of a p orbital. Every p orbital is made out of two halfs. :) In ethin every C atom has ONE p orbital.", + "video_name": "ROzkyTgscGg" + }, + { + "Q": "@10:55 there are 9 lone pairs right? then y it is taken 0", + "A": "those pairs are of Flourine (F) not of (B) so it doens t count", + "video_name": "ROzkyTgscGg" + }, + { + "Q": "How can he tell its going to be a sigma bond at 10:40?", + "A": "Because a single covalent bond is a sigma bond.", + "video_name": "ROzkyTgscGg" + }, + { + "Q": "Like it said at 11:40, in overall, is it you always fill valence electrons into sp2 orbitals first then free p orbital right?", + "A": "Yes, however this is a very unusual situation because boron does not usually follow the octet rule. Ordinarily, you would have the sp\u00c2\u00b2 and the p all filled (counting the electrons shared with the other atoms).", + "video_name": "ROzkyTgscGg" + }, + { + "Q": "at 10:45 why the number of lone pairs are taken as zero?", + "A": "Because we are only counting the electrons on boron and it has no lone pairs.", + "video_name": "ROzkyTgscGg" + }, + { + "Q": "When you squared that negative number in 2:37, does it become non negative?", + "A": "Yes. The square of a negative number is positive. The cube, however, will be negative.", + "video_name": "gluN2wxqES0" + }, + { + "Q": "At 5:20, it is assumed that tension is not equal to the force of gravity on the 3kg box because the 3kg box is accelerating. How can you assume that the 3kg box is accelerating at that point? How can you know that the box isn't standing still?", + "A": "The surface that the 5kg box is sitting on is assumed to be frictionless---meaning any force that is applied to it will move it.", + "video_name": "QKXeZFwFPS0" + }, + { + "Q": "At 2:53, isn't it 5,5 diethyldecane if you count from the closest sides to each ethyl group?", + "A": "i think you need to review your counting mechanics, because I do not see two adjacent ethyl groups on any 5,5 carbons", + "video_name": "q_Q9C1Ooofc" + }, + { + "Q": "9:05 Positives in left rod attract positives in right rod?", + "A": "Like charges repel, they don t attract.", + "video_name": "ZgDIX2GOaxQ" + }, + { + "Q": "At 12:33, how do we know that whether it's the ceiling or rather the balloon that reorients or polarise its atoms in order to create an attractive force?", + "A": "We put the charge on the balloon., not on the ceiling, right? Rubber is an insulator, so it is difficult for charge to move around.", + "video_name": "ZgDIX2GOaxQ" + }, + { + "Q": "At 11:24, if the left rod was positively charged, would the positive charges on the right rod leave to the ground instead?", + "A": "The positive charges were the nuclei, and nuclei can t really move in a solid.", + "video_name": "ZgDIX2GOaxQ" + }, + { + "Q": "At 9:10 why did he assumes protons are attracted by the electron? isn't more easy for the electrons to move to protons?", + "A": "The point is, they are attracted. It does not matter who moves.", + "video_name": "ZgDIX2GOaxQ" + }, + { + "Q": "At 9:08, he says \"these positives in this charge rod are attracting these positives\" when explaining charge by induction. But since like charges repel, shouldn't they repel instead of attracting?", + "A": "If he said that, he misspoke.", + "video_name": "ZgDIX2GOaxQ" + }, + { + "Q": "Is displacement and distance traveled the same thing? because I thought distance between two points is displacement. In here, I noticed Mr.Khan using 'distance traveled' and 'displacement' interchangeably. Like on 14:07 he has the equation he used to find 's' set up equaled to 'D'", + "A": "They are not quite the same. Displacement is a vector whereas distance is a scalar. Displacement and distance are often equivalent, but there are many cases where they aren t. For example, after completing one lap around a circular track, the distance would be the circumference of the track whereas the displacement would be 0 (because you ended up back where you started).", + "video_name": "MAS6mBRZZXA" + }, + { + "Q": "at 7:30 , why did sal subtracted initial velocity from the final velocity to find height? instead, he could multiply constant acceleration with delta time. ex} 4s * 2m/s^2 = 8 m/s", + "A": "in this case only the Vi-Vf x t = a x t^2 in other cases it may not be the same.", + "video_name": "MAS6mBRZZXA" + }, + { + "Q": "At 0:30,u assigned right to positive and left to negative.Is the right direction always the positive one and the left always negative.Or is it something we can choose?", + "A": "You can choose it however you want.", + "video_name": "MAS6mBRZZXA" + }, + { + "Q": "Could you simplify the equation at 12:55 e4ven further and say 1/2t(vi+vf)?", + "A": "Not unless the amount of time between Vi and Vf is 1 unit of time. The average of 2 velocities is still a velocity not a distance.", + "video_name": "MAS6mBRZZXA" + }, + { + "Q": "At 1:23, he says that ONE photon hits ONE electron. How do you know if it is just one photon with an energy of say, x or multiple photons with a cumulative energy of x which dislodges the electron ? Is it just an assumption Einstein took or is there a scientific reason behind it ?\nAlso we are talking about Classical Mechanics isn't the photons motion supposed to be studied by Quantum Mechanics ?", + "A": "they could have possibly altered the number of photons in experimental apparatus and observed the same result.", + "video_name": "vuGpUFjLaYE" + }, + { + "Q": "At 12:23 Why is it said that the structure on the left is the right one? ALSO why is it that we have only two resonance structures for the molecule at 12:15?", + "A": "These are isomers, not resonance structures. The five orbitals have a trigonal bipyramidal geometry. There are only two places where the lone pair can go \u00e2\u0080\u0094 the axial ot the equatorial location. The see-saw geometry is more stable because the lone pair in the axial location has less total repulsion from the other electrons.", + "video_name": "0na0xtIHkXA" + }, + { + "Q": "How do you find the conjugate acid? They were mentioned around 7:55 but it was not explained how he knew those were the conjugate bases.", + "A": "A conjugate acid/base pair are chemicals that are different by a proton or electron pair. For instance, the strong acid HCl has a conjugate base of Cl-. Remember that acids donate protons (H+) and that bases accept protons. So each conjugate pair essentially are different from each other by one proton. There s a lot of info in the acid base section too!", + "video_name": "7BgiKyvviyU" + }, + { + "Q": "At 8:36 Jay states that the ethanol molecule is not as likely to donate its proton because its conjugate base is not as stable. He also states the negative charge is localized to the oxygen. What exactly is it that prevents ethanol from donating this proton? Is it the partial negative dipole on the oxygen that causes a strong attraction to the hydrogen?", + "A": "He s comparing ethanol to acetic acid here, that s what we need to keep in mind. In acetic acid the negative charge can be spread over two oxygen atoms whereas in ethanol it s stuck on one. The ethanol isn t being prevented from donating its proton, it still happens somewhat, but when you have a resonance stabilised conjugate base like there is in acetic acid we find they are better able to act as an acid.", + "video_name": "7BgiKyvviyU" + }, + { + "Q": "I didnt understan the part when he says that the rate of the reaction is equal to the rate of O2 (time 06:37). How do we know that?\nThanks.", + "A": "The rate of reaction is equal to the, R = rate of formation of any component of the reaction / change in time. Here in this reaction O2 is being formed, so rate of reaction would be the rate by which O2 is formed.", + "video_name": "8wIodo1HD4Y" + }, + { + "Q": "At 5:55, We are losing N2O5 because it's a reactant and not a product, right?", + "A": "Sort of. N2O5 [reactant] is being consumed/used up to generate NO2 and O2 [products]. I usually think of it as the number of moles or the concentration of the reactants become less as products are being formed in the process.", + "video_name": "8wIodo1HD4Y" + }, + { + "Q": "At 07:18 he says that increase in temperature results in increase in solubility. how is that so?", + "A": "the water molecules move around when heated, then gives the salts the opportunity wedge in between them.", + "video_name": "zjIVJh4JLNo" + }, + { + "Q": "At 4:27 Sal says that the NaCl molecule breaks, isn't it that a molecule needs a lot of energy to break? Where does that energy come from?", + "A": "When the NaCl ions dissociate, the attraction between the ions is replaced by the attraction of the ions to the water molecules. Nevertheless, the process is slightly endothermic but the dissolution is favoured by an increase in entropy as the system becomes more disordered. Solutions always have higher entropy than crystalline solids.", + "video_name": "zjIVJh4JLNo" + }, + { + "Q": "Hi :)\n\nAt 7:24, it is mentioned that the molecules have the same kinetic energy. How so? If the volume of the box was decreased then the molecules kinetic energy would increase, wouldn't it?\n\nOr does it mean that all the molecules inside this smaller box all have the same average kinetic energy? But this kinetic energy is still higher than the kinetic energy of the molecules on the bigger box, isn't it?\n\nThank you!", + "A": "Me thinks the average K.E of molecules remains the same but the extra energy they gained by virtue of reduced volume is transferred as increase in heat of collision which is very minute.", + "video_name": "tQcB9BLUoVI" + }, + { + "Q": "In the 3rd example, while drawing the final products, why arent there any stereochemistry with the left carbon? (5:10 - 5:20)", + "A": "There is no stereochemistry to worry about in the left carbon because two identical groups i.e. methyl groups are attached to the carbon. Hence it is NOT a chiral carbon.", + "video_name": "b_qDLacdkFg" + }, + { + "Q": "AT 4:10, you said \"now we divide by the mass that's 3kg.\" But in your previous video while doing the chalkboard question you didn't divide it by the mass, even though it was given as 3Kg. Why is that so? Why you didn't divided it in the vertical acceleration while here you did?", + "A": "He does divide by the mass in the chalkboard question, go back and take another look. The only difference is that he just writes the mass as m and doesn t plug in a value for it. In both problems, the next step is to multiply both sides by this mass. Since the left hand side is zero, and zero times anything is zero, the masses (in both problems) vanish anyway.", + "video_name": "EEnzhdQJUYA" + }, + { + "Q": "at 2:40 you said there was a primary carbon. Would'nt that be a methyl carbon because there is only one carbon?", + "A": "primary carbon is carbon attached to only one carbon", + "video_name": "_-I3HdmyYfE" + }, + { + "Q": "At around 5:25, David makes a destructive interference wave by moving one wave source a half a wavelength forward. Later he also notes that this placement of the two wave sources will produce no sound because the amplitudes cancel each other out. But what about that one half wavelength of the sound wave at the start, that wave does not get cancelled out right? So technically isn't there a sound being produced for that half of the wavelength?", + "A": "The destructive interference occurs at a particular point in space, not everywhere at the same time.", + "video_name": "oTjTXS40pqs" + }, + { + "Q": "What is that ocean creature called at 9:20?", + "A": "It is an Opabinia. It lived during the Cambrian Era and had five eyes. It s not part of any living phylum today.", + "video_name": "MS7x2hDEhrw" + }, + { + "Q": "at 1:40, what does velocity mean?", + "A": "Velocity is a measurement which includes a speed and a direction: (ie: 40 km/h south)", + "video_name": "oRKxmXwLvUU" + }, + { + "Q": "At 8:33, Sal mentions dimensional analysis. What is dimensional analysis?", + "A": "Dimensional analysis is basically just a fancy name for unit conversion by canceling like dimensions...", + "video_name": "oRKxmXwLvUU" + }, + { + "Q": "Does anyone have any idea as to why the letter s is used to represent displacement instead of d? (at time 1:51)\nMy best guess is that s stands for Science... Not or that it is used to be the SUM of the displacement vectors...", + "A": "d is delta in calculus", + "video_name": "oRKxmXwLvUU" + }, + { + "Q": "At 0:38 he said that 5km was a magnitude, but then at 0:48 he said that 5km was the distance. Which it is?", + "A": "Both, the distance is the magnitude.", + "video_name": "oRKxmXwLvUU" + }, + { + "Q": "At 1:20 does the arrow over the V indicate *which* direction, or is it just to show that it has a direction at all?", + "A": "It is to indicate that the value represented by the letter is a vector, not a scalar. I.e. to show that it has a direction at all.", + "video_name": "oRKxmXwLvUU" + }, + { + "Q": "At 1:50, Sal says that the symbol for displacement is S, but I have been learning in my science class that displacement is X. Is one right and one wrong, or are there just other variables?", + "A": "Both x and s are used for representing displacement", + "video_name": "oRKxmXwLvUU" + }, + { + "Q": "What is the sign Sal uses at 4:46 to show a partial positive or negative charge?", + "A": "The symbol is a a lower case delta . Delta (a triangle, related to the letter D) is used for change, so a lower case delta means a small (partial) change.", + "video_name": "Rr7LhdSKMxY" + }, + { + "Q": "At 6:45, does this mean that the elements in groups 1 & 2 are more likely to be in ionic bonds than covalent bonds because it's easier to just give an electron and be positively charged and bonded or does it not matter?", + "A": "That is exactly what it means", + "video_name": "Rr7LhdSKMxY" + }, + { + "Q": "what i the sign made by Sal at 4:53 to denote the partial positivity ?", + "A": "It s a lowercase delta (Greek letter): \u00ce\u00b4", + "video_name": "Rr7LhdSKMxY" + }, + { + "Q": "At 13:13, he says that \"x\" represents the concentration of Hydronium ion [H3O]. But the -log of x was pH. I don't understand why. Can someone please explain this for me?\nThanks :3", + "A": "To you figure out the pH of any substance, the formula says: pH = -log([H3O+]) , or pH = -log([H+]) If x = [H3O+], so pH = -log(x); It s all the same thing. Sorry if my english ain t so good, I am brazillian. I hope it helped you.", + "video_name": "XZWoMXVANww" + }, + { + "Q": "hey but in case of CH3OH ( at 5:00 ) the total no of valence electrons dont match with the no of bonds as shown at 6:29 ..??", + "A": "I think you should also count the dots. CH3OH has a total number of 14 valence electrons. At 6:29, the structure shown has a total of 5 bonds, and 4 dots on the Oxygen. It means that the structure has 14 valence electrons and is correct.", + "video_name": "BIZNBfBuu1w" + }, + { + "Q": "I noticed at 2:40 he writes the formula for Methylamine as CH_3NH_2 as opposed to CH_5N, does the expression of the formula vary based on context?", + "A": "There can be variations in a general formula of an organic compound. This happens due to a phenomenon which we have named as isomerism. Simply put, there can be various structures of a general formula if not specified.", + "video_name": "BIZNBfBuu1w" + }, + { + "Q": "When drawing the diagrams, do you choose the element that has the least number of atoms in that bond for the central atom? Secondly, how do you know how to place the atoms in larger bonds (ex. CH3 NH2 at 2:45) (how to configure the diagram)?", + "A": "H atoms must always be external atoms. That leaves C and N as candidates for the central atom. The central atom is the *least electronegative atom:* C. So, C is the central atom. Attach N to the C. Then add H atoms and electrons to give each atom its octet.", + "video_name": "BIZNBfBuu1w" + }, + { + "Q": "At 9:10, it states that there would be a high potential energy assuming that q and Q are positive. Is the same true for when both charges are negative? What if q is positive, and Q is negative (vise versa as well)?", + "A": "The formula is the same and always works, as long as you put all the signs in correctly. So if Q is positive, it creates a positive electric potential V. If Q is neg, it creates a neg electric potential V. But then if you put a positive q in a positive V, it will have positive potential ENERGY (PE = qV). Same for a neg q near a neg Q (thus a neg V). But a positive q in a neg V or a neg q in a positive V will both have NEG potential energy.", + "video_name": "ks1B1_umFk8" + }, + { + "Q": "At 2:37, how can we even predict that the Eagle Nebula doesn't exist right now if the photons we are seeing currently depict it as it was 7000 years ago, and nothing travel faster than light, i.e., these photons? Shouldn't the 7000 year old photons be our most recent image of this nebula? How could we know of something that happened after this point in time if light can't reach us that fast?", + "A": "Actually, right now we can see a hint of a destructive energy burst (probably from a nearby supernova) going towards the Eagle Nebula. And what we are seeing IS the Eagle Nebula as it was 7,000 years ago. So actually, the Eagle Nebula as we know it does not exist today. It is either gone or completely disfigured.", + "video_name": "w3IKEa_GOYs" + }, + { + "Q": "At 7:31 in the video, Sal stated that the chain goes from 5' to 3'. Is it possible for it to go from 3' to 5'? If not, why?", + "A": "DNA polymerase only works in the 5 to 3 direction. This is down to the specificity of this enzyme. If you think about it, DNA replication could result in a real mess if DNA polymerase could work in both directions.", + "video_name": "0CQ5ls3Uc2Q" + }, + { + "Q": "At 1:53, Why is the fact that nitrogenous bases are forming hydrogen bonds offset their basic property? Somehow making them \"happy\" or something?", + "A": "as he said in 1:35, it is done in order to take more hydrogen protons", + "video_name": "0CQ5ls3Uc2Q" + }, + { + "Q": "At 1:32, Sal says that \"as we get more into physics, we'll see that maybe we shouldn't necessarily think of time as driving; maybe position, in some ways, is driving time.\" What is Sal referring to? Is there a relevant Khan Academy video or Wikipedia page?", + "A": "Spacetime diagrams when you study relativity have time on the vertical axis. In relativity you cannot untangle space from time. if you change position very quickly (travel near the speed of light, for example), you move through time more slowly.", + "video_name": "PRx_R9iIWk4" + }, + { + "Q": "at 9:00 it is written vt+1/2atsquare .and delta t is a very small quantityand delta t multilied by delta t gives a much more small quantity and should not be taken into consideration.then why it is writtem as t square", + "A": "The t in that equation is not the delta t of calculus, it s the time during which the acceleration took place.", + "video_name": "wlB0x9W-qBU" + }, + { + "Q": "At 6:05 wouldn't the final velocity be zero after it hits the ground?", + "A": "Final velocity refers to the speed it has when it first hits the ground, not after it lands. It would not be very useful or interesting to say that everything has a final velocity of 0.", + "video_name": "wlB0x9W-qBU" + }, + { + "Q": "7:11 I'm confused. You are shifting the numbers around, assumably to find the specific variable, but you boxed in blue the Vi+Vf( which has been moved to another part of the equation, extended and broken down in yellow) into a translation that read 2Vi, which is just Vi+Vi, right? Am I missing something, or how did Vf become a second Vi, and where did it come from?", + "A": "Sal re-wrote Vf, which he brackets at 6:25, as initial velocity plus acceleration times change in time. He then collects the two Vi s together (2Vi) and divides them by two, and also divides the acceleration times change in time by two. (Remember, we re just re-writing the V avg. part of the S = V avg. x delta T equation so it s in terms of initial velocity.) Hope that s clear :)", + "video_name": "wlB0x9W-qBU" + }, + { + "Q": "At 3:52 Sal said that if something is moving up, it's given a positive sign, but if it's moving down, it's given a negative sign. What if it's being affected by the moon's gravity? Then, it's moving up relative to earth, but down relative to the moon.", + "A": "positive being up and negative being down is just a conventional way of doing things. We can choose the y-axis to point in any direction, so long as it is perpendicular to the x-axis. It just seems natural to choose y to point upwards. So when the Earth is pulling something down, we give that a negative value. And using that same convention, then the moon above us would pull things up with a positive value.", + "video_name": "wlB0x9W-qBU" + }, + { + "Q": "At 4:03, Sal stated that a vector is positive if an object goes up and negative if it goes down. What about left and right?", + "A": "It can be whatever way you want, just make sure you stick to it for the whole problem. Personally if I m working on a problem and I have a lot of vectors going in a certain direction, I consider that direction positive and the opposite direction negative. Sometime this is right, sometimes it s left.", + "video_name": "wlB0x9W-qBU" + }, + { + "Q": "In my physics class we use the equation x = xi + (vi)(\u00ce\u0094t) + 1/2 a(\u00ce\u0094t)^2\nBut at the end of the video (by 9:27) I see Sal using the equation x = (vi)(\u00ce\u0094t) + 1/2 a(\u00ce\u0094t)^2\nWhy is the equation used in my class different?", + "A": "xi is just a measure of where you are starting out. Sal s is assigning the starting point a coordinate of zero. But if you decided to say you were starting from, say 10 feet, then you would have to add that 10 feet if you wanted to calculate your distance from zero.", + "video_name": "wlB0x9W-qBU" + }, + { + "Q": "stupid question, at 8:35 sal multiplies change in time by change in time but the first change in time is placed over 2...so why is it not half change in time multiplied by change in time? does that make sense?", + "A": "That does make sense, but that s because they will both give them same answer. Half of change in time multiplied by time written as (1/2 t)*t will give you the same answer as half of change in time squared ( (1/2 t^2) ). It s just easier to remember 1/2 at^2. You could test that by putting some numbers in for time. example if t = 5: 1/2 * 5 = 5/2 5/2 * 5 = 25/2 or 12.5 5^2 = 25 1/2 * 25 = 25/2 or 12.5", + "video_name": "wlB0x9W-qBU" + }, + { + "Q": "Sal shows that a=g (where a is a vector quantity displayed at (1:30)). My question is, would gravity ALSO be a vector quantity? If so, why isn't there an arrow placed above it?\n\nThanks :)", + "A": "Every force is a vector. If you are talking about a force of gravity, then it is a vector.", + "video_name": "wlB0x9W-qBU" + }, + { + "Q": "@ 9:20... Shouldn't the drawing only have one methyl group branching off the 1st carbon on each of the ehtyl groups branching off of first and third carbons of the ring? Doesn't the \"di\" in 1,1-dimethylethyl imply that there are only two methyl groups (instead of four like is shown in your drawing)? Such as how you only have two methyl groups in 2,2-dimethyl-hexane. Or is it different because it is an alkyl group branching off another alkyl group instead of the parent chain?", + "A": "It s sort of like an order of operations problem from arithmetic. You have to pay attention to the parenthesis and consider everything within them for each case. Solve 1,1-dimethylethyl first, then put that in place at 1 and 3 on the cyclopentane.", + "video_name": "6BR0Q5e74bs" + }, + { + "Q": "Shouldnt the 3,6,9,9-tetramethyldodecane be named as a 4,4,7,10-tetramathyldodecane\n\n06:37", + "A": "it could be 1,4,7,7-tetramethyldodecane", + "video_name": "6BR0Q5e74bs" + }, + { + "Q": "hey i think there is a mistake at 5:26 in the naming of this molecule the sum of the methyl prefix is 3+6+9+9 =27 but if we named the molecule 4,4,7,10-Tetremethylcyclododecane the actual sum is equal to 25 or am i wrong ?", + "A": "You don t sum them, that isn t the rule despite what your teacher may have said. You use the set of numbers that has a lower number at the first point of difference. 3 is less than 4 so the video is correct.", + "video_name": "6BR0Q5e74bs" + }, + { + "Q": "at 6:38, Wouldn't that be called 3,3,6,9 instead of 3,6,9,9? I mean shouldn't we start where there is more branching at a smaller no.?", + "A": "I know this question was asked 2 years ago but for anyone reding though in the future: No. Count again from the right hand side and you will see that would put the methyls on carbon #4 not carbon #3. 3 is a lower number than 4, the name given in the video is correct.", + "video_name": "6BR0Q5e74bs" + }, + { + "Q": "At 5:36, if the penny was thrown up at a velocity of 30 m/s, then it would go up, reach a velocity of 0m/s and by the time it comes down to the same point from which it was thrown, wouldn't the velocity at that point then be different than 30 m/s?", + "A": "It would be -30 m/s, since velocity is a vector. The speed at the bottom would be the same on the way down as on the way up. It has to be, because the acceleration is constant the whole time, and the distance up is the same as the distance down. (ignoring air resistance)", + "video_name": "emdHj6WodLw" + }, + { + "Q": "What is beta- plus decay ?\nIt was spoken by sal at 1:38 .", + "A": "Beta decay is a kind of radioactive decay, which occurs so that the nucleus becomes more stable. In beta- decay, a neutron emits an electron to become a proton, so that the nucleus becomes more stable. In beta+ decay, also known as positron emission, a proton emits a positron to become a neutron, to make the nucleus more stable.", + "video_name": "FEF6PxWOvsk" + }, + { + "Q": "at 2:47 sal said anti electron neutrino, well i don't understand what neutrino is?", + "A": "Neutrinos are subatomic particles produced by the decay of radioactive elements and are elementary particles that lack an electric charge.", + "video_name": "FEF6PxWOvsk" + }, + { + "Q": "At 6:03, how do you know which block it is? (ex. D block)", + "A": "Groups 1-2 are the s block Groups 13-18 are the p block Groups 3-12 are the d block The 2 rows under the main periodic table are the f block The block generally (not always) tells you which orbitals electrons are being filled in to", + "video_name": "UXOcWAfBdZg" + }, + { + "Q": "At 7:57, how are there 18 noble gases.\nAren't they just 6(+1)?!", + "A": "Sal says So the noble gasses, that s the other name for the group 18 elements, noble gasses , not that there are 18 noble gasses. Groups in the periodic table are the vertical columns that are numbered from 1-18.", + "video_name": "UXOcWAfBdZg" + }, + { + "Q": "At around 5:30, why would it be 4s2?", + "A": "b coz 4s has lower energy than 3d as it is inner orbital more close to the nucleus hence it must get fille first", + "video_name": "UXOcWAfBdZg" + }, + { + "Q": "At 5:35, Sc would have 2, not 3 valence electrons? I'm curious as to why you would not add the 2 and 1 together, since you do that with Carbon (and you add the 2s together to get 4 valence electrons).", + "A": "You do not add the 2 and 1 together because the 1 electron is part of the d block and therefore cannot be a valence electron. The d blocks cannot be used as a valence electron because they are not one of the highest energy furthest out electrons, but p blocks can be used as valence electrons. With carbon you get 4 valence electrons because you add the s and p blocks together.", + "video_name": "UXOcWAfBdZg" + }, + { + "Q": "at 1:01 Sal marks the 1st column but he doesn't mark HYDROGEN . Can some tell me the reason for this ?", + "A": "This is because H is not an alkali metal and it doesn t share all the properties of the alkali metals. It doesn t perfectly fit anywhere in the periodic table but it s usually put in Group 1.", + "video_name": "UXOcWAfBdZg" + }, + { + "Q": "At 6:59, Sal says that Carbon has four valence electrons, but the subscript for the p shell is only 2. I'm confused as to why Sal added on the electrons in the 2s shell to the 2p.", + "A": "Because the 2s electrons are also carbon s valence electrons. For main group elements it will be the electrons in the highest energy shell, both 2s and 2p are in carbon s highest energy shell.", + "video_name": "UXOcWAfBdZg" + }, + { + "Q": "At 6:31, for the cycle pentane, shouldn't there be 12 hydrogens, not 10 (because of the alkane formula Cn H2n+2)?", + "A": "For a normal pentane it would be 12 hydrogens, like: CH3CH2CH2CH2CH3 if you would now want to make a ring out of this ordinary pentane, you would have to bond the two CH3 s together. In order to do so, both would hove to lose a bond first, which are both bonds to hydrogen atoms. So that leaves 10 hydrogens for cyclic pentane.", + "video_name": "NRFPvLp3r3g" + }, + { + "Q": "at around 10:00,\nwhy doesn't the fluoride anion react with H+ and form HF??", + "A": "The Fluoride is a very small anion, and indeed, the smallest anion. So, It s electrons will be held very near to it s nucleus. We have to supply high amount of energy to make it bond.It ll be less reactive than Iodide, chloride and bromide which are considerably bigger than Fluoride and they can share their electrons to bond using lesser Energy supply.", + "video_name": "Z9Jh-Q59xso" + }, + { + "Q": "When you order the halides in order of decreasing nucleophilicity, where would OH- go? 12:33", + "A": "Good question, Sal actually answers this in the next video. In short it depends on whether the solvent is protic or not. In short, it is a stronger nucleophile than all the halides in an aprotic solvent, and not quite as strong as iodide in a protic solvent.", + "video_name": "Z9Jh-Q59xso" + }, + { + "Q": "At around 12:35 the Professor talks about transposons and conjugation. During which he said trasposons can jump from cell to cell, what I would like to know is if this process has somethig in relation with synapsis.", + "A": "No, this is a direct linking of bacteria through pili to transfer genetic material, while the signals sent across synapsis are chemical. Neuro transmitters are released from the axon terminals (end of the neurons axon) of one neuron, which then travel across the synapse to the dendrites of the recieving neuron.", + "video_name": "TDoGrbpJJ14" + }, + { + "Q": "At 8:25 the Professor talks about Archaea cells, what type of environment are these unique cells found in ?", + "A": "Thank You that makes everything clear", + "video_name": "TDoGrbpJJ14" + }, + { + "Q": "Isn't the direction of angular velocity supposed to be perpendicular to both linear velocity and the radius? At 4:10 David says that the direction of angular velocity is anti-clockwise?", + "A": "The angular velocity vector is perpendicular to the linear velocity and the radius But that still leaves two possible directions for it to point. You need to know the direction of the spin in order to know which of those two directions is the one. Specifying the direction of the spin is the same as specifying which direction the velocity vector points.", + "video_name": "garegCgMxxg" + }, + { + "Q": "At 6:46 you mentioned that Si can make 5 bonds because it has d orbitals. Being in the 3rd period and above the d block, how does Si have d orbitals?", + "A": "It is because in the 3rd shell there is 3s2 3p6 3d10 in a full shell and even before the transition metals there are d orbitals since while the 3s and 3p orbitals fill the 3d orbitals form from the electrons having more places to go. This makes all elements past neon hypervalent and thus Iron is able to have a +7 oxidation state instead of just +3 like you would expect from an oxide.", + "video_name": "KsdZsWOsB84" + }, + { + "Q": "at 6:01 , why did sal draw the graph as \"discontinuous function\" ?!\ngenerally , when i draw a graph like this case how can i decide if i'll draw it as continuous or discontinuous function ?", + "A": "The given function was defined piece-wise with a jump discontinuity at t=2. Since it was defined that way (with the jump discontinuity), you can only draw it that way.", + "video_name": "6FTiHeius1c" + }, + { + "Q": "At 7:55, Khan says that if the radius goes down, then the tangential velocity goes up.\n\nConsidering a ball on a string wrapping itself around and around, its velocity is increasing even though there is no torque acting upon it. But according to the Law of Conservation of Momentum, the momentum is conserved. But if the tangential velocity increased, then mv increases and so does the linear momentum.\n\nCan someone explain to me why this is? How can the linear momentum change without torque?", + "A": "Torque is rotational and linear momentum is linear, so torque can t change linear momentum, it can only change angular momentum. To apply conservation of momentum you have to consider the system of the ball and the object to which it is tied. The total momentum of those two is conserved. If you ignore the object to which it is tied, then you can consider the string to be exerting an outside force on the ball. The string is accelerating the ball and changing its momentum.", + "video_name": "nFSMu3bxXVA" + }, + { + "Q": "does p always mean -log? 12:17", + "A": "Well, when it s in front of something and it s a LOWERCASE p, then yes, it s always -log. Hope I answered your question well! ;D", + "video_name": "LJmFbcaxDPE" + }, + { + "Q": "9:38, in the correction, isn't the conjugate of a weak acid always a weak base? Like HCN (weak acid) has conjugate CN^- (weak base)", + "A": "HCl is a strong acid. The conjugate base, the chloride ion, is a very weak base, so no. However, the ionisation of HCl in water is not a reversible reaction (it goes to completion), so its not appropriate for a discussion of buffers, as they involve equilibrium reactions..", + "video_name": "LJmFbcaxDPE" + }, + { + "Q": "At 4:30, why do you decrease the poh when you increase the oh?", + "A": "Because pH + pOH = 14.00 at 25 Celcius", + "video_name": "LJmFbcaxDPE" + }, + { + "Q": "3:15 Sal says a force is needed to be applied in order to move the particle towards the positive side. How would this force be applied?", + "A": "Well, there might be another electrical force being applied from the other side. There might be something pushing it. There is simply some form of a force. It s abstract. If you were supposed to know it, Sal would tell you.If you need to know it in some other scenario, you ll be given some way to find it out. Unless it s in life. That s one game where no variables are necessarily provided.", + "video_name": "zqGvUbvVQXg" + }, + { + "Q": "at 5:15 you say the charge closer to the plate has a higher PE. Why is this if the E field is uniform? if F= qE then wouldnt the force be the same at both pts?", + "A": "Hi, The force on the charge of course would not vary since F=qE and Sal did not say that the Force is higher. What he said that the P.E is higher. WE know that P.E is the work done in taking the charge to that point. Also Work done is Force times the Distance. Therefore is force is constant the distance will determine the P.E. And from the video it s clear that the particle will be at a higher potential near the plate since it has to travel a greater distance to reach there. Hope it helps Cheers", + "video_name": "zqGvUbvVQXg" + }, + { + "Q": "at 4:50, what does meters have to do with electricity?", + "A": "The equation for work is Force times Distance equals work. The 2 meters represents the distance of the charge.", + "video_name": "zqGvUbvVQXg" + }, + { + "Q": "At 10:54, why did Linneas develop the division in the first place? What was his purpose?", + "A": "He simply wanted to organize the cluttered jumble of species.", + "video_name": "oHvLlS_Sc54" + }, + { + "Q": "what is sal saying at 6:21 ? how we can find kinetic energy from position time graph ?", + "A": "He s saying that the weight slows down until it reaches the maximum displacement, where it changes direction, and at that point (instant) the velocity is 0. And since KE depends on velocity, at that point KE is also 0.", + "video_name": "Nk2q-_jkJVs" + }, + { + "Q": "At 6:25, I now that the spring does not infinitely go on from experience as a kid. Help?", + "A": "That s because of friction. If there were no friction, it would go on forever.", + "video_name": "Nk2q-_jkJVs" + }, + { + "Q": "At 8:06 we made the carbocation gets attacked by water . why we couldnot we do it in the starting instead of making it atacked by hydronium ion?", + "A": "Water is too weak to attack when there is no positive charge.", + "video_name": "O_yeKo6-qIg" + }, + { + "Q": "At 0:36, He says work is energy transferred by force, Using this definition shouldn't the formula be Work = Energy times Force ?", + "A": "No. Work IS energy. when you exert a force over a distance, you transfer energy to the object you are exerting the force on. The amount of energy you transfer is force*distance.", + "video_name": "2WS1sG9fhOk" + }, + { + "Q": "When writing the overall formula at 5:55, what if the force that was applied had a anticlockwise torque? (i.e if the force was applied on top of the board, n the same end as worked out in the video) Doesn't the formula change to - Torque = F.r.cos (theta)?", + "A": "Typically, clockwise torques are negative and counterclockwise/anticlockwise torques are positive. This is because clockwise torques would cause an object to rotate in the negative direction, giving theta a negative value. Counterclockwise/anticlockwise torques would be positive for a similar reason. Thus, the formula is still \u00cf\u0084=Fr sin(\u00ce\u00b8)", + "video_name": "ZQnGh-t25tI" + }, + { + "Q": "At 5:36, why did he move the hydrogen to the other side of the periodic table?", + "A": "Every element wants to satisfy its Electron or Valence Shell. The first shell occupies 2 electrons, so Hydrogen only needs 1 more to satisfy its shell. The same goes for the elements in Group 7, they only need one more electron to satisfy their shells, so he says in theory it could be moved there.", + "video_name": "CCsNJFsYSGs" + }, + { + "Q": "If hydroxide is a polyatomic atom that is represented as OH- then how come at the minute 5:20 you write it as HO- ?", + "A": "It doesn t really matter which way around it is written, although OH- is much more common.", + "video_name": "CCsNJFsYSGs" + }, + { + "Q": "At 2:00, what is the typical oxidation state of a halogen and why?", + "A": "The typical oxidation state, or oxidation number, of a halogen is -1, mainly because halogens are so willing to gain another electron in order to fill out its octet.", + "video_name": "CCsNJFsYSGs" + }, + { + "Q": "at 5:28 you talk about having a blood vessel break in a certain part of the brain. since we have different sections in the brain for different subjects and topics such as music,personality,vision, etc. would the stroke effect your relationship with that certain subject?", + "A": "If the braintissue dies due to lack of oxygen or due to the compression of the bloodflow in that part of the brain, then those functions are lost or damaged. So it s possible you go blind, you lose the possibility to speak or understand what s bein said et cetera et cetera...", + "video_name": "xbyfeEW56Nc" + }, + { + "Q": "At 6:31, is that also called latent heat?", + "A": "Yes, you noticed right! That s precisely what latent heat is.:-)", + "video_name": "lsXcKgjg8Hs" + }, + { + "Q": "9:29 What is a sigma bond? What is a pi bond? Is pi bond in all double bonds or multiple bonds? Is a sigma bond in every single bond?", + "A": "All single bonds are sigma bonds. However, a double bond consists of 1 sigma bond and 1 pi bond. You can rotate around a sigma bond (single bond), but not a pi bond (involved in double and triple bonds), which I m sure will be important in upcoming videos. A tripple bond consists of 1 sigma bond and 2 pi bonds.", + "video_name": "u1eGSL6J6Fo" + }, + { + "Q": "At 5:12, why did Sal say straight VANILLA s and p orbitals??", + "A": "It s American slang for normal or original . It refers to the original flavour of ice cream (vanilla). Since then, many new, more exciting flavours have been invented. The phrase plain vanilla would then refer to the original or unhybridized atomic orbitals.", + "video_name": "u1eGSL6J6Fo" + }, + { + "Q": "At 14:00 methane has been drawn, but I see no 1s orbital drawn...is it there and just not mentioned, or did it get absorbed into the sp3's somehow?", + "A": "I believe that he just did not put the 1s electrons in there since they play no role in the Hydrogens bonding to the Carbon.", + "video_name": "u1eGSL6J6Fo" + }, + { + "Q": "1:33 what is an internal pressure?", + "A": "I think there is an actual name for the internal pressure of a plant that allows it to stand upright. It s called Turgor Pressure.", + "video_name": "zdvKhaQxvag" + }, + { + "Q": "At 2:06, how is it a probabilty of it happening?", + "A": "A probability of it happening is the concentration of the molecules. If you have a high concentration, you will have a high probability. If you have a low concentration, then the probability is low.", + "video_name": "TsXlTWgyItw" + }, + { + "Q": "at 3:18 whats a solvent. and how is it related to h20", + "A": "Solvent is the liquid thing that is in abundant quantity. Notice how H2O is liquid (there s a small l written next to it, see?) and the others are aqueous. So, that means, water is everywhere. So it is in abundance. And thus, it is a solvent. I can t explain any better than that.", + "video_name": "TsXlTWgyItw" + }, + { + "Q": "what the heck does 1s^22s^22p^63s^1 in the video at 1:23 mean did i miss something because it makes no sense.", + "A": "The superscripts are not exponents. They are the numbers of electrons in each shell or subshell. 1s\u00c2\u00b2 2s\u00c2\u00b22p\u00e2\u0081\u00b6 3s\u00c2\u00b9 means there are 2 electrons in the 1s shell, 2 in the 2s subshell, 6 in the 2p subshell, and 1 in the 3s subshell.", + "video_name": "akm5H2JsccI" + }, + { + "Q": "At 9:38, when the tension is being found at the bottom of the circle, is the assumption made that the velocity is the same at the top and the bottom? The number 4 was used for both, and I thought the values would be different?", + "A": "He s just showing you how the problem would be different if you have the velocity at the bottom instead of at the top. Consider it two different problems.", + "video_name": "2lcaBPLLoLo" + }, + { + "Q": "at 2:50, why do we have to change degree Celsius to kelvin?", + "A": "Because Kelvin is a measure of temperature in which 0 temperature corresponds to zero energy. C is a measure in which 0 is arbitrarily chosen. The ideal gas equation is therefore written in such a way (check the units) that it is expecting T to be in Kelvin.", + "video_name": "erjMiErRgSQ" + }, + { + "Q": "Hi, at time 8:21 in video, when doing final calculation, why is the calculation .082 divided by 303? shouldnt it be 4/(.082*303) as in 4 divided by (.082 multiplied by 303) ?", + "A": "What he did is correct. 4/0.82/303 is equal to 4/(0.82*303) the same as 4/2/2 is equal to 4/(2*2)", + "video_name": "erjMiErRgSQ" + }, + { + "Q": "At 6:14, why is there so many constant, i know in my chemistry class we only learned one. And what is the difference between all of them, is there different uses for them. And how do they come up with the constant reaction formula?", + "A": "PV = nRT only has one constant.", + "video_name": "erjMiErRgSQ" + }, + { + "Q": "at 8:21, why does Sal say \"4 divided by .082 divided by 303...\"? Wouldn't it be times 303? He used the multiplication dot when he wrote it out.", + "A": "They both mean the same thing. You can divide 4 by 0.082*303 or you can divide 4 by 0.082 and then divide it by 303. You will get the same answer. Hope this helps :)", + "video_name": "erjMiErRgSQ" + }, + { + "Q": "at 3:09, what does \"R\" mean in the equation PV = nRT?", + "A": "The R is just a constant number that relates the other four properties, called the universal gas constant. The other four can change depending on the example or situation but R will always have the same value..", + "video_name": "erjMiErRgSQ" + }, + { + "Q": "at 8:33, how did that work? why not divide 4 by ( 0.082 * 303 ), as in 4/(0.082*303) ?", + "A": "What Sal did and what you ve suggested are mathematically equivalent. Sal effectively took (4/0.082)/303, which is the same as (4/0.082)*(1/303) which is the same as 4/(0.082*303).", + "video_name": "erjMiErRgSQ" + }, + { + "Q": "what did sal mean at 2:55 ? if the mountain in the image is very plane like a plane mirror without any up\nand downs then we will be able to see the image ?", + "A": "Sal meant that mountain cause diffused reflection all around it and does not reflect specularly.", + "video_name": "sd0BOnN6aNY" + }, + { + "Q": "At 0:30, it is stated that particles move in rotation and curved paths but the kinetic molecular theory states that particles move only in straight lines. Error?", + "A": "Definitely an error", + "video_name": "eEJqaNaq9v8" + }, + { + "Q": "At 5:23, when Mr. Khan says \"slide down the slope\", shouldn't the block go flying after the first hill?", + "A": "It s a possibility. However, energy is still conserved, that is the initial PE + KE still equals the PE + KE at any place along the block s path, whatever the path truly is.", + "video_name": "kw_4Loo1HR4" + }, + { + "Q": "At 5:50 Sal says that this problem would be extremely difficult using kinematics equations... I do not understand why it is difficult using kinematics. Vi = 0, a = 9.8, (y2-y1) = 10. Use Vi^2 = Vf^2 + 2a(y2-y1). Final velocity comes out to be 14 m/s. Gravity is the only force acting on the object and our displacement is simple. Why should I not use kinematics here?", + "A": "You can, but most people find it easier to use CoE when it applies. Both will give you the same answer. Try it both ways and see what seems quicker and easier to you. Then see if you can think of a more complicated path that might be very difficult to solve with kinematics (like a curvy roller coaster, for example).", + "video_name": "kw_4Loo1HR4" + }, + { + "Q": "At minute 3:30 Sal plugs in the mass which is 1 Kg multiplied by (1/2) shouldn't it be .5 and if we divide both sides by .5 to get v^2 alone shouldn't 100/.5=50?", + "A": "100/0.5 is not 50 Try it on your calculator 100 x 0.5 is 50", + "video_name": "kw_4Loo1HR4" + }, + { + "Q": "At 1:56 if an object is in the ground it has 0 PE, so does an object on a cliff or mountain top also have 0 PE", + "A": "Potential energy depends on where you re referential is, where you define your 0 to be. You can choose your 0 to be anywhere you want, as long as you stay true to your choice and don t change it in the middle of your calculations. If your 0 is on the ground, an object on the ground has 0 PE but the one on the cliff has not, because it has altitude relative to your 0 potential point.", + "video_name": "kw_4Loo1HR4" + }, + { + "Q": "at 3:00 he says that this formula only works for a point charge or for a spherical charge. My question is: does this formula work for a wire's cross-section.", + "A": "it does but you have to apply a bit of calculus for it(or maybe Gauss law)", + "video_name": "-LtvW5783zE" + }, + { + "Q": "01:01 - 01:32 What does he mean by 'moles'?", + "A": "A mole is just a number, like a dozen. But instead of 12, a mole is 6.02 * 10^23. You could use it to count anything, but since it is a big number is is mostly used to count very small things like atoms and molecules.", + "video_name": "2f7YwCtHcgk" + }, + { + "Q": "At 3:40 you say that the energy produces 38 ATPs but I heard that it was 34, which one is correct?", + "A": "4 ATP are generated before the electron transport chain. That, in addition to the 34 ATP, makes 38 ATP.", + "video_name": "2f7YwCtHcgk" + }, + { + "Q": "at 1:54 and a few other places, Sal says a few \"moles\" of oxygen, hydrogen, etc. Bye \"moles\", does he mean molecules?", + "A": "No, he means moles. A mole is a number, like a dozen, but much larger. 6.02*10^23. A mole of hydrogen atoms is 6.02*10^23 of those atoms.", + "video_name": "2f7YwCtHcgk" + }, + { + "Q": "At 3:22 when Sal says that energy generates 38 ATPs isn't it 36 ATP?", + "A": "A very efficient cell can produce 38 TOTAL ATP from one glucose molecule, but since glycolysis requires 2 ATP, the NET gain would be 36.", + "video_name": "2f7YwCtHcgk" + }, + { + "Q": "I assumed that Sal was saying 38 ATPs total at first because he was looking at the total number of ATPs not the net. However, in 10:30 , he says the net gain of ATP is 38. My books say 36. Am I understanding this wrong?", + "A": "well the total ATPs produced in aerobic repiration should be 38... However, muscle cells & neurons produce only 36 molecules of ATP per glucose molecule. Its because the 2 molecules of NADH produced during glycolysis in muscle cells & neurons dont enter the ETC directly but through other carriers, which transfer the electrons and H+ to the cytochromes. Therefore, these two NADH molecules produce 2 molecules of ATP only, instead of the usual 3...", + "video_name": "2f7YwCtHcgk" + }, + { + "Q": "At 03:55 you mention there are 38 ATP molecules that are being released According to other sources it is 36 why is that ?", + "A": "because they add the number of ATP molecules from the first and the second step of the cellular respiration. Since the first step is produces 2 ATP molecules and the second step produces 36 ATP molecules so when we add them together it is 38 ATP molecules.", + "video_name": "2f7YwCtHcgk" + }, + { + "Q": "When Sal was talking about a net gain in ATP in the video about 9:25 in glycolysis, are the other processes in cellular respiration also have a net gain? Because Sal didn't write whether or not the 2 ATP in Krebs and the 34 in the transport chain were net gains. Thanks!", + "A": "they are. In the ideal cell you have a net win of 38 ATPs. 2+2+34=38 It s a bit confusing if you look at the pictures of it. Sometimes it just says you ll win NADH or FADH2. But they are used to win ATP.", + "video_name": "2f7YwCtHcgk" + }, + { + "Q": "At 08:48, why would you look for a resonance structure? Isn't the Oxygen in this case at a formal charge of 0 (6 - (4+2)). It doesn't make sense to me why you would push the electrons off the double bond and end up with a +O and -C as I thought nature disliked charges and prefers neutral atoms.", + "A": "Yes, it does, but the contributor is still a minor contributor to the resonance hybrid.", + "video_name": "UHZHkZ6_H5o" + }, + { + "Q": "at 1:59 how is the formal charge of oxygen negative one?", + "A": "Formal charge = valence electrons - lone pair electrons - bonds 6 - 6 - 1 = -1", + "video_name": "UHZHkZ6_H5o" + }, + { + "Q": "At 3:49, how come we start numbering at the left side for the second example, whereas Bromine is at 2?", + "A": "Generally, you want the lowest numbers possible for your substituents. There are some exceptions, such as in alcohols, where you want the lowest number on the -OH group (even if it makes big numbers for any other substituents.)", + "video_name": "nQ7QSV4JRSs" + }, + { + "Q": "At 4:28, why is it a oct-5-yn-4-ol but not 5-octyn-4-ol?", + "A": "As it was explained to me, both are acceptable, but the first way is less confusing.", + "video_name": "nQ7QSV4JRSs" + }, + { + "Q": "At 7:38 Sal says that the area of the piston = area of the base of the container but dosen't the base of container have walls on it's sides? So, the area of the base is not = to the area of piston!\nPlease explain me!", + "A": "The area of the face of the piston is the same as the area of the base of the cylinder; the piston fits snuggly into the cylinder. I an not sure why you think the area of the walls of the cylinder are involved here.", + "video_name": "obeGVTOZyfE" + }, + { + "Q": "At 5:34 how does he get \"(1) in the equation.", + "A": "He is showing that six \u00cf\u0080 electrons satisfy H\u00c3\u00bcckel s 4n+2 rule. 4n +2 = 6 4n = 6 \u00e2\u0080\u0093 2 = 4 n = 4/4 = 1 \u00e2\u0088\u00b4 Six \u00cf\u0080 electrons satisfy 4n +2 when n = 1", + "video_name": "oDigu9YxXUg" + }, + { + "Q": "From 4:11 does hank mean the actual taxonomic ' class' when he mentions class ?", + "A": "Yes, hank means classes", + "video_name": "c7Yy9v8dH8s" + }, + { + "Q": "What he calls a tetrad at 7:00, I thought (from lectures) was a bivalent - are these two names for the same thing, or is there a difference?", + "A": "There both the same because the definition of bivalent is a pair of homologous chromosomes.", + "video_name": "04gQ0bQu6xk" + }, + { + "Q": "At 7:40, why is the object exerting an equal force on the hand? I mean, after all it's the object that is getting accelerated, so the force on the object should be bigger than the force acting back on the hand, right? It seems to me like, if the forces were truly equal, nothing would move, not the hand, not the object...", + "A": "Reaction pair forces are on different objects, not the same object. I push on the chair, the chair pushes on me. How many forces on the chair? Just one. So it accelerates. If you and the chair are floating in outer space, when you push on the chair it will also push on you and you will move in opposite directions. If you masses are equal, you will have equal but opposite acceleration.", + "video_name": "By-ggTfeuJU" + }, + { + "Q": "At 6:30, wouldn't you have to throw an enormous object with A LOT of mass to accelerate backward enough to grab onto the space shuttle?", + "A": "Yeah, that would be ideal, but you probably don t have a massive object on you when you re out in space. I assume it would require more energy to move around.", + "video_name": "By-ggTfeuJU" + }, + { + "Q": "At 4:37, why is Sal saying that L goes in the same direction as current. My intuition tells me that the current is going through the L of the conductor and how can length have a direction?", + "A": "You can consider L to be displacement rather than distance or length . We know displacement is a vector while distance and length are scalars. So L has a direction! :)", + "video_name": "l3hw0twZSCc" + }, + { + "Q": "Why do you use a c instead of an equal sign? Is this intentional or just a fault of drawing?(10:04)", + "A": "It is an equal sign. Just the video has lower quality, so it looks like it is c.", + "video_name": "7vHh1sfZ5KE" + }, + { + "Q": "How can the voltage be equal at both the points (02:50)? In the previous video, Sal said that voltage is electric field times distance. Clearly, there is a difference in distance between the two points.", + "A": "Yeah that it is quite confusing, the way to think about voltage in a circuit is work being done on charge . In circuits we are assuming that the work to move a charge through a conducting wire is negligible compared to the work getting the electrons through the resistors. Of course that isn t true, work is needed just to move the electrons through a wire even if it doesn t have any resistance but that amount of work is totally negligible.", + "video_name": "7vHh1sfZ5KE" + }, + { + "Q": "at 1:12, sal says that the electrons are on the negative terminal... dont they repel??", + "A": "yes, thats why current flows when a circuit is made", + "video_name": "7vHh1sfZ5KE" + }, + { + "Q": "I might be wrong in my concepts......please correct me if I'm wrong....\n\nAt 1:55 isn't the compound supposed to be called \"2 butyl pentane\"(as the butyl group is linked to the 2nd carbon of the ring) instead of what sal tells us?", + "A": "First you number the atoms in the ring. If there is only one group attached to the ring, that ring carbon is automatically number 1. Thus the names are butylcyclopentane and sec-butylcyclopentene.", + "video_name": "TJUm860AjNw" + }, + { + "Q": "At 4:23 when discussing naming this structurewould it be appropriate to call it a dibutyl cyclopentane", + "A": "No.The common name is sec-butylcyclopentane. The IUPAC name is (1-methylpropyl)cyclopentane. A dibutylcyclopentane would have two separate butyl groups attached to the cyclopentane ring.", + "video_name": "TJUm860AjNw" + }, + { + "Q": "3:10 till 3:20 were a bit difficult to understand for me, can anyone please elaborate?", + "A": "He is saying that there are two different ways of naming the side chains (alkyl groups) \u00e2\u0080\u0094 the common names and the official or IUPAC names. There are four different butyl groups, and their names in the two systems are Common IUPAC n-butyl butyl isobutyl 2-methylpropyl sec-butyl 1-methylpropyl tert-butyl 1,1-dimethylethyl", + "video_name": "TJUm860AjNw" + }, + { + "Q": "When Sal gives us the (1,1 methyl ethyl)cyclopentane towards the end of the video (12:45) he uses two one's and a di to describe the two methyls on the same carbon. Is it also correct to just say 1-dimethyl? If so, which would be more correct because I feel like 1,1-dimethyl is more referring to two groups of methyls (an ethyl) on each side of that carbon. Slightly confusing. =(", + "A": "We use numbers to locate the substituents only when ther are many possibility for the positions of the substituents. In this case the name could be (dimethylethyl)cyclopentane because there is no other possibilty for the two methyl group to be attach on the ethyl substituent.", + "video_name": "TJUm860AjNw" + }, + { + "Q": "i think\nat 5:28 the vector denoted in blue should directed in downword direction", + "A": "The string is pulling in the upward direction", + "video_name": "_UrfHFEBIpU" + }, + { + "Q": "Could someone give me a hard question to this, i am not sure if i have got this or not, thanks! And how did at 9:28, did Mr. Khan get 200N, he said divide both sides by 1/2, that gives 50N, does it not? So what is happening here", + "A": "It would have given 50 N if it were divided by 2. Diving by 1/2 is the same as multiplying by 2.", + "video_name": "_UrfHFEBIpU" + }, + { + "Q": "At 11:36 he said \"homologous\".Is it not homozygous?", + "A": "Homozygous is when the two inherited alleles from both parents turn out to be both dominant or recessive at the same time, in the new organism.", + "video_name": "DuArVnT1i-E" + }, + { + "Q": "at 12:40 what is a genotype?", + "A": "The genotype is the genetic makeup of a person, which phenotype is they physical makeup.", + "video_name": "DuArVnT1i-E" + }, + { + "Q": "What did Sal mean when he said noise at around 5:14?", + "A": "He is referring to random changes that can occur during the budding process. The most likely change is a mutation of genes. Instead of an exact replica happening during the copying of the original, there is a error, and the end result is not identical to the original. An environmental event could also account for a change in the expression of the genes that are present, again resulting in a non-identical offspring.", + "video_name": "DuArVnT1i-E" + }, + { + "Q": "Isn't the xy pair chromosomes a girl? And the xx is a man? In the picture at 8:55 he is a girl.", + "A": "It actually depends on the species what type of chromosome pairs determine sexual characteristics; there are different sexual determination systems. For humans (and most mammals), the XY chromosomal pair denotes that you are biologically a male while the XX chromosomal pair denotes that you are biologically a female.", + "video_name": "DuArVnT1i-E" + }, + { + "Q": "At 18:07 when Sal talks about how a new combination of genes may or may not be passed on, what happens if it is not passed on, do an old combination of genes get passed on? or the genes from the other person get passed on?\nAlso can someone give me an exact definition for genotype and phenotype?", + "A": "Genotypes are genes expressed as letters. (Ex. Tt) A phenotype is the appearance expressed in words. (Ex. tall)", + "video_name": "DuArVnT1i-E" + }, + { + "Q": "Why do you throw e in there without explaining it? Please walk through the steps a little more deliberately. What is happening with e at 5:14?", + "A": "It s assumed knowledge and it should be about the most complex algebra you need to know to get you through most of chemistry. lnK which is in that equation means the natural log of the variable K. To isolate K, we need to use the inverse function on both sides of the equation, which is e. e^(ln K) = K", + "video_name": "U5-3wnY04gU" + }, + { + "Q": "at about 6:20 hank mentions a tepane, what in the world is that? I am really curious now about that.", + "A": "Pace or step.", + "video_name": "cstic6WHr2E" + }, + { + "Q": "At 9:06, how can P.E. be 5 Joules.\nWhen h=1/2d, P.E. should be equal to 5 units", + "A": "Are the units Joules? If so, what s the problem?", + "video_name": "vSsK7Rfa3yA" + }, + { + "Q": "At 3:51 , What do you mean by \"sp3 hybrid orbital gives 4 hybrid orbitals\" (Is this fixed) ?", + "A": "in sp3 orbitals there are 4 orbitals as 1 of s orbital and 3 of p orbitals", + "video_name": "BM-My1AheLw" + }, + { + "Q": "At, 8:40 - 8:42, there is repulsion between the lone pairs & the bond pairs but what about the lone pairs? Don't they repel themselves too?", + "A": "Of course they do. And they repel one another the most.", + "video_name": "BM-My1AheLw" + }, + { + "Q": "At 1:44 what is VSEPR theory?", + "A": "VSEPR theory is the theory of hybridized orbitals. It is the theory that dictates unhybridized, sp1, sp2, and sp3 hybridizations. Basically the idea is that orbitals will hybridize to form bonds with equal energy.", + "video_name": "BM-My1AheLw" + }, + { + "Q": "Around 7:45 Sal said that the radius of the observable universe is equal to 46 billion light years, does that mean the whole universe is 92 billion light years?", + "A": "The diameter of the observable universe is 92 billion ly. We don t know how big the whole universe is. We have good reason to believe it is much, much bigger than the portion we can observe. Maybe infinite, we don t know.", + "video_name": "06z7Q8TWPyU" + }, + { + "Q": "At 9:16 in the video he states that the light from the object that took 13.7 Billion years to reach us is now 46 Billion light years away. If it all began at the big bang 13.7 Billion years ago, how can anything be 46 Billion light years away?", + "A": "Light years are a measure of distance not time", + "video_name": "06z7Q8TWPyU" + }, + { + "Q": "At 5:54, why does he do a mol ratio of MnO4- over Fe2+ and not the other way around? I'm doing similar problems, and there's seemingly no rhyme or reason as to whether it should be 1/5 or 5/1. It varies from problem to problem.", + "A": "That s because it doesn t matter which way he does it. He is trying to get the moles of Fe\u00c2\u00b2\u00e2\u0081\u00ba. If he had written 5/1 = x/0.000 4000, he would still have gotten x = 0.002 000 mol Fe\u00c2\u00b2\u00e2\u0081\u00ba.", + "video_name": "EQJf8Gb8pg4" + }, + { + "Q": "At 3:36 I don't understand, if there are excess MnO4-, then how can this be the end point? Wouldn't it mean that now there are extra ions which would contribute to an extra volume, and therefore become an inaccurate value to calculate the concentration?", + "A": "The MnO4- has a purple color and the Fe2+ is colorless solution. If the Fe2+ solution is excess, it can be colorless unless the MnO4- is enough. If the color turns purple, that means the Fe2+ ion doesn t exist as Fe2+, they all turn into Fe3+.", + "video_name": "EQJf8Gb8pg4" + }, + { + "Q": "How can he assume it is an acidic solution at minute 0:25?", + "A": "The equation has H\u00e2\u0081\u00ba in it. That s an acid.", + "video_name": "EQJf8Gb8pg4" + }, + { + "Q": "At 3:48, you said that lions and tigers can make ligers, but can animals of different species make hybrids of themselves?", + "A": "Species are defined as being a distinct group that can breed within itself and produce viable, fertile offspring. Certain species (e.g. lions & tigers -> ligers, horses & donkeys -> mules) are close enough genetically that they can produce hybrids but these hybrids are sterile and not able to breed among themselves and produce offspring. Otherwise they would not represent a separate distinct species but rather a subpopulation or race.", + "video_name": "Tmt4zrDK3dA" + }, + { + "Q": "At 3:13, Sal decides to integrate with a lower bound of zero and an upper bound of infinity. Could we also have integrated from infinity to zero, thereby summing all of the rings from an infinite distance away up to the point charge at a distance of zero?", + "A": "Of course but you should then multiply the result by -1 as you reversed the limits of the integration.", + "video_name": "TxwE4_dXo8s" + }, + { + "Q": "At 5:10, Sal explains that when you dump (H^+) into the blood, the buffer system prevents the pH from going up by creating an equilibrium that bonds the H+ to the Bicarbonate. Why does that prevent the pH from going up? There is still a larger amount of H+ in the blood.", + "A": "A solution gets more acidic (lower pH) when there are more free H+ ions in it. The bicarbonate takes these free H+ ions out of the solution. H+ that is bonded to something does not affect the pH.", + "video_name": "gjKmQ501sAg" + }, + { + "Q": "I just wanted to thank you for this video. It was fantastic and it was very helpful. Just really quick question. This turtle doesn't have displacement because she is not changing position. She is just changing distance as seen at 3:33 but she doesn't move left or right? Because she is just moving forwards and backwards this is different than if she were moving left and backwards or right and forwards?", + "A": "you can be displaced forward and backward just as well as left or right. any direction will do.", + "video_name": "GtoamALPOP0" + }, + { + "Q": "5:27, where did you get the 8? I added from three and went down where it stopped and got more than 8.", + "A": "I think he might have forgotten to count 0 when he was counting down from 3.", + "video_name": "GtoamALPOP0" + }, + { + "Q": "Why he made an assumption that it is moving horizontally not vertical? at 12:58", + "A": "because objects can easily roll along the ground and maintain their speed, but it is not so easy to do that in the vertical direction. Gravity interferes.", + "video_name": "GtoamALPOP0" + }, + { + "Q": "At 12:50, doesn't the conjugate base create hydroxide ions in solution, adding to the total moles of OH-, causing [OH-] to be larger and pH to be lower? Or does acetate not affect the pH after the equivalence point?", + "A": "You are correct! It will add to the total amount of OH-, increasing its molarity. But the change is so insignificant that the change is only in the slightest. I did the whole calculation for you and found out that the concentration changes only 9 (!!) places after the decimal. This will cause only a minuscule change in the pH. Also, the higher the concentration of OH-, the higher the pH.", + "video_name": "WbDL7xN-Pn0" + }, + { + "Q": "at 4:36 why is it called The Bowman's Capsule?", + "A": "A glomerulus is enclosed in the sac. Fluids from blood in the glomerulus are collected in the Bowman s capsule (i.e., glomerular filtrate) and further processed along the nephron to form urine. This process is known as ultrafiltration. The Bowman s capsule is named after Sir William Bowman, who identified it in 1842", + "video_name": "UU366tJPovg" + }, + { + "Q": "At 4:01, could you also call it a \"vectorial field?\"", + "A": "Hadnt thought about it that way, but yes, I think you could call it a vectoral field Why do you ask? What are you thinking??", + "video_name": "1E3Z_R5AHdg" + }, + { + "Q": "At 0:44, why is an object in free fall accelerating with a negative value since it is going towards the centre of the earth", + "A": "Nature don t know you are positive or negative, you are free to choose sine conventions, either you choose negative or positive the important think is that you make your calculations right", + "video_name": "1E3Z_R5AHdg" + }, + { + "Q": "At 0:26 he says \"methanol.\" I know this is a pretty elementary question, but why does methanol end in \"ol\"? As for a question actually pertaining to the video, does anyone have classic examples of molecules being used to teach oxidation states. (like practice problems?)", + "A": "Methanol is a combination of the base methane plus an alcohol group, which tends to be simplified in nomenclature by ol . Thus, we have methanol.", + "video_name": "CuGg-Tf8lPI" + }, + { + "Q": "at @6:12 why didnt you change the final velocity vector into negative.", + "A": "Because that is the magnitude it was coming down at, he was not trying to point out the direction.", + "video_name": "sTp4cI9VyCU" + }, + { + "Q": "At 10:17 Sal said that the reason why the car moves through the curve in a curved manner rather than going straight is because of friction. Shouldn't it be because of the change of vector velocity as Sal explained earlier in the satellite, yoyo and the the object travelling in a circular path in space examples?", + "A": "the frictions is the cause of the change in vector velocity", + "video_name": "vZOk8NnjILg" + }, + { + "Q": "At 0:59, it was specified that the carbon turns into an sp2 hybridized carbon, meaning that all the substituents should be on the same plane, yet there are still wedges and dashes, indicating that the substituents of the carbon are not on the same plane. Can somebody explain this to me?", + "A": "The substituents are still in the same plane. It is just that you are looking at the plane edge-on. This puts one bond closer to you (a wedge), one bond further away (a dashed line), and one that is equidistant at both ends (an ordinary line).", + "video_name": "sDZDgctzbkI" + }, + { + "Q": "When Sal mentions that the helium core fuses into heavier elements at 6:02, why only up to iron 26? What about Uranium, gold, etc. ?\nSecondly what happens when A heavier element fuses with a light by one by somehow traveling from its shell or core to another?", + "A": "It has to do with the strength of the Strong Nuclear force. The Strong Nuclear force has a limited distance that is works over. The size of the iron nucleus is the point where the Strong Nuclear force is weakened to the point where to make a larger atom it takes more energy to push the protons/neutrons together than comes out of the process. In systems called heavy ion colliders that they use them to produce heavy elements. So as long as there is enough energy in the collision they can fuse.", + "video_name": "EdYyuUUY-nc" + }, + { + "Q": "At 2:52, he mentioned that the star was starting to collapse. What exactly is meant by collapse?", + "A": "i think he means that a while a red giant is expanding,there is also a white dwarf inside, which when the red giant sheds his outer layers, would reveal the white dwarf. but i m not sure.", + "video_name": "EdYyuUUY-nc" + }, + { + "Q": "Close to the end of a video, (12:21) it said that over many years, a white dwarf would eventually become burned out and turned into a black dwarf. Can you give me a time frame of how long that would take?", + "A": "I have see estimates for around 8 to 11 billion years for a 0.5 to 1 solar mass white dwarf to cool to be a black dwarf.", + "video_name": "EdYyuUUY-nc" + }, + { + "Q": "At 1:40, he said our sun was even hotter than it was before because it is fusing faster. Is this causing global warming then?", + "A": "no As compared to4.6 billion years ago it it hotter but global warming is caused by human activities in the mordern time(industrialisation). I would say that the solar output is stable since last 3 billion years and would be same for next 3-4 billion years", + "video_name": "EdYyuUUY-nc" + }, + { + "Q": "At 7:48 would we be able to see a he flash from Earth?", + "A": "Its not a literal flash. Its just a point in the Suns life cycle.", + "video_name": "EdYyuUUY-nc" + }, + { + "Q": "At 1:34, how is gas a fluid? I know it fills in the shape of what it is in, but how can it be a fluid? Also, at 6:30 what is that thing?t", + "A": "a fluid is a substance which has the ability to flow. liquids can flow from a state of higher potential energy to lower potential energy. in gasses, the same thing applies. they are also considered as fluids because they flow to the edges of the container or from a hot surface to a cold surface. gasses are fluids because they have the ability to flow", + "video_name": "Pn5YEMwQb4Y" + }, + { + "Q": "At 5:03 wouldn't you feel the G-force because 250 m/s > 9.8 m/s and couldn't you measure that?", + "A": "you are comparing a velocity to an acceleration. It s not 9.8 m/s it s 9.8 m/s^2. That s acceleration. 250 m/s is a velocity.", + "video_name": "3yaZ7lkQPUQ" + }, + { + "Q": "Why does it take the same amount of time to cycle regardless of the amplitude? (that is to say, if the starting postion is A/2 it still takes the same amount time to go to -A/2 and return as it would if the starting postion were A)\n\nis it because the acceleration is less at A/2 than at A so the lower velocity means it takes longer to cycle? but why the same amount of time?\n\n(around 7:30 onwards)", + "A": "Well from my understanding, the cycles both take the same amount of time because of its velocity, the one that is stretched more goes faster making it quicker, keeping a constant time, and the one that isnt stretched very far goes much slower, draging the time out even though it has less distance to cover. I m having a hard time explaining, it works well if you visualize it, imagine it and if you were to do it yourself.", + "video_name": "oqBHBO8cqLI" + }, + { + "Q": "1:25\nit said that that molecule's longest chain is 9-carbons\nbut i think that's wrong\nit's (i know this is the incorrect name, but i'm using it for an example) 2-propylheptane\n(emphasis on propyl)\npropyl means 3, but you wrote 4\nthe yellow line means it connects to the 9-carbons\nit's not the actual molecule\nso i believe the actual name is not 4-methylnonane, but 4-methyloctane!\nplease tell me if i am wrong or correct\ni'm just a bit confused...", + "A": "The carbon atom that forms part of the long chain is counted as part of part of the alkane group but not the alkyl group. And remember that the lines are the bonds, the important things are the carbon atoms which are the end-points of the lines.", + "video_name": "CFBKfgGTP98" + }, + { + "Q": "So, what would be the name of the actual neurotransmitter that is released as a response to the Glomus cell depolarizing? Would this be acetocholine or epinephrine? (6:24 in video)", + "A": "Neurotransmitters actually known to be used by the glomus cells are : dopamine, noradrenaline, acetylcholine, substance P, vasoactive intestinal peptide and enkephalins.", + "video_name": "cJXY3Cywrnc" + }, + { + "Q": "At 09:43, Sal uses Coulomb's Law to calculate the \"force generated by the ring\". Coulomb's Law defines the electrostatic force that exists between two point charges, and not that between a thin ring and a point on it's axis. He is applying the Law to calculate the latter, which, obviously cannot be justified. Has he made a mistake?", + "A": "No. He didn t make a mistake. It s like we assume a small amount of charge say dq and calculate its electric field at the axis of the coil then we tend to integrate the whole thing to obtain Electric field due to charge on entire coil.", + "video_name": "prLfVucoxpw" + }, + { + "Q": "At 0:10 why is the electric field constant? Doesn't it get weaker the further away you get from the electric field?", + "A": "Not with infinite plates.", + "video_name": "prLfVucoxpw" + }, + { + "Q": "At 7:45 and a little after, why are the oxygens positive? I thought when you have an oxygen-hydrogen bond the oxygen becomes partially negative?", + "A": "The oxygen in this case is positive because it is sharing 2 of its non-valence electrons with that hydrogen. Its 2 valence electrons are already tied up in the two covalent bonds with the two carbons, and when it gives up some of its rights to the 2 non-valence electrons to the hydrogen, it reduces its negative charge (making it positive). :)", + "video_name": "OpyTJbzA7Fk" + }, + { + "Q": "At 3:43, Sal says that the nuclear membrane starts to disappear. Does this not break the law of conservation of mass? Where did it go? And how?", + "A": "This just means it breaks down, not that it disappears into thin air.", + "video_name": "TKGcfbyFXsw" + }, + { + "Q": "At 4:48, Sal says that the chromosomes are not magenta in real life. What color are they in real life?", + "A": "I believe it depends on the dye used on the cell before viewing it under the microscope. Though I am not fully certain.", + "video_name": "TKGcfbyFXsw" + }, + { + "Q": "at 8:43, how can two chromosomes become four chromosomes?", + "A": "The chromosomes (genetic material) duplicates in the previous cell phases (interphase/prophase) that occur before the splitting in mitosis", + "video_name": "TKGcfbyFXsw" + }, + { + "Q": "At 9:05 it is mentioned that if young boys have any precocious puberty it is pathological, but that may not be always the case in young girls. Is there any reason why is it like this?", + "A": "Girls are more prone to environmental triggers for setting off puberty then boys are... Stress, changes in diet and eating habits, body weight and even sex itself can trigger puberty in women.", + "video_name": "XhYQYVQq6K0" + }, + { + "Q": "5:20 why do we only divide 4.9 by 4 and not time?", + "A": "4.9t is one term - the result of multiplying 4.9 and the change in time. If t is one, 4.9t=4.9. If t is two, 4.9t=9.8. If t is one (4.9t=4.9), then 4.9t/4=4.9/4=1.225. Dividing both by 4 would be 4.9/4/4, or 4.9t/16.", + "video_name": "P7LKEkcNibo" + }, + { + "Q": "At 3:14, why is delta-v equal to 0-initial velocity?", + "A": "THat s how you find a change, you take final minus initial", + "video_name": "P7LKEkcNibo" + }, + { + "Q": "At 5:16, why does Sal square delta t? To cancel out the units?", + "A": "No..not to cancel the units, but to Simplify the calculation.", + "video_name": "P7LKEkcNibo" + }, + { + "Q": "At around 2:50, Sal divided the equation by (-1), but the right side of the equation remained the same, as he wrote it.\n\nIt matters for the direction of the velocity. Did it stay in the same direction or not?\n\nAnd if it did, why did he not put the velocity in the velocity in absolute value?\n\n\nThanks in advance for the helpers! :)", + "A": "there was a negative symbol on both sides before he did that calculation", + "video_name": "P7LKEkcNibo" + }, + { + "Q": "At 3:14, Sal starts writing the formula for displacement. Why is he using Time Up as the time instead of Total Time? Can't we use Total Time instead?", + "A": "If he found the displacement over the total time, it would be zero. He is showing us how to find the peak height. The object reaches peak height when half of the total time has passed.", + "video_name": "P7LKEkcNibo" + }, + { + "Q": "at 6:35, will this equation calculate the total displacement or the half of displacement? because it is only using half of the time.", + "A": "I think it will calculate just how high the ball went in the air because if we calculated the whole displacement it would be 0 because it would land exactly from where we threw the ball,so it would be right at the place we started at, but i think we also calculated half the distance traveled", + "video_name": "P7LKEkcNibo" + }, + { + "Q": "At 3:05 when he multiplied the entire equation by a negative, shouldn't change of time be negative?", + "A": "That depends on your definition, you can have negative time if you wanted to take X amount of seconds of something. Like how can I cut down the time it takes me to get to work, if it takes me 60 minutes to get to work taking one route then I take another route and it takes off 20 minutes of my time its 60-20 = 40 minutes. depends on the context of the expression.", + "video_name": "P7LKEkcNibo" + }, + { + "Q": "At 4:13 Sal Khan says that the first part of the equation is the number of stars in the galaxy but my other source of information says that it is the rate that stars form. Which one is right?", + "A": "I think that the average number of stars that are formed is a better value. Stars are born, and stars die. Using the average of stars currently alive at a given time makes more sense than just using the formation rate.", + "video_name": "YYEgq1bweN4" + }, + { + "Q": "4:52 Sal said planets that are good for sustaining life preferably have a rocky core. Do he mean molten core?", + "A": "Our core isn t molten, it is a solid ball of iron, nickel, and other assorted amounts of heavy metals. The surrounding area is liquid but the core isn t.", + "video_name": "YYEgq1bweN4" + }, + { + "Q": "At 3:38, why did Sal say \" really do 'EXCITE' the electrons in the chlorophyll.....\"", + "A": "Because it means that they move faster. People often say excite rather than speed up.", + "video_name": "-rsYk4eCKnA" + }, + { + "Q": "At 2:51, why is Oxygen O2 and not just O. It is like this in my textbook as well and I do not know why.", + "A": "oxygen is actually called oxygen oxide. this is the oxygen we breath", + "video_name": "-rsYk4eCKnA" + }, + { + "Q": "@7:42 Shouldn't he do (1.00029*ans)/(1.33*8.1)??", + "A": "It would be the same thing. Apparantly his TI-85 can work by dividing a number, and then diving another number immediately after it, instead of putting parentheses around the items, but all in all, it would equate the same value.", + "video_name": "10LuSfZZa3E" + }, + { + "Q": "At 0:50 how'd do we have a large number of atoms?", + "A": "Even a speck of a substance contains a huge number of atoms.", + "video_name": "9REPnibO4IQ" + }, + { + "Q": "8:10 - Ok, what is happening here? One equation is being subtracted from another without any substitutions or anything?\n\nI thought I knew my algebra but this has me confused.", + "A": "When you have system of equation in two variables, then you want to cancel out some terms to solve for at least one variable. so he multiplied the equation and then subtracted the two in order to get rid of T2. You could substitute it as well. fell free to contact me for further clarification informjaka@gmail.com", + "video_name": "zwDJ1wVr7Is" + }, + { + "Q": "On 2:40, Sal says that oxygen and 2 hydrogen make up liquid water but i thought H2o makes up water who is right please help me!", + "A": "H2O = water. This means that a molecule of water consists of 2 H (hydrogen) atoms and 1 molecule of O (oxygen).", + "video_name": "Y3ATc9he254" + }, + { + "Q": "at 7:20 what does aq stand for?", + "A": "aq stands for aqueous . that means dissolved in water or a solution in which water is the solvent. Hope this will help.............. ; )", + "video_name": "3ROWXs3jtQU" + }, + { + "Q": "if 110.mg of fluorine-18 is shipped at 10:00 A.M,how many milligrams of the radioisotope are still active when the sample arrives at the radiology laboratory at 5:20 P.M", + "A": "It s half life is every 110 minutes, or 1 hour and fifty minutes. It will go through it s half life a total of ((7 1/3)x60)/110 times, or 4 times. You can divide 110 by 2 four times (55, 27.5, 13.75) and then 6.875 mg will be left.", + "video_name": "dnYyMHSSb8M" + }, + { + "Q": "At 12:00, if the period is the time taken to complete one cycle then what does it mean the particle will move up and down in one second (frequency)?", + "A": "The period is 1 second. That s not the frequency. The frequency is 1 per second.", + "video_name": "tJW_a6JeXD8" + }, + { + "Q": "at 2:01, we suppose that the electrons go straight from one plate to the other, right?", + "A": "The ions you mean. Positive and negative ions are the charge carriers here, not electrons. And no, here the system works differently, the positive ions move to the negative electrode and the negative ions move to the positive electrode. There they get discharged by gaining/losing electrons from/to the electrode. This is how electrolytes conduct electricity.", + "video_name": "uUhBEufepWk" + }, + { + "Q": "what is glucose at 2:53?", + "A": "Glucose is a sugar produced by plants in photosynthesis, it has a molecular formula of C6H12O6. In photosynthesis it is the result of a plant using water (H2O) and Carbon Dioxide (CO2) to make Glucose (C6H12O6) and Oxygen gas (O2). 6H2O + 6CO2 = C6H12O6 + 6O2", + "video_name": "lzWUG4H5QBo" + }, + { + "Q": "AT 5:45 you said when the volume goes down pressure increases then why does bigger balloon bursts easily as compared to small ballon?", + "A": "because bigger balloons have much more gas inside them which increases pressure significantly.", + "video_name": "WScwPIPqZa0" + }, + { + "Q": "at 6:53 why would hydrogen get one electron ?", + "A": "He explains it earlier on, at 1:14. It has plus one charge, which means that it lost an electron. Electrons have a -1 charge. Carbon is more electronegative than hydrogen, so it would take four electrons from the four hydrogen atoms. Each hydrogen atom gives an electron to the carbon, causing them to have 1 less electron, giving them 1+ for charge.", + "video_name": "OE0MMIyMTNU" + }, + { + "Q": "At 6:15, how is carbon losing electrons therefore being oxidized if it has 8e- on the other side? Or is the 8e- just to balance the charges?", + "A": "when something is oxidized it is losing electrons so the carbon in the reactant side lost 8 electrons to become the carbon on the products side. Now where will you put these 8 electrons? As i ve said they are lost or removed from the reactant so they are in product side. Hope this answered your question :)", + "video_name": "OE0MMIyMTNU" + }, + { + "Q": "at 5:37 whats the differnce between a half reaction and a normal reaction", + "A": "Take a normal reaction and now only consider the atoms being oxidized and the ones being reduced. Ignore all other atoms. Now split your equation into two parts: The reduction side: C(4-) ===> C(4+) + 8e- AND The oxidation side: 2 O2 + 8e- ===> 4 O(2-) The half equation is considering only the atoms being oxidized or reduced and where the electrons are flowing from and ending up. In this case carbon loses 8 electrons and oxygen gains 8 electrons. Hope that helps :)", + "video_name": "OE0MMIyMTNU" + }, + { + "Q": "at 6:11 what does he mean by the lion goes ger? is it suppose to be a metaphor?", + "A": "LEO (loss electrons is oxidation) goes GER (gaining electrons is reduction) it s just a way to remember whether a half equation is oxidation or reduction", + "video_name": "OE0MMIyMTNU" + }, + { + "Q": "At 9:21, how is it that oxygen is reduced only by carbon and not carbon & hydrogen? On the right side of the equation is oxygen not receiving electrons from both hydrogen and carbon?", + "A": "Hydrogen does not change its oxidation state, thus it cannot directly have been part of the oxidation/reduction process.", + "video_name": "OE0MMIyMTNU" + }, + { + "Q": "At 8:26 when he is saying that we wish to minimize the formal charge, why is doing so with one double bond preferred to doing so with two double bonds? Don't you get +1 for Sulfur, -1 for the left Oxygen and 0 for the right oxygen for the one double bond, whereas you get 0 for Sulfur and both oxygens for two double bonds? Wouldn't that be 'minimized' for Sulfur?", + "A": "Did everyone see this pop up at 9:00 ? At 9:00, I drew one of the resonance structures for sulfur dioxide. While forming two double bonds would decrease the formal charge, both ways of representing sulfur dioxide are generally accepted.", + "video_name": "3RDytvJYehY" + }, + { + "Q": "At 3:00 he mentions that Boron doesn't need to follow the octet rule but it can. Does that mean that BF3 would have four resonance structures? The one that doesn't follow the octet rule AND the three that do?", + "A": "It cannot because of the number of total Valence Electrons. Boron can follow the octet rule, but the total number of Valence Electrons prevents this. Boron normally wants 6-8 electrons.", + "video_name": "3RDytvJYehY" + }, + { + "Q": "At 12:04 it says bent, so is it 120 degrees or 104.5 degrees?", + "A": "In this instance, the bond angle will be 120 degrees. If there was a lone pair on the central atom, then the bond angle would be reduced to 104.5 degrees. See the video titled VSEPR for 4 electron clouds for an example of this", + "video_name": "3RDytvJYehY" + }, + { + "Q": "From 8:12 on, could someone please simply define and discriminate between transcription and translation?", + "A": "That is a great question! Transcription is when DNA transfers its genetic information to messenger RNA (mRNA), which carries this genetic information to a ribosome, where each codon (a set of three nucleotides) is translated to a specific protein (this part where the mRNA is in the ribosome is the translation step). Keep these in mind, and you ll be able to remember the difference! :) Note: Sal explains transcription around 8:06, and translation around 10:57.", + "video_name": "6gUY5NoX1Lk" + }, + { + "Q": "Do genes make DNA molecules or DNA molecules make up a gene (around 6:04)?", + "A": "At around 6:29 , Sal mentions section of DNA . Genes are kind of like parts of DNA that code for the expression of specific traits. Hope this helps, and please let me know if I m wrong!", + "video_name": "6gUY5NoX1Lk" + }, + { + "Q": "At 10:48 does adenine pair with both uracil and thymine?", + "A": "In a DNA molecule adenine pairs with thymine while in a RNA molecule adenine pairs with uracil. There are no uracil in DNA and no thymine in RNA.", + "video_name": "6gUY5NoX1Lk" + }, + { + "Q": "I was wondering why from 8:57 to 10:00, you multiplied -9.8 by two and took the square root of it all?", + "A": "It was - -30 = 1/2* -9.8 t^2 If we multiply both side by 2 then the half in the RHS will cancel out and we will be left with- -30*2 = -9.8 t^2 minus minus cancels out and we get- (30*2)/9.8 = t^2 t = sq. rt. of [60/9.8] t = 2.47 s", + "video_name": "jmSWImPs6fQ" + }, + { + "Q": "At 8:19 why is the 1/2 there?", + "A": "Because that s the formula", + "video_name": "jmSWImPs6fQ" + }, + { + "Q": "at 5:53 do you not write 1,2 dimethylHept-2-ene because the Methyl at 1 is part of the chain?", + "A": "Yes, the methyl at 1 is part of the chain so you wouldn t write 1,1 dimethylhex-1-ene. Although that name would indicate the molecule we are talking about, it wouldn t be listed in databases that way. 1,2-dimethylhept-2-ene would actually be written 3-methyloct-3-ene.", + "video_name": "KWv5PaoHwPA" + }, + { + "Q": "At 7:49 shouldn't Sal start from the place where the substituent is the closest i.e\nthe opposite direction", + "A": "The numbering must include the alkenes as two consecutive numbers, although you write only the lower number in the name. In cyclohexene, the alkene carbons are automatically 1 and 2. C-1 becomes the one with the methyl group, and the numering must then go in the direction Sal used.", + "video_name": "KWv5PaoHwPA" + }, + { + "Q": "4:07 Can it also be named hept-2,4-diene?", + "A": "Close. You have to keep the a of the ane ending when there is a multiplying prefix.. This makes it easier to pronounce. The name is hepta-2,4-diene.", + "video_name": "KWv5PaoHwPA" + }, + { + "Q": "At 6:00, Sal says it is \"2-methylhept-2ene\". Is it correct if I write \"2-methylheptene\" ?", + "A": "Sal is correct on this one. Since there are two important structures that have to be pointed out (the methyl group and the double bond), you need to indicate these with two separate numbers. You can t just write the 2 once and say that it applies for both of the groups. Another acceptable name for 2-methylhept-2ene is: 2-methyl-2-heptane", + "video_name": "KWv5PaoHwPA" + }, + { + "Q": "At 4:20, Rishi says the LAIV can't cause you to get sick. If you had a really weak immune system, couldn't you actually get sick? Thanks in advance.", + "A": "There are some groups of people (those with asthma, etc.) who do not qualify for the live vaccination. These people should get the killed vaccine.", + "video_name": "wDghWK_Rr_E" + }, + { + "Q": "at 1:30, 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", + "video_name": "HwkEQfsJenk" + }, + { + "Q": "If DMSO is more likely to take the left structure as Jay at 05:50 says, is it probable for it, used as the solvent in a reaction, to take the right, polar aprotic structure and increase the nucleophilicity? And are the polar aprotic solvents generally bulky, so that they, due to steric hindrance, generally do not solvate the anion of the nucleophile?", + "A": "It never has either the structure on the right or the structure on the left. It always is a resonance hybrid of the two structures, with a partial negative charge on the O atom and a partial positive charge on the S. The major requirement for a polar aprotic solvent is that it have a large dipole moment and a large dielectric constant. It does not have to be bulky. Other examples of polar aprotic solvents are acetone, dimethylformamide, and acetonitrile.", + "video_name": "My5SpT9E37c" + }, + { + "Q": "At 9:38, what are dopamine and serotonin?", + "A": "Those are neurotransmitters, chemicals which let neurons communicate with each other.", + "video_name": "TyZODv-UqvU" + }, + { + "Q": "At 8:26 in the breaking of the covalent bond, is the energy produced heat?", + "A": "this energy can be sound, heat, electromagnetic, nuclear and mechanical energy", + "video_name": "TyZODv-UqvU" + }, + { + "Q": "At 0:52 why are there 2 hydrogens connected to Carbon and", + "A": "In that structure you can only see 2 bonds to other carbons and there is not a charge indicated. With these structures you assume that the maximum possible bonds are there (4 for carbon), so there are two hydrogens bonded to that carbon.", + "video_name": "qpP8D7yQV50" + }, + { + "Q": "at 5:52 is magnesium actually originated in Magnesia?", + "A": "Yes it did from the district of magnesia. It is a place in greece.", + "video_name": "8Y4JSp5U82I" + }, + { + "Q": "At 10:10, how would you use light years to calculate diameter?", + "A": "at center of universe we would use a light in any direction and then when it will reach the end of the universe that its radius and the twice is the diameter", + "video_name": "5FEjrStgcF8" + }, + { + "Q": "at 2:39-ish a pop up comes up stating the \"size\" of the earth, is that from pole to pole?", + "A": "It is the diameter of the Earth which is acually long than from pole to pole", + "video_name": "5FEjrStgcF8" + }, + { + "Q": "At 7:42, you mention how far apart stars are. What stars are the closest together, and how close are they?", + "A": "The two closest stars every found are the stars in HM Cancri system. This system is made up of two white dwarfs co-orbiting each other with a period of about five minutes. Each stars is moving at about 500 kilometers per second around each other and have an average separation of about 80,000 kilometers from each other (a separation of around 7 earths).", + "video_name": "5FEjrStgcF8" + }, + { + "Q": "At about 5:49, what does one AU mean? What is an AU?", + "A": "astronomical unit. Average distance between sun and earth.", + "video_name": "5FEjrStgcF8" + }, + { + "Q": "I thought astrophysicists have claimed that for some time after the creation of the universe, the particles that made up the young universe weren't ionized for some length of time. So wouldn't that mean that they couldn't transmit energy (light) across distances and that light from the early star formation couldn't be visible from our home planet?\n\nI probably worded this wrong but oh well.\n\ntime: ~9:00", + "A": "Prior to about 380,000 years after the big bang the universe was too hot (above about 3000K) for electrons to be in atoms so the majority of matter had an electric charge so light could not travel freely. This is so early in the development of the universe that there was very little to see even if you could.", + "video_name": "5FEjrStgcF8" + }, + { + "Q": "At 4:28, Rishi writes pCO2 and pO2. What does p stand for?", + "A": "partial pressure", + "video_name": "QP8ImP6NCk8" + }, + { + "Q": "At 4:05, how do you pronounce 'crastholatian' acid metabolism??", + "A": "Crassulacean , after the Crassulaceae family of plants in which it was first discovered. This family includes orchids, bromeliads (of which pineapple is a member), purslane, agave, aloe and the succulent jade plant.", + "video_name": "xp6Zj24h8uA" + }, + { + "Q": "At 5:07 sal says that glass is a fluid,but how? in order to become one it should flow, right?", + "A": "Glass is made of really long and hard to move molecules. Even though they want to move, its just too slow. Glass is not really a liquid, but also it isn t a solid, properly saying. Its state is called a supercooled liquid, or an amorphous solid. That happens when a liquid is cooled beyond its freezing point, but it doesn t freeze.", + "video_name": "G4CgOF4ccXk" + }, + { + "Q": "At 2:59 when the nitrogen gets sp2 then the carbon with the negative charge gets sp3?.", + "A": "In that particular resonance structure the carbon with the negative charge would be sp3, but the real structure has all the ring atoms sp2 hybridized with the \u00cf\u0080 electrons delocalized (spread over all of the ring atoms).", + "video_name": "wvVdgGTrh-o" + }, + { + "Q": "At 2:40, I don't really understand where the numerator came from.", + "A": "To figure total parallel resistance, one adds the reciprocal of all the resistors to get the reciprocal of the final resistance of the circuit. (i.e. one adds the conductances). The 16 is the least common denominator of the various fractions he is adding. He needs to convert each fraction to 16ths in order to add the numerators. For example, the 1/4 becomes 4/16, and so on.", + "video_name": "3NcIK0s3IwU" + }, + { + "Q": "at 3:39 he begins to add up the resistance of the two resistors in series using ohms law by saying R1+R2 which gave him 3. my question is why is R3 on the vertical right hand side line not being added when it is also a resistor in series", + "A": "R3 is not in series with (R1+R2), but rather in series with [(R1+R2) in parallel with R0]. So the total resistance would be (R1+R2)*R0/(R1+R2+R0) + R3 not just R1+R2+R3", + "video_name": "3NcIK0s3IwU" + }, + { + "Q": "at 6:55 the molecule which contains 2 lone pairs and 2 bond pairs\nnitrogen has valency of only 5\nin that 2 lone pair of electrons are there so there is only one e to be shared then how can it form two bonds\nis the one bond a dative bond?", + "A": "Pretend that molecule had an -NH2 group on the end. Then pretend a very strong base came along and removed one of those hydrogens, and the electrons that were in that N-H bond stayed on nitrogen. What you get is nitrogen having 8 electrons still but only 4 of them are in bonds, the other 4 are in the 2 lone pairs.", + "video_name": "5-MM39VCwc0" + }, + { + "Q": "According to wikipedia: A parsec is the distance from the SUN (not from the EARTH) to an astronomical object that has a parallax angle of one arcsecond.\n\nSal said in 7:20, \"It's the distance that an object needs to be from EARTH in order for it to have a parallax angle of one arc second.\n\nYou could argue that it's approximately the same because 1 AU is miniscule compared to distance of a star from the earth. But still, the concept is different.", + "A": "It s not just approximately the same, it s the same to an almost immeasurable degree. We are looking at objects that are light YEARS away. The distance between the sun and the earth is 8 light MINUTES. 8 minutes / 1 year = .0015%. The distance measurements themselves are nowhere near that precise.", + "video_name": "6zV3JEjLoyE" + }, + { + "Q": "Hi all, I have a question. At 1:47, what does Sal mean when he says, \"Distance traveled as a function of theta.\"?? Thank you.", + "A": "at 1:47 sal means that if theta is changed, the distance changes because distance depends upon theta", + "video_name": "-h_x8TwC1ik" + }, + { + "Q": "At 0:30 what is a LCD?", + "A": "Liquid Crystal Display. He mentions it in the vid", + "video_name": "PSy6zQsk8z0" + }, + { + "Q": "At 7:48, it says there's a decrease in Sn2 mechanism. I understand that, but if a strong nucleophile is put in a polar protic solvent, it becomes a weak nucleophile. Then, shouldn't Sn1 be favoured over Sn2 as a minor product ?", + "A": "A polar protic solvent doesn t make a strong nucleophile into a weak nucleophile.It makes it into a weaker nucleophile. Ethoxide ion is a strong nucleophile in an aprotic solvent. It is weaker in a protic solvent, but it is still a pretty strong nucleophile even there.", + "video_name": "vFSZ5PU0dIY" + }, + { + "Q": "At 3:40 he says that the reaction would go by an Sn1 mechanism. Doesn't Sn1 only occurred in tertiary substrates? The one in the example is secondary", + "A": "No, 2\u00c2\u00b0 substrates can react via SN1 or SN2, depending on the conditions. We have two competing processes. If the nucleophile attacks faster than the leaving group spontaneously leaves, the reaction is SN2. If the leaving group leaves before the nucleophile can successfully attack, we have SN1. In this case, the methanoic acid is a very weak nucleophile, so the rate of SN2 attack is slow. Br\u00e2\u0081\u00bb is a good leaving group. so the rate of the SN1 reaction predominates over that of SN2.", + "video_name": "vFSZ5PU0dIY" + }, + { + "Q": "around 9:30 in the video he said \"total distance\"... i thought we were finding the total displacement?", + "A": "In this case, the distance and the displacement are the same, because the plane always moves in the same direction. But you are correct, if he was being super-careful, maybe he should have said displacement .", + "video_name": "VYgSXBjEA8I" + }, + { + "Q": "At 11:12, Sal uses the previous value stored in the calculator (72.222 m/s) as the final velocity. But if he had just used 72 m/s like he said during the video, then the answer we get would be slightly different, around an acceleration of 32.4 m/s^2. I know this is a very slight difference, but in the second case, the value rounds down to 32 m/s^2. Should we use the more precise value like Sal used or use the value that complies with the significant figures rule?", + "A": "follow sig fig rules. But you don t round intermediate values - you only round the final answer (to the correct number of sig figs)", + "video_name": "VYgSXBjEA8I" + }, + { + "Q": "at 4:24 where does the 2 come from in the denominator? I don't understand...it seems so random", + "A": "The 2 is used because the average (mean) velocity is being found. The mean of a set is found by dividing the sum of the numbers in the set by the number of numbers. So the average mean speed is (V1+V2)/2, Hope this helped.", + "video_name": "VYgSXBjEA8I" + }, + { + "Q": "at 11:40, shouldn't Sal use 72 instead of 72.2222.... because it's only 2 sig figs? that would make 72^2 / 160 = 32.4, which rounded to 2 sig figs is 32, not 33.", + "A": "Sal is often a bit careless about sig figs. The equation that you have written should have 2 sig figs in its answer, if that is the final answer. Remember not to discard extra sig figs until you report your final answer. You use them all during intermediate calculations.", + "video_name": "VYgSXBjEA8I" + }, + { + "Q": "At 6:02, why does the hydrocarbon chain have no polarity?", + "A": "Carbon and Hydrogen have very similar electronegativity, so the elements don t pull each other to a specific direction. Thus the hydrocarbon chain is not polar.", + "video_name": "Pk4d9lY48GI" + }, + { + "Q": "At 8:50\n\nWhy would Nitrogen grab a proton (H+) from the environment if this atom is very eletronegative?", + "A": "The atom as a whole is not electronegative, if the carboxyl tail becomes negative by losing a H+ the amino head becomes positive by gaining a H+, to make a neutral molecule.", + "video_name": "Pk4d9lY48GI" + }, + { + "Q": "At 04:07, why is it that at the 3rd carbon it is not 3-dimethyl since you have two methyl groups coming off?", + "A": "That second methyl has already been accounted for in the longest chain (it s the fourth carbon in the butane base), so you only need to name one methyl substituent at the 3 carbon.", + "video_name": "peQsBg9P4ms" + }, + { + "Q": "Hi, at 9:00 why does the #2 group move but not the #1 group?", + "A": "He is rotating the whole molecule 120\u00c2\u00b0 about the axis joining the C and #1, so those two atoms stay in place while #2, #3, and #4 rotate about that axis.", + "video_name": "peQsBg9P4ms" + }, + { + "Q": "At around 4:53, why did Sal 4*56+3*16?", + "A": "Each iron has a mass of 56 and each oxygen has a mass of 16. The total mass of Fe2O3 is calculated as 2*56+3*16. (You have a typo; should be 2*56 instead of 4*56)", + "video_name": "SjQG3rKSZUQ" + }, + { + "Q": "At 7:00, do you always multiply that number by 2 or did he only do that because it was in front of Al? Would he have not multiplied it at all if it had nothing i front of the Al?", + "A": "If you look at the reaction equation, there is a coefficient in front of Al. You multiply by the coefficient because that is the ratio in which these chemicals react. Of course, if the coefficient is 1 (in which case you don t write it just like you don t write a coefficient of 1 in algebra) there is no need to multiply.", + "video_name": "SjQG3rKSZUQ" + }, + { + "Q": "At about 7:12 sal says \"for every one molecule of this, we need one molecule of that.\" I thought Fe2O3 would have an ionic bond and therefore technically wouldn't be a molecule. Am I mistaken?", + "A": "You are not mistaken, but we are often a little sloppy in terminology. We technically should be saying formula unit when speaking of Fe\u00e2\u0082\u0082O\u00e2\u0082\u0083 or any other ionic compound instead of molecule .", + "video_name": "SjQG3rKSZUQ" + }, + { + "Q": "I'm still confuse why use the ratio of 1:2 of FE2O3 and 2Al mole ratio , 85g FE2O2 is 0.53 moles right why the aluminum must be 2(0.53)mole?", + "A": "So, the reaction asks for 1 unit of Fe2O3 for every 2 units of Al. Therefore, if you have 1*(0.53) moles of Fe2O3 then you need 2*(0.53) moles of Al", + "video_name": "SjQG3rKSZUQ" + }, + { + "Q": "At 5:18 is it okay to NOT use PEMDAS?", + "A": "No, you should always compute numbers using the correct order of operations AKA PEMDAS.", + "video_name": "SjQG3rKSZUQ" + }, + { + "Q": "Why do we round the atomic mass numbers from the periodic table? Like for Iron at 4:43, we use 56, not 55.85", + "A": "I understand that Iron has multiple isotopes and the atomic mass is an average of all those isotopes. 55.85 is the average mass of all Fe isotopes. Using 56 is simplifying a little bit...basically assuming you re using an Fe isotope with a mass of exactly 56 amu.", + "video_name": "SjQG3rKSZUQ" + }, + { + "Q": "at 6:30 did he round that with the third number?", + "A": "Yes, he did. 85 g Fe\u00e2\u0082\u0082O\u00e2\u0082\u0083 = 0.532 mol Fe\u00e2\u0082\u0082O\u00e2\u0082\u0083. Only 2 significant figures are justified, but this is an intermediate answer, so he should have carried an extra digit and then rounded off the final answer to 2 significant figures.", + "video_name": "SjQG3rKSZUQ" + }, + { + "Q": "At 4:53, Can you explain to me why you multiplied 2 x 56. I am not very clear...", + "A": "you multiply 2X56 because the atomic mass of iron is approximately 56, times two because you have two atoms of Fe. Hope this helps! :)", + "video_name": "SjQG3rKSZUQ" + }, + { + "Q": "Things I am confused about:\n- At 5:20 you say that one molecule of iron three oxide is going to be 160 atomic mass units, then\n- At 5:41 you say that one mole of iron three oxide is going to have a mass of 160 grams.\nI am confused, at either 160 is recognized as grams or atomic mass unites?", + "A": "A MOLECULE has mass of 160 amu. One MOLE of those molecules has mass of 160 grams. A mole is a number, and we picked it so that the grams to amu thing would work.", + "video_name": "SjQG3rKSZUQ" + }, + { + "Q": "At 1:31 how did you predict the subscripts of the atoms, and how they would arrange themselves?", + "A": "It s something that he just knows from past experience, and it is something that will come to you with time. When a metal is reacted with oxygen a metal oxide is formed. The subscripts are needed to make the formula work: Al^3+ O^2- The simplest way to make the charges cancel is 2x Al^3+ and 3x O^2- So the formula is Al2O3", + "video_name": "SjQG3rKSZUQ" + }, + { + "Q": "at 1:30 the iron oxide isFE2O3 why not FEO2?", + "A": "Iron (Fe) in the complex will become a (Fe)3+ ion. The oxygens are each (O)2-. Therefore, in order to balance the charges and have a compound with zero net charge, you need 2(Fe)3+ and 3(O)2-", + "video_name": "SjQG3rKSZUQ" + }, + { + "Q": "At 5:36 Why does Sal add the atomic masses of O and Fe to get the atomic mass of Ironoxide", + "A": "He added them to calculate the moles of Fe2O3 using the formula: moles = given mass/molar mass.", + "video_name": "SjQG3rKSZUQ" + }, + { + "Q": "At 11:27, in our class we say iron feroxide. Is it the same as iron three oxide as Sal says?", + "A": "Do you mean ferric oxide ? If so, that is an older term for Iron (III) oxide. It is still widely used, but it is not the IUAPC approved term. Ferroxide is a brand name of a pigment, so that is not an acceptable scientific name. But, to answer your question, you should use the method demonstrated in the video with the Roman numerals. This is the officially sanctioned term and would be understood by any chemist.", + "video_name": "SjQG3rKSZUQ" + }, + { + "Q": "at 3:36 he says Iron 3 Oxide, he means Iron 2 oxide right?", + "A": "No, Fe\u00e2\u0082\u0082O\u00e2\u0082\u0083 is Iron (III) Oxide. The number after the metal ion references its oxidation state, not how many atoms are present per formula unit.", + "video_name": "SjQG3rKSZUQ" + }, + { + "Q": "At 6:28 why asymmetric stretch is taking more energy than symmetric stretch ?", + "A": "Here s my guess: Consider a CH\u00e2\u0082\u0082 group. In a symmetric stretch, the two H atoms are going in the same direction. The group dipole moment changes considerably because both bonds are going in and out at the same time. In an asymmetric stretch, they are going in opposite directions. One bond gets longer as the other gets shorter, so the change in dipole moment is much less. It takes energy to separate positive and negative charges from each other, so the symmetric vibration has a higher frequency (energy).", + "video_name": "9GPuoukU8fM" + }, + { + "Q": "whats a solar mass as said at 1:28", + "A": "One solar mass is not the mass, but the diameter of Sol(the Sun).", + "video_name": "DxkkAHnqlpY" + }, + { + "Q": "What would almost infinite be? (5:16)", + "A": "There is no ALMOST infinite", + "video_name": "DxkkAHnqlpY" + }, + { + "Q": "Mentioned in 8:32, what are those stars in our solar system rapidly orbiting what is believed to be a black hole?", + "A": "the star are called a high velocity star.", + "video_name": "DxkkAHnqlpY" + }, + { + "Q": "even at 8:15 the structure that is given\nis it benzophenone or dibenzophenone?", + "A": "I wiki d it up It s benzophenone although some part of me really wants it to be called dibenzophenone :P", + "video_name": "wD15pD5pCt4" + }, + { + "Q": "At 7:44 the structure that is drawn\nis it acetophenone or acetophenyl?", + "A": "it s acetophenone. Phenyl is only used as a prefix--phenone is used as a suffix. (e.g. 2-phenylbutane)", + "video_name": "wD15pD5pCt4" + }, + { + "Q": "When Sal first talks about the 2nd spaceship, he says \"at exactly the same velocity as her\", but then writes and says 1.5C. He loses me at 1:30. If the 2nd ship is traveling at 1.5C and she's at .5C, how do their relative positions stay the same?\nARE we dealing with SR here? It doesn't seem Newtonian to me.\nThank you", + "A": "You are getting confused with the expressions, writing .5C means point five times the speed of light while writing 1.5C would mean one point five times the speed of light. The equation is not 1.5C its 1.5x10 to the power of 8 m/s which is half the speed of light (3x10 to the power of 8 m/s) So all the spaceships are traveling at the same speed, which is half of the speed of light. Hopefully this makes sense, have another look at the equation being written at 1:30 again.", + "video_name": "F7BU1sXtul4" + }, + { + "Q": "At 4:10, there are bulges at the cup. Is there any relations with the convex meniscus?", + "A": "Sort of. The bulge that Sal is talking about does have to do with cohesion, but in this situation the bulge is not truly a convex meniscus because it is formed by surface tension, through cohesion, rather than just cohesion.", + "video_name": "_RTF0DAHBBM" + }, + { + "Q": "At 4:54, Sal says that 'the same average kinetic energy' . What is he referring to ?\n\nThanks in advance !", + "A": "The wood and the metal have the same kinetic energy, or in other words they have the same temperature since temperature is just a mesure of the jiggling of atoms/molecules. Hope this helps ! If not, feel free to contact me", + "video_name": "6f553BGaufI" + }, + { + "Q": "At 1:00 how would the joules cancel out if we multiply them? We are supposed to divide it right? And where did the eV unit pop up from? If the unit of eV is (Joule)^2, then why is it written in the video that 1eV=1.6*10^-19 J?? I am not able to understand this part!", + "A": "I don t think you have followed the units correctly. When you multiply by 1/x that s the same as dividing by x. So when he does: y J * 1 eV / z J, both J cancel out leaving just eV. He is converting an energy value from J to eV. 1 eV = 1.6 x 10^-19 J is the conversion factor between these.", + "video_name": "nJ-PtF14EFw" + }, + { + "Q": "Why can't we have a value of energy in between the integers which you mentioned at 2:59?", + "A": "Because that s the way nature works. Energy is quantized. It was a surprising discovery, but it is true. Why it is that way, we don t know.", + "video_name": "nJ-PtF14EFw" + }, + { + "Q": "at 2:24, what is subscripts", + "A": "It literally means written below, in this case it s the smaller letter. At 2:24, he means a smaller letter to distinguish different things. For example, if I m doing a physics problem and I have 2 velocities, of a car and of a train, I could use subscripts to tell them apart.", + "video_name": "CFygKiTB-4A" + }, + { + "Q": "At 5:55, Sal did F*d, with F being 10 kg * 9.8. Why isn't F=0, because as he said, there is no net force because the elevator is going at a constant velocity?", + "A": "The way it is going at constant velocity is it must have an upward force on it equal to its weight. Otherwise it would accelerate downward (fall)", + "video_name": "3mier94pbnU" + }, + { + "Q": "A little before 3:50, sal talks about pushing upwards with the acceleration of gravity while gravity is pulling downwards with the same acceleration, would the block even move then? Because if the block moves then there isnt any work done.", + "A": "There is no net work done on the block and therefore we should not expect the kinetic energy of the block to increase, according to the work-kinetic energy theorem. But there is work done on the earth-block system, and therefore the potential energy of that system increases.", + "video_name": "3mier94pbnU" + }, + { + "Q": "At 5:15, Sal said that there's no net force, so Fnet =0. But why he take 98 N as a force?", + "A": "For Fnet to be zero the upward force must be equal to the weight (which is 98N). He is finding work done by this upward force.", + "video_name": "3mier94pbnU" + }, + { + "Q": "At 9:30, does the potential energy when it hits the ground get converted to kinetic energy? And would it have velocity 100 when it hits the ground?", + "A": "There is no more PE when you reach the ground. It s all KE at that point. And the KE then gets converted to thermal energy", + "video_name": "3mier94pbnU" + }, + { + "Q": "at 5:39 you said acceleration of gravity is 9.8 meter per second squared why is it not zero when the object is descending with constant velocity. It's not accelerating", + "A": "If the object descends with constant velocity, it is not accelerating. But that s not how objects fall. They accelerate when they fall. That s why you can jump off a short step but you can t jump off a tall building.", + "video_name": "3mier94pbnU" + }, + { + "Q": "At 3:02, why exactly are we pushing the object up with a force mg? Wouldn't it cancel with the gravity?", + "A": "If so happens then the body will stay at equilibrium rather we are pushing it with a bit greater force to overcome gravitational pull.", + "video_name": "3mier94pbnU" + }, + { + "Q": "why is gravity negative at 5:52?", + "A": "he said that the tension in the string is equal to mg..!! the net force in the vertical direction is equals zero..!! refer the video once more, carefully..!! gravity is not -ve !!", + "video_name": "3mier94pbnU" + }, + { + "Q": "If potential energy is the ability to do work (7:00), what work does the object do when it falls? Isn't this work (falling of the object) done by gravity?", + "A": "Remember, gravity is an acceleration (9.81m/s^2); it s not a force. Therefore, 10kg of an object has potential to do work WITH GRAVITY, if it s located at proper position.", + "video_name": "3mier94pbnU" + }, + { + "Q": "If you times 1/2 x 5 x 49 this is equal to 122.5 which is also 1.23x10 to the 23rd power... How does he get that answer at 1:41 - 1:58", + "A": "Are you referring to his answer of 125 joules? He s using the approximation of 1/2 * 5 * 50 there. Also, 1.23 * 10 to the 23rd power is a huge number, I don t think that is what you meant to type.", + "video_name": "3mier94pbnU" + }, + { + "Q": "at 5:40, why is force = 10*9.8? If force = m*a then shouldn't acceleration be -9.8 not 9.8, since it is downwards", + "A": "You can define the signs of your direction however you want; it s arbitrary. If you want to make down be positive, you can. You just have to be consistent throughout the problem.", + "video_name": "3mier94pbnU" + }, + { + "Q": "At about 3:12 Sal says he's applying a force of mg upwards. Is this a net force? I fi t were just a force wouldn't it be counterbalanced by the force of gravity?", + "A": "If he applies mg upward, and gravity pulls downward with a force of mg, then the net force is zero and the object will maintain its velocity.", + "video_name": "3mier94pbnU" + }, + { + "Q": "At 7:38, Sal explains why the distance between us and the object emitting the photon has expanded due to the universe. Wouldn't the photon emitted from the object still be moving? It wouldn't have stayed in the same spot, right?", + "A": "Right. It s own motion is bringing it closer, and that is offset to some degree by the expansion of space", + "video_name": "6nVysrZQnOQ" + }, + { + "Q": "in this video, at 13 minutes and 56 seconds (13:56) sal says that the distance between the two points is 46 billion light years. but isnt the universe 13.7 bilion years old, and wouldn't this imply that the distance between the two points is 13.7 light years???? i'm confused...", + "A": "Some parts of the universe may be expanding faster than light.", + "video_name": "6nVysrZQnOQ" + }, + { + "Q": "At 8:00, there's a point in space which emitted a photon 10mil. yrs ago and space is expanding between us so it takes longer to get to us. At 9:50,the photon isn\u00e2\u0080\u0099t travelling faster than the speed of light, even though it covered a greater distance.\n?\nIf space is expanding, then that photon must be travelling slower than the speed of light towards us, yet faster than the speed of light away from its origin. Ouch, my head! I realize this is getting into relativity, but can anyone expand on this", + "A": "but the light will be red shifted because it s source is moving away.", + "video_name": "6nVysrZQnOQ" + }, + { + "Q": "At 16:09, is the \"white hot plasma\" the same thing as the \"cosmic background radiation\"?", + "A": "The cosmic background radiation is the afterglow left over from the big bang. At first it was seen to be constant (the same everywhere). Now the COBE satellite shows that there are tiny fluctuations which are believed to be differences in density. This is what led to the forming of galaxies. But I m not sure what Sal means exactly by white hot plasma .", + "video_name": "6nVysrZQnOQ" + }, + { + "Q": "At 9:07, Sal said there may be a black hole at the center of the galaxy, why would this be so?", + "A": "We don t know why they are there, but it appears that most or maybe all galaxies have a super massive black hole in the center.", + "video_name": "rcLnMe1ELPA" + }, + { + "Q": "At 6:36, Sal mentions that our solar system is in the Orion Spur. Also, on a clear night, you sometimes see what looks like an arm/spur of the Milky Way. Which arm/spur is it?", + "A": "That is the entire milky way. Every arm of it is in that same plane.", + "video_name": "rcLnMe1ELPA" + }, + { + "Q": "You state at 3:45 that our images of the galaxy are artist representations. What information do they have to draw from and what do they have to make educated guesses about in their representations? What do these artists use to generate these images?", + "A": "The artists have to add the light and color. What our telescopes see is light waves of various frequencies. A lot of the light is not in the visible spectrum. The telescopes use electronic sensors to record the data. Someone has to decide what that data looks like. What wavelength should be what color? How bright is bright ? That s the artist.", + "video_name": "rcLnMe1ELPA" + }, + { + "Q": "In the picture at 12:07, there is a black space that forms a sort of horizontal line. Is that just empty space between stars? Or is it attributed to something else?", + "A": "In these pictures, the whiter parts are usually gas clouds that reflect off the light, while the darkers areas are where dust clouds partially obscure the light of stars behind them.", + "video_name": "rcLnMe1ELPA" + }, + { + "Q": "at 5:49, Sal mentions the Orion Spur. Where is that in the Milky Way?", + "A": "We re in it.", + "video_name": "rcLnMe1ELPA" + }, + { + "Q": "At 9:03 Sal said that scientists think there is a super massive black hole in the middle. Would we one day get consumed by this black hole? Is our galaxy spinning into that black hole?", + "A": "No, even a 4 million solar mass black hole is unable to get us at its distance. This black hole has not swallowed anything of significant size in millions of years.", + "video_name": "rcLnMe1ELPA" + }, + { + "Q": "At 7:40, he says that the boiling point for methane is around -164 degrees celsius. So, can methane be in a liquid form, if it is colder than -164 degrees celsius? And if so, is it present in a liquid form naturally anywhere?", + "A": "Yes. Titan, Saturn s largest moon, has clouds, rain, rivers and lakes of liquid methane.", + "video_name": "pBZ-RiT5nEE" + }, + { + "Q": "2 questions.\n1. In the first example within the first 4:00, both carbons have the same number of substituents. So couldn't you add the proton and the OH to either one of the carbons?\n\n2. at 11:50, why do you not have to worry about sterochem? Just because you are ignoring it for the sake of teaching?", + "A": "1. Correct. The alkene is symmetrical, so you can add the H and the OH to either end. 2. No. You don\u00c3\u00a8t have to worry about stereochemistry, because the product has no chiral centres.", + "video_name": "dJhxphep_gY" + }, + { + "Q": "In the previous video it was said that temp is av KE by no of molecules but in this video at 3:20 it is said that temp is total KE by no of molecules. Which one is correct", + "A": "average, he says total divded by n, which is number of molecules", + "video_name": "HvYUKRMT0VI" + }, + { + "Q": "I've noticed this in a few videos but at 8:50 he draws a 'double head' arrow to show the movement of a electron from the Bromide ion to the carbocation but only one electron is moving so shouldn't it be a 'fish hook' arrow?", + "A": "Yes, that s the convention. Most chemists consider this reaction to be a two-electron movement: Both \u00cf\u0080 electrons move to the H, and both of the electrons in the H-Br bond move on to the Br.", + "video_name": "Z_GWBW_GVGA" + }, + { + "Q": "At 5:23 Sal mentions continuing mountain chains between North America and Europe. What are some examples of this?", + "A": "The Appalachian mountains in the US, the Scottish Highlands, and the Little Atlas Mountains in Morocco were all formed as parts of an ancient Pangean mountain range.", + "video_name": "axB6uhEx628" + }, + { + "Q": "At 7:04, David says that the force of tension is pointing towards the centre. But in previous videos, David said that the force of tension is only a PULL, not a PUSH. But if the force of tension is pointing towards the centre, wouldn't that be contradictory?", + "A": "If the object that is moved around in a circle by a string, suddently lost the string, then the object would keep moving away from the center. This means that the string is pulling the object to stay in the circle. If this makes sense?", + "video_name": "FfNgm-w9Krw" + }, + { + "Q": "At 1:37, what is the angle between the plane containing two C-H bonds in CH4, and the plane containing the other two C-H bonds in the same molecule?", + "A": "90 degrees is the angle", + "video_name": "ka8Yt4bTODs" + }, + { + "Q": "At 4:15, why is the y-component 120 sin 30 degrees ?", + "A": "The y- and x-component of the velocity is computed with trig. Go back to the 1-dimensional videos for a full explanation of how to use trig to break a vector into it s vertical and horizontal components. Sal does a good job of explaining how to break a vector into it s components, and why it is useful to do so in those earlier videos.", + "video_name": "jl_gQ-eL3xo" + }, + { + "Q": "At 1:20, I believe there is a mistake. RBCs do not contain a nucleus.", + "A": "That is not a RBC and you re correct, they shed their nuclei before they enter circulation. What he is drawing is endothelial cells lining the blood vessel. Hope this helped! :)", + "video_name": "RQpBj8ebbNY" + }, + { + "Q": "AT 14:13\nIt is said, that the wavelength of that standing wave can be found using the formula\nWavelength (lambda) = 2* (Length of the tube)/ n , where n=1,2,3,.....\nBut, looking at the graph carefully, we can take n= no. of nodes...\nCan'nt we?", + "A": "If we take n as no. of nodes, we just have to be careful! It works for this case, but not for all of them, ex. if you use n as number of nodes for standing waves on strings, it will not work out :)", + "video_name": "BhQUW9s-R8M" + }, + { + "Q": "Aren't you supposed to write solute -> lowers FREEZING point at 3:17?", + "A": "Its true, check the clarifications section.", + "video_name": "z9LxdqYntlU" + }, + { + "Q": "to be clear, when the solute is added, the boiling point is lower, and when the solute is added it creates a lower vapor pressure. What does vapor pressure have to do with the boiling point because that was mentioned at about 5:45", + "A": "The standard boiling point of a substance is the temperature at which the vapour pressure of the substance is equal to the external pressure. The vapour pressure is decreased when a solute is added and thus, a higher temperature is required to bring the vapour pressure to be equal to the external pressure. This, we have a higher boiling point.", + "video_name": "z9LxdqYntlU" + }, + { + "Q": "at 6:04, sal says the solute lowers the vapour pressure but my question is if the solute particles occupy both the positions in surface as well as inside ,won't the solvent molecules (H2O) get dis-organised leading to more of the molecules escaping out of the system therby decreasing its boiling point ??", + "A": "Within the solvent and at surface, the solute molecules become surrounded by layers of associated water molecules, or shells of water of solvation. Formation of these shells reduces number of solvent (water) molecules that have enough kinetic energy to escape as a vapor, decreasing vapor pressure and increasing boiling point.", + "video_name": "z9LxdqYntlU" + }, + { + "Q": "3:50 (ish) Why would the OCH3 donate the e- to the hydrogen, instead of the e- going directly to the chlorine? Doesn't going to the H before the Cl just make this unnecessarily convoluted?", + "A": "Duh, wow. Sometimes I just miss the simplest things, I can t believe that went over my head haha thanks so much!", + "video_name": "J0gXdEAaSiA" + }, + { + "Q": "At 6:40+ does the Chloride bond with the Sodium at any point?", + "A": "no, remember that in solution the sodium and chloride would exist as ions anyways because of the ionic bonding", + "video_name": "J0gXdEAaSiA" + }, + { + "Q": "At 6:43, i'm not exactly sure what he means by \"faster than the speed of light\" because when you think about it, wouldn't the light travel that 1.5x10^8m with the ship and then travel the other 1.5x10^8m to be a total of 3.0x10^8m away from Sal in one second?", + "A": "When you measure the speed of light when traveling through a vacuum it will always travel at 3 * 10^8 m/s regardless of the velocity of the source of the light when it was emitted. So if you have a rocket going 1.5 * 10^8 m/s and they fire a laser at you they see the light as traveling at 3 * 10^8 m/s and you see it traveling at 3 * 10^8 m/s as well not 4.5 * 10^8 m/s.", + "video_name": "OIwp8m3S30c" + }, + { + "Q": "7:57 i thought the OH takes place where the O was originally at , i mean where the C is before it", + "A": "The O hasn t really moved, it s just drawn in a different position. It s still bonded to the same carbon as before.", + "video_name": "rNJPNlgmhbk" + }, + { + "Q": "At 7:26, Sal describes the fluid part as \"Although we can't call it a liquid yet\". Aren't all fluids liquids, or is there a difference?", + "A": "No, not all fluids are liquids, but all liquids are fluids. Gases are fluids. Sand can act like a fluid.", + "video_name": "f2BWsPVN7c4" + }, + { + "Q": "At around 1:30, Sal said that new land was forming. I don't get what he means by that. And also, he said that the land is pushing the two plates apart. What makes the land push the two plates apart? Is it the inside of the earth?", + "A": "He means that when the plates get pushed apart magma comes up and cools creating more land also pushing the plates apart because of the growing land. The intense heat from the core moves the mantle moving the plates.", + "video_name": "f2BWsPVN7c4" + }, + { + "Q": "At 10:07, what does Kw stand for?", + "A": "Kw= (1.0E-14) equilibrium constant for {H3O][OH-] Ka=(1.0E-7) [H3O] + C-base Kb=(1.0E-7) [OH-] + C-acid. These vales are important in determination of PH and POH of a solution", + "video_name": "3Gm4nAAc3zc" + }, + { + "Q": "At 5:28, how do you know that it can reach octet? Is there a proof or a way to determine? Does it have 8 valence electrons just because it is in the second period? Then what about other periods?", + "A": "Experiments tell us this is how atoms behave", + "video_name": "p7Fsb21B2Xg" + }, + { + "Q": "At 3:59, I don't exactly understand what you mean when you say Cytosol is the \"Fluid between the organelles.\"", + "A": "Hi, Dan! I get what you mean... So basically, suppose, that all the organelles are swimming in this swimming pool.... And instead of the water, there s something called Cytoplasm. Now, pretend that these organelles decide to leave it and get out of the pool. Now, because the organelles are out, the swimming pool changes its name to Cytosol. In a more realistic world, when all the cell organelles are taken out , the fluid that remains is called Cytosol. Hope that helps! TQ, Cookie!", + "video_name": "6UqtgH_Zy1Y" + }, + { + "Q": "At 0:24, are proteins the same thing as amino acids if you were solving codons?", + "A": "Proteins are amino acids. Protein is made up of long chains of amino acid.", + "video_name": "6UqtgH_Zy1Y" + }, + { + "Q": "3:55 If cytoplasm is everything inside cell, can we say that a cell consist of cytoplasm and cell membrane?", + "A": "no..cytoplasm is everything inside cell...everything such as cytosqueleton, cytoplasm, all organelles including nucleus, mitochondria, vesihecles and such... hope it helped", + "video_name": "6UqtgH_Zy1Y" + }, + { + "Q": "At 0:28 what is the bronchai", + "A": "the bronchi is the tubes that air goes through either the right or left lung. there are two types of bronchi, primary bronchi which are the first 2 tubes that creates a passageway to the lungs and the secondary bronchi which are the the tubes that branches of the primary bronchi. after the secondary bronchi, the bronchioles. the last one would be arterioles. hoped this helped", + "video_name": "fLKOBQ6cZHA" + }, + { + "Q": "2:30 what is diffusion", + "A": "Diffusion is the moment of a solute from a region of high concentration to one of a low concentration.", + "video_name": "fLKOBQ6cZHA" + }, + { + "Q": "At 13:15 Sal says that \"They sop up 98.5% of oxygen \" what happens to the remaining 1.5% of oxygen ?", + "A": "They pretty much stay wherever it was the other oxygen was sopped up from. If the oxygen was taken from the blood plasma, which is what I understood from the video, then the 1.5% will just remain in the blood plasma.", + "video_name": "fLKOBQ6cZHA" + }, + { + "Q": "at 1:36 , Sal said that we take in 78% nitrogen , but i know that we cannot breath in nitrogen and we take it from plants because they are the only living organisms that can take in nitrogen ?", + "A": "In fact we do dissolve a very tiny amount of nitrogen in our blood from the air we inhale. And the more the higher pressure around us. This is significant for divers who breathe under Deep Water. If a diver ascends to quickly nitrogen bubbles can be released in the bloodstream because the pressure diminishes too quickly to release the surplus of nitrogen throug normal breathing. This condition is leathal unless the diver very quickly is put in a pressuretank and is de-compressed slowly.", + "video_name": "fLKOBQ6cZHA" + }, + { + "Q": "If red blood cells have DNA then why did he say they didn't. I don't understand. 14:26", + "A": "they do have dna but they push it out to carry more hemoglobin, if you watch the entire video.", + "video_name": "fLKOBQ6cZHA" + }, + { + "Q": "At 14:35, Sal said that red blood cells don't have DNA, so they can't reproduce. At 15:55, Sal also said that they don't live long. I wonder who who makes those RBCs for us.", + "A": "At first, when produced in the bone marrow (most likely from the femur because it s the biggest bone in the body), the RBCs have nuclei. However, when they lose it the metabolism of the cell it s compromised and they live less then other cells.", + "video_name": "fLKOBQ6cZHA" + }, + { + "Q": "At 10:27, Sal says that iron is the main component. Is that the reason why if you drink blood by accident it tastes like metal?", + "A": "Yes, the hemoglobin molecule has a big-old Iron atom embedded in the complex protein.", + "video_name": "fLKOBQ6cZHA" + }, + { + "Q": "at 3:21 why do you have to do all problems in kelvin units", + "A": "The most common of the universal gas constants is in the units of ((L*atm)/(mol*K)), so in the instance of using that constant, you must be in kelvin. There are different constants for differing units, but Kelvin has the benefit of never being negative.", + "video_name": "69V-60sga3M" + }, + { + "Q": "At 3:23, why do you have to change the temperature into kelvin?", + "A": "Because 0 on the Kelvin scale corresponds to 0 heat, but 0 on the celsius scale is arbitrary.", + "video_name": "69V-60sga3M" + }, + { + "Q": "at 3:00, why does \"n\" stand for moles instead of \"m\"?", + "A": "n stands for number of molecules.", + "video_name": "69V-60sga3M" + }, + { + "Q": "At 3:35 he said that when our cells gets broken by damage we feel pain, but how about slight pain for example if you poke slightly with a toothpick to your hand? There are no visible damage done but it causes slight sensation of pain or it just kills less cells and releases less proteins who causes pain?", + "A": "Dermic and hypodermic receptors, of which there are many, have a big impact on feeling slight damage/discomfort (e.g., toothpick example). There are also different kinds of nerves that carry different sensations (ex., tiny unmyelinated C fibers produce dull, burning ache while large myelinated axons convey quick, sharp pain) I d be happy to elaborate if you like.", + "video_name": "D-oAsFIHqbY" + }, + { + "Q": "At 5:45, Sal said that the initial velocity is 24.5 but earlier he said that the initial velocity is 0. i got mixed up. Can someone clarify it?", + "A": "Earlier in the video he said final velocity is 0 m/s. I think this must be where you got confused.", + "video_name": "IYS4Bd9F3LA" + }, + { + "Q": "What makes the time up the same as the time down? (Around 1:15)", + "A": "Acceleration remains constant throughout the flight so, when it has a velocity of zero (at the top), you can know it has to be at its halfway point during the flight. Hope that helps : )", + "video_name": "IYS4Bd9F3LA" + }, + { + "Q": "is the velocity calculated by Average on 6:25 because both the rise and fall of the object is taken into question?", + "A": "No, Van. We are only dealing with the first part of the projectile-rising part, in which t=2.5s. This is because the falling part is essentially the reverse of rising part. We use average velocity because velocity is not constant, but acceleration is.", + "video_name": "IYS4Bd9F3LA" + }, + { + "Q": "At around 5:10, Sal found the initial velocity. Could you also use s=v_i*t+1/2a*t^2 and plug in 5 for t, -9.8 for a and 0 for s to find v_i? How does these two completely different methods get the same answer?", + "A": "Approaches that are algebraically the same can have different forms", + "video_name": "IYS4Bd9F3LA" + }, + { + "Q": "At 6:50 Sal talks about the energy of the system being 0. Under what conditions would the internal energy change?", + "A": "I had a look and could not see where he says the energy of the system is zero... However, the answer to your question is that internal energy = kinetic energy of the particles + potential energy of the particles. In an ideal gas, the potential energy changes are considered to be zero. Temperature is related to kinetic energy of the particles. So, a change in temp = change in KE = change in Internal energy", + "video_name": "aAfBSJObd6Y" + }, + { + "Q": "Hi, at 10:02 Sal Khan says that catalysts lower activation energy but on some other websites and in books it is written that the catalysts do not lower the activation energy . What should I follow ?", + "A": "Catalysts provide an alternate reaction pathway with a lower activation energy. The uncatalyzed pathway still has the same activation energy.", + "video_name": "__zy-oOLPug" + }, + { + "Q": "@5:07 Could you explain the activated complex a little bit clearer? I was confused whether it is the bond between diatomic molecules or whether it was a bond formed between molecules already bonded.", + "A": "It s more like a temporary phase (at a higher energy level) when the bond is first formed between the atoms of the reacting molecules, in this case an H atom of the H2 molecule and an I atom on an Iodine molecule. The activation complex is that moment when these two guys are trying to strengthen their bond and are JuSt breaking away from their original molecules to form HI . Hope I made sense to you", + "video_name": "__zy-oOLPug" + }, + { + "Q": "At around 8:00 he says that one has to add energy if its not spontaneous, I thought that even spontaneous reactions do have an activation energy so energy has to be added?", + "A": "You re absolutely right that spontaneous reactions have activation energy -- what makes them spontaneous is that there s enough energy in the environment to overcome the activation energy. This is where conditions such as temperature and pressure can effect spontaneity (think delta H as it plays in to delta G, for example). Hope this helps!", + "video_name": "__zy-oOLPug" + }, + { + "Q": "In 0:26 shouldn't it be one mole of hydrogen and one mole of iodine?", + "A": "Quite correct. It should be 1 mol of H\u00e2\u0082\u0082 and 1 mol of I\u00e2\u0082\u0082.", + "video_name": "__zy-oOLPug" + }, + { + "Q": "At time 10:08 when he says 1 to 6 wouldn't be 1 to 12 since 6O2 is 12 oxygen?", + "A": "He means 1 to 6 oxygen molecules", + "video_name": "eQf_EAYGo-k" + }, + { + "Q": "At 0:42, why is oxygen in its molecular form?", + "A": "This is a combustion reaction \u00e2\u0080\u0094 a reaction with oxygen \u00e2\u0080\u0094 and oxygen exists as O\u00e2\u0082\u0082 molecules.", + "video_name": "eQf_EAYGo-k" + }, + { + "Q": "at 9:00 couldn't Sal have put down 0.14? does it matter how you round the number?", + "A": "Actually, no he could not have written down .14. You have to look at the number with the least number of sig figs in the problem. Then you have to write your answer with that many sig figs and one more for uncertainty purposes. Since two was the least number of sig figs in the problem, Sal rounded his answer to three sig figs. Significant numbers do matter when you are doing stoichiometry problems. Never round midway.", + "video_name": "eQf_EAYGo-k" + }, + { + "Q": "At 0:42, how does Sal know that the oxygen is in its molecular state? Is it the convention?", + "A": "Yes that is the convention. If you see reacts with oxygen they mean O2.", + "video_name": "eQf_EAYGo-k" + }, + { + "Q": "At 1:00, do you always have to start by balancing the equation?", + "A": "Yes, it is necessary to balance the equation for any stoichiometry problem. Hope this helps :)", + "video_name": "eQf_EAYGo-k" + }, + { + "Q": "To find the amount of C02 and H20 we used only glucose in that ratio at 13:00, but what about 02 molecule?", + "A": "There is an excess of oxygen, so only all the glucose will be used up in the reaction. All of the moles of glucose will be used to make your products, carbon dioxide and water. There will be some oxygen left over after the reaction is complete because there are no more glucose for it to react with. Does this make sense? That s why we are only concerned with the LIMITING REACTANT or REAGENT.", + "video_name": "eQf_EAYGo-k" + }, + { + "Q": "In 8:39 why does he divide 25 by 180?? soo confused right now", + "A": "There is 25 grams of glucose The molar mass of glucose is approx 180 grams per mole If you divide like so: 25 g / 180 g/mol this will calculate how many moles of glucose there are. We always need to work in moles when using chemical equations. It s important to be comfortable doing this.", + "video_name": "eQf_EAYGo-k" + }, + { + "Q": "0:25 if there is a vacuum everywhere, then wouldn't the water just go up?", + "A": "between sun and earth, there is vacuum so why earth revolves in an elliptical orbit around the sun, by newton law of gravitation, every particle gravitate to other particles the force is the same but the acceleration is different bcoz of there difference in masses.", + "video_name": "HnfBFeLunk4" + }, + { + "Q": "At 10:59 Sal says that the field lines correspond to the trajectory of the test charge but my textbook stated that this is a common misconception. So do they or do they not? If they don't how would the trajectory of the test charge compare to the field line?", + "A": "The field lines are the force that would be exerted on a unit positive charge present in that field. Remember, it s force; not trajectory. If the charge is moving inside the electric field, the trajectory would depend on the force (and some fancy vector mechanics)", + "video_name": "0YOGrTNgGhE" + }, + { + "Q": "is Sal saying that electric fields pervade the entire universe At 2:58? How do electric field lines extend infinite distances?", + "A": "Electric fields do indeed pervade the universe, just like gravitational fields do.", + "video_name": "0YOGrTNgGhE" + }, + { + "Q": "At 4:48,how is the force of static friction is going to be 29.4 N? As we got this as a answer of budging force.", + "A": "Budging force is the term Sal uses for the maximum possible force of static friction.", + "video_name": "ZA_D4O6l1lo" + }, + { + "Q": "At 5:40, Sal mentions sperm carry either an X or Y chromosome, determining gender. Are the X and Y chromosome not carried in every sperm?", + "A": "Sperm will always carry one or the other unless they undergo nondisjunction in meiotic divisions. Remember that they are haploid, and as such can only carry one copy of each chromosome, including the sex chromosome.", + "video_name": "-ROhfKyxgCo" + }, + { + "Q": "Would writing the angle of the second ball as -38 degrees be the same as when Sal says \" 38 degrees below the horizontal\" at 7:47 ?", + "A": "It might be, if you specify that 0 is a horizontal line to the right. You need to be clear.", + "video_name": "leudxqivIJI" + }, + { + "Q": "At 4:13, If Br is so electronegative, why does it give it's electron to Fe in the first place?", + "A": "it have 7 valence electrons and wants to fufill its orbitals with 8, the FeBr3 has an open spot so that both of the compounds have 8 and therefore are satisfied", + "video_name": "K2tIixiXGOM" + }, + { + "Q": "At 2:39, When do you know when to use negative for tension pulling up or negative for the force of gravity pulling down. I tried another pulley problem using the same concept pulling up 10kg at 2 m/s^2 and the answer was 2T - mg = ma (answer 60N) instead of 2T + mg = ma ( answer 40N upward). These both give two different answers so I am a bit confused.", + "A": "You just have to decide, in each problem, which way do you want to be positive. If you decide up is positive, then it is always positive. If you decide down is positive, then it is always positive.", + "video_name": "52wxpYnS64U" + }, + { + "Q": "09:00 You're placing the oxygen on the same side as Br but you're saying that it's inversion. How come?\nAlso, I really don't understand that triangle type bond, what's that?", + "A": "See videos on stereochemistry. This video is way too advanced if you don t understand chirality or wedge and dash representations of bonds.", + "video_name": "3LiyCxCTrqo" + }, + { + "Q": "At 16:24, it is said that work is done, but deltaU is zero because T does not change, which means Q-W is 0. If work is not zero, than Q must not be zero, which contradicts with a adiabatic process? What's the problem here?", + "A": "I don t recall this process being described as adiabatic. Lots of heat comes from the reservoir to maintain T to offset the drop in T from work being done.", + "video_name": "WLKEVfLFau4" + }, + { + "Q": "At around 2:00, Jay says that one oxygen fewer is hypochlorite. Why isn't perchlorate called HYPERchlorate? For example, you can have HYPOthermia and HYPERthermia.", + "A": "Strangely enough, I believe in the past perchlorate was sometimes referred to as hyperchlorate but the name seems to have gone into disuse. Perhaps there was confusion between hypo and hyper so it was safer to drop the hyper.", + "video_name": "DpnUrVXSLaQ" + }, + { + "Q": "4:30 how do we know we should use the second half-reaction?", + "A": "To find a total cell potential we should take into account both oxidation and reduction reactions. It s not enough to know how much an element wants to be reduced, we also should check how strongly the other element wants to be oxidized, as electrons lost by one element are the electrons gained by another.", + "video_name": "fYUwEAPejbY" + }, + { + "Q": "At 7:04, Sal explained neutron stars by saying that it is just a ball of neutrons. How does this ball stay in place?", + "A": "It dosn t stay in place . All stars - including neutron stars - orbit the super-massive black hole at the center of their galaxy. Furthermore, the galaxy itself is constantly in motion. So, the neutron star does not stay just sit there. It s moving.", + "video_name": "qOwCpnQsDLM" + }, + { + "Q": "At 2:49, Sal mentioned that the electrons get captured into the nucleus. Well then, wouldn't the atom be annihilated?", + "A": "Why would it be annihilated?", + "video_name": "qOwCpnQsDLM" + }, + { + "Q": "from 4:30 to 5:00\nsure there's loads of pressure on the core of the star, but why exactly does it suddenly go supernovae??\nis there some repulsion between the neutrons??", + "A": "The collapse stops beyond the point when the neutrons are literally touching each other. The neutrons are actually smaller than normal neutrons because of this pressure. The forces trying to decompress the neutrons is incredible and they fuel the supernova.", + "video_name": "qOwCpnQsDLM" + }, + { + "Q": "At 4:00, Sal says \"should.\" Can some cancer cells be so mutated that they do not produce MHC I at all?", + "A": "Yes. Sometimes cancer cells are so mutated or too close to your actual cells that if your cyto cells attack them, they will also attack your healthy cells. That s why to be safe they don t attack them. They also don t recognize them so they don t kill them. That s why all people need help to fight off cancers since your body can t kill most cancers.", + "video_name": "YdBXHm3edL8" + }, + { + "Q": "Around 6:23 when the Hydrogen breaks off was it in a hybridised sp2 orbital with the C? and when forming the double bond with the other C does it change to a p orbital?", + "A": "Yes, at that point, the C atom is using an sp\u00c2\u00b2 orbital that is parallel to the vacant p orbital on the adjacent carbon. As the H leaves, the back lobe of the orbital becomes larger and the front lobe becomes smaller until, once the H atom is completely free, both lobes are the same size and you have a p orbital that contains two electrons. That p orbital overlaps with the adjacent empty p orbital to form a \u00cf\u0080 bond.", + "video_name": "U9dGHwsewNk" + }, + { + "Q": "Would the name of the new organic product formed at 8:39 be: 3-ethyl pentene?\nAlso, how would you indicate in the name where the double bond is?", + "A": "You would name the compound 3-ethyl-pent-2-ene or 3-ethyl-2-pentene. The 2 indicating the location of the double bond.", + "video_name": "U9dGHwsewNk" + }, + { + "Q": "At 7:45 What if someone who gets blood on their hand washes their hands right after they got the blood on their hand? Would they still get ebola?", + "A": "Not necessarily. The virus would need to enter the body through broken skin or mucous membranes, for example, if the blood on their hands got into a cut or came in contact with the eyes, nose, or mouth. Regular hand washing may remove the visible sign of blood, but the CDC recommends decontamination via an EPA-registered hospital disinfectant.", + "video_name": "xYoQQCO15GE" + }, + { + "Q": "At 6:00 what would 3.991 be rounded up to if it could only contain two significant figures? Would this result in 4.0? Or would it simply be 4?", + "A": "4.0 since the number of significant digits are preferably preserved.", + "video_name": "xHgPtFUbAeU" + }, + { + "Q": "4:45 Sal said \"a mitochondria\" but the correct singular is \"a mitochondrion\", right?", + "A": "Yes, that is correct.", + "video_name": "J30zpvbmw7s" + }, + { + "Q": "This isn't intuitive at all for me. If at 2:57 you do exactly what he said (index finger points in the direction of b and middle finger for a) with your right hand, i still get my thumb going into the screen, the same result as in the last video. How is he flexing his thumb to get it to point out of the page? I'm really confused.", + "A": "I struggled with this too, but I think if you keep you index finger straight (as in fully extended and in line with your arm), then you should be able to figure it out.", + "video_name": "o_puKe_lTKk" + }, + { + "Q": "What happens if you add to much force?\nFor example, from 4:28 on, what would happen to a 42N weight?", + "A": "The weight would accelerate upwards until gravity brings it back down. It would jump , as you can try with any lever in real life.", + "video_name": "DiBXxWBrV24" + }, + { + "Q": "At 7:28, what does spontaneously mean?", + "A": "With no additional energy / it will naturally just happen. This will also mean that delta G (change in free energy) is negative", + "video_name": "g_snytB7iQ0" + }, + { + "Q": "At 3:20, would the equation NaCl (s) --H2O--> Na+ (aq) + Cl- (aq) the same as saying NaCl (s) --H2O--> NaCl (aq) ? Or are they structurally different in solution?", + "A": "They mean the same thing, it is just that one is more specific than the other. NaCl (aq) requires knowing that this compound dissociates in aqueous solution. The other version spells that out explicitly.", + "video_name": "g_snytB7iQ0" + }, + { + "Q": "When you say in 00:40ish \"the formula we've been speaking about\".. which video is this you are referring to? Thanks.", + "A": "That formula is explained in the previous video, Putting it all together: Pressure, flow, and resistance.", + "video_name": "fy_muPF0390" + }, + { + "Q": "He only mentions \"BB\" as homozygous dominant (@11:10), but I am under the assumption that \"bb\" would be called homozygous recessive. Is this correct?", + "A": "yes you right", + "video_name": "eEUvRrhmcxM" + }, + { + "Q": "At 3:15, Two oxygens that don't have double bond have 7 electrons? doesn't it need to have 6? so the formal charge is 1?", + "A": "It has 7 electrons because of the one shared by Nitrogen. The formal charge is 1 because it has 7. Had it only 6, the formal charge would be zero.", + "video_name": "bUCu7bPkZeI" + }, + { + "Q": "So at 6:59 when the germ cells go through Meiosis, to make the gametes, does that mean the germ cells are haploid?", + "A": "first they are are diploid then after meiosis they become haploid", + "video_name": "PvoigrzODdE" + }, + { + "Q": "At 2:34 What does accreting mean?", + "A": "accretion is the gradual gathering of matter.", + "video_name": "VbNXh0GaLYo" + }, + { + "Q": "At 4:08 you say that the moon was a part of the earth ere it was hit by a proto planet named theia so if the earth and the moon is made up of same type of stuff why there is neither gravity nor life on the moon ?", + "A": "The Moon does have gravity. It cannot support life because it isn t composed in the same way as the Earth. It is smaller, mostly composed of lighter elements like the Earth s crust, and lacks a significantly active core to generate any substantial magnetic field. As a result, it isn t able to maintain an atmosphere or liquid water. Thus life isn t really able to even get started on the Moon.", + "video_name": "VbNXh0GaLYo" + }, + { + "Q": "at 2:35 sal says \"a few million years ago\" I Dont think thats right", + "A": "2:42 corrects that", + "video_name": "VbNXh0GaLYo" + }, + { + "Q": "At 6:20 should the empirical formula for water be HHO instead of H2O?", + "A": "No H20 is the empirical formula on its own.", + "video_name": "bmjg7lq4m4o" + }, + { + "Q": "3:50 what's the meaningo of those double bonds ?", + "A": "A double bond is where there are four electrons shared between two atoms. You will learn more about these in future videos.", + "video_name": "bmjg7lq4m4o" + }, + { + "Q": "At 4:53, why do you have to draw a structural formula of a carbon with 3 single lines, and 3 other double lines bonding with each other?", + "A": "Because that simply is what the structure of benzene is. Google it and you ll find many pictures that look just like that. You cannot give each carbon an octet of electrons without making those double bonds.", + "video_name": "bmjg7lq4m4o" + }, + { + "Q": "At 3:50, why is there a \"double bond\" on the hexagon of carbon atoms? What is a double bond? When should we use double bonds?", + "A": "That molecule is benzene, it has the formula C6H6. The only way for each carbon to have 8 electrons around it is to form double bonds. Double bonds simply are just another bond between the atoms. As for when to use them the dot structure videos go over this. They re often needed to make elements follow the octet rule or to minimise formal charge.", + "video_name": "bmjg7lq4m4o" + }, + { + "Q": "At 3:45 Sal draws the Benzene molecule, mentioning that every other atom is joined by a double bond, while the rest are single. What is the significance of this and how do you know what kind of bond (single, double, etc) it is?", + "A": "Benzene (a carcinogen) has 2 possible formations. Going clockwise you can start with a double bond, then a single bond, etc. Or you can do the same thing but go anti-clockwise. the 2 structures are very similar. So instead of being one or the other it is actually somewhere between the 2. Each bond is not single or double but 1.5. The 1/2 is normally shown as a circle inside the carbon hexagon.", + "video_name": "bmjg7lq4m4o" + }, + { + "Q": "At 4:28, there is a structure of benzene shown. What I wanted to know is in the formula are the hydrogens connected to the carbons connected to each other?", + "A": "Hydrogen is only capable of making a single bond, so all of the hydrogen atoms in benzene are bound only to a single atom of carbon.", + "video_name": "bmjg7lq4m4o" + }, + { + "Q": "At 3:35, Sal draws a structural formula, but some covalent bonds have two lines. What do two lines mean in structural formulas?", + "A": "It means a double bond. It s exactly how it sounds, 2 bonds between the two atoms instead of 1.", + "video_name": "bmjg7lq4m4o" + }, + { + "Q": "What happens to / with the positive electron from the battery? 3:51 \"gonna leave a net positive charge\"... Can you explain this? Thanks", + "A": "the copper wire is neutral when no battery is attached when there is a + from the battery, Cu- will be attracted then the area will have less - , thus have a net + charge hope this solve your problem", + "video_name": "ZRLXDiiUv8Q" + }, + { + "Q": "Why is it -q instead of +q in the copper wire at 5:03 because the net charge is positive since there will be more protons than electrons?", + "A": "In metals, its the electrons that do the moving. Electrons have a negative charge, so they are labeled -q.", + "video_name": "ZRLXDiiUv8Q" + }, + { + "Q": "At 6:15 in the video it discusses the difficulty of eating and digesting cellulose. Are cells in fruit not composed of cellulose, or does the plant do something magically different in the process of fruiting?", + "A": "Fruit, being made of plant cells, definitely does contain cellulose. We can t digest it, but there are so many other good things in fruit (sugars, nutrients, etc.), that we eat it anyways. Cellulose is the fiber part that is advertised as being so healthy for your digestive system, by virtue of the fact that it can t be digested. Tree branches, on the other hand, are basically pure cellulose, with nothing else, so are noticeably less appetizing.", + "video_name": "d9GkH4vpK3w" + }, + { + "Q": "@8:33 when the compound reacts with H2 and Pt, since it goes from an alkyne all the way to an alkane, does the same reaction happen twice? syn addition twice with the reagents?", + "A": "Yes, it is effectively the same reaction happening twice.", + "video_name": "RdFfIEDxo18" + }, + { + "Q": "at 5:56 you get another Na with one electron, how do you know there are plenty left over after using Na with one electron already in the first step when u started off the reaction? Same with ammonia in the next step following 5:56?", + "A": "There are billions and billions of Na atoms and NH\u00e2\u0082\u0083 molecules in the reaction mixture. The Na and ammonia are always in excess. The alkyne is the limiting reactant.", + "video_name": "RdFfIEDxo18" + }, + { + "Q": "At 9:50 in the video, 3-hexanol is explained to have a dipole-dipole moment between the O and the H, resulting in hydrogen bonding. My question is this: would there also be a dipole-dipole moment between the O and the C in 3-hexanol, and would that dipole-dipole moment be the same strength as that in 3-hexanone?", + "A": "I agree there must be some polarization between the oxygen and the carbon in the alcohol, but I don t think it would be as strong as in the ketone. In the alcohol the oxygen is pulling electron density from both the hydrogen and the carbon, which is more electronegative than the hydrogen so the electron density shift is mostly away from hydrogen. In contrast, in the ketone the oxygen is pulling electron density exclusively from the carbon.", + "video_name": "pILGRZ0nT4o" + }, + { + "Q": "around 0:34 sal shows a solar flare. what would be the effects if one of these were powerful enough to get to earth?", + "A": "If a powerful solar eruption were to be aimed at earth, humans themselves would not be affected. But it would have a great affect on Earth s electrical grid. A shock like that could short out anything that isn t shielded and it could be years before the grid is fully restored. Such an event has happened in the past around the Civil war where telegraph systems stopped working.", + "video_name": "jEeJkkMXt6c" + }, + { + "Q": "actually gravitational force is independent of mass right and in the video i saw tha sal said at4:57 as mass of the brick is larger force on the brick is also larger am i right in what i have asked", + "A": "No, gravitational force is not independent of mass. That s quite a strange idea. Gravitational force is directly proportional to mass.", + "video_name": "36Rym2q4H94" + }, + { + "Q": "At about 9:00-9:20 Sal says Earth goes into whats called \"Snowball Earth\" and ices over. Is that like an Ice Age, and if not, how are Snowball Earth and an Ice Age different?", + "A": "Snowball Earth is a period in earth s history where the whole surface of the earth was supposedly covered by ice. Snowball Earth periods are extreme ice ages. During most ice ages there was only glaciation in latitudes up to 40\u00c2\u00b0 or 50\u00c2\u00b0.", + "video_name": "E1P79uFLCMc" + }, + { + "Q": "I think there's a mistake at 7:00 minutes, how did he get 4. 75m/s?\nI've been calculating it over and over it it keeps appearing to be 3.7m/s.\nWhat's going on?", + "A": "Try changing your calculator to degrees from radians, is that your problem?", + "video_name": "_0nDUXO0k7o" + }, + { + "Q": "at 1:09 the term \"short\" is mentioned, and then again a few seconds later.\n\nplease may I know what is a short?", + "A": "The term short in this context means to short-out; it basically occurs when a conductive element comes into contact with the circuit board, allowing voltage to bypass all resistors and capacitors. When this happens, this is bad. The voltage will rush through the element instead of the board with almost no resistance and destroy many, if not all, components. The solenoid safe-guards from this issue.", + "video_name": "gFFvaLzhYew" + }, + { + "Q": "at 9:40, would that tetra molecule be cis or trans?", + "A": "That would be neither. It has the same group on all 4 positions.", + "video_name": "AiGGaJfoQ1Y" + }, + { + "Q": "at 1:53 cant the compound be named as 3-Bromo-4,6-dimethylheptane if the functional group is given the first preference ?", + "A": "It is not the functional group, but the rule of lowest numbers, that determines the numbering. In your name, the lowest number is 3. In the other name, the lowest number is 2. The lowest number wins. But the bromo wins in determining the order in which the substituents are listed in the name. So the compound really is 5-bromo-2,4-dimethylheptane.", + "video_name": "aaZ-isZs4ko" + }, + { + "Q": "at 2:48 why does it lose both hydrogen protons.", + "A": "Well..oxalic acid is a diprotic/dibasic acid, which means that it has two replaceable H atoms. Oxalic acid when it ionizes loses or liberates 2 hydrogen protons. It does this quite readily as the oxalate anion (acid with 2 H+ ions removed) is stabilized by -I effect and resonance.", + "video_name": "XjFNmfLv9_Q" + }, + { + "Q": "When writing the chemical name, does it matter the order of the elements, like are H2O and OH2 the same?\nI'm asking this because at 1:10, Sal wrote HO, but I've seen it mostly as OH.", + "A": "technically doesn t matter but it is common to write the acid part on the left and the basic part of the right", + "video_name": "XjFNmfLv9_Q" + }, + { + "Q": "at 2:30 how is one going to know it takes 2naoh to neutralize?", + "A": "Oxalic acid has 2 Hydrogen protons which are formed when it disassociates in water. Thus, 2 OH- ions are required to neutralize them. Every NaOH molecule releases only 1 OH- ions. Thus, 2 NaOH are required to neutralize the oxalic acid. Thus, when there are two H+ ions which are formed on disassociation, two OH_ ions will be required to neutralize it. Hope this helps :)", + "video_name": "XjFNmfLv9_Q" + }, + { + "Q": "At around 1:40 he is drawing the H atoms on the diagram and called them protons. Does he mean to say hydrons?", + "A": "Hydrogen atoms are just protons with one electron.", + "video_name": "XjFNmfLv9_Q" + }, + { + "Q": "AT 3:42 Sal said that the Water Molecule (H_2O) got a \"proton\" from the hydrogen ion .\n\"Can Protons be also added in a atom or molecule\", during a chemical reaction?\nI know that electrons do but can Protons tooo....?", + "A": "When we say proton in chemical reactions it means a hydrogen cation H+, it doesn t mean one of the nuclei is gaining a proton.", + "video_name": "Y4HzGldIAss" + }, + { + "Q": "1:22 what is aqueous solution??", + "A": "Solution whereby the solute is dissolved in water.", + "video_name": "Y4HzGldIAss" + }, + { + "Q": "At 9:00, why isn't that molecule designated as \"cis\" or \"trans\"? Can't you have both an R/S designation and a cis/trans designation?", + "A": "There are no double bonds and each of the 4 groups at the chiral centres are different. How could you determine cis/trans here? You can have R/S and cis/trans in cyclic molecules though.", + "video_name": "kFpLDQfEg1E" + }, + { + "Q": "At 3:36, wouldn't the longest carbon chain start at the carbon in the top right (above what Jay designated as the first carbon) and continue down to what he designated at carbon 7? That would make a continuous 8 carbon chain", + "A": "The OH group needs to be included in the main chain as it is the highest priority substituent in this molecule, even though there is a longer carbon chain.", + "video_name": "kFpLDQfEg1E" + }, + { + "Q": "In 4:55, can't I write \"5-chloro-5-methyl-3-propyl-heptan-2-ol\" instead of 5-chloro-5-methyl-3-propyl-2-heptanol\"?\n\nMy chemistry teacher taught me that the first is correct. What's the difference between the names?", + "A": "You can as long as you remove the dash between propyl and heptan. The preferred way to do it is to put the number in the middle like your first way. People don t always learn the new recommendations. It s also much easier to say 2-heptanol out loud than heptan-2-ol", + "video_name": "kFpLDQfEg1E" + }, + { + "Q": "At 1: 26, in my textbook, it shows that the name should be propan-1-ol (or propanol) and similarly the name of 2-propanol should also be propan-2-ol.\nAlso, at 4:48, according to the rules in my textbook, the name should be 5-chloro-5-methyl-3-propylheptan-3-ol.\nI am very confused now because I don't know if should put -ol at first or at last.\nPlease help me!", + "A": "Yeah ! you are correct, in my textbook too it is written as propan -2-ol. And the textbook contains the correct nomenclature", + "video_name": "kFpLDQfEg1E" + }, + { + "Q": "I thought water was already a conductor. 8:20", + "A": "It s actually not the water itself that is the conductor. All water forms hydronium (H3O+) and hydroxyl (OH-) ions, which conduct the electricity. In pure water the concentrations of these ions are very low (about (about 10^-7 mols/liter of each), so you need to add impurities (such as salts or acids) to increase the number of ions and the conductivity.", + "video_name": "Rw_pDVbnfQk" + }, + { + "Q": "At 1:37ish, wouldn't the carbons be connected slightly differently? More like a single uniform \"diamond\" shape, rather than a spread out tree.", + "A": "actually, it depends on the cooling rate. atleast what i learned when working with metals was when they were melted and cooling, if cooled slowly, they would form their perfect crystaline shapes but if quenched (dipped in water for a quicker cool) they would create many irregular crystal patterns, this irregularity is what would cause quenched metals to bend easier than slowly cooled ones. if theres a big difference in strength of a metal and its ability to bend, same metals different cooling rate.", + "video_name": "Rw_pDVbnfQk" + }, + { + "Q": "At 6:35, isn't HF held together with hydrogen bonding, not dipole-dipole forces?", + "A": "If we re getting technical hydrogen bonding is a strong type of dipole-dipole interaction.", + "video_name": "Rw_pDVbnfQk" + }, + { + "Q": "At 4:20, Sal says that when we cut something, we are breaking atomic bonds. But I thought we were breaking molecular bonds. Or are they the same ?", + "A": "What he means is that we are breaking bonds between atoms. We don t have knives or scissors sharp enough to cut atoms in pieces.", + "video_name": "Rw_pDVbnfQk" + }, + { + "Q": "At 1:46 Sal says that dinosaurs may have been smarter than us, but they couldn't of been smarter than us because if they were, they could stopped the asteroid... Right? Or, they were smart enough, but they didn't have what they needed to stop it? What do you think, because that's confusing me. (We'll probably never know)", + "A": "They were never aware of an asteroid. Even if they had tech, it would have struck unexpectedly. Like today, last year we almost got hit with an asteroid 50 feet across. We didnt know until it got close.", + "video_name": "T5DGZIsfK-0" + }, + { + "Q": "At 2:47-2:51 where did \"Milkomeda\" come from?", + "A": "To be fair, Sal didn t make it up, it is the already made name for the future galaxy.", + "video_name": "QXYbGZ3T3_k" + }, + { + "Q": "At 2:11; what is the difference between the Hydrogen atom and Deuterium??", + "A": "Deuterium is a hydrogen atom with one neutron. Protium has no neutrons in the atom. Tritium has 2 neutrons.", + "video_name": "I-Or4bUAIfo" + }, + { + "Q": "At 5:35 we know oxygen has 6 valence electrons it is making a single covalent bond with sulfur so it must be contributing one of its electrons in bonding which leaves 5 lone electrons with it doesn't it then why is he drawing 6 lone electrons with it?", + "A": "Both of the electrons in the S-O bond are coming from the sulfur.", + "video_name": "dNPs-cr_6Bk" + }, + { + "Q": "At about 5:30, the K_a of HCl is discussed. Since HCl is a strong acid, so the reaction is irreversible, and K_a is an equilibrium constant, how is this possible? I thought it was only possible to measure the K_a of a weak acid.", + "A": "Is not completely irreversible though very likely to favor porducts. That s why the KB value is so tiny Strong Acid has a very weak base", + "video_name": "DGMs81-Rp1o" + }, + { + "Q": "At about 0:45 you mention Heat of Fusion. Don't you mean Heat of Vaporization?", + "A": "We re looking at liquid becoming gaseous, in other words vaporization, so I think he meant to say heat of vaporization.", + "video_name": "hA5jddDYcyg" + }, + { + "Q": "At 9:27, why do they want to evaporate at a high KE?", + "A": "High KE means they are moving fast. The ones that are moving fast are the ones that might be able to escape the surface and be carried away.", + "video_name": "hA5jddDYcyg" + }, + { + "Q": "At 9:11, you reference the Ka value of Ammonium (taken from another video). If solving this problem requires this Ka value, would the value normally be displayed as part of the question?", + "A": "The Ka will either be given to you, or it will be possible to calculate it based on what else the equation gives you", + "video_name": "kWucfgOkCIQ" + }, + { + "Q": "At 9:20, you said that you can leave out the \"X\" because is \"X\" would have a small amount. How do you know that ? I saw that the result was small, but I just don't understand when you can leave out the\"X\"", + "A": "Most instructors say that x is very small if it is less than 5 % of the initial concentration of the acid or base. A quick test for this is if the initial concentration is greater than or equal to 400 \u00c3\u0097 K. If [Acid]\u00e2\u0082\u0080/K \u00e2\u0089\u00a5 400, x is small enough to ignore. At 9:20, [Acid]\u00e2\u0082\u0080/K = 0.0500/5.6\u00c3\u009710\u00e2\u0081\u00bb\u00c2\u00b9\u00e2\u0081\u00b0 = 8.9 \u00c3\u0097 10\u00e2\u0081\u00b7. This is much larger than 400, so you can safely ignore x in the denominator of the equation.", + "video_name": "kWucfgOkCIQ" + }, + { + "Q": "How can we predict that a neutral molecule such as ethanol or water molecule would act as a base as shown at 10:26?", + "A": "Any molecule that contains an atom with a lone pair of electrons, such as the O in ethanol or water, can accept a proton from an acid. For example. H2O: + H-Cl --> [H2O-H]+ + Cl-. The [H2O-H]+ is usually written as H3O+. Since the water is accepting a proton from the HCl, it is behaving as a Br\u00c3\u00b8nsted-Lowry base.", + "video_name": "l-g2xEV-z7o" + }, + { + "Q": "at 1:41, why does the alcohol group act like a base, when oxygen does not like to be positively charged?", + "A": "Bases remove protons, nucleophiles form bonds. Hyroxide removes the proton and so is a base not a nucleophile. If it formed a bond and stayed, then it would be a nucleophile. In step 1 it is a nuc, step 2 it is a base. Overall it is a base I belive, I could be wrong though", + "video_name": "l-g2xEV-z7o" + }, + { + "Q": "4:11 I don't understand.... 20mph per second? Can someone please help?", + "A": "If you are in your car and you go from 0 mph to 20 mph, and you do it in 1 second, then your acceleration was 20 mph per second.", + "video_name": "FOkQszg1-j8" + }, + { + "Q": "5:50 If there were no atmospheric pressure it would turn automatically into a gas?", + "A": "Yes (but it will also depend on temperature), because there is nothing holding things together. In fact, if you had liquid water in space it would freeze because it is cold and evaporate because there is no pressure at the same time.", + "video_name": "tvO0358YUYM" + }, + { + "Q": "what does he mean by sending an axon to the optic nerve at 9:42 in the video? How do you send an axon? Does he mean send a message to an axon in the optic nerve", + "A": "All the axons of ganglion cells compose the optic nerve. send would be just a figure of speech.", + "video_name": "CqN-XIPhMpo" + }, + { + "Q": "At 11:30, why do you divide mole on both sides?", + "A": "Review basic algebra - solving simple equations.", + "video_name": "VqAa_cmZ7OY" + }, + { + "Q": "At 9:03, what does the epsilon mean and what does it refer to?", + "A": "It means permittivity.", + "video_name": "VqAa_cmZ7OY" + }, + { + "Q": "At 4:57, at the bottom left of the virgo supercluster image, doesn't it say 250 million light years or am I mistaken?", + "A": "oh yeah", + "video_name": "JiE_kNk3ucI" + }, + { + "Q": "At 8:31 you talk about the universe Expanding. Does that mean the Sun will one Day be out of range for us to even see it? Please answer my question if you understanding, because the Universe is just mind blowing :)", + "A": "No, it doesn t, because gravity keeps earth near the sun. the effect of the expansion of space is only meaningful over intergalactic distances.", + "video_name": "JiE_kNk3ucI" + }, + { + "Q": "8:35 We used to be close but it took the light 13B years to catch up with us. Does this mean the galaxies are moving apart almost at the speed of light? Or some even faster?", + "A": "even faster.", + "video_name": "JiE_kNk3ucI" + }, + { + "Q": "in 8:35 sal said that the universe would keep expanding, if so, in a large amount of time, would we move farther and farther away from the sun or the other planets or galaxies?", + "A": "The expansion of space is only measurable over distances that are much, much greater than even the distance to nearby galaxies. The effect between the earth and the sun is very tiny, and in any event, the sun s gravity offsets the expansion and pulls the earth back even as the expansion of space minutely stretches it away", + "video_name": "JiE_kNk3ucI" + }, + { + "Q": "At 12:30, do the neurotransmitters bind to receptors on sodium ion channels or on the post synaptic membrane?", + "A": "Receptors are sometimes on sodium ion channels, and the ion channels are in the membrane, and sometimes the receptors are in the membrane but connected with the sodium channels with another molecules. I think they will explain us in some other video, probably next one :)", + "video_name": "Tbq-KZaXiL4" + }, + { + "Q": "At 3:50, there is just one product drawn. Shouldn't there be one more? The methylgroup is also an ortho- and para-directing activator, which means that there must be an isomer where -SO3H is next to the -CH3.", + "A": "Jay is only showing the major product, which is based on the hydroxyl being a stronger activator.", + "video_name": "iF-f2-KSw6E" + }, + { + "Q": "ok so on 5:38 he talks about hydrophobic stuff. So is oil hydrophobic?", + "A": "Yes. The reason being that oil cannot be mixed into water, instead is seprerates and that is the meaning of hydrophobic", + "video_name": "QymONNa5C6s" + }, + { + "Q": "why is the water blue at 3:39", + "A": "Blue food coloring/dye was mixed with the water in order to make it more visible on the kitchen counter (since water is clear it is difficult to see).", + "video_name": "QymONNa5C6s" + }, + { + "Q": "at 13:50 what happens to the H on the Oxygen that attacks the electrophilic carbon (leading to a cycle product)?", + "A": "During the workup , the reaction mixture is probably treated with dilute sodium carbonate solution. The hydroxide ions would neutralize the H from the oxonium ion.", + "video_name": "8-ccnvn9DxI" + }, + { + "Q": "At 8:43. why does ethanol attack the carbonyl carbon and not the oxygen as oxygen possesses the positive charge (3 bonds) while the carbonyl doesn't? Also wouldn't there be less steric hindrance if it attacked the oxygen?", + "A": "That would make the oxygen violate the octet rule", + "video_name": "8-ccnvn9DxI" + }, + { + "Q": "At 1:50, how was Sal able to infer that acceleration = gravity = -10m/s^2? Was there some kind of formula or rule he used or is that a constant of some sort?", + "A": "That s the acceleration due to gravity on the surface of the earth. We measure it.", + "video_name": "15zliAL4llE" + }, + { + "Q": "at 4:24 the equation that was used was d=v*t . Could we have used the formula vf^2=vi^2+2ad", + "A": "Yes, They ll both give the same answer as long as you know the value of a", + "video_name": "15zliAL4llE" + }, + { + "Q": "At 5:06, Sal gives us the equation delta V=Vf-Vi. Isn't it necessary for (vf-vi) to be divided by time to find the average velocity?", + "A": "No, it isn t. The change in velocity divided by the change in time gives you the acceleration.", + "video_name": "15zliAL4llE" + }, + { + "Q": "how come distance be -500m at 9:08 as told in the video??", + "A": "at 9:08 the distance is -500m because the average velocity is -50m/s the time is 10s and if they both are multiplied the answer would be -500m if you watch the video again you will find how will it come.", + "video_name": "15zliAL4llE" + }, + { + "Q": "At 6:15, how did you get 10? Did you find the square root of 100 to get 10?", + "A": "When you look at the equation, you ll realize that the change in velocity = acceleration X time. We know that the change in velocity (final velocity - initial velocity) is -100 because -100 - 0 = -100. We also know that acceleration is -10 m/s^2 because it s gravity. Then this gives -100 = -10 X t. It s clear now that t=10. Hope that helped!", + "video_name": "15zliAL4llE" + }, + { + "Q": "Sal talks about 7:07 into the video that since momentum is conserved, the speed must be adjusted to the new weight. What happens in an inelastic collision where the two objects stop dead in their tracks? Any mass times 0 velocity always equals zero, so how can momentum be conserved in an inelastic collision?", + "A": "Let s say (to make it easy) that the colliding objects have equal mass and equal speed. Note that equal speed does not mean equal velocity - the objects are headed toward each other, so one of them has velocity exactly equal to the negative of the other one. Before collision, total momentum is: m* v1 + m*v2 = m*(v1 -v2) = 0! So you see now where this is going, right? After the collision, they are stuck together sitting there, so momentum is 0. 0 before, 0 after means momentum was conserved.", + "video_name": "XFhntPxow0U" + }, + { + "Q": "you said we need the mass of the moving object, but what happens if I am not given the mass of the car? like said at 5:30", + "A": "To calculate momentum, mass is an essential ingredient. However, you might be given the mass indirectly so to say. E.g. One of the cars can move with 40N with an acceleration with 4m/s. This automatically tells you that the mass is 10kg. Thus either way, you must have the mass somehow. Or else it is impossible to calculate the momentum.", + "video_name": "XFhntPxow0U" + }, + { + "Q": "At 4:54, why can't we assume switching the positions of CH3 and Br? Since they're all single bonds, wouldn't they rotate freely anyways?", + "A": "No, that s the point. No matter how you try you ll find it s impossible to rotate them in such a way that the 2 molecules can fit on top of one another with each atom in the same place. If you cannot visualise it, a molecular model kit will be able to prove it.", + "video_name": "tk-SNvCPLCE" + }, + { + "Q": "I actually cannot understand why will the molecule be not superimposble (at 5:36).", + "A": "He is arguing, correctly, that the images are NOT superimposable because the carbon is chiral.", + "video_name": "tk-SNvCPLCE" + }, + { + "Q": "At 6:00 Sal says that an uniform electric field can be formed. But,as i have understood, it is uniform only along the plate not perpendicular to it and thus we cant construct one even with an infinitely long charged plate.(the way it is shown in the diagram i.e. perpendicular to the plate as the field is proportional to 1/d where d is the distance from the wire.\nIs this correct?", + "A": "It is close to uniform as long as the distance between the plates is much smaller than the plates. Also, it is not uniform near the edges.", + "video_name": "elJUghWSVh4" + }, + { + "Q": "At 2:58 Sal says that the upward force we would need to apply to push a certain object up is equal to the force of gravity. But wouldn't tht mean tht the net force on the object equals 0 and it would not move upwards?\nPlease help? Sorry if I'm missing something here.", + "A": "Sal is saying that after getting the object to accelerate a little then we have to apply the same force as gravity. As we have already caused the object to accelerate we then only have to keep the object moving to go up. And only by applying the same and opposite force as gravity, we can do that.", + "video_name": "elJUghWSVh4" + }, + { + "Q": "At 7:23,velocity at time t=0 should be 2 m/s right why is it 1 m/s?", + "A": "You probably mixed the concept of velocity and change in velocity (or acceleration). At t=0, the velocity David assume is 1 m/s, while the acceleration is 2 m/s^2.", + "video_name": "DD58B2siDv0" + }, + { + "Q": "at 8:05, how do we know that the velocity at 0(zero) second was 1?", + "A": "It is just an assumption.", + "video_name": "DD58B2siDv0" + }, + { + "Q": "At 6:10, shouldn't the 'd' of 'Dicyclobutyl' be in small case, i.e. 'dicyclobutyl' ?", + "A": "The D would be capitalized at the beginning of a sentence, but not anywhere else.", + "video_name": "ygXkdSKXQoA" + }, + { + "Q": "At 5:40 how would we number it if the numbers were\n1)1,2,4,6,7\n2)1,2,4,5,8\nBecause ive heard we always take the lowest sum, but what if the sum were equal?", + "A": "5 is lower than 6, the sum doesn t actually matter.", + "video_name": "ygXkdSKXQoA" + }, + { + "Q": "At 9:42 Sal draws a circle and a dot in the centre to say that the vector is pointing out of the page, though what do you draw/signal to say that the vector pointing away from you? Thank you to whoever can answer this.", + "A": "You draw a circle with an x in it. The idea is that the one coming toward you looks like the head of an arrow coming at you and the one going away from you looks like the feathers of an arrow going away.", + "video_name": "s38l6nmTrvM" + }, + { + "Q": "@ 1:35 how do we predict when something will dissociate and when it will not? Why doesn't the Carbon or any other part of the sorbate dissociate?", + "A": "This sort of thing will come to you with time doing practice problems. In general though just remember that water is not strong enough to break C-C or C-H bonds.", + "video_name": "jzcB3faNdq0" + }, + { + "Q": "What is coulom force at 6:09?", + "A": "A Coulomb force is the attractive force between positive and negative charges.", + "video_name": "q--2WP8wXtk" + }, + { + "Q": "At 6:38 Sal said \" 2s and 2p\". But aren't those 4s and 4p orbitals?", + "A": "Yes, they are 4s and 4p orbitals", + "video_name": "q--2WP8wXtk" + }, + { + "Q": "At 3:38,sal says atooms are joined by covalent bonds ......so my first question is what are covalent bonds and how can we find radius if atom is not joined to anyone??", + "A": "Covalent bonds are bonds between two atoms sharing electrons.", + "video_name": "q--2WP8wXtk" + }, + { + "Q": "At 7:15, do you have to write the CH2 as carbon bonded with 2 hydrogen atoms? Can't you just write it as CH2?", + "A": "The formula with two separate H atoms is a structural formula. The formula with a CH\u00e2\u0082\u0082 group is a condensed structural formula. You decide which one you want to use for your own purposes.", + "video_name": "pMoA65Dj-zk" + }, + { + "Q": "At 1:14 isn't the metals \"magic number\" 18, as they want to fill their d-orbital.", + "A": "Yes, but that isn t something that should come up in organic chemistry as it almost always deals with C H N O (and a few others here and there...)", + "video_name": "pMoA65Dj-zk" + }, + { + "Q": "why is hydrogen the best partner as explained by sal in 0:56?\nwhy can't other atoms be used?", + "A": "other atoms can be used but the main problem is that we have to draw other electrons of the atom also. For eg:in CO2 we have to draw the rest 4 electrons of oxygen & also number compounds of carbon-hydrogen is more than 1000.", + "video_name": "pMoA65Dj-zk" + }, + { + "Q": "at 6:30, why is the final velocity -5m/s? Wouldn't it be 0m/s because the rocket is not moving at all, it is sitting on the ground? I understand that negatives are used when the rocket is going down, but the final velocity would be when the velocity at the very end of the experiment, when the rocket lands and is sitting stationary on the ground.", + "A": "The equation of motion for a projectile does not include the effect of collisions, so the final velocity is the velocity the projectile has the moment it reaches a surface. After that point, the projectile EOM no longer holds since there are additional forces acting on it.", + "video_name": "ZZ39o1rAZWY" + }, + { + "Q": "at 11:41, why is the average velocity in the horizontal direction is 5 square roots of 3 metres per second? I know Sal said it is because it doesn't change, but why does it not change?", + "A": "Gravity only affects the velocity in the vertical direction, and since we are assuming that there is no air resistance, there is nothing to change the horizontal velocity.", + "video_name": "ZZ39o1rAZWY" + }, + { + "Q": "How can you prove mathematically that the initial velocity will be the same as the final velocity in this situation? ( 5:37 ) Can I calculate this somehow from v = at or s = 1/2(at^2)?", + "A": "There are several approaches. Some have to do with potential and kinetic energy. And it s not v = at, it s (v-u) = at, the formula most appropriate to that is v^2=u^2 + 2as, when the displacement (vertical) is zero then v^2=u^2 and since you know that the object will be moving in the opposite direction (vertically) when it lands than it was when it was launched then it is necessary that v = -u.", + "video_name": "ZZ39o1rAZWY" + }, + { + "Q": "7:08 shouldn't the 10 be positive since it is actually 5-(-5) = 5+5", + "A": "At 7:08 the equation he just finished was -5 -5 = (-5) + (-5) = -10", + "video_name": "ZZ39o1rAZWY" + }, + { + "Q": "8:46 If the answer to acceleration or velocity is \"0\", is it necessary to include units?", + "A": "It s better if you do. Best ask your teacher if you really feel like being lazy :)", + "video_name": "d-_eqgj5-K8" + }, + { + "Q": "At 7:18, the displacement is taken to be the area under the slope i.e., a triangle. why isn't the other side of the slope considered, tat would form a rectangle?", + "A": "If you go at a constant velocity of 10 m/s, the graph of that is a straight horizontal line at 10 m/s, right? If you go that velocity for 10 s, how far did you go? 100 m, right? You got that by doing 10 m/s x 10 s = 100 m, which is the area UNDER that horizontal line. Now, did we need to add the area above the straight line? No, why would we do that, right? It doesn t have to do with anything. The same idea holds when the line is tilted. The area above the line has no signficance. It s infinite, too.", + "video_name": "d-_eqgj5-K8" + }, + { + "Q": "At 9:58, Sal says that He fuses to C and O.Why does He not get fused into other elements like Lithium,Boron or Nitrogen etc.?", + "A": "It does, but lithium, boron, and nitrogen actually have a lower fusion temperature than helium so they fuse instantly.", + "video_name": "kJSOqlcFpJw" + }, + { + "Q": "at 1:12 why is hydrogen fusing into helium?", + "A": "beryllium is also an element ,heavier than hydrogen or helium but lighter than oxygen or carbon", + "video_name": "kJSOqlcFpJw" + }, + { + "Q": "In 9:26, How does the Hydrogen heat up? Is it hot in space? Is the star heating it up? If the star is heating it up, whats it's source?", + "A": "As gravity pulls in the atoms, they are confined to a smaller and smaller volume. When you compress a gas, it heats up.", + "video_name": "kJSOqlcFpJw" + }, + { + "Q": "At 0:50, it is said that the compund breaks into individual ions, when dissolved in water. But, if this happens, they will no longer be compunds. How are they be able to retain the characterictics of the initial compund?", + "A": "When they dissolve, they become a solution of the compound. It is still the same compound, but it is now dissolved.", + "video_name": "BgTpPM9BMuU" + }, + { + "Q": "At 5:31, why can't Carbon have +2 charge?", + "A": "In theory, carbon can have +2 charge, but for only like, i don t know, one millionth of a nanosecond? Carbocations are highly unstable (most of them!) and react quickly. The bigger the charge, the less stable they are.", + "video_name": "7p2qfyqiXHc" + }, + { + "Q": "At 3:35, does he mean percentage for that one drop, or for the whole plasma part?", + "A": "Those percentages are applicable for both the drop and the entirety of the plasma.", + "video_name": "5MOn8X-tyFw" + }, + { + "Q": "what does Sal mean by culum of water at 6:20 ...is the liquid in the test tube not mercury ?", + "A": "I think this is a mistake because at @6:50 he writes the density of mercury 13600kg/m-3", + "video_name": "i6gz9VFyYks" + }, + { + "Q": "At around 9:37 can some one please explain how 1N is 1kgm^2/s? I thought that force=mass*acceleration leading to the unit kgm/s^2. Thank you in advance!", + "A": "A Newton is a kg*m/s^2 (mass * acceleratin) A Joule is a kg*m^2/s^2 (Force * distance)", + "video_name": "i6gz9VFyYks" + }, + { + "Q": "At 2:43, if there is vacuum in the tube, shouldn't mercury climb up the whole tube to compensate for the difference in pressure?", + "A": "it is usual to think that, if there is a vacuum then things will naturally get sucked into that space. But actually, that only happens if there is enough pressure pushing it. The atmospheric pressure is wha pushes it and that is only big enough to get the mercury so far. The weight of mercury is also pushing against the atmospheric pressure hope that makes sense :)", + "video_name": "i6gz9VFyYks" + }, + { + "Q": "At 2:16, Sal calls the water molecule a tetrahedron. What exactly is a tetrahedron?", + "A": "if i remember corectly, a tetrahedron has 6 edges and 4 vertices", + "video_name": "6G1evL7ELwE" + }, + { + "Q": "at 2:58, why is their a bubble around... i din't realy understand.", + "A": "The bubble is supposed to illustrate that the electrons in a water molecule (and any other molecule) aren t actually stationary in one place (like we usually draw them, with the dots and lines), but are constantly buzzing around.", + "video_name": "6G1evL7ELwE" + }, + { + "Q": "@2:50 why did he split the cube/pentacyclo ring the way that he did?", + "A": "Because of the symmetry of the molecule, there are many ways in which he could have done it. The point is that he had to draw the largest ring possible (8 C atoms) that contained two bridgehead carbons. The particular one he chose was probably the easiest to draw.", + "video_name": "ayKHmN90ncc" + }, + { + "Q": "At 0:06 Sal refers to the neuron as a cell. However, the neuron has bits that are cells, like the Schwanne cells. Doesn't this make the neuron a tissue? Or is it a cell with add-ons?", + "A": "It s more like a cell with add-ons. The Schwann cells are helper cells/glial cells that specialize in helping a certain type of cell. These cells are just as important as any other cell except not so well known.", + "video_name": "ob5U8zPbAX4" + }, + { + "Q": "What is the myelin sheath and what does it do? Mentioned at 4:42.", + "A": "The myelin sheath helps keep the electrical signals insulated and protected; it is the same concept as rubber on a power cord.", + "video_name": "ob5U8zPbAX4" + }, + { + "Q": "At 5:25, it is mentioned that the effects of the impulses are combined. Does that mean that the multiple impulses are transformed into one or does it mean that the effects of each impulse are measured which will then decide whether or not access is granted to the axon. Or, are you saying the impulse effects are measured and then another signal is created and then travels down the axon?", + "A": "Thanks, you really explained it well :)", + "video_name": "ob5U8zPbAX4" + }, + { + "Q": "At 7:40, why is it quasi-static? What does quasi mean?", + "A": "that means almost such that you get almost static", + "video_name": "lKq-10ysDb4" + }, + { + "Q": "At 1:20, how come the force due to gravity is mg? In free fall particle videos earlier, I remember it being just g (-9.81 m/s^2)?", + "A": "You remember wrong. g is acceleration due to gravity, not force due to gravity. (It is also force per unit of mass.) To find the force of gravity on an object you have to multiply m by g.", + "video_name": "TC23wD34C7k" + }, + { + "Q": "at 11:59 He said that when \u00ce\u00b8=0 all forces will act perpendicularly to the plane. Then does that not mean that \u00ce\u00b8=90? Furthermore if \u00ce\u00b8=0, then how do you explain the magnitude of the normal force since mg(cos\u00ce\u00b8) = 0 [cos\u00ce\u00b8=0, mg(0)=0], the normal force should be the same as the weight of the object when \u00ce\u00b8 is zero, could someone please clear my doubts. Thank you", + "A": "Theta is the angle between the plane and the ground. When that angle is 0, the force of the weight is perpendicular to the plane. Look at the drawing.", + "video_name": "TC23wD34C7k" + }, + { + "Q": "Exactly...At 2:37. Mr. Khan literates that the notation that he will be using is unconventional. Then what is a conventional notation?", + "A": "conventional notation is scientific notation", + "video_name": "TC23wD34C7k" + }, + { + "Q": "At 2:36, I tried searching up the conventional notation for vector magnitudes but came away a little confused, so does anyone know what it is?", + "A": "Unsure what you mean exactly by conventional notation, since mathematicians and physicists can t agree, but the most COMMON notation is as follows: Math: Vector Q is located at <3,4,5> Meaning 3 units in the x-direction, 4 units in the y-direction, and 5 units in the z-direction. Physics: Vector Q is located at 3i+4j+5k, where i is the x-component of Vector Q (Qsubx), j is the y-component (Qsuby), and k is the z component (Qsubz). That s how it s usually written.", + "video_name": "TC23wD34C7k" + }, + { + "Q": "at 7:30, how can we write V+ as Vin.. isn't Vin = V+ - V-??", + "A": "Hello Karthikeyan, In this case the non-inverting input terminal (V+) is connected directly to the voltage source (Vin). You are also correct that the op-amp amplifies the difference between the input terminals: Vout = Gain * (V+ - V-) Yes these circuits can be tricky. Different things have the same names. You will need to look at the context to figure out the meaning. Regards, APD", + "video_name": "_Ut-nQ535iE" + }, + { + "Q": "at 10:54, you said ''because x is <<1\", for me to get that I had to calculate it first, so how did you know that it is much smaller than 1 without any calculations?Since when x<<1 we make assumption, that means subtracting/adding it does not make any significant difference, so from that I also wanna know if I would be wrong if I DO NOT make assumptions instead I just work it out the way it is.", + "A": "You can confidently ignore the value of x when the Kb value is of order 10^(-5) or smaller. The reason is that small Ka would mean small dissociation. Also, if you do not ignore x in the equation, you will arrive at almost the same answer (there may be a difference but it is insignificant). But, you may notice that if you do not ignore x, you will arrive at a quadratic equation which increases our effort to solve for the answer(and its going to get you the same answer). Hope this helps!", + "video_name": "223KLPnJCBI" + }, + { + "Q": "Forgive my ignorance, but when he speaks of a step-up transformer @ 1:35, what exactly happens to the voltage? I assume it isn't making free energy...?", + "A": "True, Though the voltage is increased in step up transformer, the current is decreased to make Power= Voltage*Current consant.", + "video_name": "xuQcB-oo-4U" + }, + { + "Q": "At about 1:00 the transformer is for what?", + "A": "the transformer lowers the voltage so that the alarm clock radio doesn t over heat", + "video_name": "xuQcB-oo-4U" + }, + { + "Q": "@ 9:39, he said that the copper wire works as an antenna . why does that work?", + "A": "Because as the electricity goes through it will make contact with the satellite. Hope that helps. :)", + "video_name": "xuQcB-oo-4U" + }, + { + "Q": "@8:39 how does he know that the equilibrium lies to the left? How do you know if you have more reactants than products? I'm having difficulty understanding whether to point the arrow to the left or to the right. Thanks", + "A": "If Ka > 1, the position of equilibrium lies to the right. If Ka < 1, the position of equilibrium lies to the left.", + "video_name": "BeHOvYchtBg" + }, + { + "Q": "At 7:47, I know it sounds silly but could acetic acid have acted as a base, and ACCEPTED a proton from water? For example, either the double-bonded oxygen or single bonded oxygen could have accepted the proton. Thanks", + "A": "It can happen, but that reaction is not very favourable in water as water is a much better base (which means it s much more likely to accept H+) If you added a strong acid to pure acetic acid it could happen forming CH3COOH2^+", + "video_name": "BeHOvYchtBg" + }, + { + "Q": "At 1:26 why does the Cl ion have a negative charge when it has a full octet?", + "A": "A chlorine atom has 7 valence electrons. If it has 8 (a full octet) then it has to have gained 1 electron which is why it has a -1 charge.", + "video_name": "BeHOvYchtBg" + }, + { + "Q": "At 2:40 why we do 2^x =4 Then X=? ,what does X means here?", + "A": "To be more specific, x is the order of the reaction in NO (which is the exponent for [NO] in the rate law).", + "video_name": "Ad0aaYixFJg" + }, + { + "Q": "At 5:38, by Time rate of change, does he mean the speed the electrons are moving, and doesn't this relate closely with Voltage?", + "A": "Time rate of change is always of something. Like: time rate of change of voltage, or time rate of change of position. If the time rate of change of voltage is 5 volts/second, then in the capacitor equation (i = C dv/dt) you would substitute 5 for dv/dt.", + "video_name": "l-h72j2-X0o" + }, + { + "Q": "At 13:20, I am a little confused on how you went from 0 ice to 0 degrees water ?", + "A": "For each kg of ice, you need a certain amount of energy to melt it to water. During the melting, the temperature stays the same. The amount of energy you need is given by L, the latent heat of fusion, which is in units joules per kilogram.", + "video_name": "zz4KbvF_X-0" + }, + { + "Q": "At 9:55 Sal only crossed out the I's to make the equation simpler. why is that and why didn't he cross out the R's?", + "A": "This is because I(current) is the same throughout the circuit. so Sal cancelled the I s. But the resistance keeps on changing after going through each of the resistor. so he simply cannot cancel out the R s.", + "video_name": "ZrMw7P6P2Gw" + }, + { + "Q": "13:00\n\nIs there a name for this little period where the temperature stays constant although we are adding or removing a certain amount of heat?", + "A": "Heat of vaporazation or the heat of fusion.", + "video_name": "pKvo0XWZtjo" + }, + { + "Q": "In 0:05 he says that there are only 4 truth is there are 5 states of matter.They are Solid,Liquid,Gas,plasma and Bose- Einstine compound.", + "A": "I learned there were five as well.", + "video_name": "pKvo0XWZtjo" + }, + { + "Q": "Are the polar bonds forming between the H2O molecules @ 4:06 hydrogen bonds? If not what are hydrogen bonds?", + "A": "Yes, in a hydrogen bond hydrogen is bound to a highly electronegative atom, such as nitrogen, oxygen or fluorine.", + "video_name": "pKvo0XWZtjo" + }, + { + "Q": "At round 14:02, Sal says that water takes much more time to vaporize as compared to the time period that ice takes to melt.\nWhy does this happen?", + "A": "In order to vaporize water, you have to give a lot of energy to each of the molecules so that they have enough energy to move far away from each other. To melt ice into water, you also have give the molecules energy, but you only have to give enough to break the bonds between the water molecules, and that doesn t require nearly as much energy as it does to actually pull the molecules away from each other.", + "video_name": "pKvo0XWZtjo" + }, + { + "Q": "At 4:07 when the ring breaks do the electrons in magenta need to rotate in order to form a bond with the other halogen atom(anti addition)?", + "A": "Nothing needs to rotate, the magenta electrons are not forming a new bond they are going to the Br that was in the ring. The electrons in the new C-Br bond comes from the bromide anion. It would help if Jay coloured these in.", + "video_name": "Yiy84xYQ3es" + }, + { + "Q": "At 8:50 in the video the mechanism is described as happening two more times and the result is a trialkylborane molecule. I can't think of where the other two O's have come from. I don't understand why B, with an octet around it has a negative charge.", + "A": "From another two peroxides. Formal charge = valence electrons - lone pair electrons - bonds 3 - 4 = -1", + "video_name": "00qYQahwuSQ" + }, + { + "Q": "How is Chlorine less electronegative than oxygen? 6:40", + "A": "Sal explains this in the video on trends in the periodic system (chemistry video no. 10). Simply put, chlorine (compared to oxygen) has an additional shell of valence electrons (and a lot more electrons overall) that repels the electrons of other atoms or molecules. Watch the video or look at Wikipedia for a better explanation!", + "video_name": "8qfzpJvsp04" + }, + { + "Q": "9:15 Hydrogen Flourine is HF not H-FL, right?", + "A": "Yes Hydrogen Flourine is HF.", + "video_name": "8qfzpJvsp04" + }, + { + "Q": "At 7:27 you said the electron from the hydrogen spends most of its time with the chlorine, but why doesn't the chlorine just take the electron permanently, like an ionic bond?", + "A": "hydrogen bonding can also only form if it s with the elements FON. Flourine Oxygen and Nitrogen. and it s also covalently bonded.", + "video_name": "8qfzpJvsp04" + }, + { + "Q": "At 5:19, how doe he say that the lone pair will move up angularly away from the Central Atom O ?", + "A": "The electron pairs in water point towards the corners of a tetrahedron. The bonding pairs are in the plane of the paper. One lone pair is coming angularly out of the paper, and the other lone pair is pointing angularly behind the paper.", + "video_name": "q3g3jsmCOEQ" + }, + { + "Q": "At 8:07 i did not quite understand why the tetrachloromethane molecule will have 0 D??", + "A": "Same case as in CO2. Since the power of Cl in C(CL)4 attracting the electron to themselves have the same magnitude individually, they cancel each other. Hope this helps.", + "video_name": "q3g3jsmCOEQ" + }, + { + "Q": "At 8:00 it is said that we would expect CCl_4 not to be polar, but aren't the individual C-Cl bonds polar making the molecule polar?", + "A": "Yes, the individual bonds are all polar, but they cancel each other out, so the molecule as a whole is nonpolar.", + "video_name": "q3g3jsmCOEQ" + }, + { + "Q": "1. at 12:05 , once we have the moles quantity. cant we use PV=nRT to figure out the pressure for each?\n\n2. For PV= nRT dont we always have to use Liters as the volume?\n\n3. Would the total number of moles always equall 100 moles when we add them up coming from % ?\n\nThanks for helping. and you are changing the world with your videos, not just how people are learning things.", + "A": "for number 1,yes you can , you just have to replace n with the number of moles of each molecule", + "video_name": "d4bqNf37mBY" + }, + { + "Q": "I know this might be a simple math question but dont you have to divide the entire side of the equation by 4 instead of just the 100 @ 8:52 ?", + "A": "this might help: since there are no variables or anything complicated, the entire side is just multiplying numbers. because of the order of operations (BEDMAS, or BEMDAS, or PEMDAS, or however you learned it), it doesn t matter whether you divide the whole thing by at the end, or divide one of the numbers by 4 in the middle. you re just dividing by 4! try it on a calculator, you get the same result :)", + "video_name": "d4bqNf37mBY" + }, + { + "Q": "At 4:28, why did he change oxygen from 16 to 32?", + "A": "The relative atomic mass of one oxygen atom (O) is 16, while the relative atomic mass of one oxygen molecule (O2) is twice that at 32. It depends on if you are talking about the atom or the molecule.", + "video_name": "d4bqNf37mBY" + }, + { + "Q": "At 7:52 how did you get 3 different R equations? And how can you be sure that you are choosing the right one, is it that you choose which ever one matches your units ?", + "A": "You re right - you always want to choose the R equation that matches the units you re using (or, you have to convert your units to match your R equation!).", + "video_name": "d4bqNf37mBY" + }, + { + "Q": "At 3:43 you say that the star will enlarge its radius like a red giant, but not get to the same size as a sun-sized star becoming a red giant. Does it also a experience a color change toward red, and if so what color was it in the first place? Does the creation of heavier elements in the core affect the color as well?", + "A": "No, as the stars surface gets farther from the core, it gets cooler. Color is entirely related to temperature the cooler surface glows red instead of yellow.", + "video_name": "UhIwMAhZpCo" + }, + { + "Q": "4:00-4:30 are there others stars that have different elements or have we discovered all of the elements ?", + "A": "we have discovered all the elements that naturally exist, and even if we hadn t there would have to be stars as big as the milky way to fuse elements beyond iron.", + "video_name": "UhIwMAhZpCo" + }, + { + "Q": "At 2:10 how do you know it is cosine and not tangent or sine?", + "A": "Think about the problem, if your moving something forward (applied force is greater then friction), and were to use sin0\u00c2\u00b0 then your work F(d)(0)=0 and that doesn t make sense because there is some type of work being done BC the object is moving", + "video_name": "udgMh3Y-dTk" + }, + { + "Q": "At 7:00, Sal says that astronauts can't tell whether they're in free fall near an object with a gravitational pull, or in deep space without any noticeable gravitational forces. How is this possible? Won't they feel the difference in acceleration?", + "A": "How can they feel the acceleration of free fall? The astronauts on the ISS are in free fall. What do you think they feel?", + "video_name": "oIZV-ixRTcY" + }, + { + "Q": "At 0:01 what is \"level 4\" multiplication? Does Sal mean grade 4?", + "A": "no its just to show your going in a more complicated type of multplication", + "video_name": "_k3aWF6_b4w" + }, + { + "Q": "at 1:03 where did he get a and b?", + "A": "For Ax^2 +Bx +C a*b = AC a + b = B He set the equality, then factored the resultants to obtain candidates for a and b. This takes experience and trial and error.", + "video_name": "dstNU7It-Ro" + }, + { + "Q": "why we need the slope? he mention it in min 2:34", + "A": "Since the line of reflection is not horizontal or vertical, he noted that it has a slope of 1. We use iy-intercepts and slopes to graph lines.", + "video_name": "3aDV3L8aZtY" + }, + { + "Q": "At 2:30 he takes the derivative of e^(-2x^2) with respect to (-2x^2). Why doesn't the power rule apply here?", + "A": "The power rule applies when the base is a variable and the power is a number. This is an exponential, the base is a number and the variable is in the power. They are very different functions, and therefore have different derivatives.", + "video_name": "MUQfl385Yug" + }, + { + "Q": "At 5:15 why is the answer a positive and a negative? e.g. + or - 1/2", + "A": "It s because you are taking the square root of (1/4). When you take the square root you ll have two solutions ( + or - 1/2 in this case ) since when you square each one you ll get (1/4).", + "video_name": "MUQfl385Yug" + }, + { + "Q": "At about 2:29, Sal is saying that 3a(a^5)(a^2) is 3(a^1*a^7). How? I am probably just confused on this topic, though.", + "A": "a = a^1 3\u00e2\u0080\u00a2a^1\u00e2\u0080\u00a2a^5\u00e2\u0080\u00a2a^2 = 3\u00e2\u0080\u00a2a^(1 + 5 + 2) = 3\u00e2\u0080\u00a2a^8", + "video_name": "-TpiL4J_yUA" + }, + { + "Q": "At 1:28 why is he making those markings? He draws a line and then crosses it out... as to say, what? If he wants to make it easier for himself to follow along, shouldn't he be crossing out the 2 digit and 3 digit instead?", + "A": "He circles the numbers to see which numbers he s multiplying. He s just trying to help us understand by giving us a visual. :)", + "video_name": "TqRReFvbpXA" + }, + { + "Q": "At 4:33, how would you find the area of an inscribed polygons?", + "A": "I would break it into triangles, each with a vertex at the center of the circle, then use trigonometry (or special triangles) to solve for the sides and area.", + "video_name": "LrxZMdQ6tiw" + }, + { + "Q": "At 2:10, how ar the triangles congruent by SSS? I thought SSS was a similarity postulate and the triangles are congruent through the SAS Postulate.", + "A": "SSS is both a congruency and a similarity postulate. We cannot use SAS because we haven t proven that all the central angles are congruent.", + "video_name": "LrxZMdQ6tiw" + }, + { + "Q": "At around 1:40, couldn't you take the (positive and negative) square roots of both sides?", + "A": "You could. (and then x = -2 and x = 2) Good question!", + "video_name": "bml74_PsfwA" + }, + { + "Q": "At 2:33 Sal says it will make sense. I never really got past the 2 to the 0 power. I don't understand how he took two, put a zero above it, and then turned it into a one?! How does that work?", + "A": "What he showed helped me understand why it does that, so now let me try to explain it for you: He changed the way he did the exponents to multiplying 1 times how many numbers (the number that the exponent is) to that one. So when it is 2\u00e2\u0081\u00b0 = 1 because there aren t any 2s to multiply by. So something as big as 1,000,000\u00e2\u0081\u00b0 = 1 Now let s do it regular: When you have 4\u00e2\u0081\u00b6 = 1 \u00c3\u0097 4 \u00c3\u0097 4 \u00c3\u0097 4 \u00c3\u0097 4 \u00c3\u0097 4 \u00c3\u0097 4 = 4096 Well, that is a bit too big of a number so let s do 3\u00c2\u00b2 = 1 \u00c3\u0097 3 \u00c3\u0097 3 = 9 Ask me to clarify anything.", + "video_name": "dAvosUEUH6I" + }, + { + "Q": "is there other basic rigid motions other than reflect,translate, and rotate?\n\nas said in 1:07", + "A": "Those three translations are the three basic geometric translations besides dilation.", + "video_name": "EDlZAyhWxhk" + }, + { + "Q": "At 1:09 Sal says that he doesn't like using FOIL. FOIL is really easy and is much less confusing then the way Sal did the distributive property twice even though you get the same answer. Why does Sal not like FOIL?", + "A": "FOIL won t help you if you have to expand a product that isn t two binomials multiplied together; for example, two trinomials multiplied together. It s usually better to understand what you re doing instead of relying on mnemonics. For example: (a + b + c) * (d + e + f) = ad + ae + af + bd + be + bf + cd + ce + cf", + "video_name": "JKvmAexeMgY" + }, + { + "Q": "At around 2:00-2:10, why is it when x=1 and when x=3? Why not something else?", + "A": "You can pick any x you like. 0 and 1 are frequently picked because 0*a=0 and 1*a=a. Since the multiplication is easy, you can solve the problem quicker.", + "video_name": "7QMoNY6FzvM" + }, + { + "Q": "1:47\nHow do you determine whether the parabola faces upward \"U\" or downward?\nSOS", + "A": "Clarifiction to the prior response you were given: You need to look at the coefficient of the X^2 terms or the coefficient in front of (X+b)^2. The coefficient of whatever is being squared determines the direction of the parabola. If the number is positive, then the parabola opens upward. If the coefficient is negative, the parabola opens downward.", + "video_name": "7QMoNY6FzvM" + }, + { + "Q": "At 5:00, doesn't the \"function\" Sal draws fail the vertical line test? Why does he still call it a function?", + "A": "That s called a piecewise function - they re defined like this: f(x) = { x + 1 for x > 1 x - 1 for x < 1 x for x = 1 }", + "video_name": "8VgmBe3ulb8" + }, + { + "Q": "at 4:07, when he draws the funny function graph, isn't it true that it isn't a function because it doesn't pass the vertical line test? It appears that the line would go through the open circle and the wing-shaped line on the left side.", + "A": "Perhaps he just didn t draw it clearly. I think he meant to draw an open circle as you suggested. If that was not his intention, then you are correct, it isn t a function.", + "video_name": "8VgmBe3ulb8" + }, + { + "Q": "AT 9:39, why is there a gap between the reflection about the y-axis and the reflection about the x-axis?\nAt 6:58, there was no gap.", + "A": "It s just a different equation he s graphing (I m not sure what the equation is; if anyone knows I d love to hear). It does look rather strange as a function, but it s still classified as an odd function.", + "video_name": "8VgmBe3ulb8" + }, + { + "Q": "at 0:10, he says rational #s are different from natural numbers. What exactly ARE rational numbers?", + "A": "natural numbers are the numbers you learned for counting: 1, 2, 3 ... whole numbers are the numbers of apples you might have: 0, 1, 2, 3 ... integers are positive or negative numbers that are not fractions: ... -3, -2, -1, 0, 1, 2, 3 ... rational numbers are any number that can be expressed as a fraction of integers.", + "video_name": "i1i2_9wg6N8" + }, + { + "Q": "At 0:21, what does Sal mean by \" arbrutary\"?", + "A": "Any old An arbitrary angle measure is a random angle or just any old angle", + "video_name": "0gzSreH8nUI" + }, + { + "Q": "Would 3 quadrupled by shown as a radical with a little four in the \"notch\", as a cube root is described at 4:32?", + "A": "4th roots would have a little 4 in the notch of the radical symbol. 5th roots would have a 5 in that position. 6th roots would have a 6 in that position. See the pattern?", + "video_name": "87_qIofPwhg" + }, + { + "Q": "At 5:02 Sal say's that he is going to calculate the CUBE root of 27.\nI didn't understasnd how it is calculated?", + "A": "So what Sal is saying is he is breaking it down into 3 * 3 = 9 9 * 3 = 27 So, 3 * 3 * 3 = 27. Therefore, 3 is the cube root of 27. Just like cube root of y = x * x * x", + "video_name": "87_qIofPwhg" + }, + { + "Q": "at 0:31 why when you square 49 the result is 49?", + "A": "He is squaring the result of \u00e2\u0088\u009a49, which is 7. 7 squared is 49, so (\u00e2\u0088\u009a49)^2 = 49.", + "video_name": "87_qIofPwhg" + }, + { + "Q": "At 0:58, what are Lucas numbers??", + "A": "Lucas numbers are defined in pretty much the same way as the Fibonacci numbers except that the first Lucas number is 2 instead of 1. So, for the Lucas sequence, you get: 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, ....", + "video_name": "14-NdQwKz9w" + }, + { + "Q": "The age of vinod and sanjeev are in the ratio of 5:7. Ten year later the ratio of their age will be 7:9. Find the present age.", + "A": "Let v be vinod age now and s be sajeev age now. 5c= 7v so c = 7/5 v 10 years from now, 7(c+10) = 9(v+10) so 7c + 70 = 9v + 90 or 7c = 9v +20 Substitute into c, so 7(7/5v) = 9v + 20 multiply whole equation by 5 49v = 45v + 100 subtract 45v 4v = 100, v = 25 and c = 7/5(25) = 35 Ratio of 25:35 reduces to 5:7 Ten years, v will be 35 and c will be 45 so ratio of 35:45 or 7:9", + "video_name": "W-5liMGKgHA" + }, + { + "Q": "Okay, quite possibly my concept of integration is wrong but shouldn't increasing the number of trapeziums bring the result closer to the value obtained by integrating f(x)? in this case integrating it brings the value to 7.4, which is close enough to the value obtained at 8:26 , but if i increase the no. of trapeziums to 10, the value of delx becomes 0.5, so the total becomes 3.26. it becomes less accurate.", + "A": "If you increase the number of trapeziums to 10, then \u00ce\u0094x = 0.5, and you got that the area is equal to: A = 0.5/2 [ f(1) + 2f(1.5) + 2f(2) + 2f(2.5) + 2f(3) + 2f(3.5) + 2f(4) + 2f(4.5) + 2f(5) + 2f(5.5) + f(6) ] A = 0.25 [ 0 + 2\u00e2\u0088\u009a0.5 + 2\u00e2\u0088\u009a1 + 2\u00e2\u0088\u009a1.5 + 2\u00e2\u0088\u009a2 + 2\u00e2\u0088\u009a2.5 + 2\u00e2\u0088\u009a3 + 2\u00e2\u0088\u009a3.5 + 2\u00e2\u0088\u009a4 + 2\u00e2\u0088\u009a4.5 + \u00e2\u0088\u009a5 ] A \u00e2\u0089\u0085 7.3847 Which is a much closer result.", + "video_name": "1p0NHR5w0Lc" + }, + { + "Q": "On the third example, at about 7:25, Sal says that the length marked 2 and the segment parallel to it are equal. He says both are length 2. He says \"We know that these are both length 2 [because] these are all 90 degree angles..\" -- I don't understand how that lets us assume they are equal.", + "A": "Actually, you are right. He can t assume they are equal. BUT, the reason they wouldn t be equal is because the length of either the vertical purple side or the white side (or both) would have been changed. In that case, though, the green side would have changed exactly in the same amount that the other two (white an vertical purple) would have changed, except that if they got shorter, it would have gotten longer, and vice versa.", + "video_name": "vWXMDIazHjA" + }, + { + "Q": "At 3:02 when Sal mentions altitude, what does he mean exactly?", + "A": "Altitude is a geographic term used to describe the height of land.", + "video_name": "vWXMDIazHjA" + }, + { + "Q": "Sal @ 18:00 c2= 1/3 (x2 - 2x1) you forgot the 2 from the equation above. love you Sal. you are the greatest.", + "A": "Sal corrected this error at the end of the video.", + "video_name": "Qm_OS-8COwU" + }, + { + "Q": "At 2:21, I noticed the following: 3a+ -2c. This is a bit of a silly question but when I was in middle school we were taught to write the above as 3a+(-2c) as a parenthesis was thought to be needed between the +,- signs. Is the way I was taught to write it wrong/redundant?", + "A": "Either putting parenthesis around the negative number or writing it in the form of 3a-2c is preferred for clarity. In school students are often taught to only do one operation at a time in each math step. However you may choose to combine multiple operations in a single step for speed purposes. Not following these type of conventions just increases the chance of confusion and mistakes but does not invalidate the math. To me it is similar to the difference between formal and informal writing.", + "video_name": "Qm_OS-8COwU" + }, + { + "Q": "At 3:37, he says that (if it's continuous) Psi xy = Psi yx . Is there a video where he proves that?", + "A": "It s proven in all Calc III texts, but most likely in the section that he talks about partial derivatives, it s proven.", + "video_name": "a7wYAtMjORQ" + }, + { + "Q": "At 3:00, where are the sample sets s1, s2, etc coming from. Sal is just picking out numbers without describing the process.", + "A": "The sets s1, s2 and s3 are outcomes that could be obtained by throwing the unfair dice defined by the distribution in yellow, but they are just examples and could be totally different.", + "video_name": "JNm3M9cqWyc" + }, + { + "Q": "At 2:47, he starts using numbers like two and eight that didn't fit with what he was doing a minute before. Are those numbers suppose to be there to help solve the equation or just random numbers he pulled out?", + "A": "They are just numbers he chose to plug in to the equation so we could see that the property was true.", + "video_name": "PupNgv49_WY" + }, + { + "Q": "At 3:07 Why did he multiply instead of adding and where did he get the 16 to add to the 240?", + "A": "He multiplied because when you are adding two logarithms of the same base (in this video, it was base 2) you can rewrite the logarithm as the product of the two numbers that are on the inside. log(8) + log(32) is the same thing as log(8 *32) 8*32 = 256, so we get log(8*32) = log(256) (I didn t write in the base on the logarithm, which would have been base 2.)", + "video_name": "PupNgv49_WY" + }, + { + "Q": "At 2:18 and on, what criteria is used to choose the limiting numbers 1, 2, 3/2, 5/3, 8/5 etc.?", + "A": "Its fibonacci. 1,1,2,3,5,8,13,21 1/1 2/1 3/2 and so on. Its late, but someone will probably like this.", + "video_name": "lOIP_Z_-0Hs" + }, + { + "Q": "At 4:41, in the third line, Sal writes f(x+h) without the denominator of h that it had in line 2. Why isn't this a mistake?\nIf I did the same thing with numbers, it would be as if I rewrote (3 + 5)/2 as 3 + 5/2. That IS a mistake. What's different here?", + "A": "He factored it out, which is not a mistake. This would be like doing the following: (6+10)/5 = 2 \u00e2\u0088\u0099 [(3+5)/5] This is valid because: (ab)/c = a \u00e2\u0088\u0099 (b/c)", + "video_name": "L5ErlC0COxI" + }, + { + "Q": "So if we can claim that the the limit as h\u00e2\u0086\u00920 of f(x+h) is f(x), as was stated in the video at 7:30, Why can't you evaluate it as f(x+h)g(x+h)-f(x)g(x)/h = f(x)g(x+h)-f(x)g(x)/h = f(x)((g(x+h)-g(x))/h), which would be equal to f(x)g'(x). This result is clearly wrong, but I can't see where exactly I've made a mistake.", + "A": "You need to put the entirety of the first expression in parentheses as it all must be divided by h", + "video_name": "L5ErlC0COxI" + }, + { + "Q": "At 6:00 , how come there are no restrictions on x-3y? How can we tell if there will be restrictions on a certain part or not?", + "A": "If a factor disappears from the denominator, then its restriction needs to be stated. Otherwise there d be no way of knowing that it had ever existed in the original problem. If a factor is still left in the denominator of the simplified fraction, then its restriction does not need to be stated because it is still visible and we all know that division by zero is not allowed.", + "video_name": "e7vA_S7abSY" + }, + { + "Q": "at 0:45 Sal says that 5^2/3 is equal to 25/9. Shouldn't it be 5^2/3^2 or (5/3)^2 is equal to 25/9?", + "A": "Well, he didn t say that, actually. What he said was that 5/3 squared was equal to 25/9 What he wrote as he segued to the next example was subtly different, and it is true that he should have put his Segue into Park long enough to put the 5/3 into parentheses to emphasize that he was squaring the whole fraction.", + "video_name": "bIFdW0NZ9W4" + }, + { + "Q": "at 1:25 isn't that the transitive property of equality?", + "A": "It can be taken that way. If boys=tall and Bill=tall, that s like saying x=tall and y=tall. Therefore, you can substitute x for tall and say x=y. If you write the equation as boys =tall and tall=bill, then it s like saying x=y and y=z, therefore x=z, that is more the transitive property. This really depends on your perspective, and as I debated today, it can be taken either way.", + "video_name": "GluohfOedQE" + }, + { + "Q": "At 0:57, why did Sal draw those lines over the z? Please click the time to see what I'm talking 'bout", + "A": "Some people draw a line in their z s because it helps other people tell them apart from 2 s, since sloppy z s and 2 s can look like each other.", + "video_name": "cTveNRjWQYo" + }, + { + "Q": "3:50 wouldn't length 'a' equal length 'b' then?", + "A": "You can t make that assumption. As you shift to a different point on the circle, the length of a and b will vary. If the point was very close to the x-axis, then b would be very short compared to a . If the point was close to the y-axis, then b would be very long compared to a . Hope this makes sense.", + "video_name": "1m9p9iubMLU" + }, + { + "Q": "my doubts are in the right triangle in the video.At 3:46, why is the length of the opp side b? and at 4:08, why is the adj side equal to a? what does it have to do with the coordinates of the intersection point?", + "A": "(a,b) in the video is the x,y coordinate of the line from the origin to the perimeter point on the unit circle.", + "video_name": "1m9p9iubMLU" + }, + { + "Q": "At 1:47 .... how is he sure that \" arctan( tan ( g^-1(x) - 3pi/2 ) ) \" will give out ( g^-1(x) - 3pi/2 ) ?\ni mean .... how is he sure , that ( g^-1(x) - 3pi/2 ) is restricted to the domain of tan ?", + "A": "Tangent isn t actually a completely invertible function since it outputs the same value from different inputs. So the fact that the question asks for the inverse function implies it s looking for the simplest inverse function. Since it s just looking for the simplest inverse function, we consider arctangent as if it perfectly cancels tangent.", + "video_name": "QGfdhqbilY8" + }, + { + "Q": "At 0:04 it says two sets of parallel sides. Isn't that the same thing as two sets of parallel lines. Sides on a parallelogram are lines. Even if the question says so, you can also say sets of sides. Not to be critical, just thought I'd point it out.", + "A": "Yes, two sets of parallel sides are the same things as lines. It s just another way of saying it. Just like how you might call a sphere, a ball. There might be many different ways to say that, like two pairs of parallel lines.", + "video_name": "1pHhMX0_4Bw" + }, + { + "Q": "At 3:39, why is it that we minus the dy/dx from the other side? Because it is being multiplied by the (2x-2y) on the left wouldn't we have to divide the other side by dy/dx?", + "A": "... but then we would have an answer that was for (dy/dx)^-1 = dx/dy ... which is not what we want!", + "video_name": "9uxvm-USEYE" + }, + { + "Q": "At 2:17, Sal distributes the (2x-2y) to the -(dy/dx). I understand that the answer originally is (-2x+2y)(dy/dx), and that he's just rearranging things when he writes it as (2y-2x)(dy/dx). But I don't understand how he gets (-2x+2y)(dy/dx) in the first place! I would have written (2x-2y)(-(dy/dx)). Is he simply applying the negative sign of the (dy/dx) to the (2x-2y)? That's what it looks like, but I don't understand why that is being done. Why can't the negative stay with the (dy/dx)?", + "A": "He is multiplying (2x - 2y)(-(dy/dx)) by one, but by a special form of one which is (-1)(-1). Now he has (-1)(-1)(2x - 2y)(-(dy/dx)). Since we can multiply in any order let s shift things to: (-1)(2x -2y)(-1)(-(dy/dx)). If you multiply the first two terms together, and the 3rd and 4th term together you get: (2y - 2x)(dy/dx).", + "video_name": "9uxvm-USEYE" + }, + { + "Q": "At 1:25ish. Angle BGC and DGC would also be \" Adjacent\", correct?", + "A": "Close. Adjacent angles share a ray, but neither is interior to the other. Each of those angles would be interior to angle BGD. However, the angles you mention are adjacent to each other.", + "video_name": "vAlazPPFlyY" + }, + { + "Q": "At 7:27 what about \"x\" does not equal 3?\nx=3 will make the function undefined too right?\nHelp me! I'm a little bit confused.", + "A": "Values that make both the numerator and denominator zero are undefined points (like x = -3 in this example). Values that make only the denominator zero are vertical asymptotes (like x = 3 in this example). Yes, both points are undefined for this function, but in different ways.", + "video_name": "P0ZgqB44Do4" + }, + { + "Q": "5:34 So is codomain the same as range?", + "A": "No, range is a subspace (or subset) of codomain. Range is the specific mapping from the elements in set X to elements in set Y, where codomain is every element in set Y. To concretize: Let f map X --> Y Where X = { 0, 1} Where Y = { 2, 3, 4, 5, 6...}. Let f(0) = 2 & f(1) = 3. Clearly, the range of X = [ 1, 2} where as the codomain of X = { 1, 2 ,3, 4, 5, 6..}.", + "video_name": "BQMyeQOLvpg" + }, + { + "Q": "why is 0 not in the range? it is a real number and the product of any number and zero would be zero, so I don\u00c2\u00b4t get why Sal says in 13:36 that it is not a member of the range?!", + "A": "Elements of the range are not numbers, but triples of numbers. So asking whether or not 0 is in the range makes no sense. Yes it is true that we can make the third coordinate 0, but can we make the first coordinate 5, the second coordinate 1, and the third coordinate 0 all at the same time? The answer is no.", + "video_name": "BQMyeQOLvpg" + }, + { + "Q": "What does he mean at 12:42?", + "A": "The function h maps an ordered pair onto an ordered triple. He is observing that the result of the function is an ordered triple of real numbers, an element of the range R^3.", + "video_name": "BQMyeQOLvpg" + }, + { + "Q": "At 2:30, why does a number to the negative power a decimal?", + "A": "When you have a negative exponent, you re essentially dividing the current number, like 5 squared, by the base, or 5. If you keep doing that, you get 1, 0.2, 0.04, and so on. I hope this helped you!", + "video_name": "6phoVfGKKec" + }, + { + "Q": "In 9:15 - he simplified 0.1 into 1/10, but it could have been into 10/100 as well... If you do it like that, you have root10 / root100 = root10 / 10\n\nSeems correct to me but has different answer.... why not do it this way?", + "A": "You can do it either way, but depending on what the problem is, it might be easier to do it your way or to do it Sal s way. For instance, if you had 0.2 , then that would simplify to 1/5 Sal s way; but your way, it would simplify to 20/200 , which would turn into root20 / root200 , and that s a little more messy. So, sometimes your way is easier, and sometimes Sal s is. But you can do it whichever way you prefer; they both give correct answers.", + "video_name": "BpBh8gvMifs" + }, + { + "Q": "at 2:35 shouldn't 2/(square root of) 6 be the other way around", + "A": "Sal had 2*2*2*3 inside his radical. 2*2=4, 2*3=6. So you have 4*6 inside a radical. The sqrt of 4 is a rational number ( a number that can be expressed as a fraction a/b where b doesn t = 0) so we can go ahead and work with it. We remove the sqrt of four from the radical, leaving us with 2 (the sqrt of 4) times the sqrt of 6.", + "video_name": "BpBh8gvMifs" + }, + { + "Q": "What does corresponding angles mean? [8:16] and other parts of the video. Thanks!", + "A": "Corresponding angles are created where a transversal crosses other (usually parallel) lines. The corresponding angles are the ones at the same location at each intersection.", + "video_name": "TErJ-Yr67BI" + }, + { + "Q": "At 16:03, why are you multiplying 1/4sin(t) by 2sintcost? Wasn't it ...+sin2t?", + "A": "At 15:23 Sal reminded you of the trigonometric identity: sin(2\u00ce\u00b8) = 2\u00c2\u00b7sin(\u00ce\u00b8)\u00c2\u00b7cos(\u00ce\u00b8). And even when he s writing it at 16:03, he clearly says this is just a trig identity .", + "video_name": "IW4Reburjpc" + }, + { + "Q": "at 10:00 if we substitute sin\u00cf\u0084.cos\u00cf\u0084 equals to sin2\u00cf\u0084/2 . answer turns out to be different at end. isn't it ? Terms donot cancel out each other in end", + "A": "You do get the same answer. Try again, and make sure that you evaluate it a 0 as well as a t. The integral of \u00c2\u00bdsin(2\u00cf\u0084) becomes -\u00c2\u00bccos(2\u00cf\u0084). That is evaluated at t and at 0, so we are left with [-cos(2(t))/4] - [-cos(2(0))/4] = \u00c2\u00bc - \u00c2\u00bccos(2t). The cos(2t) can be expanded into cos\u00c2\u00b2(t) - sin\u00c2\u00b2(t), so we are left with \u00c2\u00bc + \u00c2\u00bcsin\u00c2\u00b2(t) - \u00c2\u00bccos\u00c2\u00b2(t). All this must be multiplied by the -cos(t) out front, and you are left with \u00c2\u00bccos\u00c2\u00b3(t) - \u00c2\u00bccos(t)sin\u00c2\u00b2(t) - \u00c2\u00bccos(t). You will find that that will cancel with the other integral.", + "video_name": "IW4Reburjpc" + }, + { + "Q": "At 6:20, what does Sal mean by the solution satisfying the diff eq for all x's?", + "A": "In this case, it basically means writing the equation in such as a way that you have no differentials remaining and no excess variables. If the differential was in the xy-plane, then x- and y-variables are the intend. In the xyz-space, only x-, y-, and z-variables. Suitable substitutions (like here with m) are allowed.", + "video_name": "zid7J4EhZN8" + }, + { + "Q": "At 1:04 is altitude the proper term?", + "A": "YES! According the the definition An altitude is the line segment which join vertex and its opposite sides (known as base) perpendicular to it. And interesting thing about it that it is the the shortest path to reach opposite side from the vertex. A STRAIGHT PATH IS THE SHORTEST PATH!", + "video_name": "APNkWrD-U1k" + }, + { + "Q": "At 3:10 you multiply by Y' but why is the reason for this? If the product rule is just f'(x)g(x)+f(x)g'(x) which would mean from my understanding (1)(y^2) + (x)(2y)", + "A": "It s the notation that is confusing. I had a hard time with this as well. If you mentally substitute write in dy/dx here rather than multiply by y I bet you would feel more comfortable", + "video_name": "ZtI94pI4Uzc" + }, + { + "Q": "4:49 where did the +1 come from?", + "A": "That is basic factoring: 2x + 6x\u00c2\u00b2 Factors to 2x(1+3x) The same thing is happening here, only with slightly more complicated expressions.", + "video_name": "ZtI94pI4Uzc" + }, + { + "Q": "at 4:50 why does he get \"+1)y'\" and not just 2y'? it seems like there is already a y' on that side so now that he added another there should be two right?", + "A": "He just skipped one step, when he added y he got 2xy(e^xy^2)*y +y Now you can t just add this and get 2y but they both have a y so you can do this y (2xy*e^xy^2+1)", + "video_name": "ZtI94pI4Uzc" + }, + { + "Q": "I don't understand how the equation represents a surface (after 7:00). Can anyone recommend any sites that might show an animation to help me visualize it?", + "A": "This is fairly easy. Just imagine now that the only variables we have are m and b. Then you can come up with an equation that looks like this: z=x^2-2*x-2*y+2*x*y+y^2 where x is m, y is b and z is SL error. If you plot that (copy paste it into google search) you ll end up with a surface (3 variables). Here it is drawn as a parabola (z=x^2+y^2), however it resembles only some similarity with the latter. To check it just copy paste provided equations into google search and it will plot it for you.", + "video_name": "f6OnoxctvUk" + }, + { + "Q": "In 6:33 when Sal says that pi is an irrational number, if someone does find out that pi terminates or repeats does that make pi a rational number?", + "A": "Pi cannot be rational. However, if someone can prove that it terminates or repeats, then yes, it would be rational", + "video_name": "qfQv8GzyjB4" + }, + { + "Q": "At 6:31 Sal said that Pi never repeats. however, doesn't Pi always repeat?", + "A": "What he meant was pi doesn t have a pattern. You never see the same set of numbers twice. Unlike a repeating decimal such as 0.3838383838.... and so on.", + "video_name": "qfQv8GzyjB4" + }, + { + "Q": "isn't a 360 degree a cricle i'm confused and whats the difference between supplementary and complemtary at 3:14", + "A": "A supplementary is a pair of angles with 180 degrees total while complementary is a pair of angles that equal 90degrees.", + "video_name": "zrqzG6xKa1A" + }, + { + "Q": "I'm confused about the proof at 7:20. Exactly afterwards when he did 180-x+y=180? Why did he do that?", + "A": "He proved earlier that z = 180 - x , so then he could use this knowledge to replace the meaning of z: (z) + y = 180 (180 - x) + y = 180 The items in parentheses above are the same thing: we know this because it was proven earlier. This is how math proofs happen: you reuse the equations you ve already solved to help rewrite the equation you re trying to solve in a different way. That way, you reduce it into what you know is a fact.", + "video_name": "zrqzG6xKa1A" + }, + { + "Q": "At 01:26, why does he put y/x? Would it also work the other way round?", + "A": "He does that because that s how you find the answer to the problem, and no it does not work the other way around.", + "video_name": "Iqws-qzyZwc" + }, + { + "Q": "At 13:41, when Sal says that the slope is undefined, does that just mean that there is no slope for that particular line at all?", + "A": "Not really. Remember, the slope of a line is a fraction: change in y / change in x. If the slope is undefined, it is telling you that the change in x = 0 (denominator = 0). We can t divide by 0, which makes the slope undefined. If you say the line has no slope, this can be confused with a slope = 0. In this case, you have no change in Y (numerator = 0). And, you will have a horizontal line. So, to avoid confusion, it is better to say the slope = 0 or the slope - undefined. Hope this helps.", + "video_name": "Iqws-qzyZwc" + }, + { + "Q": "What is the difference between 80:1 and 1:80? He said it can go the other way around.", + "A": "Both scenarios gives you something that is 80 times as big as another object/line. So changing the order doesn t change much. However, you need to be specific to which object the 1 and the 80 belongs to. Building a miniature ship with a 80:1 ratio is a bit confusing, because the miniature ship is prob 80 times smaller instead of 80 times larger than the real one.", + "video_name": "byjmR7JBXKc" + }, + { + "Q": "How did sal in 3:55 get 12.5 from 128,000? -dazed and confused", + "A": "Well, at 3:50 Sal got 12.8 square meters (m^2), in your question you said 12.5 (maybe a typo?), but the conversion is a simple conversion from square centimeters (cm^2) to square meters (m^2).", + "video_name": "byjmR7JBXKc" + }, + { + "Q": "How many more proportion can we make from 2:4::3:6\nPlz answer. My answer is total 8 including ratio given above.", + "A": "Since a ratio is a fraction, we can create a infinite number of proportions from one ratio. Take any ratio, multiply its 2 parts by the same number and you will get an equivalent ratio. Since the 2 ratios are equal, you have a proportion. The number you select to multiply with can be any number. Since there are an infinite set of numbers, you can create an infinite set of ratios.", + "video_name": "qYjiVWwefto" + }, + { + "Q": "why in 3:55 the ecuation is equal to 1?", + "A": "try to compare with this simple numeric example 6 / 3 = 2 and then take 2 to other side dividing in the denominator and we have 6 / (3 * 2) = 1", + "video_name": "6YRGEsQWZzY" + }, + { + "Q": "At 3:49, why did he divide 2xvv' by the entire right hand side as opposed to subtracting v^2 from both sides?", + "A": "When solving a separable equation you don t want to have a term you are adding to the dy/dx (or in this case dv/dx) term. The problem is that it will make it harder to separate the variables but lets try: 2x dv/dx - v^2 = 1 2 dv/dx - v^2/x = 1/x 2 dv - ((v^2/x) dx) = 1/x dx So by creating an additional term on the left side of the equation you have a mix of terms and so you can t integrate.", + "video_name": "6YRGEsQWZzY" + }, + { + "Q": "Hi sal, at \"7:49\" you subtract the cx^3 to the left side of the equation. Wouldn't you have to divide that expression to the left side? I was confused.", + "A": "He brought the entire CX^3 term to the left side. Whereas in dividing, he would have to have left either the C or X^3 term on the right side. 1 + 2 = 3 -> 1 + 2 - 3 = 0 hope this helps!", + "video_name": "6YRGEsQWZzY" + }, + { + "Q": "At 6:56 couldn't he have taken everything as a power of e. to cancel the natural log. Or would it have become e^(ln(x) + C) which is the same as e^(ln(x))*e^c which is cx.\n\nSo it would be the same solution, so, nvm. Just figured that in the fly. Was my logic correct?", + "A": "Your logic is correct, I regualary use the approach you suggested in my Differential Equations class and the teachers does it too. I think Sal just took a different approach", + "video_name": "6YRGEsQWZzY" + }, + { + "Q": "At 3:33, how did Sal get 0.1 from the second equation?", + "A": "The -0.1 is part of the function. It was given as part of the problem definition. Sal didn t create it.", + "video_name": "GA_yxxeFYBU" + }, + { + "Q": "At 4:40 when Sal solves the integral and gets 2*ln|x-1|, can I just forget the absolute value of x-1 because of the logarithmic rules? it's the same like ln(x-1)^2 so my argument is always positive and therefore always valid for my ln. Or did I overlook something?", + "A": "Since you took the square out , you must put a modulus there as negative log isn t defined. But if the square is there, its always positive so no worries.", + "video_name": "5j81gyHn9i0" + }, + { + "Q": "Just before 2:31 you got 2*2*x*x*x**y and I did not understand how you got that because dont they factor out or something?", + "A": "That 2*2*x*x*x*y, or 4x^3y, is the greatest common factor of the two polynomials, and he factors it out of both of them.", + "video_name": "_sIuZHYrdWM" + }, + { + "Q": "say you have 6 peanut cookies and you have 6 friends two of your friends cannot eat nuts. So the ratio is 6:2 (thats how you write a ratio) Now say you baked six more cookies to give to 12 of your friends. For every 6 peanut cookies you have two friends. So what is the ratio if you have 12 cookies?", + "A": "Solving this problem is easier than it seems. The way I do it is that I turn the ratio into a fraction multiply the numerator and denominator by x (in your case,2) then turn it back into a fraction. 6:2 = 6/2 6 X 2 = 12 -------------------- 2 X 2 =4 12/4 = 12:4 By observing the diagram, we can tell the ratio is now 12:4. Hope This Helps!", + "video_name": "bIKmw0aTmYc" + }, + { + "Q": "at 2:05 how is 6/9 the same thing as 2/3?", + "A": "6/9 simplifies into 2/3", + "video_name": "bIKmw0aTmYc" + }, + { + "Q": "kate and nora each have a sum of money. the ratio of the amount of money Kate has to that of Nora is 3:5. After Nora gives $150 to Kate, the ratio of the money is 7:9. Find the sum of money Kate had initially?", + "A": "I think it goes like this Kate to Nora = 3:5 Kate to Total sum = 3:8 Kate+150 to Nora = 7:9 Kate+150 to Total sum = 7: 16 We want Kate initial sum to total moeny. 3/8 and 7/16 have different denominators and we need them the same. 3*2/8*2 = 6/16 Total sum = 150/(1/16) = $2400. Kates initial sum = 2400*(6/16) = $900", + "video_name": "bIKmw0aTmYc" + }, + { + "Q": "At about 1:09 shouldn't he have added fraction form?", + "A": "I think it is covered in the next video.", + "video_name": "bIKmw0aTmYc" + }, + { + "Q": "Why can\u00e2\u0080\u0099t there be another way to write a ratio, and can there be a negative ratio like -4:10", + "A": "Hello random stranger!! There are 3 different ways to write a ratio. Ex: 2:4 2/4 2 to 4 Hope that helps random stranger! XD", + "video_name": "bIKmw0aTmYc" + }, + { + "Q": "Ratio of boys to girls is 3:4 if 252 students attends how many are boys", + "A": "SInce ratios are the same thing as fractions, if the ratio of the boys to girls is 3:4, that means 3/7 children are boys. Therefor, you would have to find 1/7 of 252 (or 36). Then, since 3/7 children are boys, you multiply 1/7x3, or 36+36+36=108. Finally, your answer is 108 boys.", + "video_name": "bIKmw0aTmYc" + }, + { + "Q": "at 9:46 how is it that you can compare the matrices\n[a] and [b]\n[c] ___ [d]\nto the fractions a/c=b/d ??? I thought matrices were used to notate vectors, not ratios....", + "A": "We are looking at the situation where the determinant is 0. So ad - bc =0 and thus ad = bc ad/cd = bc/cd a/c = b/d", + "video_name": "UqyN7-tRS00" + }, + { + "Q": "At 0:53, he writes: zero to the second power, is 1*0*0. Why would this equation be 1*0*0? Since any number times one is that number, what would be the difference between 1*0*0 and 0*0? And where did the one come in anyway? Wouldn't zero to the second power just be written as 0*0? Maybe i'm just missing something. Thanks!\n\nLorenzo, age 9", + "A": "I m not exactly sure why he put a one there either. I think it s out of habit from other videos he s done, when taking the powers of non-zero numbers. I think one example is proving that any non-zero number is 1, like this: 5^2 = 1*5*5 5^1 = 1*5 5^0 = 1 His putting a one in front of the equation probably came from that. Perhaps someone might use that to prove that 0^0 is also one if that s his opinion.", + "video_name": "PwDnpb_ZJvc" + }, + { + "Q": "at 2:15 why so many zero and why is he talking about stuff we havent even learned yet", + "A": "Different schools go at different paces and introduce things in different orders. Now expand that idea to all the schools in your country and then expand it again to all the schools in the world. It s not possible to make a website that exactly matches every school and every teacher.", + "video_name": "PwDnpb_ZJvc" + }, + { + "Q": "Wait... at 0:43 Sal says that 0 to the first power is 0*1, but I thought it was 0*0, can anyone explain why? Thanks!", + "A": "Ah, 0^1 = 0 and 0^0 is undefined. Does that help?", + "video_name": "PwDnpb_ZJvc" + }, + { + "Q": "At 1:46 Sal says that this property extends to negative exponents as well. But 0^-1 power would be 1/0^1 = 1/0 which is undefined right?", + "A": "Yes you are correct. By definition, a negative exponent implies a reciprocal. That is, any number, x^(-1) is equivalent to 1/x.", + "video_name": "PwDnpb_ZJvc" + }, + { + "Q": "Why can he switch natural logarithm with the limit at 6:24 ? He explained it but it didn't really convince me. My textbook doesn't seem to mention anything about that kind of limit rule.", + "A": "Think about how we approach analyzing composite functions. For example, if I am looking at the lim as x --> \u00e2\u0088\u009e for sin(1/x), analyzing the sin part of the function doesn t really matter until I determine the behavior of 1/x as x --> \u00e2\u0088\u009e. Therefore, I can rewrite the limit as sin (lim as x --> \u00e2\u0088\u009e of 1/x) and this will not change the answer. Try it and see for yourself.", + "video_name": "3nQejB-XPoY" + }, + { + "Q": "At 3:25, why did Sal use the substitution. I don't get how he just defines delta(x) / x equal to 1/n.\nDid I miss something from the previous video? (I just started watching from this video)\n\nPlease help.", + "A": "Because n hasn t appeared anywhere in any equations we are free to use it how we like. we re just making the equation look different to make it easier to recognize what s going on. Sorry if my answer doesn t help.", + "video_name": "3nQejB-XPoY" + }, + { + "Q": "at 2:54, why did sal write 8? wasn't it 7?", + "A": "No it is f(7) = 8, so at x = 7, y reaches it maximum height of 8. Range has to do with possible ys.", + "video_name": "sXP7VhU1gYE" + }, + { + "Q": "At 2:13, he says that the formula is clean, what does he mean by that?", + "A": "When he says that the formula of the volume of the cone is clean, he means that the cone is EXACTLY 1/3 of the volume of a cylinder. As you can see in the video, the volume of a cylinder is h(pi)*r^2, and the area of a cylinder is exactly 1/3 of that, which is known as 1/3*h(pi)*r^2. So when he says clean, he means that the volume of a cylinder is exactly 1/3 the volume of a cone.", + "video_name": "hC6zx9WAiC4" + }, + { + "Q": "Why is f(x,y)=p(x,y)i+q(x,y)j a function of 't' as Sal mentions around @15:28", + "A": "Well, f(x,y) is a function of x and y. But if we re following the path defined by r(t) = x(t)i + y(t)j then our x and y are themselves just functions of t, so f(x,y) becomes f(x(t),y(t)), in short it depends completely on t (though indirectly through x(t) and y(t)). I.e. f(x(t),y(t)) becomes f(t).", + "video_name": "t3cJYNdQLYg" + }, + { + "Q": "5:48\nhow does variable summation applies to 1", + "A": "There are a few ways to think about it. One is, when i is 1, then 1 is still 1. When i is 2, then 1 is still 1 right? When i is some number k, then 1 is still 1. When i is N, 1 is still one. So when you sum along the index i, 1 is simply added to itself again and again N times. So the answer is N. The other way to think about it, which is essentially the same is this. Since i is never 0, we can rewrite 1 as i/i. Then Sum(1)=Sum(i/i)=1/1+2/2+3/3+...+(n-2)/(n-2)+(n-1)/(n-1)+n/n=1+1+1+...+1+1+1=N.", + "video_name": "sRVGcYGjUk8" + }, + { + "Q": "Around 3:30 Sal references the Calculus playlist--I'm not even CLOSE to that playlist yet. Am I watching these videos too soon? It seems like the Statistics playlist is showing up really early on my practice map and I may not have the skills to successfully accomplish the unit. Do you think this could be true? I did okay up through standard deviation, but z-scores, empirical rule and some references are throwing me off!", + "A": "This is like a side tour, sightseeing in a cool neighborhood. You don t need to move into the calculus house to work in statistics. For example, I think the formula for the Standard Deviation of a uniform distribution is (b-a)/sqrt(12). I wanted to know, Why 12? I asked Doctor Math and he (Doctor Anthony) gave me an explanation that I (frankly) didn t understand, but trust. I don t need to know where the 12 came from to use the formula, but I find it comforting to know that someone knows.", + "video_name": "sRVGcYGjUk8" + }, + { + "Q": "At 2:05 Sal says that the line he just drew was called a transversal, because it transversed across the other two lines. But what does it mean to transverse?", + "A": "To transverse means to intercept.", + "video_name": "H-E5rlpCVu4" + }, + { + "Q": "At 5:00, if we were given the measure of the yellow angle in the second diagram, could we find out what the measure of the green angle was? If so, how?", + "A": "No, you would not. Since the two angles exist on different lines, and the lines are not parallel, then there is no way to know for certain if the angles would compliment each other or not.", + "video_name": "H-E5rlpCVu4" + }, + { + "Q": "Hi friends :-) I have a question for you-\n1> at 6:27 \"Sal\" proved us that alternate interior angles are equal , right? so, here is my question ?\nwe know that :- b=c,f=g\nnow b and c are vertical angles and we also know that b = f (corresponding angle) so why can't we say that c = f ,right? and why not alternate exterior angles?", + "A": "Ok, so you said b=c,f=g. Which says b=c and f=g. If you look back at Sals blackboard on the video there is no comma, it simply says b=c=f=g which means they are ALL equal, so yes , c does equal f and c equals g, and b equals g etc. etc.. As for alternate exterior angles, the same rule applies. a=d=e=h. They are all equal.", + "video_name": "H-E5rlpCVu4" + }, + { + "Q": "At 3:11 Sal says that lim kf(x) = K*limf(x)\nx-->c x-->c\nshouldn't it be equal to lim k * limf(x)\nx-->c x-->c", + "A": "At 3:11 if one takes lim k, one will just get K because it is not a function, so one could put it as a function as g(x)=K, but then it would always return K and it would always approach K no matter where you get your limit. so instead of taking lim K, you just use K because K is the limit of K. This is because it is a constant, not a variable. so for example, 2f(2) where f(x)=2x will get you 2(2*2) which is 2*4 which is 8. Hope that made sense.", + "video_name": "lSwsAFgWqR8" + }, + { + "Q": "At 2:44 How do I solve this question?\n\n(3r^3-19r^2+27r+4) / (r-4)", + "A": "3r^2+31r-87-344/r-4", + "video_name": "UquFdMg6Z_U" + }, + { + "Q": "It took me a minute to figure this out, but I wanted to check if I am right. At 4:30, the +1 -2/3x can not be simplified because it can also be stated as + 1x^0 - 2/3x^-1, which makes the x terms different. Is this correct?", + "A": "You are correct. 1 is a constant term (x^0) and is not a like term with (2/3)x^(-1).", + "video_name": "UquFdMg6Z_U" + }, + { + "Q": "1:47 why did you add -4x on that side? Not as in addition but you rewrote it as a subtraction sentence using -4x . -8 doesn't have a coefficient so why did Sal do that? I thought it was X minus X or X plus X. Really Confused Here !", + "A": "In order to graph an equation, it is easiest if it is in y=mx+b form. Therefore you want y alone on the left. Since the 4x is hanging out with the 2y, by subtracting it to both sides it helps get y all by itself.", + "video_name": "V6Xynlqc_tc" + }, + { + "Q": "At 2:50 Sal says that the point at beginning of the interval is a relative maximum point. How do we know that to be true when the points on both sides of the point in question have to have a y-coordinate equal to or less than it, but then everything to the left of the point Sal was referring to was undefined?", + "A": "Well, that means that there is nothing to the left so it only needs to worry about the existing or defined parts of the graph.", + "video_name": "zXyQI4lD4wI" + }, + { + "Q": "At 02:52, Sal says that the point (3,-8) would be a relative maximum point but how is that possible? The function is only till -8. How can we assume that the function will have the greatest value considering the points around it? I hope I made my question clear.", + "A": "Sal told us at the beginning of the video that the domain was closed, that is, it included the end points. The domain is [-8,6]. On this particular graph, if we start at x=-8, and move towards the right on the x axis, the next immediate f(x) is less than it was at x=-8. Because we are on a closed interval, that makes the point (-8, 3) a relative maximum. (Make sure you put your x coordinate first when referring to a point on a graph\u00f0\u009f\u0098\u008a.)", + "video_name": "zXyQI4lD4wI" + }, + { + "Q": "At 4:06, wouldn't 6/13 plus 6/13 be equal to 12/13? How does it add to zero?", + "A": "The term in the original equation was MINUS 6/13. Sal then added POSITIVE 6/13 to both sides. That s where the zero came from. When combining terms (or numbers) in algebra, you always have to take note of the sign as well as the numerical amount.", + "video_name": "XD-FDGdWnR8" + }, + { + "Q": "at 4:45 is Sal writing (e^ln2)^u or (e)^ln2*u? I mean e^ln2 equals 2 and 2 is raised to the power u...so why should it be the latter and not the former?", + "A": "if you remember your logarithmic rules, you will know that log(x^y) = y*log(x)", + "video_name": "C5Lbjbyr1t4" + }, + { + "Q": "At 6:01 we have,\n\n= exp [u*ln(2)] / ln(2) + C\n\nWhy can't we substitute u=ln(x) now and use ln(x)ln(2)=ln(x+2) ? i.e.,\n\n= exp [ln(x+2)] / ln(2) + C\n= (x+2) / ln(2) + C\nCan anyone see what I'm doing wrong?", + "A": "You ve confused the property a little bit; ln(x)*ln(2) is not equal to ln(x+2). Rather, ln(x) + ln(2) = ln(2*x), and ln(x)*ln(2) = ln(2^(ln(x))). Hope that helps.", + "video_name": "C5Lbjbyr1t4" + }, + { + "Q": "At 5:00, why does the integral of e^(au) become 1/a * e^(au)? Where did the 1/a come from? Thanks!", + "A": "The chain rule, I presume would be the answer, since the expression uses a function of a function ( the thing you wrote up). Hope that helps :)", + "video_name": "C5Lbjbyr1t4" + }, + { + "Q": "at 0:42,what does reciprical mean?", + "A": "The reciprocal of a fraction is simply the fraction flipped over. For example, the reciprocal of 6/9 is 9/6.", + "video_name": "yb7lVnY_VCY" + }, + { + "Q": "1:15 what does he mean", + "A": "He means that if the weekend was a square split into 20 parts, one of those parts would be spent studying for a single subject (math, science, english, history, etc)", + "video_name": "yb7lVnY_VCY" + }, + { + "Q": "At 2:07, why do you have to do:\n(4y^2 -6y) + (10y - 15)\ninstead of\n(4y^2 +10y) + (-6y - 15) <-- it's clearly not the same thing right?\n\nThanks", + "A": "Either way works as long as you can factor it, as both expressions are equivalent. One factors to 2y(2y-3) + 5(2y-3) = (2y+5)(2y-3) The other equals 2y(2y+5) - 3(2y +5) = (2y+5)(2y-3) Hope this helps!", + "video_name": "u1SAo2GiX8A" + }, + { + "Q": "(9:40 p.m.) Please help me with this problem. I've been out of school for years and I'm preparing the the GMAT. x^2 - 4x + 4 > or = 0", + "A": "Factor it as (x-2)^2, and then you find that it s 0 when x is 2. So you test on either side of 2 to find what the sign will be. If you plug in 1 it s positive, and when you plug in 3 it s positive, so your solutions are all real numbers.", + "video_name": "u1SAo2GiX8A" + }, + { + "Q": "In 4:21 how did he get the m to ?(at 5:13)", + "A": "I use a simple example whenever I can. Say 10>0. If you change the sign on 10, then -10<0. The same exact change happens if there are multiple numbers, as long as you change all of the signs. BTW, if you have numbers on both sides of inequality, say, 10>9, you just change signs on both sides and flip the arrow. -10<-9. Hope this helps.", + "video_name": "xdiBjypYFRQ" + }, + { + "Q": "Hi,\n\nwhen sal took any vector from the original subset V and multiplied it with a vector from the \"orthogonal complement\" subspace at 10:05 , he found that their dot product was equal to 0.\nHow can we be sure that this is the case? I mean, the orthogonal subspace is supposed to have the vectors that are orthogonal to a specific subspace of vectors, not to any in V. I hope I made my question clear...", + "A": "thats the definition of an orthogonal complement... the z axis is the orthogonal complement of the xy plane in a 3 dimensional space. obviously, any vector on the z axis will be orthogonal to vectors in the xy plane, even though the xy plane is a 2 dimensional subspace.", + "video_name": "zlI8mx8Hc8o" + }, + { + "Q": "At 4:04 why is the x negative?", + "A": "The x is negative because after going down 4 for the change in y (negative 4), you have to go six to the left to meet up with the line again, (negative six). Going up is positive, going right is positive, left and down are negative.", + "video_name": "R948Tsyq4vA" + }, + { + "Q": "At about 4:10. Why do the negatives cancel out. Because wouldn't it be -4/6??", + "A": "Review your sign rules. A negative divided by a negative = a positive. So, -4 / (-6) = +4/6", + "video_name": "R948Tsyq4vA" + }, + { + "Q": "at 3:38 how does he get negative change in y? I get why the x is cause he's moving in the opposite direction but the change in y seems the same as the first example at 2:10. why is it different?", + "A": "In the first example, he was going from a lower point to a higher point, so there was a positive change in y. In the second example, he is going from a higher point to a lower point, so the y is going down. There is a negative change in y. Another way to think about it is this: The y value is going from 1 at the starting point to -3 at the ending point. You get from 1 to -3 by subtracting 4, so the change in y is -4.", + "video_name": "R948Tsyq4vA" + }, + { + "Q": "At 2:20 Sal says that the slope is 2/3. I am kinda confused about how you would draw that line using the information found out? Can someone please help me?", + "A": "Okay, using the information Sal mentioned at 2:33 in the video you can t draw a line on a graph. This is because the equation of any linear line on a Cartesian plane can be delfined by the formula y=mx+b. Since we know that m, or the slope equals 2/3 we can add it in the equation. Without any point known on the line, though, we can t solve the equation because any point s coordinates could be plugged into the equation along with the slope to solve for b. Therefore the line is undefined. Hope this helps!", + "video_name": "R948Tsyq4vA" + }, + { + "Q": "at 0:55 when you are talking about the starting point, what if a certain graph/problem does not give you a certain starting point. Would you start at (0,0)", + "A": "A problem would not be worded like that, it would be more clear.", + "video_name": "R948Tsyq4vA" + }, + { + "Q": "2:28 How the heck did he get a NEGATIVE 32?! What made it negative???? That concept has never been explained to me before!", + "A": "because he multiply 8 * (-4) :) if you have 8(3x - 4), youll have 8 *(3x) + 8*(-4) and this is 24x + (-32), which is basically 24x - 32 :) in this case you have 8(3/8 x - 4 ) so you are left with 3x - 32", + "video_name": "PL9UYj2awDc" + }, + { + "Q": "at 2:06 how do you go from 1 to 3", + "A": "I think Sal is trying to show you that the slope remains constant across the entire line. He started with 2/1 Then, he picked another 2 points and the slope was 6/3. You need to recognize that these are = values. If reduce / divide 6/3, you get 2/1. Same slope. He could have gone up 10 and to the right 5. he would still be on the line. Slope would be: 10/5, which still = 2/1. Hope this helps. Hope that helps.", + "video_name": "MeU-KzdCBps" + }, + { + "Q": "After looking at 5:08, does that mean the slope of a graph basically is a rate of change in a table and graph? In a nutshell, the rate of change and the slope of a graph is the same, right?", + "A": "Yes you are correct. Adding on to that, it can really be applied to Physics. For example, if you found the slope for a velocity over time graph, you get the velocity. See, isnt that cool? like how everything is connected in this universe.", + "video_name": "MeU-KzdCBps" + }, + { + "Q": "2:00 What if the line is not strait so the slope cannot only have one number?", + "A": "Good question, you re getting a bit ahead of yourself though. There are other types of equations that will describe curved lines.", + "video_name": "MeU-KzdCBps" + }, + { + "Q": "What does Sal mean at 3:30 when he says \"Let's see if we can break down 115 any further\"? What method does he use, and how does it work?", + "A": "He is literally trying to factorize or break down 115 as much as possible.The method he has showed you is prime factorization . In this you find 2 numbers that when multiplied give you a certain result. you keep doing this until you only have prime numbers.It can also be called a factor tree.", + "video_name": "O64YFlX1_aI" + }, + { + "Q": "At 1:44 how is it a ray without a arrow on the other end?", + "A": "Think of it with everyday things. Take for example sun rays. they go in one direction until they hit an object (us, the atmosphere or a mirror ect.). Do they have arrows? As long as one line looks like it is going to continue on and on, they it should be considered a ray.", + "video_name": "DkZnevdbf0A" + }, + { + "Q": "at 5:28 , I dont understand why Sal put +(-14). it is so confusing.", + "A": "He meant 6 plus negative 14, which is 6 minus 14. Hopefully this helped you.", + "video_name": "-4bTgmmWI9k" + }, + { + "Q": "what is a checker board pattern? Sal mentions it at 0:20", + "A": "A checkerboard pattern is when every other square is black or white both in the horizontal and vertical directions. With numbers instead of colors, it could look like this: 1 0 1 0 1 0 1 0 1", + "video_name": "u00I3MCrspU" + }, + { + "Q": "I don't understand the intersect stuff @2:52. Is there a video that talks about this? Or could someone explain it for me? Thx :)", + "A": "What don t you understand about it", + "video_name": "VTlvg4wJ1X0" + }, + { + "Q": "4:14, Shouldn't it be the first n+1 squares since we're starting at 0 or do most people start at 1 so it's the first n squares? If the latter, why is Sal starting at 0?", + "A": "I think he started at 0 to eliminate the D term (in the previous video). Our Sigma in this starts at 0, also, so he had to start at 0 to evaluate the formula.", + "video_name": "MkGXR8umLco" + }, + { + "Q": "Okay at 2:13 on question 4 he says Z is 1 but then he says that Z is over 4. I'm really confused about that how can he say one thing but it mean another?", + "A": "The equation is 1/4 * Z So to solve you do: 1/4 * Z/1 (remember Z/1 is still equal to Z) Then you multiply across, first the two numerators (1*Z which equals 1Z or Z) then the two denominators (4*1 which equals 4) And your final answer is Z/4", + "video_name": "aoXUWSwiDzE" + }, + { + "Q": "@ 4:45, Sal skips from question 6 to question 10.\nCould he possibly either do a re upload where he does all the questions, or maybe someone provide the answers to the rest of the questions so that those who are working directly from the sheet can see if their workings are correct.", + "A": "He is not trying to answer all the questions. The whole point of these videos is to help you understand the concepts. The only reason you could think these videos are not doing their jobs is if, even after you watch the video, you are confused on the topic. If that is true, you might want to try talking to a teacher or parent to help you delve further into the topic. After all, they probably know different ways to help you learn. Not everyone is a visual learner and learns through videos.", + "video_name": "aoXUWSwiDzE" + }, + { + "Q": "From 15:32 to 15:43, Sal mentions his wife being a doctor, and if people don't see the decimal point they'll overdose on medication. What does he mean by that?", + "A": "If you are suppose to give a patient 3.2 mg of some medicine And, instead you lose the decimal point and give them 32mg of medicine. You will have given your patient 10 times the amount of medicine they should have. Depending on the medicine, this can have drastic consequences.", + "video_name": "trdbaV4TaAo" + }, + { + "Q": "In 6:22, how does it have 23 zeros? 602200000000000000000000 (phew) only has 21 zeros.", + "A": "He was saying 23 digits after the 6.", + "video_name": "trdbaV4TaAo" + }, + { + "Q": "In the video, at 11:10, Sal said that scientific notation can be used to express any number in an easier way. Does that imply fractions and integers too? Or is it only natural numbers?", + "A": "I m really not sure. I think so, but I don t think that includes repeating decimals. I m somewhat new to scientific notation too.", + "video_name": "trdbaV4TaAo" + }, + { + "Q": "at 8:04 Avogadro's number is written as 6.022 x 10^23 but shouldn't it be 6.022 x 10^20 because there is 20 zeroes after the 6022?", + "A": "Everything is fine in the video, notice that there is a dot between 6 and 0. Of course 6.022x 10^23 = 6022x 10^20, but 6022x 10^20 is not a scientific notation, because scientific notation is a number that is at least 1 and less than 10 multiplied by a power of 10.", + "video_name": "trdbaV4TaAo" + }, + { + "Q": "At 2:00 Sal says Avogadro's number has \" 6 followed by the 23 digits or the 6022 followed by 20 zeros\". Then at 7:15 we multiply 6*10^23, that is 6 followed by 23 digits. At 8:01 we do 6.022*10^23. My question is why does he multiply it by the power of 23 ? Isn't the answer now have 6 and 26 digits now?", + "A": "In both cases, the leading digit before the decimal point is just the 6 . In 6.022 , the other 3 values are to the right of the decimal point. The 10^23 moves the decimal point from where it is currently located in the number. Another way to compare them... You originally stated 6022 followed by 20 zeroes. In this situation, the decimal point is at the end of 6022. To get to 6.022 we only moved the decimal 3 places. So, we need 20+3 = 23 as our exponent. Hope this makes sense.", + "video_name": "trdbaV4TaAo" + }, + { + "Q": "So, for clarification, scientific notation is an easier way to write 12,000,000,000,000. So how do you know where to put the decimal place in, say, 6,510,000,000,000? Is there a way to know? I'm sorry if its in the video, I'm only at 3:46.", + "A": "The scientific notation formal format is x*10^y, where 1 <= x < 10 and y is an integer. In other words, when writing in scientific notation, the number you multiply the power of ten must be between 1 (included) and 10. Here are the numbers you suggested as an example: 12,000,000,000,000 = 1.2*10^13 6,510,000,000,000 = 6.51*10^12", + "video_name": "trdbaV4TaAo" + }, + { + "Q": "I don't get problem 13 at 8:31\nCan anyone help me?", + "A": "For the 2 triangles to be similar the corresponding angles all have to have congruent measurements. For obvious reasons, angle DBE is the same on both tri. For the other 2 corresponding angles to be proven to be congruent, the 2 sides AC and DE must be parallel to eachother. This is true because the transversal of line AB would make the 2 corresponding angles of the triangle congruent ecause of the corresponding angles of the transversal are these angles. This is true for the other transversal as well.", + "video_name": "bWTtHKSEcdI" + }, + { + "Q": "weren't all the sides on the paralellogram on 10:34 the same?", + "A": "There are four paralellograms: Rhombus, Rhomboid, Rectangle, and a Square. The square is the only paralellogram must have four equal sides. While a Rhombus can have 4 equal lengths, for this problem, it is not a given that this is the case. We are looking for proof only that triangles inside the paralellogram are congruent. The answer to your question is the angles could be the same, either way, you should be able to get the right answer even if they were not.", + "video_name": "bWTtHKSEcdI" + }, + { + "Q": "At 5:40, Sal says that if you have two sides and an angle, you can figure everything else out. The problem here is that SSA Congruence is NOT a valid congruence. SSA Congruence includes two sides and an angle. This is because you most likely end up with two solutions for the third side. Does he mean that if you are given two sides and an angle and the angle is between the sides, then you could find everything else?", + "A": "I think when you have a SSA triangle you would just list both possible answers. Like if you were asked to find side C of an SSA triangle you say C=x or C=y", + "video_name": "VjmFKle7xIw" + }, + { + "Q": "At 2:50, how did you get 1/4?", + "A": "1/2 divided by 2 = 1/4 he got the 1/2 because sin 30 = 1/2", + "video_name": "VjmFKle7xIw" + }, + { + "Q": "At around 4:30, why do you need to take the reciprocal of both sides to solve the law of sines?", + "A": "The goal was to isolate the variable. There are several ways of accomplishing this, but since the variable was in the denominator, taking the reciprocal of both sides seemed a useful choice.", + "video_name": "VjmFKle7xIw" + }, + { + "Q": "at 12:16 why does Sal evaluate one of the Sin(t)'s at Pi all of a sudden (instead of Pi/2)? I got for that problem:\n2Pi + 2 and sal has 4 + 2Pi. Is this a mistake?", + "A": "The second expression with a sine was sin(2t), which, evaluated at pi/2, is sin(2pi/2)=sin(pi)=0", + "video_name": "wyTjyQMVvc4" + }, + { + "Q": "Wouldn't it be 1/2 +pi^2/8? if not, what happened to the +1 at 10:23 ?could someone please help, because I don't understand where that 1 went.", + "A": "The 1 was multiplied by the sin(t)*cos(t) function inside the integral. The square root of negative sine squared plus cosine squared is one.", + "video_name": "uXjQ8yc9Pdg" + }, + { + "Q": "At 1:37 why would it be mm squared?", + "A": "when you do an area it is always in mm squared or square mm (or whatever measurement it is in. This is because it would take that many 1mm x 1mm squares to fill up the area of the circle. don t forget a circle is a 2D shape, i may not have used candy for an example on area but just pretend it s the circle bit on one side of the candy lol", + "video_name": "ZyOhRgnFmIY" + }, + { + "Q": "At 2:47\nDo you get the same anwser if you do 3.14 times R and just add the second power?", + "A": "Not quite. Because of PEMDAS, you square R, then multiply that by pi, or 3.14. Squaring 3.14r would get a completely different answer.", + "video_name": "ZyOhRgnFmIY" + }, + { + "Q": "At 1:30, why does Sal say that the answer is still squared, after already squaring the radius?", + "A": "the units are squared, not re-squaring the numbers. Areas are always in square units, Volumes are in cubed units.", + "video_name": "ZyOhRgnFmIY" + }, + { + "Q": "At 1:53, why after you have squared 8 (64) do you still leave it squared?", + "A": "Because the equation to find the area of a circle is \u00cf\u0080 r2. Therefore to find the area you have to have the radius squared and then you multiply it by \u00cf\u0080. So when you square 8 you get 64 and to find the area you multiply it by \u00cf\u0080 ( \u00cf\u0080 r2 ). He leaves 64 that way because its r2 ( 8*8 ). \u00cf\u0080*64=Area. Hope you got your question answered !!", + "video_name": "ZyOhRgnFmIY" + }, + { + "Q": "@ 1:18 how did he get 64 mm from 8 mm", + "A": "he found the square root of the radius of the circle", + "video_name": "ZyOhRgnFmIY" + }, + { + "Q": "2:59 doesnt he mean to say millimeters sq?", + "A": "You can say square millimeters or millimeters squared. Either is correct.", + "video_name": "ZyOhRgnFmIY" + }, + { + "Q": "Starting from 0:45, why do we do \"radius^2\", or to be more specific, why \"^2\" to come to the conclusion of the area? any explanation of this somewhere?", + "A": "It comes from a higher branch of mathematics called calculus, which is really good at deriving formulae for areas of shapes. When you try it for a circle, the r^2 pops out of the formula.", + "video_name": "ZyOhRgnFmIY" + }, + { + "Q": "at 1:35 how does prime factorization work?", + "A": "prime factorization is making a number as small as it can by only using prime numbers", + "video_name": "DKh16Th8x6o" + }, + { + "Q": "When you're drawing a vector with given points (for example, (1,2) for vector v @ 12:57), how do you know what direction the vector is going in? Sal keeps drawing the vector going up but why can't it go down?", + "A": "One Can Draw A Vector In Two Cases. 1)A Point Through Which The Vector Passes And Its Inclination(Angle)With Respect To Any Of The Co-ordinate Axes Are Known Or 2)Minimum Of Two Points Are Known Through Which The Vector Passes. One Can Draw A Vector Through A Single Point In Arbitrary Direction Only.", + "video_name": "r4bH66vYjss" + }, + { + "Q": "At 19:40, it is said that \"2x -y -z +3x\" must be equal to 0 in order for b to be valid.\nIsn't it that we have then:\nif b is valid => 5x -y -z = 0\n(i.e. not yet \"<=>\". Necessary condition only).\nThen b is in the plan of equation 5x -y -z = 0, in other words:\n\"the plan of equation 5x -y -z = 0\" is included in C(A). Finally, as C(A) is a plan (dim C(A) = 2), then C(A) = \"the plan of equation 5x -y -z = 0\". (now we have \"<=>\" . b is valid <=> 5x -y -z = 0 )", + "A": "He states Ax = b at 14:00 ish, and asks what are all the possible b s, which form C(A). So if you find out that Ax forms a plane, that equality gives you equivalence .. Ax forms a plane <=> All the b s form a plane, because LHS = RHS (or in other words the validity of b is given). At least that s how I d interpret it.", + "video_name": "EGNlXtjYABw" + }, + { + "Q": "I'm so confused.. at about 11:00 Sal decided to factor out 27\u00c2\u00b712x^2 - 4x^6 = 0 to 4x^2(27\u00c2\u00b73-x^4) = 0 .. When I was doing it on my own I multiplied the constants and got 324x^2-4x^6 = 0, factoring out to 4x^2(324-x^4) = 0... Is this an example of where BEDMAS is really important?", + "A": "You forgot to divide the 324 in your final equation by 4. :-)", + "video_name": "zC_dTaEY2AY" + }, + { + "Q": "I think at 19:00 the way this notation is formed is as x --> 3(neg. side)\nThe arrow meaning approaching 3 from the negative side.", + "A": "Hay Bennet! Join us as a life-long learner! We can use guys like you in KA. It s been a year since you ve asked this question, & I haven t seen you around since! Miss you around! :)", + "video_name": "zC_dTaEY2AY" + }, + { + "Q": "At 3:41, I thought that you put dots over the top of repeating decimals. Can you do both?", + "A": "Some students learn to write repeating decimals by putting dots over the repeating numbers, but in this case Sal puts a line over the repeating numbers. However If you want to use Sal s method you can but if you were taught to put dots, its better you do that and yes, you CAN use both lines or dots for your answer. Hope that helped !!", + "video_name": "Y2-tz27nKoQ" + }, + { + "Q": "At 1:50 he says that [sq rt]of 3x3x13 = [sq rt] of 3x3x[sq rt] of 13......Why does x13 = [sq rt] of 13? What did I miss?", + "A": "Basically Sal is saying sqrt(3*3*13). Both 3s and the 13 are under the square root symbol. What he is doing is taking out the sqrt(13) , so that sqrt(3*3*13)=sqrt(3*3)*sqrt(13) I hope this helps you.", + "video_name": "cw3mp8oNASk" + }, + { + "Q": "0:42, 3 doesn't go into 11 3 times. or am i missing something?", + "A": "You are missing something. Since 117 (if I add digits, they =9, so I know that it is divisible by three and 9). When he says 3 goes into 11 3 times, he then multiplies and subtracts (11-9) and drops down the remainder of 2 and divides 27 by 3", + "video_name": "cw3mp8oNASk" + }, + { + "Q": "Aight a question, Should i watch this after watching the exponent properties playlist?\nBecause im going in order and this one goes first, but sal says at 1:38, and we know this by our exponent properties.", + "A": "then by using Sal s advise watch the exponents video.", + "video_name": "cw3mp8oNASk" + }, + { + "Q": "Ask a question...I don't know why at 2:04 he crosses out the 3 ?!", + "A": "As he explained in the video, the square root of 3*3 is the same thing as saying the square root of 9. The square root of 9 is 3, so he simplified the square root of 3*3 that he had written down into just 3.", + "video_name": "cw3mp8oNASk" + }, + { + "Q": "At 1:55 it is explained that 5 sqrt 3*3 (also 5 sqrt 9) equals 15. Sal crosses out one of the 3's and writes a little 3 above the radical. Could someone explain this to me or lead me to a video explaining it?", + "A": "He is just using the basic definition of a square root. Square roots reverse the process of squaring a number. 3^2 = 9 So, sqrt(9) = 3 If you don t understand this concept, you need to go back to the videos that introduce square roots. Use the search bar and search for introduction to square roots to find the video.", + "video_name": "cw3mp8oNASk" + }, + { + "Q": "Which video (and where) explains why you can add up the digits of a number to see if it's divisible by 3 like at 0:25 - 0:36?", + "A": "go to pre- algabra and in the factors and multiples section you will find divisablity tests at the top of the list and it explains the rule for 3 in the first video", + "video_name": "cw3mp8oNASk" + }, + { + "Q": "at 1:48 sal splits the square root.why?", + "A": "He does show to show you that the sqrt(3*3)=3 so that can be taking out of the entire radical.", + "video_name": "cw3mp8oNASk" + }, + { + "Q": "At 0:09, Sal said that 117 is not a perfect square. What does that mean?", + "A": "It means that a any number times itself won t equal 117", + "video_name": "cw3mp8oNASk" + }, + { + "Q": "At hte first why did you pick x how do you know that was x 2:35", + "A": "He did not know that it was x (which isn t a number anyway). He just picked x as a variable or as a placeholder for an unknown value. He could have put in T, Delta or Cow, and the results would be the same in the end. The variables would just have wonky names, so he picked x, which sounds sensible.", + "video_name": "1uWZNW5PF-s" + }, + { + "Q": "At 6:13, Sal got 2 differant answers for 2 sides of a square. How did he get the 2 answers?", + "A": "To get the dimension on the left side of the large rectangle, he added the lengths of a side of each square on the left. To get the dimension on the right side of the large rectangle, he added the lengths of a side of each square on the right. Since we know opposite sides of a rectangle have equal length, we can set up an equation (13x+7y=8x+9y) to solve for the ratio of x to y (x=2/5*y).", + "video_name": "1uWZNW5PF-s" + }, + { + "Q": "At 3:56 isn't it negative 3/2", + "A": "No: -6/-4 = 3/2 Those minus signs cancel He plugs -2 into 6(x+1)/(x-2) = -6/-4 = 3/2 looks correct", + "video_name": "oUgDaEwMbiU" + }, + { + "Q": "At 1:10, I don't get why do you start multiplying (-3x -2). It's getting me confused.", + "A": "If you have a variable, like X in a fraction, you usually want to get that variable isolated. So in order to get X by itself you have to multiply both sides by the denominator. When that happens, the side with the fraction has its denominator cancelled out, but what you do to one side, you must do to the other. So that is why he had to multiply both sides by (-3x-2). Hope this helped!!", + "video_name": "PPvd4X3Wv5I" + }, + { + "Q": "At 4:30, the distance formula is mentioned. what is the distance formula? And why is it the same thing as the Pythagorean Theorem? I thought they were two completely different formulas.", + "A": "The distance formula is a formula you can use to find the shortest distance between any 2 points on the coordinate plane. You are correct that the distance formula and Pythagorean theorem are 2 different things but the distance formula is derived from the Pythagorean theorem. The distance formula is: d = \u00e2\u0088\u009a[(({x_1} - {x_2})^(2)) + (({y_1} - {y_2})^(2))]", + "video_name": "iATjsfAX8yc" + }, + { + "Q": "7:10-end you ended up calculating the area of the circle at the start and not the rate of change (I think). r was a function of t, and if you think about the problem just generally thinking about it, the rate of change should not be linear b/c the formula for area is quadratic. In fact, now that I am looking back, I think that this is because you solved for circumference rather than area.", + "A": "A = pi\u00e2\u0080\u00a2r^2 d/dt(A) = d/dt(pi\u00e2\u0080\u00a2r^2) d/dt(A) = pi\u00e2\u0080\u00a2d/dt(r^2) d/dt(A) = 2\u00e2\u0080\u00a2pi\u00e2\u0080\u00a2r\u00e2\u0080\u00a2d/dt(r) dA/dt = 2\u00e2\u0080\u00a2pi\u00e2\u0080\u00a2r\u00e2\u0080\u00a2dr/dt dr/dt = 1 r(0) = 3 dA/dt = 2\u00e2\u0080\u00a2pi\u00e2\u0080\u00a23\u00e2\u0080\u00a21 dA/dt = 6\u00e2\u0080\u00a2pi C = 2\u00e2\u0080\u00a2pi\u00e2\u0080\u00a2r d/dt(C) = d/dt(2\u00e2\u0080\u00a2pi\u00e2\u0080\u00a2r) d/dt(C) = 2\u00e2\u0080\u00a2pi\u00e2\u0080\u00a2d/dt(r) dC/dt = 2\u00e2\u0080\u00a2pi\u00e2\u0080\u00a2dr/dt dr/dt = 1 r(0) = 3 dC/dt = 2\u00e2\u0080\u00a23\u00e2\u0080\u00a21 dC/dt = 6", + "video_name": "kQF9pOqmS0U" + }, + { + "Q": "At 4:04: Why can you rewrite d/Dt [pi*r^2] as pi*d/dt [r(t)?", + "A": "Because pi is a constant, and you can do that with constants when you are taking derivatives.", + "video_name": "kQF9pOqmS0U" + }, + { + "Q": "at 1:36 why does sal multiply a/b with n/n and m/n with b/b", + "A": "I think he did it so he would have the same denominators for both fractions.", + "video_name": "HKUJkMQsGkM" + }, + { + "Q": "At 0:55 could b^1 also be b^0?", + "A": "Only if b = 1.", + "video_name": "X6zD3SoN3iY" + }, + { + "Q": "At 5:34, Sal says that the notation for the length/magnitude of a vector is notated by using double lines around the vector, like this.\n||a||\nCan somebody explain why we use this \"double absolute value\" notation to signify the magnitude of a vector?", + "A": "Well, maybe just as a convention sort of .Someone kept that symbol and maybe we are using it.", + "video_name": "WNuIhXo39_k" + }, + { + "Q": "when he means the length of vector.. does he mean the magnitude of the vector. is it another word for magnitude or is it completely different things. please explain... thanks (4:44 min)", + "A": "i think it s exactly the same thing", + "video_name": "WNuIhXo39_k" + }, + { + "Q": "1:58 Why is 3+5i a complex \"number\"?\nIt consists of 2 numbers... Real and Imaginary.\nCouldn't it be called \"complex numbers\"?", + "A": "Z is the complex number, comprised of a Real Part (5) and an Imaginary Part (3i).", + "video_name": "SP-YJe7Vldo" + }, + { + "Q": "at 3:18 why do we choose y-axis as imaginary and x-axis as real part ,is there any proof for it??", + "A": "It s just a natural representation. The key point here is that the imaginary axis and the real axis must be perpendicular to each other. Imagine rotating your graph by 90 degrees, now the imaginary axis is the horizontal one.", + "video_name": "SP-YJe7Vldo" + }, + { + "Q": "As discussed in 0:57, you divide the numerator and the denominator by the same number. However, for 30/45 and 54/81, do they both have to be divided by 5?", + "A": "No. You see, you could factor out 5 ONLY from 30/45, since both 54 and 81 are not divisible by 5( 54/5=10.8, and 81/5=16.2). You then get 6/9. 3 is divisible by both 6 and 9.You get 2/3. This is can no longer be factored. Now, for 54/81, you see automatically (if you know you re times tables) that 54 and 81 are divisible by 9. You get 6/9.Like 30/45, you see that the numerator and denominator are divisible by 3.You get 2/3. 54/81 and 30/45 are equivalent. I hope this helped.", + "video_name": "Io9i1JkKgN4" + }, + { + "Q": "which formula is used here Square root at 6:00", + "A": "the distance formula (:", + "video_name": "GiGLhXFBtRg" + }, + { + "Q": "At 3:59, why is Sal using 3 coordinates? Its only the supposed to be x and y correct?", + "A": "its a triangle so he has to use three points", + "video_name": "GiGLhXFBtRg" + }, + { + "Q": "What is tangent? At 0:15.", + "A": "A tangent is a line on the outside of a circle or curve that only touches at one point.", + "video_name": "ZiqHJwzv_HI" + }, + { + "Q": "I don't understand the end behaviors @4:25", + "A": "End behavior is what the function looks like when it reaches really high or really low values of x.", + "video_name": "tZKzaF28sOk" + }, + { + "Q": "At 0:33 what does \"zen\" mean", + "A": "The voice recognition software got a bit confused. I m pretty sure Sal says and we essentially picked no y s then .", + "video_name": "_hrN4rVCOfI" + }, + { + "Q": "at 3:04 couldnt he just added 5 to 35 and add 20?", + "A": "Well, he could have, but doing that is basically doing exactly what he did do. He probably chose to do it how he did because if you aren t working with time then you would have to subtract, and he want s us to build good habits in problem solving.", + "video_name": "UhMM68fq9FA" + }, + { + "Q": "so at 2:32 it says that all four base angles are congruent,but is the angle at the top congruent to them also?", + "A": "Not necessarily, Because the sides of the rhombus do not necessarily have to be equal to one of the diagonals. However, if you have a rhombus with angles 60 and 120 degrees, then the shorter diagonal will split the rhombus into two equilateral triangles and so the vertical angle of the triangle will be also equal to the other two base angles (ie, all the angles will be 60 degrees).", + "video_name": "_QTFeOvPcbY" + }, + { + "Q": "At 3:05, why is it just answer 17 but at 3:31, 5 is 25?", + "A": "He is squaring each number. So at 3:05 he squares the squared root of 17, the square root of 17x the square root of 17 equals 17. The square root of 17 is a number slightly bigger than 4, because 4x4 equals 16, so this is just a little bit more than that. At 3:31 he square 5. 5x5=25 The concept is that if you square each number you can compare the numbers without the radical signs........", + "video_name": "KibTbfkoPTs" + }, + { + "Q": "It states at 4:56 that zero is a positive number. I thought all positive numbers have an opposite. If they do then what is zero's opposite?", + "A": "Yes, all numbers, either positive or negative, should have the opposite, except 0.", + "video_name": "XHHYA2Ug9lk" + }, + { + "Q": "At 3:28, Sal says that he can do multiplication in any order, but thought you had to go from left to right.", + "A": "You can do multiplication in any order because of the commutative property of multiplication, which means that you ll get the same answer no matter what order you put it in.", + "video_name": "XHHYA2Ug9lk" + }, + { + "Q": "@0:28 Why is it 2cm?? Really confused", + "A": "That is because 2 is the height. When you look at it, two cm is the line coming up that makes the figure 3D, so that is why it is the height. Also, the length and the height make the base and they intersect before the height comes up at the edge.", + "video_name": "feNWZEln6Nc" + }, + { + "Q": "At about 1:35, you mention that 5 and 12 are relatively prime. What exactly does that mean?\n\nThe more I think about this, the more puzzled I become. I guess I'm having trouble with how prime-ness can have different degrees. The one solution that I've come up with isn't exactly satisfying: that the two numbers together 'may as well be'/ are 'as good as' prime, since they only have one as a common factor and all primes have 1 as a common factor.", + "A": "12 is not a prime, but if you consider that you are only allowed to divide by 1 and 5 (the factors of 5), then 12 would be a prime. 12 can be divided by 2, 3, 4, 6, but not by any factor of 5. So 15 and 8 are also relatively prime. You could also say: two numbers are relatively prime if they don t share any factors. For example 15=3*5 and 8=2*2*2", + "video_name": "jFd-6EPfnec" + }, + { + "Q": "at 2:1 l don't understand", + "A": "What Sal means is that you need a certain amount of cleaning product (bottles in the numerator) to clean a certain fraction of the bathroom. As in the video, you need 1/3 of a bottle of cleaning product to clean 3/5 of the area of a bathroom.", + "video_name": "2DBBKArGfus" + }, + { + "Q": "At 1:48, isn't the vector drawn vector (a+b), not vector (a-b)?", + "A": "No, it is a - b. To draw a + b, you d put vector b s tail at the head of vector a (i.e. chain them together). Draw some vectors on paper with roughly correct coordinates and give it a go.", + "video_name": "5AWob_z74Ks" + }, + { + "Q": "i kind of get but killo means 1,000 or 1,000,000 on 00:14", + "A": "Kilo means 1,000.", + "video_name": "9iulv2QvKwo" + }, + { + "Q": "The question is to write an equation, so should we stop at 6:46?", + "A": "We could have stopped but he wanted to solve for the answer.", + "video_name": "jQ15tkoXZoA" + }, + { + "Q": "2:32 how is the opposite and adjacent line of theta can become sin theta and cos theta? i thought sin is like opposite over adjacent something like that..", + "A": "In the unit circle, the hypotenuse always equals 1 (it s the radius of the unit circle). Since sin(\u00ce\u00b8)=opposite/hypotenuse, and the hypotenuse equals 1, you can say that sin(\u00ce\u00b8)=opposite/1, or sin(\u00ce\u00b8)=opposite. It s the same idea for cosine. This only works for the unit circle, though. You can watch the videos on the unit circle if you haven t already.", + "video_name": "Idxeo49szW0" + }, + { + "Q": "I really don't get how he looks at the length at about 4:40 and says \"So this is square root of 2 over 2\" is it something he memorized or can you calculate it based on the slope?", + "A": "Sal wasn t looking at the length, really, but rather at the angle Theta (derived from the slope): Theta is -45 degrees. That means that the right triangle he draws is isosceles (with hypotenuse = 1, since this is a unit circle), and a quick calculation (or a good memory) tells us that both of the legs must therefore have a length of sqrt(2)/2.", + "video_name": "Idxeo49szW0" + }, + { + "Q": "At 3:53, what does factorial mean?", + "A": "A FACTORIAL is when a number has the little ! next to it. That means that you multiply that number with every number before it and stop when you get to 1. For example: 5! = 5 x 4 x 3 x 2 x 1 = 120 Hope this helps! :)", + "video_name": "W7DmsJKLoxc" + }, + { + "Q": "How do you know for sure if it's a conic? I mean, what if you try to simplify it and then you can't multiply it by a number so that it has the form ((x+a)^2)/b)+((y+c)^2)/d)=1? For example, what if, at 3:58, the number on the right wasn't 100? What would you do then?", + "A": "I m going to call the number on the right z. If z wasn t a square root, Z= (sqrt(z))^2, right? So you work with that. You would go sqrt(z) in the direction needed.", + "video_name": "cvA4VN1dpuY" + }, + { + "Q": "At 0:30 how is 36 the least common multiple of 12 when doesn't it have to not be 1? I don't understand this.", + "A": "It is not the least common multiple (lcm) of 12 but of 12 and 36. 12=12, 24, 36, 48, 60, 72 36=36, 72 36 is the least multiple 12 and 36 have in common. decompositing method. 12=2*2*3 36=2*2*3*3 So the lcm=2*2*3*3=36", + "video_name": "znmPfDfsir8" + }, + { + "Q": "At 1:39 why did you put 2 times 3 times 3", + "A": "Because 2 x 3 x 3 = 18. (In more detail, 2x3 = 6. 6x3= 18.) Same reason with 12. 2x2 = 4 4x3=12. So that s why you see: 2x2x3 Why do we need to do this? Because we need to gather some set of numbers that can be multiplied to get both number 12 and 18, in order to find the Least Common Multiple. LCM: 2x2x3x3 = 36 <--- 2x2x3= 12 and 2x3x3 = 18", + "video_name": "znmPfDfsir8" + }, + { + "Q": "at 1:39 why did you did you put 2 times three times three?", + "A": "2*3*3 is the prime factorization.", + "video_name": "znmPfDfsir8" + }, + { + "Q": "1:24 We're allowed to pick numbers at random? Is that \"legal\"?", + "A": "The idea is to pick points to plot the graph. Which ones you use isn t important as long as you can draw the plot with enough precision. The more points you pick, the more accurate your graph will be around those points.", + "video_name": "rgvysb9emcQ" + }, + { + "Q": "1:16-1:46 he does the translation visually. Is there any way to do it with an equation.", + "A": "Yes, to translate a figure 2 spots to the right you just add 2 to its x value. So E (3+2,3) -> E (5,3).", + "video_name": "XiAoUDfrar0" + }, + { + "Q": "at 5:09, i dont understand how it is the same distance", + "A": "Most transformations, translations, rotations, and reflections all end up with an image that is congruent to the pre-image, so same parts of congruent figures are congruent. The video has the rotation slightly off.", + "video_name": "XiAoUDfrar0" + }, + { + "Q": "At 4:30 how does Sal go from B/60*-5 into -b/12?", + "A": "Multiply: b/60 * -5/1 = (-5b)/60 Cancel out common factor of 5 and you get: -b/12 Hope this helps.", + "video_name": "Q0tTfe2lKIc" + }, + { + "Q": "At around 6:11 , how is it possible that X can be less or equal to -3? Wouldn't that make the square root negative?", + "A": "No, because the absolute value of anything less or equal to -3 is larger than 3, i.e. it is more than 3 removed from zero. Subtracting 3 from something larger than 3 gives a positive outcome, and hence a real solution to the problem. For instance x = -4. Abs value (-4) = 4 4 - 3 = 1 Square root (1) = 1.", + "video_name": "U-k5N1WPk4g" + }, + { + "Q": "Take the answer of problem at 4:51 . And, let x=12. So, f(x)=(sqrt)9 and\n(sqrt) of 9 has 2 values: 3 and -3. Which means, f(12) = -3 or f(12)= 3 which is not possible according to the definition of a function. How can this be explained??", + "A": "The notation \u00e2\u0088\u009a9 exclusively denotes the POSITIVE value. Its corresponding negative root is denoted as -\u00e2\u0088\u009a9. However, when a positive value does not exist, the radical sign may be used to indicate the negative real value. Eg. ^3\u00e2\u0088\u009a-8 = -2.[The cube root of -8, that can be expressed on a number line, is -2, because (-2)*(-2)*(-2) = -8] That s only when we used symbols; when we say, or write, square root of a certain number, it refers to all applicable values.", + "video_name": "U-k5N1WPk4g" + }, + { + "Q": "At around 4:25, Sal said the square root couldn't be a negative number, so x would have had to be 3 or more. Wouldn't it have to be 4 or more because 3 - 3 = 0?", + "A": "As Sal says: there is nothing wrong with the expression sqrt(0). Its just zero.", + "video_name": "U-k5N1WPk4g" + }, + { + "Q": "Mr Sal at 3:43 you said\nF(x)=square root of x-3greater or equal to 0\nHow can it be equal to 0, if I plug 0 in place of x i would get -3 which is wrong??", + "A": "Notice the subtle distinction. Sal did not say that x was greater than or equal to 0, but that x-3 was. So x must be greater than or equal to 3.", + "video_name": "U-k5N1WPk4g" + }, + { + "Q": "Why Sal did say at 6:28 the domain of function f(x) = sqrt(abs(x)-3) is x\u00e2\u0082\u00acR | x<=-3 and x>=3 ?\nIts a mistake? We can have a positive square root of 0 ?", + "A": "At this point, Sal says the domain is all real values of x such that x is less than or equal to -3 and greater than or equal to 3. When that value is in the denominator, then the domain is x<=-3 and x>=3 because the denominator cannot be 0. They were two separate equations.", + "video_name": "U-k5N1WPk4g" + }, + { + "Q": "So in 0:38, you said that you can add up all the digits (154 adding up to 10 in the video). Does that method always work? I mean, I understand that 5 would not be able to go into 154 because the result always ends in either 0 or 5 as mentioned, but I'm just a bit confused. Could someone possibly explain if the method really works for all numbers?", + "A": "Lets tell parts of division 15\u00c3\u00b75=3 15=dividend formula=d \u00c3\u00b7=division sign 5=divisior formula=D 3=quotient formula=q 0=remainder formula=r Euclid was a great mathmatician who made a division statement (Divisior\u00c3\u0097quotient)+remainder =dividend Eg=lets take 67\u00c3\u00b76=11 (6\u00c3\u009711)+1=67", + "video_name": "5xe-6GPR_qQ" + }, + { + "Q": "I think \"9:50\" does not need a proof as they're just i j k l unit vectors.", + "A": "9:54 A proof may be simple, but still needed. That is the case here.", + "video_name": "JUgrBkPteTg" + }, + { + "Q": "at 7:19 sal said it was equal to 112 it is equal to 108 You may do the check if you want 36+108 is 144", + "A": "Well, yeah, I guess. But I think he was a little rushed.", + "video_name": "s9t7rNhaBp8" + }, + { + "Q": "During the video at about 7:10 Sal goes a little to fast,I don't understand the\nrest of the formula. I'm struggling with the last few steps.I know 6 squared is\n36 (side A)and the hypotenuse(side c)12 squared is equal to 144.after this point\ni'm lost. I don't know my square roots real well and I struggle with formulas that\nare more than 3 steps. I know w/lots of practice i will get it.any \"positive\" tips\nmuch appreciated.", + "A": "144-36 = 108, not 112. Other than that, you are correct once you adjust the incorrect values.", + "video_name": "s9t7rNhaBp8" + }, + { + "Q": "From @7:45 to @10:36 , what are you trying to achieve when you convert the matrix to reduced row-echelon form?\n\nI thought you were trying to turn row 2 and 3 to zeros, like you did with the 2x2 matrix.\n\nWhy do you have to convert it to row-echelon form?\n\nThank for the videos btw, they've been really helpful.", + "A": "rref is the solution for the system of equations represented by the augmented matrix. You re finding the vectors v such that Av = lambda*v - i.e., the solution for (lambda*I - A)v = 0; i.e., rref ( [ (lambda*I - A) | 0 ] ).", + "video_name": "3Md5KCCQX-0" + }, + { + "Q": "At about 5:30, Sal has 9x36/2, then he divides the 36 by 2, getting 9x18/1. Why doesn't he divide the 9 by 2 also?", + "A": "36/2 is 36 divided by 2. So then he gets 9 x 18 becuz 36 divided by 2 is 18. Even if you do 9 x 36 and 9 x 2 then you will get 324/18 which is still 18.", + "video_name": "jFSenp9ueaI" + }, + { + "Q": "At 4:21 , the standard deviation of thesample size is given is given as 0.5s why do we have to determine it.", + "A": "because the other one we determined is the standard deviation of the sampling distribution of the sample mean.", + "video_name": "-FtlH4svqx4" + }, + { + "Q": "At 2:11, how do you know where to subtract the 2 from, like can you subtract it with any of the numbers on the other side of the equation?", + "A": "It s basic equation balancing. To isolate the variable, you have to get rid of the 2 in the equation. To do so but not change the equation, you have to minus 2 from both sides so that technically it s still the same equation just simplified down so the 2 is gone.", + "video_name": "qsL_5Y8uWPU" + }, + { + "Q": "what is the triangle at 1:00 for?", + "A": "It is the greek letter delta, which is commonly used today in modern applications of science and mathematics to represent a change or difference. Just like how we use pi in geometry, theta in trigonometry, lambda in calculus, phi to represent the golden ration, and more.", + "video_name": "f4MYCepzLyQ" + }, + { + "Q": "At 3:02, Sal talks about slope-intercept form. Can anyone give me an explanation of what that is and how it can be used to find average rate of change.", + "A": "y = mx + b is slope-intercept form", + "video_name": "f4MYCepzLyQ" + }, + { + "Q": "At 4:00 Sal says 350/360 is = to 35/36 What rules dictate this?", + "A": "That s how you simplify a fraction. Divide the top and bottom numbers by the same factor (in this case 10) to simplify. Another example: 3/6 = 1/2 because you divide the top and bottom numbers by 3.", + "video_name": "tVcasOt55Lc" + }, + { + "Q": "Could you cross multiply at 1:32 ?", + "A": "You mean turning it into a = ====1 ------ ------- 1.8pi 360? If so, then yes", + "video_name": "tVcasOt55Lc" + }, + { + "Q": "4:25 I don't understand why 5(7k(k+3)-(k+3)) becomes 5(k+3)(7k-1)", + "A": "Try this : If you had for say, 6(k+3) - (k+3), you could clearly say that it is equal to 5(k+3) right? Which is equal to (6-1)(k+3). Same thing is happening in here. You have 7k(k+3)-(k+3) and you are free to transform it into (7k-1)(k+3).", + "video_name": "R-rhSQzFJL0" + }, + { + "Q": "Hi at 1:03 - 1:06, Sal mentions finding a number whose product is 7 * -3. Why isn't he simply referring to the number -3 as his product?\n\nThanks in advance.", + "A": "The product of two numbers is the number that results from multiplying two numbers together. For example, -3\u00c3\u00977 equals -21. In this instance, -21 is the product. I hope this helps!", + "video_name": "R-rhSQzFJL0" + }, + { + "Q": "At 1:10, why can we not write {(-1)(-52)}^1/2 = {(-1)^1/2}{(-52)^1/2} ?", + "A": "I believe it would be mathematically incorrect, because sqrt(-1 x -52) is sqrt(52). However, sqrt(-1) x sqrt(-52) is not the same as sqrt(-1 x -52) because sqrt(-1) x sqrt(-52) is equal to sqrt(-1) x sqrt(52) x sqrt(-1) = -1 x sqrt(52) which is not the same as sqrt(-52). Sorry you got an answer to your question 2 years after you asked it, hopefully this helps! ;-} By the way, I can do the special effects for the iron-man movies, and am coming out with The last Days . if your interested.", + "video_name": "s03qez-6JMA" + }, + { + "Q": "At 3:35, why is it i*\u00e2\u0088\u009a4*13 and not i^2*\u00e2\u0088\u009a4*13? I thought that by definition i^2= -1", + "A": "i^2 = -1 i = \u00e2\u0088\u009a(-1)", + "video_name": "s03qez-6JMA" + }, + { + "Q": "At 2:04, Sal says that I can not split sqrt(-1 x -52) into sqrt(-1) x sqrt(-52). Can I go the opposite way? Would it be mathematically correct to simplify: sqrt(-1) x sqrt(-52) into sqrt(-1 x -52)?", + "A": "I believe it would be mathematically correct, because sqrt(-1 x -52) is sqrt(52). However, sqrt(-1) x sqrt(-52) is not the same as sqrt(-1 x -52) because sqrt(-1) x sqrt(-52) is equal to sqrt(-1) x sqrt(52) x sqrt(-1) = -1 x sqrt(52) which is not the same as sqrt(-52). Sorry you got an answer to your question 2 years after you asked it, hopefully this helps! ;-}", + "video_name": "s03qez-6JMA" + }, + { + "Q": "at 9:01 Sal messed up right? Isn't it supposed to be 365!/362!/(365)to the third??", + "A": "Yes; he did mess up at 9:01", + "video_name": "9G0w61pZPig" + }, + { + "Q": "on 0:59 he is a horrible stock investor\nVote up if u agree", + "A": "There isn t enough info to know. -- The problem didn t tell you the time frame. If the portfolio went up in 1 month by 25%, that would be fantastic! -- If the overall market is down for the year by 20% and this person s portfolio went up 25%, that would also be fantastic! -- If it took 20 years for his portfolio to grow 25%, that would not be good, unless his goal was to project his portfolio (low risk). Then, it would be good.", + "video_name": "X2jVap1YgwI" + }, + { + "Q": "4:48 Hey, does anyone know why Sal puts the = sign like a smiley face? =D", + "A": "It s not an equal sign, but rather an arrow. He just draws it in a way that it doesn t look quite connected. This is actually a common way to note progression of steps in mathematics.", + "video_name": "X2jVap1YgwI" + }, + { + "Q": "What's the next step if the number doesn't come out to be exact like 13*16 for 208? (2:19 in video)", + "A": "you go and find the number of ones. example: 114 = 7 * 256 + 16 *13 (D) + 0 * 1 there are 0 1 s. if the number were 115, then it would be 7D1 because there an extra one as supposed to 7D0 = 114. hope this helped", + "video_name": "NFmDz1dQyPU" + }, + { + "Q": "At 4:21, Sal says that that 0i is the same thing as 0 + i. Wouldn't be 0 times i? I am confused.", + "A": "No, he says that i is the same thing as 0 + i , which is true. You are right that 0i is just 0 times i , not 0 + i . So 0i is the same thing as just 0 .", + "video_name": "A_ESfuN1Pkg" + }, + { + "Q": "at 0:45 why is i2 + to -1?", + "A": "The definition of i is : the number that its square is equal to -1. So: i^2 = -1 by the definition of i itself.", + "video_name": "A_ESfuN1Pkg" + }, + { + "Q": "At 5:47 Sal says the x value has to be between 0 and 10. Why isn't it between 0 and 15?", + "A": "Because the piece of card is only 20 wide, and x can be at most half the width.", + "video_name": "MC0tq6fNRwU" + }, + { + "Q": "At 7:40, why did he set a maximum y value? Isn't that already determined since x cannot be greater than 10?", + "A": "Right. He knows that the maximum x-value is 10, but he doesn t know what the maximum y-value is. The y-value represents the volume of the box, which can get pretty big depending on the dimensions. (width, depth, height)", + "video_name": "MC0tq6fNRwU" + }, + { + "Q": "At 7:17, is it only a statistical question if you mention \"in 2013\" before you added it in the last example, or can it be statistical either way?", + "A": "Without the in 2013, it is kind of a complicated case. You have to think about what you want to consider. if you say throughout the history of the schools or since 1800, then this does become a statistical question no matter how you look at it. However, considering other things (like in 2013), you have concrete numbers that you can check the difference of, making it not a statistical question", + "video_name": "qyYSQDcSNlY" + }, + { + "Q": "There is one point at \"2:25\" that I really want it to be clarified. I think that \"integral f(t) d(t) from a to x\" should be \" F(x) - F(a)\" instead of \"F(x)\". Please help me Im so confused!", + "A": "The integral f(t) d(t) from a to x would equal F(x)-F(a). I believe Sal is simply using F to put the integral as a function of x. Any letter or symbol would do, some calculus books write it as A(x) instead of F(x). They tend to use A because the formula seen in the video is an area accumulation formula (A for area). Whatever x you put into F(x) would give you the amount of area you have accumulated from a to x.", + "video_name": "C7ducZoLKgw" + }, + { + "Q": "At 4:19, Sal explains that every continuous function has an antiderivative, according to the Fundamental Theorem of Calculus. I learned in Calculus A that only continuous functions have derivatives. Is this an inference from the Fundamental Theorem?", + "A": "No. The fact that every continuous function is a derivative (has an antiderivative) has nothing to do with the fact that only continuous functions have derivatives. The FToC is not necessary to show that continuity is a condition for differentiability.", + "video_name": "C7ducZoLKgw" + }, + { + "Q": "At 0:58, it doesn't really matter what size the camel is, since it's infinite, you'll always end up with the whole page covered.", + "A": "No, actually it does matter. If you make the next camel too big, then you will end up needing more than the page to draw all the camels. If you make the next camel too small, then you will not use up all the space on the page.", + "video_name": "DK5Z709J2eo" + }, + { + "Q": "If we do not include two set of numbers can we make the brackets face opposite directions? For example at 5:06 we do not include \"-1 and 4\" Sal wrote them like this (-1,4). But instead of writing parentheses can I write them in such form ]-1,4[", + "A": "no you cannot. If you write it like that, then you re saying that -1 and 4 are not included in the function and the result would be a syntax error. three thumbs up!", + "video_name": "UJQkqV2zGv0" + }, + { + "Q": "I'm sort of curious about why you would write the inclusion of real all real numbers except for one as (-\u00e2\u0088\u009e,1). If you are including all real numbers except for one, would it not look like [-\u00e2\u0088\u009e,1)? @8:42", + "A": "you can t actually reach infinity, so use ( rather than {", + "video_name": "UJQkqV2zGv0" + }, + { + "Q": "At 0:50 can anyone tell me why the yellow line's slope is going to be the negative inverse?", + "A": "Because they are both perpendicular lines!!", + "video_name": "0671cRNjeKI" + }, + { + "Q": "at 5:08\nisn't this the formula of Explicit geometric sequence ?", + "A": "In a geometric sequence, the input value is multiplied. Here it is the power.", + "video_name": "G2WybA4Hf7Y" + }, + { + "Q": "sal at 1:08 instead of moving the 5 cant u move the 4 and then add 8 to the other side", + "A": "Yes but the way Sal did it is easier.", + "video_name": "g6nGcnVB8BM" + }, + { + "Q": "at 3:11 could he use substitution instead of elimination?", + "A": "Of course. He can do anything.", + "video_name": "f7cX-Ar2cEM" + }, + { + "Q": "what does sal mean when he says at 0:21 when he says \"scaling up\"?", + "A": "By scaling up Sal means multiplying the equation by 2. This scales up all the values in the equation by 2.", + "video_name": "f7cX-Ar2cEM" + }, + { + "Q": "at 3:10 isn't pi 3.14 not 3.5 ?", + "A": "correct pi is 3.14 rounded to two decimal places. But Sal is showing that 4*pi is less than 14. Since 4*3.5 is 14, and pi is less than 3.5 then 4*pi must be less than 14. Hope that helps", + "video_name": "EvvxBdNIUeQ" + }, + { + "Q": "i didnt understand from 1:07-1:47 about the circle", + "A": "it is about pi from 1:07 to 1:47 about the circle", + "video_name": "EvvxBdNIUeQ" + }, + { + "Q": "At 2:42 why is it 14 r squared?", + "A": "Because when you times a r by a r you get r squared and 7 times 2 you get 14 so 14r^2", + "video_name": "EvvxBdNIUeQ" + }, + { + "Q": "At 3:55 What does he mean by principle root?", + "A": "The principal root is just the positive square root. For instance: \u00e2\u0088\u009a9 = \u00c2\u00b13 But the principal square root of 9 is just 3.", + "video_name": "McINBOFCGH8" + }, + { + "Q": "At 4:28 wouldn't it be 2x=C", + "A": "You had the equation x^2+x^2 = c^2. Which is 2(x^2)=c^2 which is 2*x*x=c*c When you take the square root of each side, you have to take the square root of both the x*x and the square root of 2. so you get (Square root of 2 * x)=c", + "video_name": "McINBOFCGH8" + }, + { + "Q": "At 4:59, why is it bn and vn, instead of bk and vk?", + "A": "There s no error here. b belongs to Rn, otherwise original equation Ax=b, where A is nxk matrix would not make any sense. v is a projection of b to the column space, but it still is a member of Rn, hence it also has n components.", + "video_name": "MC7l96tW8V8" + }, + { + "Q": "@ 4:05 he says it goes down 2/3's then he says its 1 and 1/3. How does he go from 2/3's to 1/3rd? I get the whole thing that 1/ 1/3rd makes 4/3rds, but he went down 2/3rds??", + "A": "When he went down 2/3 it was from 2! The line was 2/3 below 2. So if you look at it in terms of the line being above 1 the line is actually 1/3 above 1. So therefore the line is at 1 1/3.", + "video_name": "9wOalujeZf4" + }, + { + "Q": "At about 10:10, he said that the y-intercept was 0. So why does the graph line still have a slope?", + "A": "The y-intercept doesn t have to do with the slope; it just shows where the sloped line crosses the y-axis. So, a graph line can have a slope and y-intercept 0, such as y=x, where the slope is 1 and the y-int 0. The line just crosses the y-intercept at the origin.", + "video_name": "9wOalujeZf4" + }, + { + "Q": "Hold on.. how did he get 4/3 as the y-intercept in 4:05..?", + "A": "The slope = -2/3. Sal has a point at (-1, 2). He needs to move one uni to the right to get to the y-axis. The slope tells him that as he moves 1 unit to the right, the y-coordinate will decrease by 2/3. Sal finds the y-intercept by doing: 2 - 2/3 = 6/3 - 2/3 = 4/3 Hope this helps.", + "video_name": "9wOalujeZf4" + }, + { + "Q": "At 1:10, is that a different way of expressing it using a sigma?", + "A": "In this video, he is discussing sequences, which are just lists of numbers. The sigma, or summation notation comes into play when you are calculating series.", + "video_name": "_cooC3yG_p0" + }, + { + "Q": "I dont understand the part at 6:61", + "A": "Do you mean 7:11? Basically, to prove the quadratic formula Sal is completing the square and then moving everything to one side of the equation.", + "video_name": "r3SEkdtpobo" + }, + { + "Q": "At 6:00, why did he simply not just take the square root of b squared and leave it as b?", + "A": "Because you can t distribute square roots like that. You could if the terms in a radical are products or quotients, but when they are sums and differences(i.e. adding and subtracting), you can t distribute a radical.", + "video_name": "r3SEkdtpobo" + }, + { + "Q": "At 5:45, when we take square root of both sides, why does the right side end up with a \"plus or minus\" designation while the left side stays only positive?", + "A": "| Because the equation on the left has implied positive domain because it is represented with a (term)^2 and that represents that any term within the brackets which were positive or negative will result in a positive output. While on the right, we do not yet know the domain of the right so it is correct to assume that there could be a negative root. I m sorry if i have confused you. :(", + "video_name": "r3SEkdtpobo" + }, + { + "Q": "At 4:00 and 10:00, why is is cos(2a) a minus but sin(2a) is a plus?\n\nAlso which video did I miss? I am so confused here. I don't ever remember learning this in my high school precalc class.", + "A": "You have to review the formula of cos(a+b) = cos(a)*cos(b) - sin(a)*sin(b) From there, you can write cos(2a) as cos(a+a), then go on. You see why the minus in here. That is trigonometry. Go back to the beginning and learn the formula come from.", + "video_name": "a70-dYvDJZY" + }, + { + "Q": "at 8:22 how did he get 1-2sin^2(a)?", + "A": "It s one of your identities. cos(2a) = cos^2(a) - sin^2(a) sin^2(a) + cos^2(a) = 1 => cos^2(a) = 1 - sin^2(a) cos(2a) = 1 - sin^2(a) - sin^2(a) cos(2a) = 1 - 2sin^2(a)", + "video_name": "a70-dYvDJZY" + }, + { + "Q": "At 4:25 isn't cos(2a) = cos(3a - a) = cos(3a)*(cos)a + sin(3a) * sin(a)", + "A": "You could work it out like that, which would eventually simplify to what he had: cos(2a)=cos^2(a)-sin^2(a); this is one of the double angle formulas", + "video_name": "a70-dYvDJZY" + }, + { + "Q": "1:25 How are two inscribed angles that are subtended by the same arc equal to each other?", + "A": "For any given arc, there can be any number of inscribed angles that subtend it, but only one central angle will subtend that same arc. Since the inscribed angle theorem tells us that any inscribed angle will be exactly half the measure of the central angle that subtends its arc, it follows that all inscribed angles sharing that arc will be half the measure of the same central angle. Therefore, the inscribed angles must all be congruent. Hope this helps!", + "video_name": "h-_BDon5oes" + }, + { + "Q": "At 1:47, he does 3*-2, and represents it as -2+-2+-2. Can't he also say 3, -2 times?\nIf you took three twice away from zero, it would still equal -6.", + "A": "Yes, you are correct, but in this video, he only shows one way but the way you are thinking is definitely correct, they are the same. It is like saying 3*4 is equal to both 3+3+3+3 and 4+4+4. Hope this helps.", + "video_name": "47wjId9k2Hs" + }, + { + "Q": "At 1:17, I get confused. Can you help?", + "A": "Ok, so a negative times a negative equals a positive because the negatives cancel out, but if it s a negative times a positive (or vice versa) there s nothing to cancel out that negative so the answer remains negative.", + "video_name": "47wjId9k2Hs" + }, + { + "Q": "AT 1:39 the regrouping of the problem from -2 x 3 was changed to 3 x -2. Would this be an example of commutative property ?", + "A": "Yes! The communicative property states that the order does not matter for numbers added or multiplied.", + "video_name": "47wjId9k2Hs" + }, + { + "Q": "At 2:55 he said that the negative cancels out the negative and makes a positive product. Then according to that, wouldn't a positive cancel out a positive, making a negative product.", + "A": "No, that isn t how it works. A negative times a negative is a positive, and a positive times a positive is a positive. But a negative times a positive is a negative, and a positive times negatives is a negative. So, basically, if you are multiplying two of the same thing (like two positives, or two negatives), you get a positive. If you are multiplying two different things (one negative and one positive), you get a negative. So no, a positive does not cancel out another positive. I hope this helps.", + "video_name": "47wjId9k2Hs" + }, + { + "Q": "At 3:41 in the graph we can see a vertical asymptote at approximately x=3, why is this and what is its significance?", + "A": "That is simply due to the fact that 6x^5-100x^2-10 has a zero around 2.57. Because this expression is in the denominator of the rational function, there is a horizontal asymptote (because you can t divide by zero!). However, the vertical asymptotes have nothing to do with the horizontal asymptotes (limits at infinity).", + "video_name": "gv9ogppphso" + }, + { + "Q": "why does Sal say at 4:30 \"principal square root\"", + "A": "Because the \u00e2\u0088\u009a means principal square root, not square root.", + "video_name": "egNq4tSfi1I" + }, + { + "Q": "So, at 2:50, if we assume the root didn't always indicate the principal square root, could we say that x could be either positive or negative?", + "A": "Yes it can be either or", + "video_name": "egNq4tSfi1I" + }, + { + "Q": "Im stuck at 3:10, i dont know how sal has p(x)=f(0)+f\"(0)x.\nIs this like linear approximation or something?", + "A": "First of all, he said p(x)=f(0)+f (0)*x just one prime And yes, this is a linear approximation! Does it remind you of anything? Perhaps point slope form? if y=mx+b, y is p(x), b is f(0), and m is f (0).", + "video_name": "epgwuzzDHsQ" + }, + { + "Q": "Can someone explain the equation for when g(x)?\n5:16", + "A": "are you confused about why the function is called g(x) and not f(x)? if so they mean the same thing . it is like a name for the function", + "video_name": "riXcZT2ICjA" + }, + { + "Q": "at 8:20, why does G(2) = 1 instead of 4?", + "A": "Because that s part of the function - it says square x unless x = 2 where g(x) gives you a 1", + "video_name": "riXcZT2ICjA" + }, + { + "Q": "At 1:25, why is f(x) = D?", + "A": "i think you are getting confused by his arrows...", + "video_name": "riXcZT2ICjA" + }, + { + "Q": "Wait a minute, at 9:20 Sal says that when x approaches to 2, the value of g(x) would be getting really close of 4, but shouldn't it be 1? Since when x = 2 <=> g(x) = 1?", + "A": "g(2) is in fact 1, given by the dot. However, the limit is different. Remeber g(x) = y. To understand limit, try putting your pencil on the graph and trace it. As you trace it toward x=2, you see that y=g(x) is getting toward 4 and not 1.", + "video_name": "riXcZT2ICjA" + }, + { + "Q": "I don't really get it. At 00:53, why can't you reduce x-1/x-1 to equal to 1?", + "A": "This is only true if x does not equal 1. If x were to equal 1 then you d have 0/0 which is indeterminate. Therefore the division only works for most cases, but it only takes one counterexample to make a conjecture false. So limits will allow for the case up to but not including the problem point.", + "video_name": "riXcZT2ICjA" + }, + { + "Q": "in the video at 4:24 Sal says that we can get infinitely closer to one. If we can get infinitely closer to one doesn't that mean that we can never approach one?", + "A": "True. Yes, we can always get closer and closer to one but the function actually never reaches one.", + "video_name": "riXcZT2ICjA" + }, + { + "Q": "At 7:30 Sal has drawn a parabola with a gap at the point (2,4).\n\nA point takes up zero space right? It has no size? So how can something have a gap in it if the gap doesn't cover any actual space? How big is the gap? Surely a gap is between two points.\n\nCan someone please help me understand this?", + "A": "At this point it has size 0. The gap is just for understanding that there is no defined point at that x coordinate.", + "video_name": "riXcZT2ICjA" + }, + { + "Q": "9:38 he says its 4 we're getting to but how do you get for without a graph", + "A": "In later lessons you will learn different techniques to do it algebraically. This is just a video introduction of limits, so I recommend you watch other lessons about limits.", + "video_name": "riXcZT2ICjA" + }, + { + "Q": "At 9:20, how is g(x) approaching the value of 4 if it is a hole? Why isn't the limit 1 because it's an actual point?", + "A": "The limit as x approaches 2 of g(x) does not have to equal g(2). The value of this limit (if any) is determined by the behavior of g(x) near, but not at, x = 2. Since g(x) is near 4 when x is near (but not at) 2, the value of this limit is 4. The fact that g(2) = 1 has no effect on the value of this limit. Note that the fact that the value of this limit does not match the value of g(2) indicates that g(x) is discontinuous at x=2. Have a blessed, wonderful day!", + "video_name": "riXcZT2ICjA" + }, + { + "Q": "At 1:17; what's the difference between infinity and 1/0 ?", + "A": "Infinity (symbol: \u00e2\u0088\u009e) is an abstract concept describing something without any bound or larger than any number. In mathematics, infinity is often treated as a number While the expression a/0 has no meaning, as there is no number which, multiplied by 0, gives a (assuming a\u00e2\u0089\u00a00), and so division by zero is undefined. Since any number multiplied by zero is zero, the expression 0/0 also has no defined value; You can also prove it by the concept of limits. Try it out yourself.", + "video_name": "riXcZT2ICjA" + }, + { + "Q": "At 1:33, isn't that the Riemann's zeta function?", + "A": "Good question! That would be Riemann s zeta function, evaluated at z = 2. In general, this function is sum n=1 to infinity of 1/(n^z), where z is a complex number (that is, a number of the form a+bi where a and b are real numbers and i is the square root of -1). This function is defined when the real part of z (that is, a) is greater than 1. Have a blessed, wonderful day!", + "video_name": "k9MEOgcc5KY" + }, + { + "Q": "4:06: Wouldn't it be easier to say TRANSPOSE instead of ADJUGATE?! At least would be better to say that T is something that is more used when it comes to studying matrices more? (\u00c3\u008d know its the same thing but might confuce students like me who are having exam about this and never heard of adjugate and instead of TRANSPOSE T)", + "A": "Adjugate of matrix A is Transpose of Cofactor matrix of A", + "video_name": "ArcrdMkEmKo" + }, + { + "Q": "I rally didn't get what you men't by when the video got to 3:29 to 4:00 that was really confusing to be honest", + "A": "I think he was just trying to illustrate what he was multiplying. He shows you closer to 4:30 what he means, and how it all works out.", + "video_name": "j3-XYLnxJDY" + }, + { + "Q": "At 08:36, why doesn't \"x-1 = +-4\" become \"x = +- 5\"?", + "A": "@James.p.french: He couldn t simplify to x=+-5 because x is not equal to that. He could ve simplified it to the solution x=5 or x=-3.", + "video_name": "lGQw-W1PxBE" + }, + { + "Q": "At 3:45 isn't it possible that b is -2? I mean if you were to ignore the first table and before knowing c and d. Or am I wrong?", + "A": "Remember b>0 and b=/= 1", + "video_name": "Iz6IVf8frjw" + }, + { + "Q": "1:00 Is doing this method also the same as using the foil method kind of?", + "A": "Yes, this is basically the intuition behind the foil method. It s showing how the distribution property can be used twice to obtain the quadratic in standard form, which is essentially the foil method :)", + "video_name": "Xy8NKUoyy98" + }, + { + "Q": "At 0:28 Sal Said that an Odd Function Implies j(a) = - j(-a). Is this equivalent to -j(a) = j(-a) the more well known definition of an odd function? Or did Sal make a mistake?", + "A": "Multiply both sides by -1. They re the same.", + "video_name": "zltgXTlUVLw" + }, + { + "Q": "At 3:19, why does Sal divide by 7?", + "A": ".7 x 10 will equal 7. .7 represents 79 percent of the full price.", + "video_name": "d1oNF88SAgg" + }, + { + "Q": "At 1:48 Sal states that m=-4w+11 and proceeds to plug that into the other equation that we derived. But couldn't Sal simply plug that right back into the same equation that we got that from. So couldn't Sal use one equation to solve for two unknowns by plugging back in the m in terms of w?", + "A": "Try it. 100*(-4w + 11) + 400*w = 1100 -400*w + 1100 + 400*w = 1100 1100 = 1100 That s called a tautology. It s a true statement, but it s not providing any useful information. When you plug the value of m from one equation into another, your w terms don t cancel each other out, leading to a meaningful result of the form w = value", + "video_name": "2EwPpga_XPw" + }, + { + "Q": "What does Mister Khan mean when he says, \"open parentheses\", at, 3:48-3:50? What does he mean specifically? Obviously he means that the parentheses are open. but what does the phenomenon of the open parentheses imply?\n\nThat is my question for the day. I hope it was relevant. Goodbye. Reuben.", + "A": "Open the parentheses means to open it up and compute the operations inside and operations having to do what s inside the parentheses. The distributive property is an example. Here s to show: -2 ( 9x+4 ) -- Opening the parentheses would be distributing the two to the things inside. => -2 ( 9x+4 ) = -18x-8 I hope I answered your question.", + "video_name": "rCGHUXSd15s" + }, + { + "Q": "At 2:53, Sal says that the kite has perpendicular lines at an angle of 90 degrees. Do all quadrilaterals with perpendicular lines have to have it at an angle of 90 degrees?", + "A": "There seem to be a couple of questions in your question. First the definition of perpendicular is any 2 lines that form a 90 degree angle. So anything that refers to the word perpendicular is implying that the angle is 90 degrees. For clarification, the video is talking about the diagonals of the quadrilateral intersecting at 90 degrees. This is a property of a kite. Also squares have this property, so they are also kites. However (non-square) rectangles do no have this property, so are not kites. Hope this helps.", + "video_name": "inlMrf2d-k4" + }, + { + "Q": "what did sal mean by the congruent side could be opposite to each other on 1:45", + "A": "This is answered at 2:12 with a color picture of a parallelogram. In a quadrilateral, a shape with four sides, any two sides are either going to be adjacent (share an angle or endpoint) or opposite (do not touch or share an angle or endpoint). We are dealing with 2 pairs of congruent sides. Congruent sides or line segments have the same length. So, if you have two pairs of congruent sides in a quadrilateral, you will either have a parallelogram of a kite.", + "video_name": "inlMrf2d-k4" + }, + { + "Q": "At 1:44, if a pair of congruent sides are adjacent, does it affect the fact that it is congruent?", + "A": "No. Like in triangles, if it is a scalene triangle, all sides will be adjacent, but sense there are no congruent, or equal, sides, then there will be none. Even in a kite, if you think about it, there will be un-congruent ( I just made that word up ) sides that are, in face, adjacent. Please vote for this answer if it was helpful to you! :D", + "video_name": "inlMrf2d-k4" + }, + { + "Q": "At 1:02,can a kite also be a diamond?", + "A": "yes, as it is of the same shape", + "video_name": "inlMrf2d-k4" + }, + { + "Q": "at around 2:00 to 2:11 what is adjacent", + "A": "Next to or adjoining something else.", + "video_name": "inlMrf2d-k4" + }, + { + "Q": "At 5:19, how is a rhombus also going to be a kite?", + "A": "a kite has two pair of congruent (equal) adjacent (next to) sides. A rhombus has 4 congruent sides, which means each pair of adjacent sides is congruent. Therefore every rhombus is a kite.", + "video_name": "inlMrf2d-k4" + }, + { + "Q": "In 0:39, I don't understand the part where it says that there are a bunch of different Xs. How is that possible?", + "A": "Multiple variables (Same ones) can be in an inequality. Ex: x + x + 1 =23", + "video_name": "UTs4uZhu5t8" + }, + { + "Q": "Around 3:00...\nWait, isn't 39.9999(9repeating) equal to 40?\nSince 0.99999(9repeating) is equal to 1,\n39 + 0.99999... =? 39 + 1", + "A": "No it is not one or 40 because it is a decimal. When it is point somethine it is smaller than the rounded number", + "video_name": "UTs4uZhu5t8" + }, + { + "Q": "4:29 Why did the symbol > did not reversed to < hence you subtracted negative", + "A": "You re right. The symbol only reverses when multiplying or dividing negative numbers.", + "video_name": "UTs4uZhu5t8" + }, + { + "Q": "At 4:19, why is the square root of 2 x the square root of 2 equal to 2?", + "A": "Because sqrt(2) * sqrt(2) = sqrt(4) And, sqrt(4) = 2", + "video_name": "s9ppnjgmiyk" + }, + { + "Q": "At around the 6:15 mark, if the interval of convergence included 1 or -1, would the radius of convergence still be 1?", + "A": "To determine the radius of convergence, do not worry about whether the endpoints are included or not. The radius of convergence would be one regardless of whether or not the endpoints were included.", + "video_name": "DlBQcj_zQk0" + }, + { + "Q": "In this video Sal uses 6x+2 to get the solution, yet the problem has 6x-2.?? This is at 5:26/10:57 in the video:", + "A": "The quality of those questions weren t the best, if you look closely you can see that the equation really is 6x+2. I had to tilt my screen a little bit before I could tell if it was a plus or a minus.", + "video_name": "_HJljJuVHLw" + }, + { + "Q": "8:52, what is equiangular ?", + "A": "Equiangular means that all the angles of the polygon/shape have equal measure. For example an equiangular triangle would have three angles which all have a degree measure of 60.", + "video_name": "_HJljJuVHLw" + }, + { + "Q": "At 4:00 and again at 5;10, Sal says that 6x+2 is the largest angle, how can he tell?", + "A": "Among all the angles, ie, 2x, 6x, 4x - 6, 2x - 16 and 6x + 2, In 6x +2 you are multiplying x 6 times and further adding a 2. Try assigning x a value, u will find that 6x + 2 is the largest.", + "video_name": "_HJljJuVHLw" + }, + { + "Q": "At 4:01, isn't it supposed to be 6x-2 and not 6x+2?", + "A": "I thought so too. Probably we can t see it clearly, when I rewatched I thought I saw a hint of the vertical line in the +.", + "video_name": "_HJljJuVHLw" + }, + { + "Q": "at 4:10 Sal mentions that it is ar^k power. Why do the k power instead of nth power?", + "A": "k is the index, where k=0,1,2,3,...n So it would mean ar\u00e2\u0081\u00b0+ar\u00c2\u00b9+ar\u00c2\u00b2+ar\u00c2\u00b3+...+ar^n", + "video_name": "CecgFWTg9pQ" + }, + { + "Q": "The example at 8:05 if they asked f(-2) would it be does not exist as the line has an open circle", + "A": "f(-2) would be undefined or does not exist because of the open circle. However, the limit as x->-2 exists and it s 4 as Sal demonstrated.", + "video_name": "nOnd3SiYZqM" + }, + { + "Q": "At 5:25,when sal wrote the general limit of F(X) as x approaches 4,didn't he forget the minus sign in front of 5?its -5 and not 5", + "A": "Yes he did indeed forget the minus sign although he recognized that by editing in a correction box in the bottom right hand of the screen.", + "video_name": "nOnd3SiYZqM" + }, + { + "Q": "I've been thinking about this for a while and I can't figure out how to find the limit of an asymptote. At 6:20 as x=>3- is it negative infinity or undefined?", + "A": "Recall that an asymptote is just a line that a given function or curve tends to (gets closer and closer to). At 6:20, the asymptote is x = 3. However, if you actually meant to find the limit of f(x) as x -> 3\u00e2\u0081\u00bb, it is -\u00e2\u0088\u009e.", + "video_name": "nOnd3SiYZqM" + }, + { + "Q": "At 5:29, I thought the limit of f(x) as it approaches 4 would not exist because it is a corner? Aren't corners not differentiable? Does it or does it not exist?", + "A": "The derivative of the function at 4 and limit of the function as x approaches 4 are not the same thing. The derivative does not exist at 4 because of the sharp corner. But the function is continuous at 4, and so the limit is just f(4).", + "video_name": "nOnd3SiYZqM" + }, + { + "Q": "At 12:22 Sal wrote that N(A) = N(rref(A)). Does that stay true if we exchange rows when we are reducing the matrix to the rref?", + "A": "If you had 2 simultaneous equations (not matrices) in x and y, and you exchanged rows, how would that affect the solution?", + "video_name": "qvyboGryeA8" + }, + { + "Q": "At 5:43 shouldn't the third row be 0 -1 -2 -3? since u r subtracting 4 from each element.", + "A": "A logical thing to do is what you are describing which is to replace the third row by the third row minus four times the first row. What Sal is doing is kind of the reverse but it works too. He is replacing the third row by the first row multiplied by four and then subtracting the third row. Both ways work and we see that they just differ by a factor of -1. I would have done it the way you suggest in your question and then multiplied by -1 but either way you get the same result.", + "video_name": "qvyboGryeA8" + }, + { + "Q": "At 15:00, the equation for projv(x) is\nA(AT A)-1 AT x where AT = A transpose and -1 means inverse\nThis formula seems like it should reduce to x since\n\n(ATA)-1 = (A-1)(AT-1) by the rule for inverse of a product\nso (A A-1) (AT-1 AT) = I I and IIx = x?\nWhat am I missing here?", + "A": "The answer is that A and AT are rectangular, not square so they have no inverse. (ATA) is invertible if A originally had linearly independent columns as per video 106 \u00e2\u0080\u009cLin Alg: Showing that A-transpose x A is invertible\u00e2\u0080\u009d", + "video_name": "cTyNpXB92bQ" + }, + { + "Q": "At 2:10, why is e^(-st) * e^(at) combine to e^(a-s)t instead of e^(a-s) ?? Wouldn't the -t and t combine to cancel??", + "A": "For multiplying terms which have the same base, (x^a) * (x^b) = x^(a + b). So, e^(-st) * e^(at) = e^(-st + at). Take out the common factor, t from (-st + at) => t(a-s), which gives us e^(a-s)t", + "video_name": "33TYoybjqPg" + }, + { + "Q": "At 2:50, why is theta taken as the obtuse angle, and not the acute angle?Isn't cos (-60)= -1/2 also?", + "A": "cos(x) = cos(-x)", + "video_name": "eTDaJ4ebK28" + }, + { + "Q": "At 12:05, what if there is bigger angle like 100 pi instead of 3pi?\nDo you still keep going around the unit circle to find out where you finally land up and then calculate the x coordinate?", + "A": "You could go around the circle 50 times to finally figure out where you land. However, if you understand that 2\u00cf\u0080 radians is a full circle, then you can save yourself a lot of trouble. 100\u00cf\u0080 = 50\u00e2\u0080\u00a22\u00cf\u0080 This means 100\u00cf\u0080 is the same as 50 full circles, and you end up on the same point on the unit circle as 0 radians. When this happens we say 100\u00cf\u0080 is coterminal to 0.", + "video_name": "eTDaJ4ebK28" + }, + { + "Q": "When he says that it looks more like an ellipse at 2:20, what is an ellipse, please?", + "A": "Basically, an ellipse is an oval. More technically, here s the definition from wikipedia: In mathematics, an ellipse is a curve on a plane that surrounds two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. As such, it is a generalization of a circle, which is a special type of an ellipse that has both focal points at the same location.", + "video_name": "eTDaJ4ebK28" + }, + { + "Q": "at 9:00, shouldn't we square it and add then take square root?", + "A": "Only if you are working with the magnitude (unit vector etc.). However in this example Sal is purely working with the vector itself in full (not the unit vector) and he s simply adding the two vectors together to get the resultant.", + "video_name": "6Kw2nIwWYL0" + }, + { + "Q": "Why is around 2:30 mins in... (1/3) dividing 3x but on the other side it is multiplying!", + "A": "He s saying that multiplying both sides of the equation by the fraction (1/3) is the same as dividing both sides of the equation by 3.", + "video_name": "kbqO0YTUyAY" + }, + { + "Q": "I got lost at 3:00 when Sal wrote 9 - 2x", + "A": "pretend 5=x. 9-2x=-1", + "video_name": "kbqO0YTUyAY" + }, + { + "Q": "6:54 anyone happen to know what the name of the theorem is or where to find out? I seem to remember better if I have a name for these things. Thanks for any help.", + "A": "I think it s called the Base Angle Theorem . Hope that helps a lil... :)", + "video_name": "nMhJLn5ives" + }, + { + "Q": "what 12:00 in night?", + "A": "12:00 at night is also known to many as midnight.", + "video_name": "ftndEjAg6qs" + }, + { + "Q": "Is it correct to say three-oh-five for 3:05", + "A": "I don t know. Though I think it would be five-past-three.", + "video_name": "ftndEjAg6qs" + }, + { + "Q": "how can i know that xy=5. at 5:53", + "A": "Look at the video. He says, that he has more of these xs and ys. He only gave us a hint how heavy xy is.", + "video_name": "h9ZgZimXn2Q" + }, + { + "Q": "This makes no sense to me once he jumps to the other scale. Essentially what he did was subtract \"x\" from the left side, and ended up with 5 on the right (in which case, the right should be 8 -x, NOT 5.) We don't have a scale in real life to keep \"adding blocks until it equals out\", this is useless, plus this automatically means x = 3 (and thus y = 2.)\n\nCan someone explain the leap in logic starting at 2:20 in the video?", + "A": "The way he put the x and y on the left and the 5kg on the right was NOT derived from previous knowledge. In other words, someone came up to you and told you x+y=5 .", + "video_name": "h9ZgZimXn2Q" + }, + { + "Q": "at 1:58 , why did sal divide the numerator by ( x-1 ) , shouldn't it be divided by (x^2 - 1) .\n\nWas this done to actually find factors for which x-1 could be eliminated .", + "A": "Sal divided the numerator by the factor (x-1) to check whether (x-1) was a factor of the polynomial (x^3 - 1), which it is. He was trying to split the numerator into factors so that he could cancel out the factor (x-1) in the main expression. The reason for doing this is because he does not want the denominator to be 0 when he plugs in x=1 to find the limit of the expression algebraically.", + "video_name": "rU222pVq520" + }, + { + "Q": "And what if at 3:15 x=(-1) ? Is the function undefined there or we can say that as \"x\" does not equal \"1\" it neither equals \"-1\" ?\nThank you.", + "A": "The function is undefined at x = 1 and x = -1. For purposes of this problem we don t care that the function is undefined at x = -1 because we re taking the limit at x = 1. As Sal points out, we also don t have to be concerned that it isn t defined at x = 1 because the operation involved in taking a limit doesn t require a function to be defined at the point where you re taking the limit.", + "video_name": "rU222pVq520" + }, + { + "Q": "I lost you at 1:53 when you said x goes in x^2 times, then backtracked and said \"actually lemme do..\" I am so confused -_-. How do you factor this problem.", + "A": "As far as I understood it, he used polynomial division after he had factored the denominator.", + "video_name": "rU222pVq520" + }, + { + "Q": "In 5:02 he says AB is congruent to segment AC but he wrote AC before AB", + "A": "In Geometry the order only matters when you say AC and AB individually. a is congruent to a, while C is congruent to B. saying CA is congruent to AB would be incorrect. Tell me if it is still unclear, I m not the best explainer", + "video_name": "7UISwx2Mr4c" + }, + { + "Q": "Sal uses a calculator throughout the video however, calculators are not allowed in my school so can someone explain how he got 10.7 around the 2:40 mark?", + "A": "Honestly, if you re not allowed calculators, you should probably just leave the answer in terms of tangent, sine, or cosine unless it s an easy value to find. 65\u00c2\u00b0 isn t an easy value to find, so this should be an acceptable answer: a = 5*tan(65\u00c2\u00b0) (this is actually a more exact answer than 10.7)", + "video_name": "l5VbdqRjTXc" + }, + { + "Q": "At 4:50 why doesn't he multiply both sides by 5 instead of multiplying them by \"b\"?", + "A": "If you multiply both sides by 5 you would get this: 5cos65 = 25/b Our goal is to get b on its own so multiplying by 5 doesn t help.", + "video_name": "l5VbdqRjTXc" + }, + { + "Q": "At 5:54 he says \" you could of solved this using the Pythagorean theorem... But there is an issue if im not mistaken:\n\n10.7*10.7 + 5*5 does not equal to 11.8?", + "A": "I don t think there is an issue he just wanted to solve using the trigonometric functions because that is what we had just been working on. Just to show, 10.7*10.7 = 114.49 5*5 = 25 114.49+25=139.49 And the square root of 139.49 = 11.8 a^2+b^2=c^2 so don t forget to square root everything.", + "video_name": "l5VbdqRjTXc" + }, + { + "Q": "At 2:13 don't you mean to say 7 7 and 9", + "A": "It s just a minor mistake. You can see that it s 7, 7, and 9. Besides, the videos are still awesome at teaching the topic!", + "video_name": "LEFE1km5ROY" + }, + { + "Q": "At 0:00, under the Stem column, why is there a 0?", + "A": "Hi Nikki. Good question. When you have a stem and leaf plot, you always have to have something on the stem side in order to have something on the leave side. So, when we want to put numbers such as 3, 7, or 9 (one digit numbers) we put a 0 on the stem side so that the value of the number doesn t change, but there is a stem for the leaves be on. :) Hope that makes sense. Syliva", + "video_name": "LEFE1km5ROY" + }, + { + "Q": "At 5:03, Sal says we can find the points (the numbers which will make both sides of the equation equal to 0). Why is it so?", + "A": "It s the same point he used to get the formula, P = (4, 9) . He used the 2 points, the variable point Z = (x, y) and a given point P = (4, 9) to get (y-9)/(x-4) = -4; so if he lets Z = (4, 9), then Z and P are the same point, and he gets (9-9)/(4-4) = 0/0, or 9-9 = -4(4-4), or 0 = 0. (Why he s saying this, I don t know).", + "video_name": "LtpXvUCrgrM" + }, + { + "Q": "@1:18 why when Sal convert 6/3 + 1/3 to 2 1/3, he emitted the (+) sign ?", + "A": "because 6/3+1/3 is equal to 2 1/3. 2 1/3 is a mixed number, so even though you say two and one third, the number you write down secludes the and.", + "video_name": "xiIQQNufFuU" + }, + { + "Q": "At 1:00, Sal said \"if y is zero..\" he then plugged in zero to the problem to find 2 1/3. How did he know y was zero. I'm lost.\n\nThanks.", + "A": "We re looking for the x-intercept. This is the point where the line crosses the x-axis. What do the coordinates of a point on the x-axis look like? They look like (x , 0). Just like for the y-intercept, the coordinates are (0, y).", + "video_name": "xiIQQNufFuU" + }, + { + "Q": "at 3:21, do you always have to flip the numbers over?", + "A": "nope, but it makes it alot easier", + "video_name": "Zm0KaIw-35k" + }, + { + "Q": "At 2:28, how come he used multiplications to solve pentagon when there was more than 1 of the same numbers, when he didn't use multiplication when he was working out the rectangle", + "A": "For the rectangle, he could ve done 2*5 + 2*3 to get the perimeter of the rectangle. I think he used multiplication for the pentagon because he would have to write 2 five times, which would take too much space. If we understand that we re adding 2 five times, that just 2 multiplied by five.", + "video_name": "9uwLgf84p5w" + }, + { + "Q": "Why doesnt he write 5c in 5:31?", + "A": "It s simpler/cleaner to just call it c. It is a constant of unknown quantity. Sure, it s 5 times something, but it s also 1 times something too.", + "video_name": "QxbJsg-Vdms" + }, + { + "Q": "At 0:24, what does he mean by derivative?", + "A": "At 0:24, Sal refers to the word derivative. A derivative of a function is the slope of the tangent line to a curve at a particular point on the curve. In this video, Sal shows how to find the antiderivative of a function using the power rule. Keep watching the video to find out what the power rule does.", + "video_name": "QxbJsg-Vdms" + }, + { + "Q": "At 5:09 how do you transition from x^-1/-1 to -x^-1 ?", + "A": "Dividing by -1 is the same as multiplying by -1, because it only changes the signal of the expression.One easy proof : (-1)^2= 1 =a/a -> {(-1)^2}f(x)=1f(x) -> -f(x).-1=-1f(x)/-1, now divide both sides by -1 and its done -f(x)=f(x)/-1 .", + "video_name": "QxbJsg-Vdms" + }, + { + "Q": "At 2:31, Sal writes x^(n+1). Does the denominator \"n+1\" apply to the whole thing or just x? (i.e. does it read ((x^(n+1))/(n+1) or (x/(n+1))^(n+1)?) Does it matter either way? Thanks!", + "A": "The whole thing. It is [(x^(n+1)]/(n+1). And yes it matters!", + "video_name": "QxbJsg-Vdms" + }, + { + "Q": "at 0:17, Sal said that if the denominator is the same, you just add the numerator and then the denominator stays the same? I just dont get it. Is it the same on the problems without the same denominators?", + "A": "no you do not add the denominator you add the numerator", + "video_name": "EJjnEau6aeI" + }, + { + "Q": "Does the endpoint always have to be the first letter when naming a ray?\nFor example at 1:27 the ray is labelled ray JH and J is the endpoint.", + "A": "Yes. Because the arrow always points to the right when naming a ray, the endpoint of the ray must always be the first letter.", + "video_name": "w9jEq6dmqPg" + }, + { + "Q": "um on 5:05 when you mentioned about GE as a ray, can GC also be a ray?", + "A": "yeah...... Im pretty sure your right that GC could be a ray too", + "video_name": "w9jEq6dmqPg" + }, + { + "Q": "I don't understand why you need to have two points for it to be a ray. Anyways there are points in between the endpoint A and the arrow (4:41 in the video)", + "A": "The first point serves to show where the ray is starting from. The second point is needed to show in which direction the ray is going. For example, if we just said ray E, it would be confusing. Is it going towards A, towards, F, or towards some other point not even drawn on the graph? Two points are needed in order to show origin and direction.", + "video_name": "w9jEq6dmqPg" + }, + { + "Q": "At 2:40 he mentions CE and CF. Which one would be better to use? or does it matter at all?", + "A": "It depends on the direction that you want to go in.", + "video_name": "w9jEq6dmqPg" + }, + { + "Q": "0:25\nIs the line of symmetry compulsory to be diagonal or horizontal to the object?", + "A": "Any line where you can fold an object and the two sides match one another is a line of symmetry. Go to Google search images and search for line symmetry .", + "video_name": "LrTn4cvsewk" + }, + { + "Q": "at 0:35 , how does he split 60 into 6 * 10 ?", + "A": "because 6 * 10 is 60, and the order of multiplication doesn t matter.", + "video_name": "jb8mFpA1YI8" + }, + { + "Q": "At 10:04, how do you remember which way to move the decimal if it's a negative exponent?", + "A": "okay heres an example -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 Negative is backwards, so just think about it like you have 2^-3 that would be 0.125", + "video_name": "i6lfVUp5RW8" + }, + { + "Q": "at 2:11 why is the line dotted instead of solid?", + "A": "A dotted line symbolizes < or > A solid line symbolizes \u00e2\u0089\u00a4 or \u00e2\u0089\u00a5", + "video_name": "CA4S7S-3Lg4" + }, + { + "Q": "at 1:20 sal says the negative cancel out. What does it mean to cancel out", + "A": "(+)(+)=(+) (-)(-)=(+) (+)(-)=(-) there is two negative, so he cancel out, because negative times or divid negative is equal to positive", + "video_name": "bQ-KR3clFgs" + }, + { + "Q": "when he takes the two out front of the integral at 2:55, do you have to do that to get the correct answer or does hat just make things easier?", + "A": "It makes things easier since you would not have to factor it out in the end after taking the integration.", + "video_name": "n-iEqLhGfd4" + }, + { + "Q": "at 6:47\nDose Sal notice this too?: b, h, c, and i are all right angles.", + "A": "If they were, yes. However, it is not given that those angles are right angles. For all we know, they could be 89 or 91 degrees or anything else close to right. Great observation though.", + "video_name": "95logvV8nXY" + }, + { + "Q": "5:44 into the video, why do you put the 2 on the outside of the square root sign?", + "A": "This problem deals with simplifying a 6th root. So, we have to find factors with an exponent =6. If we find any, then we can find the 6th root for that item. Sal has 6th root( 2^6). This can be simplified to 2. Another way to look at it is to use rational exponents: 6th root( 2^6) = 2^(6/6) = 2 The exponent of 6/6 reduces to 1. 2^1 = 2. Hope this helps.", + "video_name": "iX7ivCww2ws" + }, + { + "Q": "At 0:40, why did Sal say to turn the fraction on it's head?", + "A": "First off, notice that multiplying a number by 1/5 gives you the same answer as dividing it by 5. 5 and 1/5 are reciprocals, which means that when you multiply them you get 1 (5/1 is 1/5 flipped over). We use this property to help us divide fractions. We just multiply by the reciprocal instead. The easiest way to do that is to just flip over the fraction.", + "video_name": "tnkPY4UqJ44" + }, + { + "Q": "At 0:16, what does it mean by multiplying its reciprocal?", + "A": "The reciprocal of a fraction is the inverse of it; you basically take a fraction, flip it over, and that s its reciprocal. 3/4 is the reciprocal of 4/3, and 4/3 is the reciprocal of 3/4. Do you get that? When dividing by fractions, we turn the division problem into a multiplication problem: we take the divisor and find it s reciprocal, and then we just multiply. For example 1/2 \u00c3\u00b7 3/4 = 1/2 x 4/3 = 4/6 or 2/3", + "video_name": "tnkPY4UqJ44" + }, + { + "Q": "i am confused at 0:35 i think you switch it to multiplication", + "A": "When you divide by a fraction, it is the same as multiplying by the reciprocal. So if you have 3/8 divided by 1/2, lets say, it would be the same as multiplying 3/8 by 2/1.", + "video_name": "tnkPY4UqJ44" + }, + { + "Q": "At 0:43, is it necessary to multiply each side of the inequality by the reciprocal of -5 or can you just divide each side by -5 and still get the same answer?", + "A": "You can divide both sides by -5 and get the same answer.", + "video_name": "D1cKk48kz-E" + }, + { + "Q": "The example Sal gives at 5:51,\n(2(x+3)(x-1))/ (x+3)^2(x+1) I don't understand why x at -3 isn't a removable discontinuity. If you put -3 in the original equation without simplying, you get 0/0.\n\nThank you.", + "A": "A removable discontinuity would divide COMPLETELY out of the denominator. In this case, after the division there is still a factor of ( x + 3 ) left in the denominator, so that takes precedence over the fact that a single ( x + 3 ) was able to be divided out and indicates an asymptote at x = -3 instead of a removable discontinuity.", + "video_name": "TX_mx3qULpw" + }, + { + "Q": "At 02:35, Sal says that pi/2 there is equal to 3.5 pi over seven, how does that work out? Really trying to wrap my head around this. Why did he choose the number 3.5?", + "A": "Sal noted that quadrant I contains angles from 0 (X-axis) to pi/2 radians (Y-axis). Because he was discussing the angle of 2pi / 7 radians, he converted pi / 2 to sevenths. Half of 7 is 3.5. So he checked to see if the given angle was between zero radians and 3.5pi / 7. Because the denominators of the angles were the same, it was then easy to compare the numerators and see that 2 pi / 7 radians is less than 3.5pi / 7 radians . Ttherefore the angle of 2 pi / 7 lies in quadrant 1.", + "video_name": "fYQ3GRSu4JU" + }, + { + "Q": "Infinagons?? 3:05", + "A": "infinigons are polygons that have an infinite number of sides.", + "video_name": "D2xYjiL8yyE" + }, + { + "Q": "At 4:28 Sal finishes the Pascal Expression for (a+b)^4. He starts at a^0. Why not a^1?", + "A": "Because that s the level at which Pascal s triangle starts (2:30)", + "video_name": "v9Evg2tBdRk" + }, + { + "Q": "I see many people have questions about this: at approx 4:03, he flipped both sides of the fraction. I understand the concept of doing the same thing to each side of an equation. But what prompted him to do this for the purpose of this problem? I want to understand so I can apply this to other problems.", + "A": "When your variable is on the bottom(of a fraction), you generally want to get it to the top(of the fraction). When he was done simplifying the left side of the equation, he saw that the variable that he was trying to solve for was on the bottom(of the fraction). This probably prompted him to flip both sides of the equation, or to take the reciprocal of both sides of the equation.", + "video_name": "gD7A1LA4jO8" + }, + { + "Q": "At 4:08 Sal defines the range of f(x) as all real number such that f(x) is greater than or equal to 0. Why is it not all real numbers such that x is greater than or equal to 0? I don't really understand in this case the significance of f(x) as a function vs. a variable.", + "A": "X has to do with the domain, not the range, so if you were looking for domain, you would be fine. On the other hand, f(x) has to do with the range (this is functional notation f(x)= mx + b rather than perhaps what you are more used to in the slope intercept form y = mx+b), so that is why he says what he did.", + "video_name": "96uHMcHWD2E" + }, + { + "Q": "At 4:03 Sal places a line after the Real number notation. what does this bar mean?", + "A": "The bar means such that, so it would read all real numbers such that f(x) is greater than or equal to zero. That is also the language he used in the video.", + "video_name": "96uHMcHWD2E" + }, + { + "Q": "At 0:30, Mr.Khan asserts that a domain is \"The set of all inputs over which the function is defined.\"\n\nIf that is the case, then in the last video, at the last example, wouldn't the domain be x = 1 and x = 0?\n\nAm I missing something?", + "A": "No that would have been the range, you put in \u00cf\u0080 and 3, and get out 1 and 0.", + "video_name": "96uHMcHWD2E" + }, + { + "Q": "At 3:17, does the term \"parabola\" refer to the shape of the graph, or something else? I have NEVER heard that term before!", + "A": "The word parabola refers to the U-shape of the graph. That is the name of that shape. The equations / functions that create parabolas are quadratics. Hope that helps.", + "video_name": "96uHMcHWD2E" + }, + { + "Q": "What is a \"porabola\"? 3:20", + "A": "A parabola is a two-dimensional, mirror-symmetrical curve, which is approximately U-shaped.", + "video_name": "96uHMcHWD2E" + }, + { + "Q": "At 3:48, why can't x be negative? .", + "A": "The domain (values of x) is any real number. It s the range (values of y) that cannot be negative. That s because y = x^2 , and we know that squaring anything (whether x is positive or negative or zero to begin with) cannot produce a negative result.", + "video_name": "96uHMcHWD2E" + }, + { + "Q": "at 7:20 why do you ignore the denominators when solving the equation?", + "A": "Both sides of the equation have the same denominator, so multiplying the numerators on both sides by the denominator cancels them out, which has the same effect as ignoring them. Example: x/3 = y/3 Multiply both sides by the denominator 3: 3 * (x/3) = (y/3) * 3 3x/3 = 3y/3 Simplify: x = y It s the same result as ignoring the denominators.", + "video_name": "S-XKGBesRzk" + }, + { + "Q": "4:13 to 4:30 is confusing", + "A": "double lines mean that that angle is the same as the other angle with the same two lines.", + "video_name": "wRBMmiNHQaE" + }, + { + "Q": "why does he put hash marks on the angle markers ? like at 4:40", + "A": "He puts hash marks on the angle markers to show that the marked angles are congruent. If he didn t put hash marks on the angle markers, the (previously marked) angles would be considered congruent to the other two angles.", + "video_name": "wRBMmiNHQaE" + }, + { + "Q": "at 1:16 Sal put a decimal point and some zeros on the 63 would he be able to put a decimal and zeros on the 35 without changing the question", + "A": "yes, the decimals don t change anything because they have no value. 0.00 = 0 35 + 0.00 = 35 the decimals just help with solving the problem", + "video_name": "xUDlKV8lJbM" + }, + { + "Q": "Why e^-u at 2:33.I dont get it!", + "A": "Basic property of powers in a fraction: those on the bottom are negatives of those on the top. 1/x = x^(-1) Therefore, 1/e^u = e^(-u) to get rid of the fraction.", + "video_name": "ShpI3gPgLBA" + }, + { + "Q": "Is RSH at 2:39 a real theorem? Or just another name for the HL postulate?", + "A": "RSH is actually the HL congruence Theorem", + "video_name": "q7eF5Ci944U" + }, + { + "Q": "At 2:25, why did Sal used inverse of Sine to calculate the Radian angle (am I using that terminology right?) instead of just normal Sine? how do you know when to use the inverse calculation?\n\nALSO, we us 2pi because that'll give us a full circle revolution back to the starting, correct? But why is there a need to multiply it with a n integer? Can the answer just be 0.34 + 2pi?", + "A": "The sine function takes an angle and gives you the ratio of the side lengths. If you have the ratio of the side lengths and you are looking for the angle instead, this is when you would use the inverse of the sine function. And, since sine is a periodic function, the value will repeat infinitely. The 2pi*n is necessary to give ALL of the answers, as opposed to only the answers in the first rotation.", + "video_name": "NC7iWEQ9Kug" + }, + { + "Q": "At 2:11 in this video, why does Sal use the dot instead of the regular multiplication sign, the regular times symbol?", + "A": "In *Algebra and above, there are things called variables, which are symbols to represent numbers. x is used as one of these variables, so Algebra people use a dot as the multiplication symbol.", + "video_name": "xkg7370cpjs" + }, + { + "Q": "At around 7:05, he said that 2(pi radius) = 360degree, but afterwards he said that 2(pi RADIANS) = 360degree. Why is this so? I know that radian is an angle, and radius is a length, but how can they be used as the same variable in such an equation?", + "A": "Listen again even more carefully from about 5:40 to 7:15. Sal said that 2pi radiusseses SUBTEND an angle of 360 degrees and that 360 degrees is the SAME as an angle of 2pi radians. Hope this is of use to you!", + "video_name": "EnwWxMZVBeg" + }, + { + "Q": "At 0:07 Sal mentions that Stewart has a negative amount of money in his account; how is that possible?\n\n\nIs it because he's in debt?", + "A": "It is impossible to achieve a negative amount of money in your account unless you take something that isn t yours. So to answer your question, yes, it means he is in debt", + "video_name": "fFdOr8U4mnI" + }, + { + "Q": "so at (0:19) twice as much means multiply the age or halve it", + "A": "If the problem says something it s twice as much, it means the amount is two times the value. In this case, Jared is twice as old as Peter. This means he is two times older than peter. If peter is 5, Jared will be 10 since 10 is twice as much as 5.", + "video_name": "bS6EmYzpou4" + }, + { + "Q": "You lost me from 0:36", + "A": "It is like that because, let s say if x = 0 and we know that y = x+2 so: y = x+2 y=0+2 y=2 So, there the coordinates will be (0,2) Hope it made sense.", + "video_name": "RLyXTj2j_c4" + }, + { + "Q": "At 5:02 He says that a 2 - tuple is not a member of 3D real co-ordinate space. Why is that? Can't we just say that a 2 - dimensional vector has zero value for the z-axis? Can't we imagine 3-d space consisting of a lot of planes stacked up?", + "A": "the keyword is 2 tuple . you can t have a 2 tuple that has x y and z components, that s all. but you can represent a 2 dimensional vector as a 3 tuple, it s just that one component will always be zero.", + "video_name": "lCsjJbZHhHU" + }, + { + "Q": "At 1:55, he says 'neither of these have any imaginary parts'. Does this mean it cannot have x or y or n or any unknown number in it?", + "A": "No, it means that only Real numbers are components of that vector, rather than the option of complex numbers as well, such as the square root of negative 1.", + "video_name": "lCsjJbZHhHU" + }, + { + "Q": "8:35 does that also mean that g(x)-h(x) and h(x)-g(x) are also solutions?", + "A": "Yes, it does. 0 - 0 does equal 0. In fact any linear combination of g and h will be solutions. You can do a*g(x) + b*h(x), where a and b are any constants, and that will be a solution.", + "video_name": "UFWAu8Ptth0" + }, + { + "Q": "at 5:58, he says that if g(x) is a solution then c1*g(x) is also one, does this mean that 0 is a solution to all of these?", + "A": "Homogeneous systems have a few properties, and one of those properties is that they always have at least one solution, the trivial solution, 0. The goal is to find the non-trivial solutions in most cases.", + "video_name": "UFWAu8Ptth0" + }, + { + "Q": "At 0:15, how does the second prize relate to the first prize? Doesn't the first prize have a predetermined ticket, thus making it an independent event?", + "A": "The first prize is a independent event, yes. But the second prize is dependent on the first prize because the ticket drawn for the first prize is not but back in.", + "video_name": "Za7G_eWKiF4" + }, + { + "Q": "I know this is simple, but I just wanted to reassure myself. At around 8:27 when Sal multiplies the triangles, the formula is b times hieght divided by 2. Now does that only count for that one half of the triangle? Is that why he had to multiply it once more? Also, hypothetically, if I were to encounter a triangle such as this again, would I do the method shown here to find its area?", + "A": "(base x height)/2 is the formula for the whole triangle, and every other triangle you ll ever see.", + "video_name": "vaOXkt7uuac" + }, + { + "Q": "2:02 i was taught like 29+59+?=180\n? = 180 - (29+59)\n? = 180 - 88\n? = 92 degrees.\n\ncan i do it in this way also?", + "A": "Yes, although this method might not work with more complicated multi-step equations. This method does work however for interior triangle angles.", + "video_name": "eTwnt4G5xE4" + }, + { + "Q": "In 1:37 Sal wrote 59+29+x=180, and he wrote 180-59-29=x, why he is subtracting if the original operation is addition? Can you add those two numbers, and subtract the total by 180 and you will get the missing angle?", + "A": "Both ways end up giving you the same answer for x. You can just use the way that is the easiest for you to use.", + "video_name": "eTwnt4G5xE4" + }, + { + "Q": "Is it possible to have a matrix the entries of which are other matrices? Like, in 3:15, when Sal says a matrix can be used to represent the intensity of pixels, maybe you could have a matrix with a cell for each pixel, but the entry is an actual 3x1 matrix that represents the RGB components of this pixel. Does this actually exist?", + "A": "I m also asking this because when I attended some lectures about the Standard Model of Particle Physics, the lecturer kept talking about polymatrices . I cannot say I fully understood the lectures, not even understood, I attended them just for a challenge. Also, my Linear Algebra concepts where almost none (though they are improving now). But despite all this, I deduced he was talking about matrices inside matrices, although might be I deduced wrong. When I try and look up polymatrix , I find no results.", + "video_name": "0oGJTQCy4cQ" + }, + { + "Q": "At 1:08 - 1:13, Sal mentions radians. What are they?", + "A": "Radians are basically units used for measuring angles. In a circle, if finding the radians of a circle, it would be that particular sectors arc length.", + "video_name": "D-EIh7NJvtQ" + }, + { + "Q": "At 0:47, when they are talking about more open and less open are they ever going to give names to those angles", + "A": "less open means acute and more open is obtuse, and if the angle forms a right angle it is 90 degrees", + "video_name": "D-EIh7NJvtQ" + }, + { + "Q": "AT 3:05 and 3:56 what is the difference between the number lines?", + "A": "When the inequality is equal or less than/greater than we use a closed circle (solid dot) as in the first number line. When it is less than/greater than we use an open circle as in the second line.", + "video_name": "ilWDSYnTEFs" + }, + { + "Q": "at the 9:23 shouldn't it be -1 = f\"(y)", + "A": "He corrects himself at 9:41", + "video_name": "Pb04ntcDJcQ" + }, + { + "Q": "1:32 sal said 20 when it is actually -20, isn't it?", + "A": "It was just a mistake, and they put an infobox at the bottom-right when the mistake comes along to fix what he says.", + "video_name": "H0q9Fqb8YT4" + }, + { + "Q": "According to 3:58, is it safe to say that a ray (or 2 rays closed together) has 0 degrees angle and a line has 180 degrees angle?", + "A": "You can do that if you show where the vertex is.", + "video_name": "92aLiyeQj0w" + }, + { + "Q": "At 3:50 Sal mentioned that we knew b was negative so he changed the inequality. What do we do if we don't know for sure if b is negative or if it could be both?", + "A": "Can I use a condition |A| =/> |B| ? *absolute value of A has to be same or higher than absolute value of B", + "video_name": "0_VaUYoNV7Y" + }, + { + "Q": "At 1:01 in the video, Sal said you need to find the common denominator, which he made 18. It makes sense, but would it also work to make the denominator 6 instead of reducing at it at the end? So instead of having 3/18 and 12/18, you had 1/6 and 4/6?", + "A": "Yes... if you reduce 3/18 before you even start, you get 1/6 Then, you can use a common denominator of 6. Great work in seeing that option!", + "video_name": "8Eb5MWwcMMY" + }, + { + "Q": "at 3:10 he breaks 10 down into it's prime numbers. if there is a number all alone do you always have to break it down?", + "A": "I quess you mean break down 10 in its primenumbers like 10=2times5. this is not necessary. remember that the goal was to make the fraction as simple as possible. In that case you make the denomenator as simple as possible. not the numerator. for instance: 2/4 you make it 1/2 3/9 you make it 1/3 6/3 you make it 3/1 so remember 10 is the same as 10/1 which you would simplify to 10. and besides 10 is easier to write than 2times5.", + "video_name": "gcnk8TnzsLc" + }, + { + "Q": "where did the 1/3 come from @4:27 ? is it possible to just reduce the fraction\n27/1 * 2/3--> 9/1 * 2/1 = 18 and 8/1 * 2/3--> becomes 16/3=8 so 18/8 is 9/4 ?? would that work for all other problems?", + "A": "An exponent of 2/3 is not the same as multiplying by 2/3. If you have 9^2, you don t do 9*2. You must do 9*9. An exponent of 2/3 tells you that you need to find the cube root of the base, then square the result. 27^(2/3) = cuberoot(27)^2 = 3^2 = 9 (not the same as your value of 18) 8^(2/3) = cuberoot(8)^2 = 2^2 = 4 (not 16/3, which is your value) Hope this helps.", + "video_name": "S34NM0Po0eA" + }, + { + "Q": "Could what he showed at 1:38 be applied to logarithms in the same way it is showed here?", + "A": "Yes. for example, log(125)25=2/3 because the cube root of the square of 125 (15625) is 25. The cube root of 125 is 5, and 5^2 is 25.", + "video_name": "S34NM0Po0eA" + }, + { + "Q": "at 4:48 does 3/2=9/2 instead of 9/4?", + "A": "No, 3/2=9/4 because you are squaring both the numerator and the denominator. Therefore: 3^2=9 2^2=4 So, (3/4)^2=9/4", + "video_name": "S34NM0Po0eA" + }, + { + "Q": "at 0:17 if i flip the sides i mean write 11+a would that still be the same as a+11 is int that the commutative law of addition or it doesn't count when we use a variable?", + "A": "You got it! a + 11 is equivalent to 11 + a via the commutative law.", + "video_name": "640-86yn2wM" + }, + { + "Q": "In 2:40, Sal said if it goes 6 down but moved his cursor 6 sideways. Why?", + "A": "He said if x goes down by 6. It means 6 in the negative direction of the x axis (left). He should had said decrease instead of down to make it less confusing.", + "video_name": "uk7gS3cZVp4" + }, + { + "Q": "At 0:50 seconds why did you made the slope zero and cancel it out?", + "A": "He wants to find the y-intercept, which is the point where the line crosses the y-axis. This point obviously has to be exactly on the y-axis. For a point to be exactly on the y-axis its x value has to be exactly zero. So he substitues the 0 for x in the line`s equation to find the y value of this point, which allows him to find the coordinates of the y-intercept.", + "video_name": "uk7gS3cZVp4" + }, + { + "Q": "At 1:11 how do you know that b is on the y intercept and how do you know y will be on zero?", + "A": "1) What is x where the y axis crosses the x axis? What is the x coordinate of the y axis? 2) What is x where any line intersects the y axis? Now, all the points (x, y) on the line satisfy y = mx + b . What is the x coordinate of the point on the line where the line intersects the y axis? What is the equation for the point on the line at x=0? (y = m*0 + b; or y = b).", + "video_name": "uk7gS3cZVp4" + }, + { + "Q": "at 8:00 Sal shows that lim u->0 of ln (Z)= ln (lim u->0 of Z). Is this a property of limits that I don't remember?", + "A": "It s the property of limits having to do with continuous functions. If f is continuous, then lim_{x->c}f(g(x)) = f(lim_{x->c}g(x)). basically you can move the limit inside a continuous function.", + "video_name": "yUpDRpkUhf4" + }, + { + "Q": "How did the substitution that u is equal to 1/n get thrown in? At 9:16, Sal gives the example that the limit as n goes to infinity of (1+1/n)n is e, yet the limit being discussed in the problem is as u goes to 0, not infinity.", + "A": "As n goes to infinity, 1/n will go to zero (limit as n->infinity of 1/n = 0) because one over a really big number is very close to zero. Therefore, when we substitute u for n, we change the limit from n->infinity to u->0.", + "video_name": "yUpDRpkUhf4" + }, + { + "Q": "at 3:10 how did we get exactly 1/delta x * ln(1+ delta x/x)??\ni'd like to see more detailed way of getting 1/delta x * ln(1+ delta x/x)", + "A": "a/b is the same thing as 1/b * a. In this case, the a is a complicated looking thing, but the rule still works. the b is \u00ce\u0094x.", + "video_name": "yUpDRpkUhf4" + }, + { + "Q": "At 5:27, Sal says \u00ce\u0094x=\u00ce\u00bc, but I thought \u00ce\u0094x=x\u00ce\u00bc.", + "A": "He never said (delta)x = u He said if (delta)x approaches 0, then u also approaches 0, as they are directly proportional.", + "video_name": "yUpDRpkUhf4" + }, + { + "Q": "In 0:45. How could we say that we are multiplying dx and the function if dx is just a notation that we are integrating with respect to x?", + "A": "Let me explain dx to you. dx is not a notation. It is used like a notation in evaluating intergals, but it is basically an infinetly small value of x (think of it as limit approaching zero). So, f(x)*dx means a rectangle with height of f(x) and base of an infinetly small number, so that it could be used for intergrating area under curve more accurately than using rectangle with base 1 or 2. Hope this helped you a bit. If not, please check out Sal s lesson about intergration.", + "video_name": "btGaOTXxXs8" + }, + { + "Q": "at 16:14, how do we know that m,n,p must be 527, 11, 40. In other word, how do we know for sure that cannot be any other m,n,p that result the same value of area?", + "A": "The question indicates that m and p are relatively prime , which means the fraction m/p is not reducible to any other integers. Also, it says that n is not divisible by the square of any prime, which means the number under the radical cannot have any perfect squares factored out. These instructions rule out any other m, n, or p that can give an equivalent correct answer.", + "video_name": "smtrrefmC40" + }, + { + "Q": "At 12:06, how did you get 2 (25/2) ^2 (1 + sine theta) from 2 (25/2) ^2 + 2 (25/2)^2 sine theta?", + "A": "The expression 2(25/2)^2 + 2(25/2)^2sin theta has two terms. Both of these terms has a common factor 2(25/2)^2. Sal pulled this factor out of both terms. Let s make a substitution so it might be easier to see: let x = 2(25/2)^2. Then the expression becomes x + xsin theta. We pull the x out to become x(1 + sin theta). This is simple factoring out, or Sal sometimes calls it undistributing. We can redistribute the x to both terms by multiplying through to get x + xsin theta.", + "video_name": "smtrrefmC40" + }, + { + "Q": "At 5:52 pm what if it ask what is 39 percent of 700 how would you solve that?", + "A": "Best thing for this problem would be to divide 700 by 100 to get the amount of 1% (7) then multiply 7 by 39 to get 39% of 700 which is 273.", + "video_name": "FaDtge_vkbg" + }, + { + "Q": "at 7:45, why does the Eigenvector equal span (1/2, 1), not span (1, - 1/2)?", + "A": "these are equivalent, since (1,-1/2) is in the span of (1/2,1) and vice versa. So it doesn t matter which one you choose, both statements are correct.", + "video_name": "3-xfmbdzkqc" + }, + { + "Q": "at 1:24, Where on earth did Sal swipe that 2 from?", + "A": "I think Sal recognized 30 = 6*5 = 2*3*5. That s why he tried multiplying it by 2. Don t wrap your mind around it too much. I tend to like this approach better: Let a = 5x\u00c2\u00b2 The expression would then be a\u00c2\u00b2 - 6a + 9 You now know how to solve it.", + "video_name": "o-ZbdYVGehI" + }, + { + "Q": "At 1:27 where did the 2 come from?", + "A": "Sal is using the pattern created by squaring a binomial. Here s the pattern: (a+b)^2 = a^2 + 2ab + b^2 Here s where the 2 comes from... use FOIL and multiply (a+b)(a+b) ... (a+b)(a+b) = a^2 + ab + ab + b^2 Notice... the 2 middle terms match. When you add them you get 2ab. That s where the 2 comes from. Hope this helps.", + "video_name": "o-ZbdYVGehI" + }, + { + "Q": "at 1:00 isn't profit a second variable?", + "A": "Because the problem gives you the value for Profit, a second variable is not needed. You could use a variable, but you would immediately swap it out because you know the value of the variable. Hope this helps.", + "video_name": "roHvNNFXr4k" + }, + { + "Q": "At 3:21,how is S the same thing as 9/9?", + "A": "s is not 9/9. if it was, Sal would have gotten rid of the s. any number times 1 is itself, and 9/9 = 1. so 9/9 * s = s * 1", + "video_name": "vBlR2xNAGmo" + }, + { + "Q": "at 2:10 sal says between that and that why do we have round down or up for example can 1,251 be rounded to 1,250 rather then 1,300", + "A": "Yes it can! But not if you are rounding to the nearest hundred. If you were rounding to the nearest 50, you WOULD round to 1,250. But 1,250 does not have only zeros after the hundreds place, so in rounding to the nearest hundred that would not be right.", + "video_name": "fh8gkPW_6g4" + }, + { + "Q": "Why did Sal draw two lines over the angles at 1:18?", + "A": "To show that both angles became one angle", + "video_name": "jRrRqMJbHKc" + }, + { + "Q": "At 3:52, why did Sal say 10 to the 3rd power instead of 10 cubed?", + "A": "10 to the 3rd power is the same thing as 10 cubed. They are just two different ways of saying the same thing. Similarly, 10 to the 2nd power is the same thing as 10 squared.", + "video_name": "YJdCw2fK-Og" + }, + { + "Q": "At 2:16 the sign is little bit confusing. More explanation. Thanks", + "A": "Sal wrote b < x < c. Between the points b and c on the x-axis, but not including those points, the function is negative. Notice, as Sal mentions, that this portion of the graph is below the x-axis. That is your first clue that the function is negative at that spot. Hope this helps.", + "video_name": "KxOp3s9ottg" + }, + { + "Q": "why is it not factorial at 2:14?", + "A": "Because when you are allowed to use a letter more than once, you do not need to take it out of the possibilities for the next letter. You can use HHH, as Sal said. So you don t need to make it 26x25x24 because the numbers reset every time you add a new slot.", + "video_name": "VYbqG2NuOo8" + }, + { + "Q": "At 6:00 he swaps a row with another and add a -ve sign. If further down the computation process, if we have to swap another row, do we add another \"-\" sign thus making the Det. positive again..or does the minus stay no matter the no. of row-swaps?\n\nThanks", + "A": "Yes, each row or column swap results in the determinant being multiplied by -1. If you do an odd number of swaps, the determinant is therefore negative, and a positive number of swaps keeps it positive.", + "video_name": "QV0jsTiobU4" + }, + { + "Q": "At 5:54, why exactly did you combine C1 and C2 to have the constant C? Aren't you supposed to solve for C2 and C1 separately?", + "A": "C\u00e2\u0082\u0081 and C\u00e2\u0082\u0082 are just constants, numbers, and they are subtracting each other, so not only it makes sense to combine them into a single constant, but it would be impossible to find their values independently. You would end up with and equation in the form C\u00e2\u0082\u0081 - C\u00e2\u0082\u0082 = 0, and there are an infinite number of possibilities here.", + "video_name": "DL-ozRGDlkY" + }, + { + "Q": "At 4:36 shouldn't the integral be equal to e^ (1 - x^2)/ 2*(1 - x^2) ?", + "A": "No, I m not sure where you re getting (1 - x\u00c2\u00b2). This is an integral best done with u-substition: u = - x\u00c2\u00b2 du = - 2x dx so 1/2\u00e2\u0088\u00ab -2x e^-x\u00c2\u00b2 dx = 1/2 \u00e2\u0088\u00ab e^u du = 1/2 e^u + C = 1/2 e^-x\u00c2\u00b2 + C", + "video_name": "DL-ozRGDlkY" + }, + { + "Q": "Wait. So are all of the foreheads blue, or not? because if they're all blue it should only take 2 times. (as in open lights shut lights open lights shut and everyone is gone.) At 0:09 that's what it said, but... ok this is getting confusing", + "A": "every person would see a number of blue foreheads. if I HAVE a blue forehead I see one less than the total number of blueforeheads. If I have other than blue forhead I see the total number of blue foreheads. everone would leave on the number of blue foreheads seen plus one. So all blue foreheads would leave on the total number of blue foreheads time the light goes out, while the other foreheads are wating for the total number of blue foreheads plus one.", + "video_name": "-xYkTJFbuM0" + }, + { + "Q": "At 3:32, is anything better than Sal using the word \"DUDE\" in an educational context?", + "A": "No, no there isn t.", + "video_name": "-xYkTJFbuM0" + }, + { + "Q": "so does that mean that 1.999....=2? I hope it does, i lost track after 1:26", + "A": "I think this was already answered for you, but I m not sure so I will. Yes, 1.999.... is equal to 2. Think about it as (1 + .999....) = 2.", + "video_name": "TINfzxSnnIE" + }, + { + "Q": "At 07:42: You will never reach _____ steps or 1/3: What is the blank?", + "A": "The blank is infinity", + "video_name": "TINfzxSnnIE" + }, + { + "Q": "At 3:24 how does infinity minus 1 still equal infinity?", + "A": "because it was declared as a rule in math. I know that isn t a great answer but it works. The best answer is because its not a real number. When we add something to a real number we get that number plus 1. Since infinity is not bound by the laws of real numbers it doesn t have to behave that way. I suppose you could say it operates above the laws of real numbers in the hyper-real number space.", + "video_name": "TINfzxSnnIE" + }, + { + "Q": "At 2:35 she did a thing where she said anything equals anything, when all she said was that:\n\nX = 0\n42 * 0 = 0\n42x = x\n0=0\n\nYou should get 0 = 0, which is true.\nCorrect me if I'm wrong please", + "A": "Her last step from 42x=x was to divide both sides by x, getting 42=1. Then you can subtract 1 from both sides to get 41=0. Divide by 41 to get 1=0. And multiply by any number c to get c=0. So any number equals 0. But her work is invalid, because she defined x=0. So when she divided by x, she was dividing by 0, which is undefined precisely because of this issue it raises.", + "video_name": "TINfzxSnnIE" + }, + { + "Q": "at 3:55, how did he come up with 10-9/12? help?", + "A": "The 10-9/12 came from the right side of the equation: 5/6 - 3/4 and in order to subtract 3/4 from 5/6 we need to have like denominators. The LCM for 5/6 and 3/4 is 12, therefore 5/6 = 10/12 and 3/4 = 9/12 Which gives us 10/12 - 9/12 or 10-9/12 = 1/12", + "video_name": "DopnmxeMt-s" + }, + { + "Q": "at 2:19 i didnt hear what sal said what did he say", + "A": "he said ...times minus nine...", + "video_name": "DopnmxeMt-s" + }, + { + "Q": "At 2:34 couldn't you factor out both the 3 and the 5 to get 15? Wouldn't 15(a+b)=2 be correct?", + "A": "3a+5b=2 To factor, both terms must have a same common factor. Meaning to factor out a 3, the b-term must have a factor of 3 as well. Likewise, to factor out a 5, the a-term must have a factor of 5. Since neither have any common factor, you can t factor it. And certainly, neither of them has a factor of 15.", + "video_name": "CLQRZ2UbQ4Q" + }, + { + "Q": "WHat does recipocral mean? 3:01", + "A": "the reciprocal means the opposite of a number", + "video_name": "bAerID24QJ0" + }, + { + "Q": "At 4:20 how did you multiply the fraction -4/3 to the fraction 10/13.\nI was quite confused there.....", + "A": "To multiply fractions: 1) Multiply the numerators: -4 (10) = -40 2) Multiply the denominators: 3(13) = 39 3) This creates the fraction -40/39. 4) To change to a mixed number, divide -40 by 39. The remainder becomes the new numerator: -40/39 = -1 1/39", + "video_name": "bAerID24QJ0" + }, + { + "Q": "At 2:05, how did you get pi. When he said m 10 instead of 8r - 13 < 10. Hope this helped.", + "video_name": "x5EJG_rAtkY" + }, + { + "Q": "I'm curious: In the first problem, why didn't we rewrite y=x^x as \"log base x of y = x\" and take the derivative of that? I tried it, but I get a different answer (I get y*ln(x) ).\n\nThen, another question: at 5:09 Sal says \"If we haven't solved this, you can just keep taking the natural log of this...\" - I tried that ( ln(ln(y))=xln(x)+ln(ln(x)) ), and I get a different answer (I get y*ln(y)*(ln(x)+1+1/(x*ln(x)) ).\n\nWhat am I doing wrong?", + "A": "y = x^x ln(y) = ln(x^x) ln(y) = x\u00e2\u0080\u00a2ln(x) d/dx(ln(y)) = d/dx(x\u00e2\u0080\u00a2ln(x)) d/dx(ln(y)) = d/dx(x)\u00e2\u0080\u00a2ln(x) + x\u00e2\u0080\u00a2d/dx(ln(x)) d/dx(ln(y)) = d/dx(x)\u00e2\u0080\u00a2ln(x) + x\u00e2\u0080\u00a21/x\u00e2\u0080\u00a2d/dx(x) d/dx(ln(y)) = d/dx(x)\u00e2\u0080\u00a2ln(x) + x\u00e2\u0080\u00a21/x\u00e2\u0080\u00a2dx/dx d/dx(ln(y)) = d/dx(x)\u00e2\u0080\u00a2ln(x) + x\u00e2\u0080\u00a21/x d/dx(ln(y)) = d/dx(x)\u00e2\u0080\u00a2ln(x) + 1 d/dx(ln(y)) = dx/dx\u00e2\u0080\u00a2ln(x) + 1 d/dx(ln(y)) = ln(x) + 1 1/y\u00e2\u0080\u00a2d/dx(y) = ln(x) + 1 1/y\u00e2\u0080\u00a2dy/dx = ln(x) + 1 dy/dx = y\u00e2\u0080\u00a2(ln(x) + 1) y = x^x dy/dx = [x^x\u00e2\u0080\u00a2(ln(x) + 1)]", + "video_name": "N5kkwVoAtkc" + }, + { + "Q": "4:24 how does sal equate D/V from V=D/T?", + "A": "V = D/T Multiply both sides by T: VT = D Divide both sides by V: T = D/V", + "video_name": "Uc2Tm4Lr7uI" + }, + { + "Q": "At 2:58 he says 3/4, Can anyone tell me where he got that from? And also where'd he get 2(distance to gift store) from?\n\nThank you :)", + "A": "45 minutes * 1 hour/60 minutes = 45/60 hours (since minutes cancel out). Both 45 and 60 are divisible by 15 so you can simplify it to 3/4 (hours). The distance to the gift store is the same as the distance from the gift store since he is taking the same path in both directions, so you can view it as 2 * distance to the gift store.", + "video_name": "Uc2Tm4Lr7uI" + }, + { + "Q": "At 3:05, how do you convert the minutes into hours?", + "A": "multiply by 60 since there are 60 minutes in an hour. Hope this helps!", + "video_name": "Uc2Tm4Lr7uI" + }, + { + "Q": "in the first example, at 2:11 you have simplified it to -sqrt5/sqrt35, the proceed to rewrite this as -sqrt(5/35) and end with the result of -sqrt(1/7).\n\nWhen solving this on my own, after i reached the step you were at at 2:11, I simplified it to:\n-sqrt5 / (sqrt7)(sqrt5) and cancelled the sqrt5 to end with -1/sqrt(7).\n\nI believe these are both correct, as your example of the whole fraction under the radical could simplify to my form, however which would be considered the most simple answer?", + "A": "They are both equivalent. It depends on how your instructor wants the answer to be really. Both are simple enough. Later on you ll learn to rationalize the denominator, so you ll most likely require to do that. You simply multiply - 1/\u00e2\u0088\u009a(7) by \u00e2\u0088\u009a(7) / \u00e2\u0088\u009a(7) which will give -\u00e2\u0088\u009a(7)/7. P.S. He mas an error, forgetting to include his negative sign.", + "video_name": "suwJmCrSDI8" + }, + { + "Q": "At 5:30 sal says that the limit of f(c) as x approaches from the negative direction does not exist.\nHow is it?\nWhat does the point over the hole mean?", + "A": "Think of a simpler formula, where if x < c, then f(x) = 1; and where x >= c then f(x) = 2. If you are determining the limit from the left (ie the lower direction) your limit would equal 1, but the value for c derived from f(x) is actually 2 - thus the limit does not exist, because: lim f(x) (x->c-) = 1 f(c) = 2 -John", + "video_name": "kdEQGfeC0SE" + }, + { + "Q": "At 3:48 I don't understand how the 2 gets under c^2 and disappears from the other side. Is it being added, subtracted, multiplied, or divided?", + "A": "The 2 dissapears on the left side because the expression is divided by 2 on both sides.", + "video_name": "tSHitjFIjd8" + }, + { + "Q": "at 8:21 I don't understand wouldn't you divide instead of multiply?", + "A": "b/c you re multiplying it by the inverse", + "video_name": "tSHitjFIjd8" + }, + { + "Q": "So at 1:16 I understand that the slope is rise over run and that the line has a negative slope because its going down, but why is going right positive for x and left is negative?", + "A": "on a graph onthe x axis the right side is positive while the left is negative", + "video_name": "AqFwKecNaTk" + }, + { + "Q": "5:01 what are assymptotes? (I don't think I spelled that right)\nSal keeps mentioning them but I think if I don't know what they are I'm not going anywhere with hyperbolas....", + "A": "an asymptote is a line that the function gets infinitely close to but never touches. You draw them on your graph before you draw your hyperbola (using dotted lines).", + "video_name": "pzSyOTkAsY4" + }, + { + "Q": "at 5:15 sal says that the asymptotes are the negative slope of each other. can i say that they are perpendicular lines with the same y-intercept?", + "A": "yes for the perpendicular but no for same y intercept, because in more complex examples there will be horizontal and vertical shifts which will make the y intercepts of each asymptote different. Try searching for examples of hyperbolas with shifts and see their graphs to understand more.", + "video_name": "pzSyOTkAsY4" + }, + { + "Q": "At 7:40, Sal got rid of the -b^2, how is that possible?", + "A": "As x approaches infinity, the b\u00c2\u00b2 term becomes less and less significant. For example, consider x = 1,000,000 and b = 5 .", + "video_name": "pzSyOTkAsY4" + }, + { + "Q": "At 4:25 when multiplying b^2, why does the x^2 get moved from the numerator?", + "A": "x^2 is still part of the numerator - just think of it as x^2/1, multiplied by b^2/a^2. you could also write it as a^2*x^2/b^2, all as one fraction... it means the same thing (multiply x^2 and a^2 and divide by b^2 ->> since multiplication and division occur at the same level of the order of operations, both ways of writing it out are totally equivalent!). hope that helps", + "video_name": "pzSyOTkAsY4" + }, + { + "Q": "at 2:30, wouldn't those equations result in the same shape? if not, how are they different?", + "A": "the equation x2/a2-y2/b2 has the x-axis as the major axis while the equation y2/b2-x2/a2 has the y-axis as the major axis.", + "video_name": "pzSyOTkAsY4" + }, + { + "Q": "But when we are graphing g(x)=2-x at 8:00, should't the line be moved more upwards on a y-axis?\nThank you!", + "A": "If you notice 2 is the y-intercepts in the equation y = -x + 2 in the form y = mx + q", + "video_name": "rOftmuhGLjY" + }, + { + "Q": "At 3:21, how Sal got 1.5 the original population, did he assumed that or there is some logic behind it.", + "A": "He said he wanted the population to increase by 50% over 20 years. So, it ll be 150% of the current population, or 1.5.", + "video_name": "-fIsaqN-aaQ" + }, + { + "Q": "Around 4:15 when he found du, why did he keep the ln(2) if it is a constant? Isnt the derivative of a constant 0? Or did he use the product rule?", + "A": "yes he did use the product rule.", + "video_name": "1ct7LUx23io" + }, + { + "Q": "At 5:16, Sal puts a negative sign in front of the inverse of ln8. Is it correct that it should be an equal sign? As far as I can tell, the solution works out only if ln8 is not negative.", + "A": "It actually is an equal sign, but it is very hard to see it the way he wrote it . :)", + "video_name": "1ct7LUx23io" + }, + { + "Q": "At 0:52 how is their a 2/3 in 5/3 x 2/5? You aren't multiplying anything by 2/3. I understand there is a 2 and a 3 in the equation but that isn't 2/3 like the fraction.", + "A": "With the commutative property for multiplication, you can move the factors around within the numerator and denominator, so you can see the 2/3 fraction that way and factor it out 0:51.", + "video_name": "yUYDhmQsiXY" + }, + { + "Q": "At 1:18, are you sure it's 2 by 3 because I'm pretty sure it's 3 by 2?", + "A": "This way of identifying matrices is arbitrary: we all agree (or: most of us do, I think! :) to name the rows first and the columns second. (The first matrix in the video is 2X3, the second is 3X2.) We (or they) could have reversed the order, but since that s the way others do it, so will I (if I can remember it!).", + "video_name": "OMA2Mwo0aZg" + }, + { + "Q": "At 3:36, Sal mentions that there is a positive derivative and then zero and then a negative derivative after the critical point x=2. But the graph has a negative slope. How is it that it's positive then?", + "A": "The graph is of the derivative not of the original function. This means that when the derivative is positive the function has a positive slope and when the derivative is negative the original function has a negative slope. And the derivative is equal to zero at the function s critical points of +2 and -2.", + "video_name": "pInFesXIfg8" + }, + { + "Q": "Other than visually (3:44) how do you know if the derivative is positive or negative before the critical point.", + "A": "The simple way to do that is to pick a convenient point just before and just after the critical point and plug those values into the first derivative to see whether it is negative or positive.", + "video_name": "pInFesXIfg8" + }, + { + "Q": "At 10:40 Sal said that t does not have to be time, so what other things can t be?", + "A": "Maybe you re trying to describe the path of a complicated music box dancer that moves as you turn a crank. In that case, the independent variable might not represent time but the number of rotations that you gave the crank from its resting place, but traditionally in parametric equations we d call it t even though it isn t about time in that case.", + "video_name": "57BiI_iD3-U" + }, + { + "Q": "in 10:24 when Sal uses pi and pi/2 for his time, is there a reason why he couldn't use 90 or 180?", + "A": "Khan is using angles in radians probably because it is more intuitive rather than in degrees. cos(90\u00c2\u00ba) = 0 = cos(Pi/2) Both expressions are equivalent (just mind the angle units)", + "video_name": "57BiI_iD3-U" + }, + { + "Q": "3:20 Commutative property of addition 704 = 700 + 4 or 4 + 700\n3:30 Associative property of addition 18 + (4 + 700) = (18 + 4) + 700", + "A": "that is 3th grade math for asossitive property and 6th grade math for comunitive property", + "video_name": "jAfJcgPGqgI" + }, + { + "Q": "At 2:18 talking about the passage from the purple curve to the yellow segment of the function, he said a slope is not defined there because we could draw a lot.\nYet a unique limit for that point exists, so it should also exist a derivative right?\n(The same happens between the blue and the orange segments at the end.)", + "A": "just because a limit exists does not mean that a function is differentiable, although it is one of the conditions of that. For a function to be differentiable, the derivative from the left side of the point must be equal to the derivative from the right using one sided limits.", + "video_name": "eVme7kuGyuo" + }, + { + "Q": "at 5:00 how slope of that line is constant, that line rising up so it shouldn't be constant :S", + "A": "The slope of any line as always constant! I can show you algebraically: d/dx (ax+b) = a which is a constant. I can also explain it graphically: The slope of a line is always constant. Therefore, its tangent line is also of constant slope. Even if a line rises, the slope is constant. A rising line simply means a positive slope.", + "video_name": "eVme7kuGyuo" + }, + { + "Q": "At 3:55, the red colored line is increasing, but is in f(x)<0. So, I get that it will have a constant f'(x) slope, but shouldn't it be in f'(x)<0.", + "A": "Yes, f(x) is negative, but f (x) (or F Prime) will be positive, since it is essentially the slope of the line and the slope at that point is positive.", + "video_name": "eVme7kuGyuo" + }, + { + "Q": "At 2:15 it says the numbers are equivalent ,how is that?", + "A": "As I understand, it means that both formulas will give you the same number; so it doesn t matter how you go about finding the area, either with formula a or b, both will provide the same result and therefore are equivalent.", + "video_name": "Q3wfb0CPhIY" + }, + { + "Q": "At 2:03, what is the reciprocal?", + "A": "Reciprocal means to turn the fraction upside-down. For example, the reciprocal of 3/4 is 4/3. The reciprocal of 3 is 1/3, because 3 is really 3/1. Also, if you multiply any number by its reciprocal, you will get one (which I think is what nguyensongthienphuc was saying). So 4/3 * 3/4 = 1.", + "video_name": "K2b8iMPY11I" + }, + { + "Q": "Again 11:53:\nHow do I get from [x]B to [Ax]B ?? that is [x]B = [Ax]B algebraically?", + "A": "Sal is not saying that [Ax]_B = [x]_B. He wrote that D[x]_B = [Ax]_B. We have the rule that some vector v can be expressed in alternative coordinate systems by: C [v]_B = v, and [v]_B = C^-1 v. Ax is some vector. Therefore, we can apply the rule to it. x is also some vector. Therefore, we can apple the rule to it.", + "video_name": "PiuhTj0zCf4" + }, + { + "Q": "At 4:31, is it really possible that there are problems like-(-(-2))?", + "A": "Yes it is possible, but you don t see it much.", + "video_name": "3-aryZYsoxU" + }, + { + "Q": "what is the angle is an obtuse angle and the protractor isnt big enough to measure it? D:If you dont understand, 3:00\nwell the angle there is acute, but it LOOKS like its obtuse, and then you cant read the angle! D:", + "A": "you measure whats missing instead. then subtract it from 360. use the protractor to extend a ray so you have a strait line and measure the angle you created and subtract that from 360 to find it in degrees", + "video_name": "dw41PMWek6U" + }, + { + "Q": "@ 1:09\nWe get to the expression\n-2.7+ -5\nWhat's one thing that tells us not to solve 7-5 first but multiply the first two values and only then take the difference?\nI'd be very thankful", + "A": "PEMDAS rules always apply. Multiplication is always before subtraction. FYI, your expression as written contains no multiplication. The dot for multiplication has to be raised up: -2 * 7 + (-5). In your expression, you just have a decimal number -2.7 - 5 = -7.7", + "video_name": "uaPm3Tpuxbc" + }, + { + "Q": "At 2:12 he said that he is going to give it to the 10 hundreds. But are you going to give it to the hundreds or tens?", + "A": "It said he meant 10 tens", + "video_name": "QOtam19NQcQ" + }, + { + "Q": "At around 20:08, Sal denotes that P_1 is a vector and only draws a half arrow, (though I assume he meant to draw a full arrow).\nIs there a significant notational different between a full arrow and a half arrow above a variable?", + "A": "There is no difference. Some people, myself included, often find themselves writing half arrows , as you labeled them, instead of full arrows , because they are faster to write.", + "video_name": "hWhs2cIj7Cw" + }, + { + "Q": "At 14:00 why did Sal do b-a instead of b+a ? I thought you had to add vectors together to get the resultant vector. Can someone clarify this for me ?", + "A": "I have the same question. I don t have a good intuitive answer. But if you plot the vectors mentioned in the video we can see that a-b or b-a is the only vector that passes through the tip of the 2 vectors.", + "video_name": "hWhs2cIj7Cw" + }, + { + "Q": "At 21:30, he mentions that P2 can sub in for P1, and earlier he mentioned that (P1 - P2) can also be (P2-P1). I understand all of that, but can they both sub in at once without any consequences? Can you have (P1 + t(P1 - P2)) and (P1 + t(P2-P1))? And vice versa with P2 as well.", + "A": "Are you asking if P1 + t(P1 - P2) = P1 + t(P2-P1)? Because if so, the answer is no, the two t s would be different at each point on the line it creates depending on which point is in each position in the equation. If you separate it into two equations using the same points and different t s, then the lines will overlap at every point, but having two equations for the same line is redundant.", + "video_name": "hWhs2cIj7Cw" + }, + { + "Q": "At 0:42why did Sal write 4000+500=3000", + "A": "Look at the original problem at the top of the screen. Sal is not saying 4000+500=3000. He is writing the problem out using numbers. The original problem as + ? that Sal has not yet written in. But, by the end of the video, he does.", + "video_name": "a_mzIWvHx_Y" + }, + { + "Q": "@ 7:10. Wouldn't x = 2 also cause the answer to be undefined? (2-2)(2+1)=(0)(3)=0?", + "A": "Yes, but since we re not canceling the (x -2), it s not necessary to include that as a condition.", + "video_name": "7Uos1ED3KHI" + }, + { + "Q": "At 7:19 how did you come up with negative one? is it opposite from x+1? How do you come up with what is not defined?", + "A": "The fraction is not defined where its denominator goes to zero. You are correct that you set: x+1=0 to see what value of x would cause a problem. x= -1 would make the denominator = 0, so x cannot equal -1.", + "video_name": "7Uos1ED3KHI" + }, + { + "Q": "could you just divided the 3x^2+3x-18 by 3? I was very confused by Khan's whole \"grouping\" process at 10:48", + "A": "You could divide the whole expression by 3, and then factor from there. However, Sal is trying to explain another way that can be used to factor. On some trinomials, it is difficult to find the correct factors by guessing. A more organized approach is to use grouping.", + "video_name": "7Uos1ED3KHI" + }, + { + "Q": "Why was there no condition in the first problem (at 2:28) ? Shouldn't it have a condition that states x is not equal to -1/3? If x = -1/3, then the denominator would be equal to zero.", + "A": "wait until you finish the video until commenting", + "video_name": "7Uos1ED3KHI" + }, + { + "Q": "at 6:30 what does he mean?", + "A": "He is doing what is called FOIL. in the problem (x+5)(x+1), you first multiply the x in both parentheses, then the x in the first and the 1 in the second, then the 5 and the x and then the 5 and 1. the FOIL means: F-first (the two x s) O-outside (the x and the 1) I-inside (5 and x) L-last (5 and 1) Hope this helps clear things a little!", + "video_name": "7Uos1ED3KHI" + }, + { + "Q": "At 7:28 how come it is x does not equal 1 instead of x does not equal 1 AND 2?", + "A": "You are correct that x\u00e2\u0089\u00a01 and x\u00e2\u0089\u00a02 and you can list that if you like. However, it is traditional not to list any that remain obvious. But, it is not incorrect to list both of them. I personally prefer to list all of them, despite the tradition, just because I might do some later calculations that makes it difficult to tell where the forbidden values of x are.", + "video_name": "7Uos1ED3KHI" + }, + { + "Q": "At 7:28, (x+5)/(x-2) is not defined for x = -1, but is it defined for x=2?", + "A": "I believe that when we are deciding which term will make a problem undefined we usually go with the one we are dividing by. So if your are canceling out an (x-1) from the numerator and denominator, even if there is another term present, that is the one that cannot be 0 because it is the one that the problem is divisible by.", + "video_name": "7Uos1ED3KHI" + }, + { + "Q": "at 1:49 how do u get 3(3x+1)", + "A": "Sal starts with 9x+3 in the numerator of the fraction. He used the distributive property to factor out the GCM = 3. 9x + 3 = 3 ( 9x/3 + 3/3) = 3 (3x + 1). Hope this helps.", + "video_name": "7Uos1ED3KHI" + }, + { + "Q": "At 7:15, Sal said that x cannot equal -1. However, x also cannot be equal to 2, based off of the answer he got. Why wouldn't you put x cannot equal negative 2 in the final answer, as that would also make the expression undefined?", + "A": "Now that the expression has been simplified to (x+5)(x-2), it is obvious that x cannot be equal to 2, but the fact that x could also not be equal to -1 (otherwise division by 0 resulted) in the original non simplified expression has been lost, so we add the condition as a reminder. You see, we can set x=-1 into (x+5)(x-2) without a problem, but we could not set x=-1 in the original expression - and this simplified expression is based on that.", + "video_name": "7Uos1ED3KHI" + }, + { + "Q": "At 10:45... could you also write (3x-6)(x+3) as 3(x-2)(x+3), or is my thinking quite erred?", + "A": "You sure can. No, you re right. Take the 3 out of the 3x-6 to get 3(x-2)", + "video_name": "7Uos1ED3KHI" + }, + { + "Q": "How do we do it from slope-intersect form? 00:59", + "A": "Starting from 5x + 3y = 7, you subtract 5x and divide by 3, so 3y = - 5x + 7 or y = -5/3x + 7/3. He graphed 7/3 as the y intercept, then go down 5 over 3 to get second point. These are not very neat numbers to work with.", + "video_name": "MRAIgJmRmag" + }, + { + "Q": "at 1:30 why does 1/2 B become 1B, but H does not become 2H?", + "A": "The commutative law lets us rearrange the right hand side anyway we want. So, it becomes: (2)(1/2)(bh) 2 * 1/2 => 2/2 => 1 So, we end up with: 1*bh which is bh and now we ve got rid of the 1/2 by moving it to the left hand side.", + "video_name": "eTSVTTg_QZ4" + }, + { + "Q": "At 3:53, Where did you get the y=2(2) from, please explain", + "A": "Because in the Magenta equation we said X=2 you can bring that over into the other equation as X. This only works in systems though", + "video_name": "GWZKz4F9hWM" + }, + { + "Q": "When sal added the two 7x at 2:09, together aren't you supposed to add also the exponents?", + "A": "No, he is just combining like terms. If you have 7 apples and add 7 apples, you get 14 apples not 14 squared apples. You add exponents when you multiply variables, so (7x)2 = (7x)(7x) = 49 x^2. or 5x * 3x^2 = 15 x^3.", + "video_name": "xH_GllPuymc" + }, + { + "Q": "At 14:00 could not SQ RT 39/3 be SQ RT 13 ?", + "A": "sqrt(39)/3 is different from sqrt(39/3). Sqrt(39)/3 means square root of 39 is then divided by 3, while sqrt(39/3) means square root of the value that is 39/3, or 13.", + "video_name": "i7idZfS8t8w" + }, + { + "Q": "At 9:45 why can we not square the negative root thereby getting (36 +- 84)/36?", + "A": "That is not the square of (6 \u00c2\u00b1 \u00e2\u0088\u009a\u00e2\u0088\u009284)/6 For reference: (n + \u00e2\u0088\u009ap)\u00c2\u00b2 = n\u00c2\u00b2+ p +2n\u00e2\u0088\u009ap (n \u00e2\u0088\u0092 \u00e2\u0088\u009ap)\u00c2\u00b2 = n\u00c2\u00b2+ p \u00e2\u0088\u0092 2n\u00e2\u0088\u009ap [n + \u00e2\u0088\u009a(\u00e2\u0088\u0092p)]\u00c2\u00b2= n\u00c2\u00b2\u00e2\u0088\u0092 p +2n\u00f0\u009d\u0091\u0096\u00e2\u0088\u009ap [n \u00e2\u0088\u0092 \u00e2\u0088\u009a(\u00e2\u0088\u0092p)]\u00c2\u00b2 = n\u00c2\u00b2\u00e2\u0088\u0092 p\u00e2\u0088\u00922n\u00f0\u009d\u0091\u0096\u00e2\u0088\u009ap", + "video_name": "i7idZfS8t8w" + }, + { + "Q": "At 13:34, Sal simplified the fraction, but I''m not clear how he did it. What happened to the two? Does this simplification leave the square root of 39 alone?\nThanks", + "A": "Yes, just think of the sqrt 39 as some ugly thing multiplied to the 2. When you have (-12 +or- 2*sqrt39) / -6 , there are 3 distinct terms: the neg 12, the 2*sqrt39, and the neg 6. All 3 of those terms have 2 as a factor. That is, neg 12 = 2*neg 6 2*sqrt39 neg 6 = 2*neg 3 So all three terms have a factor of 2, so the 2 can be factored out by dividing each term by 2. That leaves neg 6 sqrt39 neg 3", + "video_name": "i7idZfS8t8w" + }, + { + "Q": "At 13:23, why doesn't he divide the number inside the radical by 2?", + "A": "Terms are things we add or subtract. They are held together by multiplication and division. The numerator only has 2 terms : -12 and 2*sqrt39. Both of those terms were divided by 2 to get -6 and sqrt39. But, if the numerator had been -12 + 2 + sqrt39, (in other words, 3 terms) and then we divided by 2, we would get -6 + 1 + (sqrt39)/2 ( Of course, that would simplify to -5 + (sqrt39)/2. )", + "video_name": "i7idZfS8t8w" + }, + { + "Q": "Isn't there a small mistake at 16:10 ? Sal says \"a little less than one\", where the graph shows a little less than 0 ...", + "A": "he says maybe close to zero but i little bit less than that", + "video_name": "i7idZfS8t8w" + }, + { + "Q": "at 4:16 why did it change to 10 why didn't you put 100?i,m sorry i am so very new to this", + "A": "the 100 was under a square root and then he took the square root of 100 to get 10", + "video_name": "i7idZfS8t8w" + }, + { + "Q": "At 0:05 Sal says that the quadratic formula is at least top 5 most useful formulas. I wonder what other formulas would be as useful as the quadratic formula.", + "A": "off the top of my head: the Pythagorean Theorem <-this is certainly one of the most useful if not the most useful formula, Area of a Triangle (you can usually break other shapes into a series of triangles), Combinations/Permutations, and maybe taking an Average.", + "video_name": "i7idZfS8t8w" + }, + { + "Q": "At 7:11, Sal describes the system as existing in R4, but isn't it also safe to describe this as 4 column vectors in R3?", + "A": "For this system of equations Ax = b , A , not the system, is 4 column vectors. x is an R^4 variable vector, each row is a plane in R^4 , and Ax is constrained to b , an R^3 column vector of constants.", + "video_name": "JVDrlTdzxiI" + }, + { + "Q": "11:30. To have an infinte number of solutions does one needs to have free variables AND a row of all Zeroes? The video was unclear on this point but alluded to it.", + "A": "row of 0 s is not a necessary condition, e.g. x1 - x2 = 5 x1 - x2 + x3 = 3 reduces to 1 -1 0 | 5 0 0 1 | -2 ` with x2 being free. The solution is (x1, x2, x3) = (5, 0, -2) + x2(1, 1, 0) If you think of a row being a constraint to the solution(s), a row of zero s seems to indicate one that is a linear combination of the remaining one s i.e. it is a superfluous constraint.", + "video_name": "JVDrlTdzxiI" + }, + { + "Q": "At about 2:08, are we just supposed to assume the solid has the same volume as the shell?", + "A": "Conceptually, we begin by estimating the volume of the solid by adding together the volumes of thin shells that make up the solid. As the shells get thinner and thinner, the estimate of the volume of the solid becomes more accurate. The limit of this sum as the thickness of the shells approaches zero is the integral, which is equal to the actual volume of the solid.", + "video_name": "6Ozz3J-LRrY" + }, + { + "Q": "at 4:32, why doesnt the pi/sqrt(2) distribute to the c? I dont think that it matters, but I would like to know.", + "A": "You re on the right track when you say I don t think it matters. The variable c stands for an arbitrary (unspecified, unknown) constant, which could be any real number. If you multiply an arbitrary constant by some other constant such as \u00cf\u0080/\u00e2\u0088\u009a2, you re still left with an arbitrary constant, so we continue to call it c and don t bother to multiply it by another constant.", + "video_name": "8Yl_u_Otcjg" + }, + { + "Q": "At 1:15 he changes 25% into a decimal. So does that mean that percent is basically the same thing as decimals?", + "A": "yes, a percentage is always a decimal. You can arrive at the decimal by dividing the number by 100. So 25% = 25/100 = 0.25", + "video_name": "JaScdH47PYg" + }, + { + "Q": "At 4:30, why does Sal say that you can't simplify -21/20? Can't you simplify it to\n-1 1/20? Or is it -21 over +20? :(", + "A": "First of all you can t simplify one part of the fraction when you want to simplify a fraction you must do it for both numerator and denominator and in this fraction you can t simplify it any further because there isn t any common factor between them (21)=3*7 (20)=4*5 hopefully this helps you", + "video_name": "pi3WWQ0q6Lc" + }, + { + "Q": "In 1:42 I don't get it.", + "A": "this is totally new exercise as 2 fractions times each other that means u can write them in one fraction and the value is still same. in 2 fractions numerators r always times each other and denominators r always time each other but numerators and denominators r always divide that is why Sal wrote 5 x 3 (numerators) and 9 x 15 (denominators). hope this will help.", + "video_name": "pi3WWQ0q6Lc" + }, + { + "Q": "why at 1:18 does neg. numerator over pos. denominator (-3/+7) become the whole fraction neg. ?", + "A": "You may be aware of the mathematical rule which dictates that if you divide a negative by a positive, you get a negative. A fraction basically means to divide the top number, or the numerator, by three bottom number, the denominator. EXAMPLE: -2/4 We know that +2/+4 is 1/2, so we can simplify -2/4 to -1/2, or -0.5 I hope this this helps!", + "video_name": "pi3WWQ0q6Lc" + }, + { + "Q": "at 5:05 is he writing out what he did in the model?", + "A": "Yep, that is correct. Sal (the speaker) just replaced the equation with absolute values, which are the lines on both sides of the subtraction.", + "video_name": "DPuK6ZgBGmE" + }, + { + "Q": "At 4:58, Sal says X squared equals -1. Shouldn't it be 1?", + "A": "No. He has x^2 + 1 = 0 You must subtract 1 from both sides to isolate x^2 (remember, we use the opposite operation to move items to the other side of an equation). This creates Sal s version: x^2 = -1", + "video_name": "uFZvWYPfOmw" + }, + { + "Q": "At the 1:53 mark he says something like \"you could probably draw a better freehand diagram\". My opinion: I definitely cannot. This guy seems to be good at explaining math in these videos-who is he?", + "A": "He s Richard Rusczyk (yeah, I probably butchered his name), but if you look him up on google you can find more info about him. He s pretty famous.", + "video_name": "rcLw4BlxaRs" + }, + { + "Q": "At 1:15... I know this is right, I just need an explanation.\n\nHow does x^2 go into x^3 and x^4?", + "A": "5 goes into 15, 3 times (5*3=15) 8 goes into 16, 2 times (8*2=16) 9 goes into 54, 6 times(9*6=54) x^2 goes into x^3, x times (x^2 * x=x^3) x^2 goes into x^4, x^2 times (x^2 * x^2 = x^4)", + "video_name": "MZl6Mna0leQ" + }, + { + "Q": "At @5:08 you say that the span of T is V but couldn't you also say that it is T itself since a span, unlike a basis, doesn't necessarily need to have linearly independent vectors?", + "A": "T was just S with one extra vector. V in the example was Span(S) = Span(T). V in theory should have infinitely more vectors than T.", + "video_name": "zntNi3-ybfQ" + }, + { + "Q": "At 4:55, it says a sub i is equal to a sub i minus i times 9/10. Is this supposed to be i-1?", + "A": "It s confusing... the dot is actually the multiplication symbol, not a dot on a i . So, Sal does have i-1", + "video_name": "DY9Q3qNmZnw" + }, + { + "Q": "At 3:30 the instructor immediately went to subtracting. But I thought the order of operations was PEDMAS so shouldn't the division go first? The way I did it, was first doing all the divisions then I found the last equation to be (d/ac)-(d/bc)", + "A": "The division bar in the middle of a fraction asks as a grouping symbol. When you have 2 terms in the numerator of a fraction or even 2 terms in the denominator, there are implied sets of parentheses the numbers in the numerator / denominator. So, Sal did the parentheses 1st by subtracting the 2 fractions in the numerator, then doing the division. Sometimes it s easier to see a simpler example: (2+3) / 10 You add 1st = 5 / 10 Then, you divide = 0.5 or 1/2", + "video_name": "_BFaxpf35sY" + }, + { + "Q": "At 8:16, how did he get A^2=3/4 h^2?", + "A": "Simple algebraic solving techniques. if you take h to be c like it is normally represented, and assume a^2 + b^2 = c^2... and take the 30-60-90 side ratio definition where the side opposite the 30 degree angle is c/2, or hypotenuse/2, then (c/2)^2 + a^2 = c^2. Subtract (c/2)^2 from both sides... you get a^2 = c^2 -(c/2)^2. Fraction stuff... a^2 = (4c/4)^2 - (c/2)^2 so a^2 = (3/4c)^2.", + "video_name": "Qwet4cIpnCM" + }, + { + "Q": "at 0:23, where did you get the radical 2 over 2 from?", + "A": "That was explained in the earlier video about 45-45-90 triangles.", + "video_name": "Qwet4cIpnCM" + }, + { + "Q": "At 7:46 how to you get 4?", + "A": "(1/2) squared is (1/4). This multiplied by h is (h/4).", + "video_name": "Qwet4cIpnCM" + }, + { + "Q": "I'm confused about what happens to the negative at 2:37", + "A": "you have (2*(1-3^100))/(-2). then the 2s cancel out: (1-3^100)/(-1). negative from the -1 goes to the top: -(1-3^100)/1. 1 in denominator goes away: -(1-3^100). distribute negative: -1+3^100 rewrite order: 3^100-1", + "video_name": "AXP5PGSaaYk" + }, + { + "Q": "At 3:10 when Sal factors out the five from the equation, why does he not put the newly factored equation in brackets with a five on the outside?", + "A": "In order to get rid of the 5, Sal divided both sides of the equation by 5, giving (5x^2 - 20x + 15) / 5 = 0/5, which simplifies to x^2 - 4x + 3 = 0. You don t need to include the 5 as a factor in the left-hand side because you divided both sides by it.", + "video_name": "MQtsRYPx3v0" + }, + { + "Q": "Okay, so at 2:36 when he finds integers that multiplied equal 3 and added equal -4, then moves on using that information? What if you have numbers that don't work? I have the equation x^2 +2x+3=0. Nothing works with this. Is there another way to solve this and graph it as a parabola? Please help.", + "A": "This is because this parabola does not have x-intercepts. You can check it by completing the square: y=(x+1)^2+2 is always positive, which means that every point of the parabola has a positive y value, which means that it is above the x axis. The fastest way to check it though is to evaluate its determinant b^2-4ac and see that it is negative,and therefore has no real zeroes.", + "video_name": "MQtsRYPx3v0" + }, + { + "Q": "7:30 in the video sal has written -24-10_/5 should the answer be -(-24-12_/5)", + "A": "What Sal wrote is correct. After rationalizing the denominator then simplifying we have: 24 + 12sqrt(5) / -1 Because we are dividing the numerator by negative one, we take the opposite of each of its terms: 24 + 12sqrt(5) / -1 -(24 + 12sqrt(5)) -24 - 12sqrt(5)", + "video_name": "gY5TvlHg4Vk" + }, + { + "Q": "how did he turn 1/4 into a whole number at 3:05", + "A": "he multiplied 12 to 1/4, and that equals 3", + "video_name": "GmD7Czmol0k" + }, + { + "Q": "At 2:25, Sal uses the chain rule for the derivative of (2+x^3)^-1. Would it not work if he just used the power rule and left it at that?", + "A": "No, the power rule applies only when you have x to the n, not when you have some function of x raised to the n. You can see this with an example like (x^2)^3. If you just apply the power rule, you get 3(x^2)^2, but we know that s wrong because (x^2)^3 is x^6, so the answer has to be 6x^5 or something equivalent. You get the right result when you apply the chain rule.", + "video_name": "GH8-URjRQpQ" + }, + { + "Q": "At 2:25 are you supposed to add the negatives together? Can't you use the old fashioned way too?", + "A": "If you are talking about the negatives of 70, 10, 15, and 21, keep in mind that you can only add them together when they possess the same exponent amounts.", + "video_name": "D6mivA_8L8U" + }, + { + "Q": "at 1:17, what if there isnt a exact weight given?how would you solve?", + "A": "If there is not an exact weight given then there is to little info to discover an exact answer.", + "video_name": "z1hz8-Kri1E" + }, + { + "Q": "what is a parabola 0:00 to 2:46", + "A": "It is the line you get when you graph a quadratic.", + "video_name": "v-pyuaThp-c" + }, + { + "Q": "how did she make that shape?! at 4:30", + "A": "She drew a circle out of dots, then drew more circles with the points being their centers and alternated colors between the shapes made by the circles overlapping.", + "video_name": "v-pyuaThp-c" + }, + { + "Q": "I want so bad to be able to draw the heart thing at 4:29 can someone explain how or make a program maybe??? because I can't understand lol", + "A": "you could take two circles and roll one around the other tracing one point on the edge; OR you could make dots in the shape of a circle ,choose one dot to be a point on the edge of all circles and use the others as centers", + "video_name": "v-pyuaThp-c" + }, + { + "Q": "At 1:10. why does he make 4.1 to 41?", + "A": "Moving the decimal around is like multiplying or dividing by 10, so he notes that 4.1 hundredths is the same as 41 thousandths (4.1 x 10^-2 = 41 x 10^-3).", + "video_name": "ios3QL9t9LQ" + }, + { + "Q": "A, B and C are collinear, and B is between A and C. The ratio of AB, B to AC, C is 1:4\nIf A is at (-7,-8) and B is at (-3,-5), what are the coordinates of point C?\nI got the x and y values by subtracting and got 4 and 3. But, when I went to find the ratios of 4 and 3 i'm told to multiply 4 by 1:4 to get 16. And 1:4 by 3 to get 12. But, in the video i'm told to find the ratios by dividing to get 4 1:4=1 so which am I supposed to be doing?", + "A": "I think you are thinking correctly, but I am not completely sure. Setting up proportions and cross multiplying, For x coordinate, AB/AC = 1/4 and if AB is 4, then 4/AC = 1/4 and AC = 16 in x direction For y coordinate, AB/AC = 1/4 and if AB is 3, then 3/AC= 1/4 and AC = 12 in y direction If I start at A and move these distances, then C (-7+16, -8+12) or (9,4)", + "video_name": "lEGS5ECgFxE" + }, + { + "Q": "At 0:03, the word collinear is mentioned. What exactly is collinear?", + "A": "It means you can draw a line through all the points.", + "video_name": "lEGS5ECgFxE" + }, + { + "Q": "I was just wondering, at 1:05, why is point B said to be 2/5 of the way from A? Shouldn't it be that the total distance from A to C is 7 (add both sides of the ratio to find the total number of parts) and then B should be 2 parts out of this total distance? Thus, B is 2/7 of the way? I'm not entirely sure of whether or not I am correct, but I'm assuming I've made some error.", + "A": "Your error was in saying the total distance from A to C is 7. The problem states that AC is 5 when it says the ratio of AB to AC is 2 : 5. In other words, the 2 : 5 ratio is a ratio of a part to the whole, not a ratio of the lengths of 2 portions of the whole.", + "video_name": "lEGS5ECgFxE" + }, + { + "Q": "At 1:35 I solved it as 8^1/4=2, where as in the video its 8^1/3=2. Im Not sure if im missing something of if Sal made a mistake?", + "A": "8^(1/3) is the cube root of 8, which is 2. (2^3)^(1/3)=2^(3/3)=2^1=2 8^(1/4) is the fourth root of 8, which is not 2. 16^(1/4) is the fourth root of 16, which is 2.", + "video_name": "eTWCARmrzJ0" + }, + { + "Q": "At the 0:53 problem how does Sal get to an Answer of 1/3 ? What is the work not shown here ?", + "A": "Let s start with 8^x =2. When the variable is in the exponent, it is useful (where possible) to express both sides of the equation using the same base. Since on the righthand side there is a 2 to the first power, ask yourself whether 8 can be expressed as a power of 2? So we end up with (2^3)^x which is the same as 2^3x. And we then have 2^3x = 2^1 as the equation. The bases are the same, so the exponents must be equal. Therefore 3x = 1 so x = 1/3 Hope you find this useful!", + "video_name": "eTWCARmrzJ0" + }, + { + "Q": "on 2:37 how does negitive turn into a fraction", + "A": "That is a basic property of exponents. The rule is: a\u00e2\u0081\u00bb\u00e1\u00b5\u0087 = 1/a\u00e1\u00b5\u0087", + "video_name": "eTWCARmrzJ0" + }, + { + "Q": "@1:25, I still dont get it... is something wrong with me? 8^1=8 and 8^0=1, but how do you get.... i dont know; is there another video i can watch to buff up my understanding of this?", + "A": "any number raised to the power 0 is 1, you can think of it like this: x^3 = x*x*x x^2 = x*x which is x^3 divided by x x^1 = x which is x^2 divided by x x^0 = 1 because any number divided by itself is equal to 1. Also, you can think of 8^1 as being 8*1, and 8^2 as being 8*8*1, since any number multiplied by 1 is just itself you don t need to display the 1, but this does explain why 8^1=8 hope this helps :)", + "video_name": "eTWCARmrzJ0" + }, + { + "Q": "Don't get the second problem at 0:42.\nAre there like any practice problems for this?", + "A": "2^3 = 8; therefore the cube root of 8 is equal to 2, right? Another way of writing cube root of 8 (remember: that s the square root sign with a little 3 above the check mark) is 8^(1/3). Notice that the exponent is 1/3. That is why the Log (base 8) of 2 is 1/3.", + "video_name": "eTWCARmrzJ0" + }, + { + "Q": "The equation is -4x+7. Shortly after the 4:00 mark, Sal replaces the x with -1 and then says, \"4 times -1 = -4\". Shouldn't it be -4 * -1?", + "A": "He misspoke and says 4*-1=4, but what he really meant is -4*-1=4 and he completes the equation as if he had said that correctly. It does not change the problem because he just misspoke and didn t write the incorrect statement down", + "video_name": "nGCW5teACC0" + }, + { + "Q": "at 1:12, why is the y coordinate of the point g(-1)?", + "A": "At this point Sal has drawn a blue line representing g(x), and wants to plot the point on that line where x = -1, so the y-coordinate has to be the value that the function g assigns to the x-value -1, which is g(-1). Possibly you just lost Sal s train of thought here, but if this doesn t make sense after this explanation, it might help to review function terminology before you proceed, as similar references will come up often.", + "video_name": "nGCW5teACC0" + }, + { + "Q": "Why does Sal draw a triangle in front of X at 2:16?\ndoes that mean change?", + "A": "Yes, it does! The triangle is actually the Greek letter Delta. When used this way, it means change .", + "video_name": "1F7LAJEVp-U" + }, + { + "Q": "At 1:57 Why can he take the radical sign off the right and stick it on the left of the equation? I feel like I missed a step or something. I can't figure out why he did that.", + "A": "Oh, right. Thank you. It makes total sense now. I must have been trying too hard and missed it.", + "video_name": "aeyFb2eVH1c" + }, + { + "Q": "Can someone elaborate why at 1:50 Sal chose to take the positive square root.", + "A": "The values here will be positive. The thing squared is (x+2) and the minimum value possible for x is -2. Therefore, 0 (-2+2) and up is the set of possible values. Since the values are positive (well, technically nonnegative) the principal/positive square root is sufficient.", + "video_name": "aeyFb2eVH1c" + }, + { + "Q": "At 2:13, Sal makes note of domain and range. I am familiar with the concept, but am unsure of why it is important.", + "A": "A domain is a certain range in which the function remains applicable. In many cases, if the domains are not constrained to a certain range, the function could be meaningless. For example, if S(x) in a function stands for the number of students in a classroom, the domain of x must be greater or equal to 0. Otherwise, this functon is meaningless. I hope you see how it works :)", + "video_name": "aeyFb2eVH1c" + }, + { + "Q": "why do we ignore the decimals at 0:40?", + "A": "thanks to kwymberry", + "video_name": "JEHejQphIYc" + }, + { + "Q": "At 0:17, Sal says that multiplying decimals is the same as multiplying whole numbers. Why is this true?", + "A": "He means it s ALMOST the same, but not all the same.", + "video_name": "JEHejQphIYc" + }, + { + "Q": "At 2:13 - 2:17, How come they remove the 0 at the very end? I know that it has no meaning but why?", + "A": "They remove it because it has no meaning and it is simpler to express the number without it.", + "video_name": "JEHejQphIYc" + }, + { + "Q": "Wait is this stuff a joke? Especially 3:42 are there really such diseases?", + "A": "Don t worry, all of them are made up, except maybe the mind-blown syndrom. If you show hexaflexagons to your friends, they could very well be disbelieving at the amazing-ness.", + "video_name": "AmN0YyaTD60" + }, + { + "Q": "At 1:01, Does Vi make two Mobius Strips tied together? Does that mean a hexaflexagon is a mobius strip?", + "A": "Right-o! A hexaflexagon s unique ability to make that weird twist and end up with multiple sides is caused indirectly by the mobius strip it s made out of!", + "video_name": "AmN0YyaTD60" + }, + { + "Q": "At 1:50 what did you say?", + "A": "At 1:50 the speaker said So we can change the order of the numbers without changing the answer . Hope this helped ! :)", + "video_name": "uHHnwafYivk" + }, + { + "Q": "At 1:43 what is the difference in tangent line and secant line?", + "A": "A tangent line touches the curve at one point whereas the secant line intersects at two points. The secant slope can be found by simple slope eq: y2 - y1/x2-x1 The tangent slope is found by f(x) - f(a)/ x - a. Hope this helps", + "video_name": "BYTfCnR9Sl0" + }, + { + "Q": "8:20 but 1/2 squared is 1/4 :'<", + "A": "The ambiguity of not having parenthesis. If you are referring to the blue writing I think it is (1^2)/ 2 and not (1/2)^2 since he substituted in 1 for x in x^2/2.", + "video_name": "vhMl755vR5Q" + }, + { + "Q": "At 1:28 do you have to do it height times width times depth in that order?", + "A": "Yes, the formula for volume in rectangular prisms is: V=B*L*H V=volume B=base L=length H=height.", + "video_name": "I9efKVtLCf4" + }, + { + "Q": "0:39 i dont understand the math from here on", + "A": "the video shows how to find the volume from there on for example lxwxh= 2x4x3", + "video_name": "I9efKVtLCf4" + }, + { + "Q": "At 1:05, Can we use any symbol (\u00c3\u00ab, \u00c3\u00a6, \u00c2\u00b4\u00c2\u00ac or \u00c2\u00a4) represent an unknown number?", + "A": "I think that s a yes, since Mr. Khan says you could use a smiley face.", + "video_name": "Tm98lnrlbMA" + }, + { + "Q": "At 2:16, it could have been (Star) + 1 = ... I don't know... Smiley Face). We didn't have to say \"y = x + 1\".", + "A": "It could have been. But people thought letters were more simpler.", + "video_name": "Tm98lnrlbMA" + }, + { + "Q": "For the graph that Sal draws beginning at 1:35, what does the Y axis represent? I understand how the probability of the event is represented by the area under the curve, but doesn't that mean the Y axis doesn't chart probability, but something different? Is it the probability of the probability? ;)", + "A": "Yes, the y axis charts something different. The y value at each value of x (or possible outcome) is the rate of change of the area under the curve as the interval (range of possible outcomes) increases or decreases. This ensures that the area under the curve in any interval (range of outcomes) is always equal to the probability for that interval.", + "video_name": "Fvi9A_tEmXQ" + }, + { + "Q": "At 5:07 Sal says that the two statements P(|Y-2|<.1) and P(1.9= 0 gives Y-2<.1 wich gives Y < 2.1 solving |Y-2|<.1 for (Y-2) < 0 gives -Y+2<.1 wich gives -Y<-1.9 wich gives Y > 1.9 Search for lecture about absolute value for more explanation.", + "video_name": "Fvi9A_tEmXQ" + }, + { + "Q": "At 1:23, why is it plus or minus the square root? Why not just square root?", + "A": "A square root undoes a power term, but a power term can hide information. Think what happens if you have x^2 and x = 1, you get 1 right? But if x were to equal -1 you would still get one. So if you were to solve with out putting the + - you only get half of the answer. This will become really big when you start solving quadratic equations.", + "video_name": "RweAgQwLdMs" + }, + { + "Q": "How does Sal know at 6:34, 6:38, and 6:46 that y=x^2, xy=12, and 5/x+y=10 are not linear equations without graphing them first?", + "A": "Linear equations have specific formats. For example, here are some of their formats: 1) Ax + By = C where A, B and C are integers 2) y = mx + b where m and b are numbers None of Sal s equations look like the examples above. y = x^2: this has an exponent on x which makes it non-linear xy = 12: this has x and y being multiplied which doesn t occur in a linear equation 5/x + y = 10: this has x in a denominator which doesn t occur in a linear equation Hope this helps.", + "video_name": "AOxMJRtoR2A" + }, + { + "Q": "At 4:55, on the sketched graph I noticed that some values of h(x) were actually smaller than some values of f(x)(check out the minimum of h(x) and the maximum of f(x)), if the inequallity is right, shouldn't the values of h(x) always be bigger than f(x)'s?", + "A": "This means above and below,(Recall [f(x)=y] so its like saying f(x) s y value < g(x) s y value < h(x) s y value Were only comparing the function evaluated at the same x-values (x is the input y [which is equal to f(x)] is the output)", + "video_name": "WvxKwRcHGHg" + }, + { + "Q": "What does Sal mean by \"wacky functions\" at 6:54?", + "A": "He means functions that are complex or difficult to manipulate algebraically.", + "video_name": "WvxKwRcHGHg" + }, + { + "Q": "Wait, I don't understand something. At 2:50, Sal squared the numbers 15 and 20. Why? What was the need to square them? He then added them, got 625 as a sum, and then found the positive square root of it--25--and deemed that number the length of the rope. Isn't there a more simpler way to solve the problem?", + "A": "Pythagorean theorem: a^2+b^2=c^2 in this case: 15^2+20^2=c^2 you re trying to figure out c (length of rope) so 625 answer -- from that square root of 625 is 25", + "video_name": "JVrkLIcA2qw" + }, + { + "Q": "In 2:05 when Sal said that... when you know two sides of the triangle you calculate the the hypotenuse...My question is that can you calculate the hypotenuse or any one of the sides if you only know ONE side of the triangle?", + "A": "In general, no, unless you know something else about the triangle. There are techniques using trigonometry that will let you find sides if you know one side and one angle (other than the right angle).", + "video_name": "JVrkLIcA2qw" + }, + { + "Q": "at 1:44 he shows that (7) (5) means the same thing is 7x5\nwhat is the reasoning or history for why a number inside a ( ) means to multiply. I would love to understand the thinking behind that better.", + "A": "Like most shortcuts... laziness. I suspect that if you look back far enough, some symbol was regularly used for multiplication... but anything you do that much begs for simplification so at some point someone said how about we call it multiply if there is just no operator and put in the operator if it is anything else ... This works pretty well so we kept it.", + "video_name": "Yw3EoxC_GXU" + }, + { + "Q": "I thought that dx meant that the integral was done relative to the variable x. So at around 3:16 he brings the dx to the middle of the equation. Doesn't that affect the e to the power of .... somehow? Also why is dx being treated as a variable?", + "A": "It doesn t affect the integral at all. dx is essentially meaning a small change in x (think of a minuscule delta-x). It is for all intents and purposes in integration a dummy variable: like any other variable in an expression, you can move it around subject to the laws of multiplicative association. dx is what ultimately creates the +C at the end as well, because of this treatment as a dummy variable. Yet another question in this section that goes to blaming Leibniz.", + "video_name": "b76wePnIBdU" + }, + { + "Q": "At 3:26, where did the dx go? Can I just leave it out? And if yes, why?", + "A": "The dx is still there at 3:26. It s between the two functions in the integral.", + "video_name": "b76wePnIBdU" + }, + { + "Q": "@2:01 Can you please explain how you used the notation du/dx as a fraction?\nHow can we pretend that it's a fraction?", + "A": "Remember that slope is \u00ce\u0094y/\u00ce\u0094x, change in y over change in x, and that IS a fraction. Well dy/dx (or du/dx) is the same deal, just that we are dealing with infinitesimals, which we call the differential difference, that is dx is what happens to \u00ce\u0094x in the limit when \u00ce\u0094x approaches zero, thus dy/dx, du/dx are fractions.", + "video_name": "b76wePnIBdU" + }, + { + "Q": "i do not understand 4:09 it is a little hazy can someone please explain it to me??", + "A": "it s to easy he seperates the inequality into two peices so it will be more easy to solve", + "video_name": "A3xPhzs-KBI" + }, + { + "Q": "at 8:30 i dont get the dif. between \"and\" and \"or\". i went on the practice questions and it said something about \" the first inequality is included........\". im so confused i kept on getting it wrong help!", + "A": "OK. What you have to do is to first solve the first inequality and then the second.", + "video_name": "A3xPhzs-KBI" + }, + { + "Q": "At 1:58, why does he divide by ten?", + "A": "he divided by ten because if you look after you solve the 9x6 which was what was in the parentheses you then solve the 54/10 because in order of operation division is after parentheses, exponents, and multiplication and since there is none of that you divide which comes after multiplication in order of operations.", + "video_name": "STyoP3rCmb0" + }, + { + "Q": "At 1:15 Sal says \"We could either do the 6 divided by the 10 first ... or we could do the 9*6 first\"\n\nWhat happened to BIDMAS?\n\nCan someone explain?\n\nI know the answers will be the same but then where does the principle apply then and how?\n\nThanks", + "A": "Im not familiar with the term BIDMAS but we used PEMDAS meaning parentheses are done first followed by exponents then you can do either division OR multiplication with addition or subtraction as the last operation. I was taught that multiplication and division are equal as far as the sequence of their operation is performed. The same goes for addition and subtraction. It just depends on what operation you are most comfortable performing first.", + "video_name": "STyoP3rCmb0" + }, + { + "Q": "At 3:00 how is how is 9 * 0.6=5.4 . isn't the product of a multiplication problem always bigger then the numbers you are multiplying?", + "A": "not always because when you multiply by a number less than 1 in a multiplication the biggest number gets smaller. 0.6 is 6/10 * 9 is 54/10 and that is 5.4", + "video_name": "STyoP3rCmb0" + }, + { + "Q": "in the video @ 4:54 i do not understand the part where the instructor of the video multiplied 4*84 to get the sum of the previous four tests.\n\n80 + 81 + 87 + 88 = 4 * 84 ? <--- how is this possible, i think its cool but do not understand how that works. thanks!!", + "A": "80+81+87+88=80+80+1+80+7+80+8=(80+80+80+80)+(0+1+7+8)=4*80+16=4*(80+4)=4*84", + "video_name": "9VZsMY15xeU" + }, + { + "Q": "at 1:27, what in the world is he doing??? I mean, i don't get it. Where did the .25 come from??", + "A": "Did you study long division yet? 4 s into 29 go 7 times with 1 left over. So we do not throw the 1 away, but instead put a decimal point and carry on. We always put a 0 after whatever digit we are left with, so the 1, becomes 10, so how many 4 s go into 10.....? two 4 s go into 10 with 2 left over. Once again put a 0 after the 2 and we get 20, 4 s into 20 go 5 times with none left over. Our final answer is 7.25. :)", + "video_name": "9VZsMY15xeU" + }, + { + "Q": "The ratio of chocolate bars to taffy pieces in a candy shop is 7:3, the total amount of candy is 3000. Then the candy store buys 32 more chocolate for there new daily order. How meny chocolate bars and taffy pieces are there?", + "A": "3000*Candy=3*700*Chocolate+3*300*Taffy=2100*Chocolate+900*Taffy 2100+32=2132 the answer is 2132 chocolate bars and 900 taffy pieces", + "video_name": "MaMk6-f3T9k" + }, + { + "Q": "At 14:50, you do what you've done many times before and write matrix multiplication as the sum of the each product of the column in the matrix and the row (1 scalar value) in the vector. However, this multiplication is actually defined in the opposite way (first row * first column = entry1,1) etc. Why are you using a different definition for matrix vector multiplication?", + "A": "The two definitions of matrix multiplication are actually equivalent. The definition Sal uses is, however, generally more compact and also carries useful geometric intuition (although not necessarily easier for numerical calculations). From your typical definition, you would find that the first element of the product is v1,1*x1 + v2,1*x2 + ... + vn,1*xn. However, by taking the vector sum in the definition Sal uses, you also obtain the same result.", + "video_name": "ondmopWLiEg" + }, + { + "Q": "Where does the (x-a)^2 come from? [at 1:35]", + "A": "We put it in ourselves to create an equation that could be used to solve for the question mark.", + "video_name": "bNQY0z76M5A" + }, + { + "Q": "At 9:11 why is +9/4 when moved to the right side of the equation not a -9/4?", + "A": "Well, as you probably know from the video, this method is call completing the square . In this step, Sal took the coefficient in front of the x, which is -3. To find the constant we must add to the left-hand side, we do ((coefficient/2)^2), which in this case gives ((-3/2)^2) = 9/4. When adding 9/4 to the left-hand side, in order to keep the equality between both sides of the equal sign, we must thus add 9/4 to the right-hand side of the equation.", + "video_name": "bNQY0z76M5A" + }, + { + "Q": "at 12:30 wouldn't the answer be 4.55?", + "A": "These are the two values we have to get the answer for x: 3/2 and \u00e2\u0088\u009a(61/20) and we know that x can equal 3/2 plus or minus the value of the square root. so, 3/2 +- \u00e2\u0088\u009a(61/20). We can just get the values of both of the terms and add/subtract appropriately. 3/2 is 1.5 and \u00e2\u0088\u009a(61/20) is 1.74642... So we can solve thusly x = 1.5 + 1.74642 x = 3.246 or x = 1.5 - 1.74642 x = -0.246", + "video_name": "bNQY0z76M5A" + }, + { + "Q": "At 4:12, why is the square root of 9 equal to +/- 3?", + "A": "because, nomatter the numbers is positive or nagetive if it be squared, it will become positive. so square +3 =9 square -3 =9 =====\u00e3\u0080\u008b square root of 9 =+3/-3", + "video_name": "bNQY0z76M5A" + }, + { + "Q": "at time 10:45, can anyone explain to me how we get the +/- square root of 61/20. specifically, the reason why we have +/- the square root. what rule is that?", + "A": "I don t know if this will help or not but I ll try to explain. So basically you re wondering why should there be a positive + and negative - square root, right? Think about any squared number really does have two possible square roots, the positive and the negative ones. For instance \u00c2\u00b1\u00e2\u0088\u009a9= -3 or 3 Because if we square (-3)^2=9 (\u00e2\u0086\u0092Notice that this different from -3^2 which is equal to =-9) and 3^3=9", + "video_name": "bNQY0z76M5A" + }, + { + "Q": "At 4:05, why can't you solve the equation as\n(x-2) = 9 (x-2) = 9\nx = 11 x = 11\nWhy do we instead need to take the square root of (x-2)^2 and of 9 to get\n(x-2) = +-3?\n\nIsn't the former how we've been solving these equations up until this point?", + "A": "The ones that you solved before always had the other side was 0 which would allow you to do this. If you have (x-3)(x+4) = 12, you should not have said x - 3 = 12 or x + 4 = 12 which would give you wrong answers. You would have to multiply to get a trinomial, subtract 12, and refactor if you could or use quadratic formula to see if there are factors. Also, if you put your attempted answer back in as a check (x-2)^2 = 9, you would have (11-2)^2 = 9 or 81 = 9 which is an impossibility.", + "video_name": "bNQY0z76M5A" + }, + { + "Q": "At 10:52, there is a fraction underneath a radical, the square root of 61/20. While Sal uses his calculator to solve it, I want to know how you would simplify a fraction under a radical like that without a calculator. My math teacher takes off points on tests for leaving answers as fractions under radicals, but it's not quite the same as simplifying a radical that is just a whole number, so I'm confused on how to do this. Also, is this process similar if you take the cube of a fraction instead of the square?", + "A": "First of all, 61 is a prime number so in a radical it remains. With 20 you can factor it into 4 and 5, so it can be written as \\ \u00e2\u0088\u009a20 = 2\u00e2\u0088\u009a5 So now we have \u00e2\u0088\u009a61 / 2\u00e2\u0088\u009a5, which is an OK answer as long as radicals in the denominator are permitted. To get rid of the radical in the denominator, multiply \u00e2\u0088\u009a61 / 2\u00e2\u0088\u009a5 by \u00e2\u0088\u009a5/\u00e2\u0088\u009a5 and we have: (\u00e2\u0088\u009a5)(\u00e2\u0088\u009a61)/(2)(\u00e2\u0088\u009a5)(\u00e2\u0088\u009a5), which can be simplified to \u00e2\u0088\u009a(61*5)/10 = \u00e2\u0088\u009a305/10. So now you only have a radical in the numerator.", + "video_name": "bNQY0z76M5A" + }, + { + "Q": "at 5:48 why do they equal zero", + "A": "That s simply the problem statement; at 5:37 Sal starts a new quadratic equation as another example.", + "video_name": "bNQY0z76M5A" + }, + { + "Q": "At 4:10, why does it become +/- 3, instead of just 3?", + "A": "the sqare root of 9 = +/-3 because in algebra, whenever you square a positive OR negative number, the answer is always positive.", + "video_name": "bNQY0z76M5A" + }, + { + "Q": "At 0:35 why does it have to be greater or equal to? Why not less than or equal to or equal to.", + "A": "Because you can t take the square root of anything less than 0.", + "video_name": "4h54s7BBPpA" + }, + { + "Q": "i do not understand from 0:22 to 0:56", + "A": "Sal realised that he ll be unable to find the square root of the quantity within the radical if it s negative. So he sets up the inequality to show that that quantity (2x-8) has to be either zero or positive.", + "video_name": "4h54s7BBPpA" + }, + { + "Q": "at 1:45 i still do not really understand why after adding 64 you must also subtract 64 from 9. Could someone explain I'm a bit confused.", + "A": "When we make changes to an expression, we need to make sure that the new version is equivalent to the prior version. If you just add 64, you have changed the value of the original expression. The new version would not longer be equal to the original. The identify property of addition says we can add zero to any expression and it doesn t change the value of the expression. Thus, by using: +64 and -64, Sal is adding zero to the expression (+64 - 64 =0). Hope this helps.", + "video_name": "sh-MP-dVhD4" + }, + { + "Q": "In 0:44 , how did Khan get 2ax from (x+a)^2? Can someone explain how and why it works?", + "A": "(x+a)\u00c2\u00b2=(x+a)(x+a). When you multiply it out, you get x\u00c2\u00b2+ax+ax+a\u00c2\u00b2. Simplify it you get x\u00c2\u00b2+2ax+a\u00c2\u00b2", + "video_name": "sh-MP-dVhD4" + }, + { + "Q": "At 3:18 of the video, how does Sal get that x= \u00e2\u0080\u00934 or x= 3 from the \"(x+4)(x-3)=0?\"", + "A": "When we get down to the factored formula (x+4)(x-3)=0, then we use the zero property principle that the others have described to finish the solution. The next step is to set each factor equal to zero by itself and solve. (x+4) = 0 x + 4 -4 = 0 -4 x = -4 First solution for x (x-3) = 0 x-3 +3 = +3 x = 3 Second solution for x", + "video_name": "swFohliPgmQ" + }, + { + "Q": "At 0:55, Sal draws a circle, but from an equation like the one in the video, is there any way to figure out exactly how large the circle is?", + "A": "The constant term is 25, so the radius of the circle is sqrt 25 = 5.", + "video_name": "swFohliPgmQ" + }, + { + "Q": "At 3:27 Sal is telling that angle AEB and angle ECB are congruent because they are corresponding angles but the line l and line m are not parallel. If they are corresponding angles, they have to be parallel. But how he did this?", + "A": "Corresponding angles are actually any two angles in that position. They are only congruent if the lines are parallel, and vice versa. Also, if two corresponding angles are labeled as congruent, the lines are parallel, end of story", + "video_name": "6dIMIBO_2mc" + }, + { + "Q": "At 7:27, shouldn't it be 1 /\u00e2\u0088\u009a2, rather than \u00e2\u0088\u009a2/2?", + "A": "The second fraction \u00e2\u0088\u009a2/2 is the same as the first fraction 1 /\u00e2\u0088\u009a2, just with a rationalized denominator. The 2 forms are equivalent.", + "video_name": "mSVrqKZDRF4" + }, + { + "Q": "What if we tried to find dy/dx by explicitly defining y in terms of x first, just like Sal did at 0:47. Would we have to find dy/dx separately for both the positive and negative roots? What would we do afterwards?", + "A": "Yes, since when we define it explicitly we get 2 equations (for a different one, we could get 4, there s an example of this, called a... fleur or something, it s 4 loops, obviously to define it as a correct function you have to limit it, since it loops back on itself). The two functions give you different slopes in terms of which one you re using. When you use y = +sqrt(1 - x^2) you re getting dy/dx for that function, the top half of our circle.", + "video_name": "mSVrqKZDRF4" + }, + { + "Q": "at about 4:30, when Sal is taking the derivative of y^2, why is he using the chain rule and not the power rule?", + "A": "He s using both. The chain rule is required here because we re differentiating with respect to x and the expression includes y. We re able to do this by treating y as a function of x. This means that y\u00c2\u00b2 is actually a composition of two functions: the squaring function applies to whatever function would turn x into y. We don t necessarily know what that function is, but that s okay, it s why we re doing implicit differentiation instead of normal (explicit) differentiation.", + "video_name": "mSVrqKZDRF4" + }, + { + "Q": "at 3:14 can someone explain how d/dx (y^2) = dy^2/dy ? how does the denominator of dx turn into dy?", + "A": "First, notice that d/dx (y^2) has a different variable for the function, and the variable we re taking the derivative with respect to. This brings to mind chain rule, that is, if y is a function of x, like y(x). The chain rule says in this example says that d/dx (y(x)^2) = d/dy (y^2) * d/dx (y(x).", + "video_name": "mSVrqKZDRF4" + }, + { + "Q": "At 2:20, you said \"the length of u1\" but you just showed u1. Does it matter which way you do it?", + "A": "Here the letter u is meant to stand for unit vector , so you don t need to write ||u1|| .", + "video_name": "rHonltF77zI" + }, + { + "Q": "what is the thing that sal did 2:43 called?", + "A": "I think improper fraction or mixed number/fraction.", + "video_name": "RPhaidW0dmY" + }, + { + "Q": "at 2:18 what if you have a number that can't be divided normally", + "A": "At 2:18, Sal cancelled out a common factor. If there are no common factors to cancel, then you just multiply. For example: 7/4 * 11/5 = 77/20 = 6 17/20 Hope this helps.", + "video_name": "RPhaidW0dmY" + }, + { + "Q": "at 3:19 he said 2x5. = 12 and I am pretty sure it = 10 so I'm just confused", + "A": "Yeah, your right, he made a mistake, but if you watch for about two seconds longer, he actually corrects himself. \u00f0\u009f\u0091\u008dgood job on catching his mistake though.", + "video_name": "RPhaidW0dmY" + }, + { + "Q": "At 1:51 you simplify the numerator of one fraction, but then simplify the denominator of the other fraction. How is it that you can do this? I thought you had to simplify the denominator of the same fraction.", + "A": "You can do this if you are multiplying fractions. If you multiply first, you get (7/4)*(36/5)=(7*36)/(4*5). Now you have all the numbers from the original two fractions in the same fraction. So it really doesn t matter at what stage you simplify. I hope this helped you. And remember that this is allowed only in multiplication, not in any other operation.", + "video_name": "RPhaidW0dmY" + }, + { + "Q": "at 2:37 you only did the denominator for the first fraction and for the second fraction you only did the numerator, why didnt you do all of both fractions?", + "A": "At this point in the video, Sal is cancelling out (dividing out) a common factor. As long as the fractions are being multiplied, we can cancel out a common factor from any numerator with the same factor in any denominator. The only numerator and denominator values that share a common factor are the 36 and the 4. Five (5), the remaining number in a denominator is not a common factor of 7 or of 9. This is why no other numbers were cancelled. out. hope this helps.", + "video_name": "RPhaidW0dmY" + }, + { + "Q": "At 0:34 what do you mean by geometric and arethmatic mean because I'm confused?", + "A": "Geometric and arithmetic mean have different meanings in some areas of math. For now just use the mean you ve learned so far.", + "video_name": "k5EbijWu-Ss" + }, + { + "Q": "WHY is 5.5 = to 5 feet,6inches? SAL said so at 3:31-3:37", + "A": "Because 1 foot is 12 inches. Compare this to for example hours and minutes. 1.5 hours is one hour plus half an hour, or 1 hour 30 minutes. Likewise, 5.5 feet is 5 feet and half a foot, or 5 feet and 6 inches.", + "video_name": "k5EbijWu-Ss" + }, + { + "Q": "At 4:43, is a capital Sigma only used for sample sums?", + "A": "Per Wiki, a capital Sigma when used by mathematicians indicates summation. A capital Sigma has other uses in other fields like physics and economics. Here s the Wiki link for a more nuanced answer.", + "video_name": "k5EbijWu-Ss" + }, + { + "Q": "At 1:23 , how many ounces is a ton?", + "A": "There is 32,000 ounces in a ton.", + "video_name": "Dj1rbIP8PHM" + }, + { + "Q": "At 6:46, Sal says the function would be defined or all other real numbers except the ones specified. But shouldn't x not be equal to 0 either? Because if x=0, then the denominator would again become 0, hence resulting in an undefined solution. Is that correct?", + "A": "We have h(x)=(x+10)/((x+10)(x-9)(x-5)). In that case, h(0) = (0+10)/((0+10)(0-9)(0-5)) = 10/((10)(-9)(-5) = 1/45", + "video_name": "n17q8CBiMtQ" + }, + { + "Q": "At 1:25, Sal shows us the outer angle. What is the use for these outer angles in the real world?", + "A": "In some math problems, if you are only given the outer angle, you can still solve for the remaining angles. Angles help in many things such as the job of construction workers, carpenters when deciding table lengths, etc.", + "video_name": "QmfoIvgIVlE" + }, + { + "Q": "What does he mean at 0:31 when he says fair coin?", + "A": "He means a coin with one head and one tail that has an equal chance of flipping one or the other.", + "video_name": "cqK3uRoPtk0" + }, + { + "Q": "At 3:28 why is the probability range between 0 and 1? I understand that beyond 1 we have a certainty of something happening, but why 1?", + "A": "In statistics, 1=100%. One hundred percent is is absolute certainty. You can t be more certain than that.", + "video_name": "cqK3uRoPtk0" + }, + { + "Q": "At 4:36, why didn't Sal distribute the 2 to AC and BD?", + "A": "The Distributive Law only applies to cases of multiplication over addition. The distributive property would not apply in this case, as it is 1/2AC*BD, not 1/2(AC+BD)", + "video_name": "3FManXv4mZM" + }, + { + "Q": "0:03 how do you now its a rhombus", + "A": "And it was a given.", + "video_name": "3FManXv4mZM" + }, + { + "Q": "In 1:12, How did Sal get 1 from i^25?", + "A": "Sal got one from i^100, not i^25. he said that since 4x25=100, then i^100 is the same thing as (i^4)^25. i^4 is equal to 1, so 1^25=1. Finally, Sal deduced that i^100=1", + "video_name": "QiwfF83NWNA" + }, + { + "Q": "At 1:12, isn't 100 also divisible by 5?, and since 5 is larger, wouldn't i^100 be i?", + "A": "When working with powers of i, we always use 4 to divide the exponent (regardless of what factors the exponent has) because the values of the powers of i repeat in groups of 4. That way, by using the fact that i^4 is 1, it makes the problem simpler.", + "video_name": "QiwfF83NWNA" + }, + { + "Q": "At 5:20 Sal says regarding i^96 that \"This is i^4, and then that to the 16th power\". Shouldn't he have said that \"This is i^4, and then that to the 24th power\" instead?", + "A": "Yeah... But the result wasn t wrong.", + "video_name": "QiwfF83NWNA" + }, + { + "Q": "At 5:18 he said 8 games and 16 somgs. How does this meets the first constranit?", + "A": "The first constraint is songs + games must be greater than or equal to 15. 8+16=24 which is greater than 15.", + "video_name": "BUmLw5m6F9s" + }, + { + "Q": "Hay,\nI was just wondering, at 5:24 Khan began to solve for the variables using the standard form. He started to graph it at 7:22. If someone has to graph an inequality converting it to standard form, do you have to use the same interval as in the standard form or can you adjust it due to the converted slope-intercept form?", + "A": "Just use intecepts", + "video_name": "BUmLw5m6F9s" + }, + { + "Q": "in 9:37 I thought the question said that a total of 15 games should be purchased, i was just wondering if it was relevant?", + "A": "Sal actually said that at least 15 items were purchased. Like English, mathematics is a language. It is important to read the words very carefully, especially in word problems.", + "video_name": "BUmLw5m6F9s" + }, + { + "Q": "What does Congruent mean? 1:25", + "A": "Congruent means that 2 or more shapes look exactly the same in shape and size.", + "video_name": "tFhBAeZVTMw" + }, + { + "Q": "At 7:46, I would like to make sure that I have the correct answer for the \"cliffhanger\". Is it 20x^9\nThanks", + "A": "Yes, you have the correct answer. Good job. Looks like they cut the video off too quickly.", + "video_name": "iHnzLETGz2I" + }, + { + "Q": "at 2:04 when p^2 = 2p, why wouldn't you solve it as sqrt(p^2) = sqrt(2p)", + "A": "You could do it that way, you d get p = \u00e2\u0088\u009a(2p). The solution would be the same (0 = \u00e2\u0088\u009a0, 2 = \u00e2\u0088\u009a4). It s just easier the way Sal does it, p(p-2) = 0, where you can clearly see the solutions are 0/2.", + "video_name": "ZIqW_sXymrM" + }, + { + "Q": "At 4:06, why did Sal multiply 3x and 12 by 1/3?\n\nCouldn't you divide each side by 3 to isolate the variable?\n\nI was taught to use inverse operations. The inverse operation of multiplication is division.\n\nSo why did Sal not use inverse operations to solve 3x=12?", + "A": "Multiplying by 1/3 is the exact same thing as dividing by 3. Remember how to divide fractions? If you have 2/3 divided by 5/6 it is the same as 2/3 times 6/5, right. Remember you can write whole numbers, such as 12 and 3 as 12/1 and 3/1, So 12/3 = 12/1 / 3/1 = 12/1 * 1/3 = 12 * 1/3. So you see, multiplying by 1/3 is the same a dividing by 3. Great Question! Keep Studying! 12/3 = 12/1 * 1/3", + "video_name": "_y_Q3_B2Vh8" + }, + { + "Q": "at 4:05 why didn't he do 3x/3 and 12/3", + "A": "Multiplying by 1/3 and dividing by 3 are the same operation, so your way is the same as Sal s, it just looks a little different", + "video_name": "_y_Q3_B2Vh8" + }, + { + "Q": "At \"2:03\" is the answer Sal has not the correct one, so he has to use another formula to finish the problem?", + "A": "Sal explains earlier (at 0:28) that this problem will have only one solution because there s only one way the absolute value of something can be 0 since the only number with an absolute value of 0 is 0.", + "video_name": "GwjiR2_7A7Y" + }, + { + "Q": "How come at 5:37 you had to take the inverse cosine and could not leave the answer as cos(19/20)?", + "A": "In this example we are solving for theta. Notice that theta is stuck inside the COS function when we say: cos(theta) = 19/20 To get theta out in the open we take the inverse cos of both sides: arccos(cos(theta)) = arccos(19/20) theta = acrcos(19/20) theta = 18.19 degrees Notice that arccos and cos are inverse function as they undo each other.", + "video_name": "Ei54NnQ0FKs" + }, + { + "Q": "What is an arbitrary triangle? it mentions that term in the video at 1:23. Thank you!", + "A": "It basically means a random triangle. He is paying no attention to side lengths or angle measures. It s not a term you need to know, don t worry.", + "video_name": "Ei54NnQ0FKs" + }, + { + "Q": "At 2:25, can't you also add 9x to both sides first instead of subtracting 12x?", + "A": "Yes! You can also add 9x to both sides, instead of subtracting 12x. The reason why Sal had subtracted 12x from both sides was that it is often preferred to have x on the left side. He ends up with: -21x - 3 = 18", + "video_name": "YZBStgZGyDY" + }, + { + "Q": "At 1:17. Sal says that 12x + 18 cannot happen because x has a coefficient and 18 is a regular number. If this is correct, how did he get 3 + 4x = 12x?", + "A": "He did 3*4x, not 3+4x.", + "video_name": "YZBStgZGyDY" + }, + { + "Q": "At 5:10, there should and maybe there is only one x for ( x^2=9 ) as, x = sqrt(9), which is equal to 3, ( by principal squareroot ), not -3!, -3 = -x right, as its the same number 3, & hence, -3 ^ 2 = 9 should always be written as -x ^ 2, for any*, any number even for infinity", + "A": "That is not correct. -3^2 = -9 and you cannot take the square root of a negative number. (-3)^2 = 9. If you have -3 = -x, that is the same as x = 3, so it still is the primary square root. The reason this is one place where we do not just take the primary square root is because we are talking about x intercepts of a quadratic, so the answer is x = +/- 3.", + "video_name": "mbc3_e5lWw0" + }, + { + "Q": "at 5:11 why did he put a 1/2 sign as the exponent", + "A": "He used 1/2 as the exponent to explain to us that polynomials can t have fractional or decimal exponents (although other numbers can have them).", + "video_name": "Vm7H0VTlIco" + }, + { + "Q": "At 0:16, How would you turn that into a linear equation?", + "A": "Good Question. first take the change of your y and x points. which is y( 7) and x(4). now we need to find the slope. to find the slope lest divide our y difference by our x difference: 7/4 now we have our slope! now so far we have Y=7/4x+b at 2:30 Sal was confirming about the dotted line. as we know we are now trying to find the y-Intercept. looking at the graph we can see that the y-Intercept is -7 so now we get!( Drum roll!) Y=7/4X+(-7) or: Y=7/4X-7 Hope This Helps! =)", + "video_name": "wl2iQAuQl7Y" + }, + { + "Q": "At 4:02, we go from d=5m/s * 1h to 5 m*h/s which is cool because we did 5m/s * h/1. But then he just writes 3600/1 s/h without any symbols. Are we just multiplying 5m*h/s * 3600/1 * s/h or what is happening here. Im not really used to adding things into a middle of equations without reasons like simplification etc.", + "A": "Right, there are 3600 seconds in an hour (because there are 60 seconds in a minute and 60 minutes in an hour so 60*60=3600 seconds in an hour). It s 3600 seconds/1 hour, or 3600 s/1 h.", + "video_name": "hIAdCTNi1S8" + }, + { + "Q": "At 2:30 and 2:37, didn't Sal mean a1, a2 and a4 rather than a1, a2 and aN?", + "A": "I believe so. Notice that he switched back. His 4 s do look like n s.", + "video_name": "CkQOCnLWPUA" + }, + { + "Q": "At 3:30 just when I learned that parenthesis most be solved first. But, I also learned about the Distributed Property. SMH", + "A": "Whenever you have parenthesis, do the math inside the parenthesis first, then use the distributive property. 4(11-3)= 4(8)=32 If you want something to help you remember the order of operations, try PEMDAS. Parentheses Exponents (if necessary) Multiplication (this includes the distributive property) Division Addition Subtraction", + "video_name": "tuVd355R-OQ" + }, + { + "Q": "In 9:09, you write an equation which I don't understand. Could you explain it again, please?", + "A": "But why does he put the twelve in brackets then?", + "video_name": "tuVd355R-OQ" + }, + { + "Q": "8:19 How can 7 be written as 35/5?", + "A": "35/5 is the same thing as 7.", + "video_name": "tuVd355R-OQ" + }, + { + "Q": "@4:42 I didn't understand how you got 3/2. The way i did it was i divided 3 by 2 and got 1.5 .", + "A": "they re really the same thing, 1.5=3/2", + "video_name": "tuVd355R-OQ" + }, + { + "Q": "at 8:19 why is seven written as 35? I thought it would be 8/5 plus 7/1", + "A": "Seven is written as 35/5, not 35. Remember that if I have 35 and divide it by 5 I get 7. It s the same as when you re reducing a fraction: When you reduce a fraction, you divide the top and bottom by the same number. You can also multiply the top and bottom by the same number. In this case, Sal multiplied the top and bottom of 7/1 by 5, which gives (7*5)/(1*5) = 35/5. Hope this helps", + "video_name": "tuVd355R-OQ" + }, + { + "Q": "At 2:11 Khan says that 0.6 goes into 12 two times but doesn't 6.0 not 0.6 go into 12 two times..?", + "A": "he moved the decimal point one place to the right, so instead of it being .6 into 12 it was 6 into 120. He was doing the first part of the problem , 6 into 12 goes twice, so you put a 2, then six goes into 0 zero times so you put a zero. The 2 and the zero together is 20.", + "video_name": "tuVd355R-OQ" + }, + { + "Q": "At 1:40 shouldn't it be (y^3)/2 (instead of (y^3)/3)?", + "A": "Okay, this is corrected later at 2:46", + "video_name": "0pv0QtOi5l8" + }, + { + "Q": "I'm a little confused about Sal's second table that he draws in green later in the video. Does this signify that the inputs and outputs have changed? At 2:56 you can see the table has written that x is 5, and f \u00e2\u0081\u00bb\u00c2\u00b9(x) is -9. Is 5 now the input, and -9 is the output? Or is x the range and f \u00e2\u0081\u00bb\u00c2\u00b9(x) is the domain?", + "A": "In the inverse function, the domain and the range are switched. domain->range range->domain", + "video_name": "KzaPBzFFLRM" + }, + { + "Q": "At 8:34, she sang something about unary. i dont that that makes sense. help me!", + "A": "Pick a number. 13 for example. In the decimal system (base ten) it is written 13, 1 ten and three 1s. In the binary system (base two) it is written 1101, one 8, one 4, no 2s, one 1. In the unary system (base one) it is written 0000000000000, one 1, another 1, another 1, another 1, another 1, another 1, another 1, another 1, another 1, another 1, another 1, another 1, and another 1.", + "video_name": "sxnX5_LbBDU" + }, + { + "Q": "at 0:40 why is y make x =0", + "A": "The y-intercept just means where the line crosses the y axis. Any point on the y-axis has a x value of 0, because you aren t moving left or right, you are just going either up or down. So the y-intercept is where the line crosses the y axis, and that point will have a x value of 0.", + "video_name": "405boztgZig" + }, + { + "Q": "Why are you multiplying it by 0? 0:22 of the video.", + "A": "I didn t see any multiplication by zero at 0:22. There is some at 0:49. At this point Sal is looking for the x-intercept (where the line crosses the x-axis) which is when y is zero, so he s plugging in 0 for y in the given equation 2y + \u00e2\u0085\u0093x = 12 and solving for x.", + "video_name": "405boztgZig" + }, + { + "Q": "At around (0:17) he says that the points aren't above or below the x axis....how do you figure out whether or not the point is above or below the x axis?", + "A": "Hi Alice. What Sal means by the x-intercept not being above or below the x-axis is that this point is the point on the line where the line intercepts the x-axis. Finding this means that we have to set y equal to 0, and doing so means that we do not move above or below the x-axis, and that we only move along the x-axis. Hope that helped!", + "video_name": "405boztgZig" + }, + { + "Q": "7:43. Isn't 1 -3 -2, not 2, or are you saying the absolute value?", + "A": "Sal is using absolute value in this video, and that is why your a little confused. \u00f0\u009f\u0098\u0089", + "video_name": "GdIkEngwGNU" + }, + { + "Q": "When Sal say's: du is going to be equal to the derivative of x^4+7 \"with respect to x\" (1:16). What does he mean with the last bit? Would it be possible to have a different variable than x and if so what would happen then?", + "A": "With respect to x means that the equation is being derivated in the form d(u)/d(x), as the equation is written in terms of x. It is possible to have a variable other than x- If we had an equation that was, for example, y=3z-1, we would derivate y with respect to z because the equation is written in terms of z. hence dy/dz = 3. Hope this helps!", + "video_name": "Zp5z0wa0kgo" + }, + { + "Q": "At 3:10 why does Sal use the \"ln\"? i know ln means natural log but why is this used?", + "A": "All the formulas in calculus involving log use the log with base e or ln. The formula used here is \u00e2\u0088\u00ab (1/x) = ln|x|", + "video_name": "Zp5z0wa0kgo" + }, + { + "Q": "At 2:56, I'm really confused about where the 1 came from. Can someone please explain? Thank you", + "A": "Example: 5/3 = (1/3)*5, right? You had du/u and did the same thing as above, so du/u = (1/u)*du.", + "video_name": "Zp5z0wa0kgo" + }, + { + "Q": "At 3:24 where does the du go? I do understand that 1/u = ln |u| then we put the constant +C . Bu I can not seem to understand what happens to du and where it goes...? Thank you!", + "A": "It disappears the same way dx does when you do a regular integration without a u-substitution. For example, the integral of x dx is (x^2)/2 + C, and the integral of (1/x)dx is ln|x| + C. We re using the same process when we integrate after a u-substitution, but now we re integrating with respect to u, so the integration needs du to work instead of dx.", + "video_name": "Zp5z0wa0kgo" + }, + { + "Q": "At 10:45 he takes the \u00e2\u0088\u009a200 and converts it to 10\u00e2\u0088\u009a2. That lost me completely. What math should I learn so that makes sense? Thank you in advance!", + "A": "The key to simplifying square roots is to take out any perfect squares and leave any non perfect squares inside. So if we notice that 200 = 100 \u00e2\u0080\u00a2 2, we see that 10^2 can be taken out as a 10 and 2 has to stay in. If we prime factor it, we have 2 \u00e2\u0080\u00a2 2 \u00e2\u0080\u00a2 2 \u00e2\u0080\u00a2 5 \u00e2\u0080\u00a2 5, and again \u00e2\u0088\u009a200 = \u00e2\u0088\u009a4 \u00e2\u0080\u00a2 \u00e2\u0088\u009a2 \u00e2\u0080\u00a2 \u00e2\u0088\u009a25 or 2 \u00e2\u0080\u00a2 5 \u00e2\u0088\u009a2", + "video_name": "E4HAYd0QnRc" + }, + { + "Q": "i have doubt about these kind of linear equation which at 7:12 have many solution due to rank of matrix is 2 and order of matrix is 3 * 2", + "A": "No, it s a simple system of two variables. There is one solution for A and another for B.", + "video_name": "hbJ2o9EUmJ0" + }, + { + "Q": "at 5:21 you said that unbiased variance = (n-1)*\u00cf\u0083\u00c2\u00b2/n. we know that (n-1)/n is a increasing function. So how come value decrease as n at 9 compared to at 8", + "A": "That s because the graph is from randomly picked samples and there is some error in this process.", + "video_name": "Cn0skMJ2F3c" + }, + { + "Q": "Mr. Khan,\nAt 2:52 of the video you mentioned how to write domain. Does {x/x\u00e2\u0082\u00acR} work too to write the domain because I was taught this way?", + "A": "Yes, you could use that when the domain = (-infinity, infinity). The domain and range are sets, so either interval notation is used to describe the set. Or, you could also use set notation which is what you have.", + "video_name": "-DTMakGDZAw" + }, + { + "Q": "I'm a little confused what the (base) is... 0:53", + "A": "Usually, the bottom side of a parallelogram is thought of as the base, but any side of the parallelogram can be chosen as the base when using the A = bh formula. Once a side is chosen as the base (b), the height (h) must be the perpendicular distance from the side chosen as the base to the side parallel to this base. (Note that the height, h, is usually not the length of a side of the parallelogram.) Have a blessed, wonderful day!", + "video_name": "hm17lVaor0Q" + }, + { + "Q": "At 1:05 What does the triangle on x+3 stand for?", + "A": "It s not a triangle, it s delta . In this case it means that you have to find the absolute value of x1 (which is -3) minus x2 (which is 0). The result is 3.", + "video_name": "81SseQCpGws" + }, + { + "Q": "At 5:41 why do we multiply P(A) by P(B)", + "A": "As the events A and B are independent, meaning the outcome of event A does not affect the outcome of event B, then we can calculate the probability of both A and B taking place by multiplying the P(A) with the probability of B. This holds for independent events. But we must be careful about what we are calculating according to the problem we are trying to solve.", + "video_name": "RI874OSJp1U" + }, + { + "Q": "At 0:30 what is sal trying to say??", + "A": "At 0:30 Sal is explaining the significance of the constant of integration added in the end. \u00e2\u0088\u00ab2xdx = x^2 + C The +C is added as the derivative of a constant is 0. So the derivative of x^2, x^2 + 1 or x^2 + e or x^2 + \u00cf\u0080 or in general x^2+C is the same each time.", + "video_name": "MMv-027KEqU" + }, + { + "Q": "i don't really get what sal says at 4:05 can some one help", + "A": "That order doesn t matter in combinations.", + "video_name": "iKy-d5_erhI" + }, + { + "Q": "How do I solve this problem?\n: a ski resort has started to keep track of the number of skiers and snowboarders who bought season passes. The ratio of the number of skiers who bought season passes to the number of snowboarders who bought season passes is 1:2. If 1250 more snowboarders bought season passes than skiers, how many snowboarders and how many skiers bought season passes?", + "A": "ratio of skiers to snowboarders 1:2 nbr of skiers = 1 * x = 1x nbr of snowborarders = 2 * x = 2x how many more snow boarders than skiers = 2x -1x = x so x should be equal to 1250 so nbr of skiers = 1x = 1 * 1250 =1250 nbr of snow boarders = 2x = 2 * 1250 = 2450", + "video_name": "tOd2T72eJME" + }, + { + "Q": "i don't get 0:32", + "A": "Think of it this way: You take a ruler and measure 7cm on the map. That whole 7cm is 10km in the real world. :)", + "video_name": "tOd2T72eJME" + }, + { + "Q": "What about a ratio like 1/2:3/4", + "A": "A ratio of 1/2:3/4 is a complex fraction (fractions within a fraction). It would need to be simplified by dividing the 2 fractions. 1/2 / 3/4 = 1/2 * 4/3 = 2/3", + "video_name": "tOd2T72eJME" + }, + { + "Q": "2:22\nWhy can't we count the Probability of \"not catching a sunfish 3 times\" as well 1/2*1/2*1/2?\nAs each time of not catching a sunfish means catching a trout, which has the same probablity.\nThank's!", + "A": "There are 8 equally likely possibilities: SSS, SST, STT, STS, TTT, TTS, TSS, and TST. So the probability you said: 1/2*1/2*1/2 could also be said as: P(not get a sunfish)*P(not get a sunfish)*P(not get a sunfish) which would be the fifth possibility: TTT. Not getting a sunfish three times in a row, however, could be any of the last seven possibilities. I hope this helps! :)", + "video_name": "86nb02Bx_5w" + }, + { + "Q": "At 0:24, why did Sal say 10+10+6? That's 26, instead of 16...", + "A": "Oh, no. Sal said 10+6, not 10+10+6. That s where your trip was.", + "video_name": "vbGwcvXgDlg" + }, + { + "Q": "At 7:35, Sal enters some values into the calculator which are close to -4. What would happen on the calculator if we tried to enter -4 into the function replacing x??", + "A": "When we substitute -4 for x, the equation becomes (-4)^2/(-4)^2-16. We can simplify this expression to 16/16-16 which then becomes 16/0. It s impossible to divide by 0 because nothing times 0 is equal to 16. There is no way to get 16 (or any other number) by multiplying by 0. The expression x^2/x^2-16 becomes undefined when x=-4 and when x=4 because there are no possible outputs from those inputs.", + "video_name": "2N62v_63SBo" + }, + { + "Q": "At 16:59 Sal explains how to get the horizontal asymptote. Is it possible to ever have a negative horizontal asymptote?", + "A": "Yes, a horizontal asymptote can be any y value. It s location is determined by the coefficients of the variables, which can be any number (the coefficients that is).", + "video_name": "2N62v_63SBo" + }, + { + "Q": "In 3:40, Sal writes |-2-3|, while on the number line, we normally subtract the lesser number from the greater one, i.e. |3-(-2)|, right?", + "A": "As long as you subtract the 2 numbers and take their absolute value, you will create the same result: |-2-3| = |-5| = 5 |3-(-2)| = |5| = 5 So, pick the version you are more comfortable with.", + "video_name": "t4xOkpP8FgE" + }, + { + "Q": "At around 7:10, why did Sal do 16-2=14 instead of 2+16=18?", + "A": "At 3:00 and at 4:12 or so, he explanes that the change in y is 14 because one point is at +2 and the other is at +16. and if you count that on the graph they are 14 spaces apart.", + "video_name": "WkspBxrzuZo" + }, + { + "Q": "in 1:16 does m equal slope?", + "A": "In y=mx + b, m is always the slope, and b is always the y-intercept", + "video_name": "WkspBxrzuZo" + }, + { + "Q": "At 0:32 Sal said \"all the rectangles\" but there was actually one square .", + "A": "A rectangle just means a shape with four sides & four right angles, so technically all squares are rectangles.", + "video_name": "nLY2bzRfQyo" + }, + { + "Q": "At 1:41, it is 4.", + "A": "Yes, 4 would be the correct opposite for -4.", + "video_name": "2Zk6u7Uk5ow" + }, + { + "Q": "I am confused at 4:35 the video lost me, i am so confused", + "A": "He s basically saying you need all of the factors for both of the numbers and if you leave one out or forget one your answer will be wrong. Hope this helps!", + "video_name": "1Vb8t7Y-pI0" + }, + { + "Q": "um... in 3:6-11 what do you mean by distribute? that i so confused", + "A": "Distributing is multiplying the number outside the parentheses by everything inside the parentheses 9(1+99) Aka 9*1 and 9*99", + "video_name": "XAzFGx3Ruig" + }, + { + "Q": "At 4:15 mins into the video, Sal says that since 999 is divisible by 9, everything before it is divisible by 9, hence 2.999 is divisible by 9. But 4.9 is not divisible by 9. What am I missing here?", + "A": "let s look here. i think 4*9 is indeed divisible by 9. 4*9 = 36. is 36 divisible by 9? yes, because 36/9 is 4, a whole number. also to do a multiplication sign, use an asterisk (shift-8) on your keyboard instead of a decimal.", + "video_name": "XAzFGx3Ruig" + }, + { + "Q": "Around the 1:36 mark in your video, I did not understand it when you said that you would multiply the number by 3 jumps. I get the jump part, but i do not get the multiplication part. By that I mean, why would you multiply 8/3 by 3? I would appreciate it very much if anyone could help me figure this out!", + "A": "You have to flip one of the numbers you are dividing and then multiply the flipped number with the other number(in this case 3) to get your answer", + "video_name": "f3ySpxX9oeM" + }, + { + "Q": "at 2:20 , how are we telling that they are parallel", + "A": "Because of the right angles. It requires a 180 degree angle to make a line fold back over itself, or to be parallel. At 2:20, the top of the square forms a 90 degree angle with the side, and the side forms another 90 degree angle with the bottom. Adding these up, we get 180 degrees, meaning the top and bottom lines are parallel. The same thing is true with the two sides. I hope this answers your question! :)", + "video_name": "wPZIa3SjPF0" + }, + { + "Q": "At 0:13, how are you able to tell that the opposite sides are parallel?", + "A": "107+73=180 degrees, so the opp sides are parallel by same-side interior/consecutive interior angles", + "video_name": "wPZIa3SjPF0" + }, + { + "Q": "At 1:45, how can we say that two pairs of opposite sides are parallel ?\nIs it just by observation or anything else ?", + "A": "If they ever touch, then it won t be parallel, but they have to continuously have the same space between them.", + "video_name": "wPZIa3SjPF0" + }, + { + "Q": "At 1:24, Sal mentions that 2 is a factor of (x^3 - 8). How did he come up with that?", + "A": "If 2 is a root of a polynomial, then (x-2) is a factor. The polynomial is x^3-8. Set that equal to 0 and solve: x^3-8=0 x^3=8 (x^3)^(1/3)=8^(1/3) x=2. So 2 must be a root, and therefore (x-2) is a factor. You can divide x^3-8 by (x-2) and get the quotient of x^2+2x+4. This is how you derive the difference of cubes formula.", + "video_name": "6FrPLJY0rqM" + }, + { + "Q": "In 2:45, who is blaise pascal?", + "A": "Blaise Pascal (1623-1662) was a French mathematician, physicist, writer, philosopher, and inventor. Pascal s earliest work was in the field of fluids, where the Pascal (Pa), a unit of pressure, was named after him. He then worked to invent the calculator. He became the second inventor of a calculator. Additionally, he basically created the field of projective geometry and worked on probabilities.", + "video_name": "Yhlv5Aeuo_k" + }, + { + "Q": "At 1:34 how come that's the highest prime number known to man isn't there a higher prime number?", + "A": "There are an infinite number of primes, but it is very difficult to prove that a really large number is prime. So, we know that there is a higher prime number, but we don t know what it is. This video is slightly out of date, though, because the highest prime known to man is now 2^57,885,161 \u00e2\u0088\u0092 1.", + "video_name": "Yhlv5Aeuo_k" + }, + { + "Q": "At 0:14, did she choose Ulam for any specific reason? Is he just a random person that she chose or does he have something to do with sick number games?", + "A": "Ulam is a famous mathematician", + "video_name": "Yhlv5Aeuo_k" + }, + { + "Q": "For 1:40, do you have to represent if it's a natural number, integer, etc..", + "A": "When using sigma notation to express sums, it is implied that we re working with integers (which are a superset of natural numbers). Usually we re only working with the natural numbers, but there s nothing preventing starting at a negative index.", + "video_name": "5jwXThH6fg4" + }, + { + "Q": "I don't get the part on 4:34.\n\nOk if you are taking the -sqrt of (x-1)^2 doesn't that equal -(x-1), thus the final value equal (-x+1).\n\nFor example the negative sqrt of 9:\n\n=-sqrt(9)\n=-(3)\n=-3\n\nSomeone tell me if I'm wrong cause I'm confused on that part on how even with negative square root he still gets (x-1).", + "A": "So I read the answer above and yh... I still don t exactly get it. Does it have to do with the fact that x<= 1 ensuring a negative number so when you get a -sqrt of (x-1) you keep it like that so the answer doesn t go positive or is that completely unrelated.", + "video_name": "Bq9cq9FZuNM" + }, + { + "Q": "At 4:57 how do you know when to take the negative square root or positive one? I didn't get how in the video. Also if you could tell me, is this level of math algebra 1 or 2? They should do a better job of subdividing the algebra category between the 1 and 2.", + "A": "Whether you take the positive or negative root depends on which side of the graph is present. That s why Sal kept the for y >= -2 and x <= 1 pulled along to every step, to remember which side to use.", + "video_name": "Bq9cq9FZuNM" + }, + { + "Q": "I'm confused. Khan says there is only one x term at 1:55. Can someone help me with this?", + "A": "Look at the second line. There is a 3x, a -3x, and there is a x by itself near the middle. Since the -3x cancels out the 3x, the x by itself is left. hope this helps :)", + "video_name": "DMyhUb1pZT0" + }, + { + "Q": "I understood everything until 1:24. Why does he insert a \"1\" in front of the parenthesis? I mean, where does that come from? He then multiplies \"-1 * -4\", to get a value of 4.... I'm confused why is the 3x ignored? Thanks for any clarification you can provide.", + "A": "He inserted a 1 to show that the ... - ( ... is also equal to ... -1 ( ... The 3x was not ignored because it was already distributed with the - (or -1), making -3x, as shown in 1:20.", + "video_name": "DMyhUb1pZT0" + }, + { + "Q": "At 5:30 you gave the formula of how to find the area of a quadrilateral but it was quite confusing. Could you please explain it again?", + "A": "Pretty much, with the edges, you form right triangles. Then, you find their area and then add that to the area of the regular quadrilateral. :0)", + "video_name": "gkifo46--JA" + }, + { + "Q": "At 5:07 Sal says S parameter describes the angle between radius and x-z plane. Has he mistaken it for x-y plane, considering the way he uses the parameter afterwards?", + "A": "Yes, he meant to say x-y plane. A little box pops up in the lower right corner of the screen with the correction.", + "video_name": "owKAHXf1y1A" + }, + { + "Q": "at 7:36 how do you get your limits of integration? I understand that you did by inspection, but how would you do it by making the two equations equal to each other ?", + "A": "In that example, Sal is integrating with respect to y. To solve for zero and one analytically, we could make the equations equivalent to each other and solve. Here s the example: sqrt(x) = x^2 x = x^4 This last equation is true only when x = 0 or x = 1.", + "video_name": "WAPZihVUmzE" + }, + { + "Q": "At 1:46. I do not understand the purpose of the 1/7 * 7, nor where they even came from, nor what allows him to write them there to begin with.", + "A": "To use u-substitution you have to identify a function u such that a constant multiple of the derivative of u appears in the integrand. In this case the function u is 7x+9. The derivative of 7x+9 is 7. Therefore a constant multiple of 7 must appear in the integrand. Because it does not, Sal multiples the expression by 1 in the form of (1/7 * 7 = 1). In this way he makes sure 7 appears in the integrand therefore facilitating u substitution.", + "video_name": "oqCfqIcbE10" + }, + { + "Q": "Are du and dx able to just be treated like normal variables?\n@5:30 he treats the dx as another variable, to be multiplied with the 7", + "A": "Yes, when using Leibnitz notation, you can think of them as quantifiable numbers. What they really mean is this - an infinitely small change in the given variable. For example, du is an infinitely small change in u. dx is an infinitely small change in x. Then, if we think of it this way, du/dx as giving the slope makes sense! The change in u over the change in x gives slope! Long story short, you can treat them as actual numbers - infinitely small changes in a variable.", + "video_name": "oqCfqIcbE10" + }, + { + "Q": "You took the average change from 2000-2003 and then 2003-2004 and averaged it out, but why couldn't you just use 2002-2004? 2:27", + "A": "It s mathematically equivalent (and easier) to take the average for 2002 to 2004 (which would be (S(2004) - S(2002))/2) as you suggest. However, the problem specifies that we are to solve by finding the slope of the two secant lines and averaging those slopes, so that is the approach used in the video.", + "video_name": "fI6w2kL295Y" + }, + { + "Q": "\"it is a function of time\" can someone rephrase that please, in a very simple way @1:00", + "A": "A function of time meaning that as time passes the number of things change. In this example as the year goes by the number of stores built is increased which can be represented by a function with respect to time. A function being something along the lines of y = x + 1.", + "video_name": "fI6w2kL295Y" + }, + { + "Q": "At 0:46 Sal Khan said 30.42 but meant 30.24", + "A": "This is a known error in the video. There is a box that pops up and tells you Sal made an error and provides the correct info.", + "video_name": "Hrjr5f5pZ84" + }, + { + "Q": "At 1:10, Sal says that the perimeter is length+width+length+width, can't you do length*2 and width*2 ?", + "A": "Yup... depends on weather you are faster at addition or multiplication:)", + "video_name": "CDvPPsB3nEM" + }, + { + "Q": "At 8:24 Sal combines X(-b-2a) and X(-a-2b) and is left with only a single X coefficient, I was sure this would be 2X. Can someone please explain why it remains a single X coefficient? Thanks.", + "A": "Because the both 2s in -b-2a and -a-2b would be simplified and that would make it a single X coefficient.", + "video_name": "Vc09LURoMQ8" + }, + { + "Q": "Why does Sal use (1 2, -1 0) matrix at 6:21 ?", + "A": "He s just giving an example of a transformation. Since any matrix can be seen as a transformation, he just choose one at random.", + "video_name": "MIAmN5kgp3k" + }, + { + "Q": "Would it work if at 1:50, instead of factoring as he did, could we just FOIL? I would only think to do it that way if I knew beforehand that the result should look a certain way.", + "A": "I don t think I understand your question too well... Sal didn t factor at that point in the problem, he just distributed the entire sin expression with the (5 - 3y )", + "video_name": "-EG10aI0rt0" + }, + { + "Q": "At 2:35, when Sal subtracts the 3Sin(5x-3y), what happened to the dy/dx that was being multiplied to it? Could the 3Sin(5x-3y) even be subtracted without the dy/dx?", + "A": "Yes, you are correct. We are subtracting 3sin(5x-3y)dy/dx. This is exactly what Sal did. He just didn t mention dy/dx out loud.", + "video_name": "-EG10aI0rt0" + }, + { + "Q": "at 1:24, how can there be 4 possibilities, one person only have 3 options and not his own self. right?", + "A": "The 4 means that the first person involved in shaking hands can be any of the 4 people. The 3 means that the second person involved in shaking hands can be any of the remaining 3 people not counting the person identified as the first person.", + "video_name": "boH4l1SgJbM" + }, + { + "Q": "1:43\n\nWe were taught about radial symmetry. Is rotational and radial symmetry the same?", + "A": "rotational and radial symmetry is generally the same, but radial symmetry is usually used in biological contexts", + "video_name": "toKu2-qzJeM" + }, + { + "Q": "1:23 how did he get 6 as his exponent ?", + "A": "at 1:23 he was subtracting 6 from 2 because there was 2 exponents", + "video_name": "AR1uqNbjM5s" + }, + { + "Q": "AT 9:20 would 5/4 x^-1 y also be correct", + "A": "It generally would be considered incomplete. Final answers should have positive exponents. And, we would multiply the items together to show them as one fraction. This is why Sal is showing the answer as 5y / (4x)", + "video_name": "AR1uqNbjM5s" + }, + { + "Q": "if at 1:05 L = 1 and R = 0 then that is 01001100110 - a binary number, will someone find what it represents?", + "A": "Bin 01001100110 = Dec 614 If you were to switch them, with L=0, R=1, Bin 10110011001 = Dec 1433", + "video_name": "Gx5D09s5X6U" + }, + { + "Q": "At 2:06, could we take the y and pull it to the front similarly to how we pulled x to the front earlier in the video since it's an exponent?", + "A": "The Y is not an exponent. We re not raising 5 to the Y power. Rather, it is the result of raising the 5 to some power, i.e., 5 to the what power equals y? So the answer is no.", + "video_name": "RhzXX5PbsuQ" + }, + { + "Q": "At 0:20 can we move the x out in front first, instead of applying the quotient log property first? And then apply the quotient log property?\n\nIf not...is there a certain order in which log properties should be applied (like BEDMAS)??? Thanks in advance :)", + "A": "You can t move the x in front first, because not the whole factor is to the xth power. if we had log(25/y)^x we could. otherwise the whole term, so both log25 and log5 would be times 5, which is wrong. I hope this helps you, English is not my first language, so I don t know if I explained it well enough!", + "video_name": "RhzXX5PbsuQ" + }, + { + "Q": "at 2:00, why x(2 - log_5(y)) = 2x - log_5(y) and not 2x - xlog_5(y)?", + "A": "The 2 resulted from the expression log_5(25) , which was being multiplied by x. There were no parentheses to distribute the x to the second term ( -log_5(y) ), so it was unaffected by it.", + "video_name": "RhzXX5PbsuQ" + }, + { + "Q": "At 1:46, I got confused. If something is \"over\" something else, does that mean divide that number by the bottom number?", + "A": "Yes but do you see that x was being divided by 4 then multiplied by 4 so there is no reason to go through all that math when there opposites it would be like adding 4 to five and getting nine then subtracting $ and getting five again", + "video_name": "p5e5mf_G3FI" + }, + { + "Q": "at 2:05 it says add one shouldn't it say add 3?????", + "A": "Hey, you re right! That s funny.... well, he got the answer right anyhow.", + "video_name": "p5e5mf_G3FI" + }, + { + "Q": "At 3:30, how does he know that the question is linear?", + "A": "He knows at 3:30 because the equation can be plotted as a line. This means it will be straight no matter how far you extend it, and will not curve or bend anywhere. It is constant and will always remain so. I hope that helps :)", + "video_name": "OWPVZoxNe-U" + }, + { + "Q": "At 4:46, Sal says that there is only one way to get to the cube below the starting point. Isn't that logic flawed because it is a three dimensional object? Couldn't he go to the right an infinite number of times and then go down? Or go to the right one, go down one, and wrap around the cube?", + "A": "You are not travelling along the surface of the cube, you are traveling through the cube itself. Therefore, there is no wrapping around the cube. There is no going right an infinite number of times, because you can only go right twice. You are able to move right twice, down twice, and forward twice. All that matters is the order in which you do those moves.", + "video_name": "wRxzDOloS3o" + }, + { + "Q": "At 8:43, how does Sal automatically determine that x is 8 or 2. In the equation above, shouldn't x be -8 or -2 since x is getting subtracted by those two numbers?", + "A": "No. Since it is -5, he would have to add 5 to both sides to isolate x. Therefore, it would be 5 plus or minus 3, giving him 8 and 2. If he subtracted 5, the left side would have -10 + x and the right side would have -5 plus or minus 3. This would not be possible. He would have to add 10 to both sides to isolate x, giving him x=5 plus or minus 3.", + "video_name": "55G8037gsKY" + }, + { + "Q": "why do you find the square root of (4x+1 )squared and 8 around 1:30?", + "A": "Since we are trying to solve for x, we want to isolate x on one side of the equation. in order to do that, we have to cancel out as much stuff on the left hand side of the equation as possible. In this example, if we take (4x+1)^2 = 8 and we take the square root of both sides, we are left with 4x+1=sqrt(8), and we are one step closer to isolating x.", + "video_name": "55G8037gsKY" + }, + { + "Q": "At 1:40, what does Sal mean by positive or negative square root. If the square root on one side is positive, shouldn't the square root on the other side be positive, too?", + "A": "Technically, we would get two equations: 4\u00f0\u009d\u0091\u00a5 + 1 = \u00c2\u00b1\u00e2\u0088\u009a8 -(4\u00f0\u009d\u0091\u00a5 + 1) = \u00c2\u00b1\u00e2\u0088\u009a8 Since the two equations are equivalent, we can discard one of them, leaving us with: 4x + 1 = \u00c2\u00b1\u00e2\u0088\u009a8", + "video_name": "55G8037gsKY" + }, + { + "Q": "at 10:09 why is it plus or minus 1, when we square?", + "A": "When you square, you multiply a number by itself. And -3*-3 = 9 as well as 3*3 = 9. So there can be two solutions, when you take the square root of something (9 in my example). It s different when you cube a number. -3*-3*-3 = -27 which is not the same as 3*3*3 = 27.", + "video_name": "55G8037gsKY" + }, + { + "Q": "At 1:50, why does Sal write \u00e2\u0088\u009a8 as \u00e2\u0088\u009a4*2, and how would I know when I should?", + "A": "You can simplify any square roots if they are the product of a perfect square and another number. For example, the number 24. The \u00e2\u0088\u009a24 is the same thing as the (\u00e2\u0088\u009a4*6). We know that \u00e2\u0088\u009a4=2 so, we bring it outside the \u00e2\u0088\u009a sign. We result with 2\u00e2\u0088\u009a6. Same thing Sal did, just with different numbers.", + "video_name": "55G8037gsKY" + }, + { + "Q": "At 5:30 can you simply the fraction even more than that? Can you separate the fraction into 2 parts?", + "A": "It appears you are talking more @4:10 where he ends with the fraction (-1 +/- 2 \u00e2\u0088\u009a2)/4. You cannot simplify the fraction anymore than that, but you could separate it into parts, and you could separate it into two different solutions. Separating into parts to get -1/4 +/- \u00e2\u0088\u009a2/2 does not look as neat and compact as what he has, but it is equivalent.", + "video_name": "55G8037gsKY" + }, + { + "Q": "What does Sal mean when he says, \"vanilla like\"? I am guessing he means not-so-complex-looking, like at 4:48.", + "A": "In the U.S, an object can be described to be as plain as vanilla , which means that something is plain and simple like vanilla ice cream. You are correct in that he means not-so-complex-looking.", + "video_name": "55G8037gsKY" + }, + { + "Q": "At 5:29, how did he get 4 times 2?", + "A": "It s because 2 and sqrt(2) were squared separately, therefore you have 4 times 2. You can also think of 2sqrt(2) as sqrt(8) and when you square it, you ll get 8 which is 4 times 2.", + "video_name": "55G8037gsKY" + }, + { + "Q": "At 2:35, how does drawing a perpendicular line to the base prove that it is an equilateral triangle?", + "A": "I think he started the video already saying that the triangle was equilateral. He is not trying to prove that part.", + "video_name": "SFL4stapeUs" + }, + { + "Q": "At 0:58 how did he get 90, and if its 90/100 why couldn't the other fraction be 80/100?", + "A": "1st question: he got 90/100 because that = 9/10. he has to + them and you have to have a common denominator. 2nd question: because 8 is in the 100ths place. so you could have it 80/1000. so 9/10 + 8/100 = 90/100 + 8/100 = 98/100 sal makes it easy to understand.", + "video_name": "qbMe4f2yvKs" + }, + { + "Q": "At 3:06, he switched but i didn't get why?", + "A": "I believe Sal is trying to show you that you can multiply the 2 numbers ignoring the decimal points. Then, you can set the decimal point in your answer after completing the multiplication.", + "video_name": "4IWfJ7-CYfE" + }, + { + "Q": "at 0:04 why are the decimals not lined up? aren't they supposed to be lined up when you are multiplying?", + "A": "No, when you multiply, you line it up by how many numbers there are, so in 3.14 and 53.4, you line up the 4 with 4, 1 with 3, and 3 with 5, it doesn t matter where the decimal is. You only line your digits up when you are adding or subtracting.", + "video_name": "4IWfJ7-CYfE" + }, + { + "Q": "I couldn't hear you at 0:25", + "A": "0:20 - 0:30 is What i want to do in this video is test whether any of these four numbers satisfy either of these inequalities. i encourage you to pause the video and try these numbers out, does zero satisfy this inequality? to see what he is saying pause the video and press c on the keyboard for captions or you can scroll down a tiny bit and next to About there is Transcript. Click Transcript to see what he is saying.", + "video_name": "Yh4TXMVq9eg" + }, + { + "Q": "Around 3:10 why not take a proportion like 37% instead of 30%?", + "A": "Look at the null hypothesis. A value of 37% does not satisfy the null hypothesis of p<=0.30. When choosing a value of p, we need to satisfy the null hypothesis, and to choose a conservative number (one which will be less likely to reject the null hypothesis. In this case the largest value allowed by the null, which is 0.30).", + "video_name": "1JT9oODsClE" + }, + { + "Q": "at 1:50 how do you divide?", + "A": "You don t, you multiply the improper fraction by the recipricole of 1/5, which is 5/1", + "video_name": "xoXYirs2Mzw" + }, + { + "Q": "cane someone pls explain wat sal is trying to say at 3:45 - 4:52?", + "A": "Hi, We need to divide 9.2 by 11.5. As division with decimals get a bit confusing, Sal does the below-mentioned step. 9.2/11.5 = 9.2 *10 / 11.5 *10 ==>92/115 (Multiplying both numerator and denominator by 10, thereby we are not changing the value of the fraction). If you are still confused, take out a calculator and perform both the functions [9.2/11.5 and 92/115]. You will get the same answer. This is the trick in fractions. Hope this helped you.", + "video_name": "EbmgLiSVACU" + }, + { + "Q": "at 5:07 i got confused.", + "A": "There, 15 goes into 75 ----> 5 times r 1. To review it, when he was writing 5*5 = 25 in the division table, after writing 5, he takes 2 to add with (1*5). But, instead of writing 2 there, he faultily wrote it as 7. Then, after finding the error, he rectified it.", + "video_name": "gHTH6PKfpMc" + }, + { + "Q": "at 0:24, he asks what 6250 divided by 25 is. What's the answer?", + "A": "250. @Victoria Fine, you mean pie as in I LIKE PIE or pi as in 3.141592465?", + "video_name": "gHTH6PKfpMc" + }, + { + "Q": "At 2:50 couldnt you multiply both sides by 5, and then subtract by 0.6?", + "A": "Yes, you could. You are right. Good observation. There are multiple ways you can solve this problem.", + "video_name": "BOIA9wsM4ok" + }, + { + "Q": "Can someone help me here?\nAt 5:15 rather than distributing the 0.5 to both r and 2.75, he just divided r and 3 by 0.5. If 0.5 can be only divided by r and 3 then why is 2.75 inside the parentheses with r? Wouldn't dividing 0.5 only by r and not by 2.75 create an imbalance?", + "A": "Sal just liked to show you another way to solve that problem, and it is more simple way too.", + "video_name": "BOIA9wsM4ok" + }, + { + "Q": "At 0:47, what does it exactly mean to have a slope of 1?", + "A": "A slope of 1 means that for every unit the line goes along the x axis, it goes up the y axis 1 unit.", + "video_name": "5a6zpfl50go" + }, + { + "Q": "at 0:06 y=x+3 how do i sketch the graph if x is x square", + "A": "You can t. It s not a linear problem then. The way to graph it is like the quadratics, or other x^2. The y intercept is now the vertex. the line will look like a U.", + "video_name": "5a6zpfl50go" + }, + { + "Q": "i don't get the whole rate system. if you have the ratio how do you get the rate? for ex: 8 boxes can hold 48 books the ratio is 48:8 but how do you figure out the rate?", + "A": "Your rate will be 6 because how much does 1 box hold it holds 6 if you divide,if you need any help comment! :D", + "video_name": "qGTYSAeLTOE" + }, + { + "Q": "By saying that one is going 35 miles per hour, in ratio form would be 35:1, but could it also be expressed the other way around? for example, 1:35, saying that in every hour one is going 35 miles. Is is the same thing?", + "A": "yes it would be the same thing except it has to due with how it is worded. say if the problem said miles per hour it is 29:1 58:2 and so on but if it is hours per amount of miles 1:29 2:29", + "video_name": "qGTYSAeLTOE" + }, + { + "Q": "At 1:13, why is theta written in radians?", + "A": "Because it is easier to measure sin cos and tan that way.", + "video_name": "sjUhr0HkLUg" + }, + { + "Q": "At 8:15, Isn't PI transcendental number, so it is not a real number.\nSo is the graph wrong ?", + "A": "\u00cf\u0080 is both transcendental and real. Transcendental just means that the number isn t the root of a polynomial with rational coefficients. \u00e2\u0088\u009a2 is irrational, but not transcendental, since it s the root of x\u00c2\u00b2-2=0.", + "video_name": "sjUhr0HkLUg" + }, + { + "Q": "at 3:18 , Sal goes 3pi/2. Isnt it 3pi/4?\nIf im wrong can someone tell me why?", + "A": "Sal is right, it s 3pi/2. Maybe you got confused because Sal mentioned that we got 3/4 of the way , but you have to remember that the whole way is 2pi. So each quarter is pi/2 and 3*pi/2 is 3pi/2", + "video_name": "sjUhr0HkLUg" + }, + { + "Q": "At 5:50, on the mounting of the graph, why the connection between the points [\u00ce\u00b8,sin(\u00ce\u00b8)] of the table, was made for curved lines instead of straight lines?\nIn other words, why the graph of sin(\u00ce\u00b8) is not like this: /\\/\\/\\/\\/\\/\\/\\/\\/\\/\\ ?", + "A": "You can check this in different ways. If you want to be really confident, just take many points between 0 and pi and take the sine, you will get this smooth line. It s easier to follow the unit circle, as seen from 2:20 - to get from 0 to pi/2 Sal goes along a curved path - this has to be on the graph of the sine als well.", + "video_name": "sjUhr0HkLUg" + }, + { + "Q": "at 6:48 sal says with arcsin we only have to draw the first and fourth quadrants. why is this? I saw somewhere else that sine is between 1 and -1, but I still don't understand this.", + "A": "arc sin is a function, and as such it cannot have different outputs for the same input. If we included the second and third quadrant, we would get two solutions for most input values, so we wouldn t have a function.", + "video_name": "JGU74wbZMLg" + }, + { + "Q": "At 7:14, how does Sal know to put the y-axis point in that spot? Is it just an estimate? It seems that the result of the problem would depend on the accuracy of the placement of that point and therefore an estimate would not work.", + "A": "In this example, it is a 30-60-90 triangle. He draws the triangle as a visual aid, not as a means of actually calculating the angle. More generally, you might use a sketch like that to estimate the quadrant but use a calculator if you needed the actual result.", + "video_name": "JGU74wbZMLg" + }, + { + "Q": "Hi. In the video you were trying to find the arcsin of rad3/2. Since sin = y/r would not the hypotenuse(r) of the triangle at 8:13 be 2 and not 1? That would make the other sides = rad3 and 1 respectively. 1^2 + rad3^2 = 2^2. I don't understand why one side of the triangle you drew would be rad3/2.", + "A": "the hypotenuse is the radius of the unit circle, which is always 1", + "video_name": "JGU74wbZMLg" + }, + { + "Q": "At 6:02 he writes the range for a general arcsin function, but just to confirm, that's the range for all arcsin functions?? Or am I missing something. Because for the example problem he did at the end, he didn't state the domain and range, but I thought restricting the range was necessary to make the sine function valid. Could someone please clarify?", + "A": "i think you mean all inverse trig functions rather than all arcsin functions. and to answer your question, the range of all inverse trig functions are not the same due to the shape of the graph.", + "video_name": "JGU74wbZMLg" + }, + { + "Q": "What are Radians? 00:14", + "A": "Radians are a different form of measurement of an angle. They act no differently than degrees. They are much like different forms of currency. The Canadian Dollar and the U.S. Dollar serve the same purpose, but have different values. In the same way that a U.S. Dollar has more value than a Canadian Dollar, Radians have more value than degrees. 180 degrees is equal to 1 pi radians.", + "video_name": "JGU74wbZMLg" + }, + { + "Q": "Why didn't Sal round up to 1.4 from 1.47? Wouldn't that be more accurate? 10:01", + "A": "Sal DID round UP. The calculator showed a NEGATIVE 1.047..... which is between - 1.05 and -1.04 The larger number (the one furthest to the right on the number line) is -1.04..", + "video_name": "JGU74wbZMLg" + }, + { + "Q": "At 5:58 it says that the range of theta/arcsin is being less than or equal to pi over 2 and greater than or equal to minus pi over 2. Can it be equal to these numbers? Can the range equal positive pi over 2 or negative pi over 2, or was this a mistake?", + "A": "the range can be pi/2 or -pi/2 because it s still a one to one function", + "video_name": "JGU74wbZMLg" + }, + { + "Q": "At 1:50, Sal says that the sin is the height, but I'm pretty sure that is not usually sin. What special circumstances makes sin the height?", + "A": "Hello Kevin, Height, including negative heights, is an appropriate description for SIN(X). You see, SIN(X) gives the vertical component and COS(X) gives the horizontal component. If this is a fuzzy answer it will make more sense when you get to the unit circle. Regards, APD", + "video_name": "JGU74wbZMLg" + }, + { + "Q": "Don't get 2:55 to 3:55", + "A": "That s an example of using Heron s Formula.", + "video_name": "-YI6UC4qVEY" + }, + { + "Q": "At 1:36 what does he mean by \"third variable S\"", + "A": "I think he meant to say the fourth variable (three sides of the triangle being the first three), but the ordinal number used to refer to it is irrelevant. s = the semi-perimeter of the triangle. That would be (a + b + c) / 2.", + "video_name": "-YI6UC4qVEY" + }, + { + "Q": "I was wondering. How come at 4 29 after he has worked it down to the square roots of all of them. How come it is 7? What happens if each number was to not have a perfact sqaure in it? Like a triangle with the sides: 8:10:12? What would happen? What one would you pick?", + "A": "Hi Fuller! If the triangle had sides 8, 10, and 12, then the semiperimeter would equal 15. So, the answer is the square root of 8x10x12 which is the square root of 2x2x2x2x5x2x3x2 which is 2x2x2x the square root of 3x5 which is 8 times the square root of 15.", + "video_name": "-YI6UC4qVEY" + }, + { + "Q": "4:12-4:20 i got confused who can help me ???", + "A": "oh ok thanks for the help ..i really appreciated it", + "video_name": "-YI6UC4qVEY" + }, + { + "Q": "at 1:29 what does Sal mean by \"nice trick\"?", + "A": "He s referring to the formula (Heron s formula) itself.", + "video_name": "-YI6UC4qVEY" + }, + { + "Q": "Principal root of a aquare root fnction? What does he mean by this? It is approximately 5:45...", + "A": "Principal root is the positive one of the two roots", + "video_name": "rYG1D5lUE4I" + }, + { + "Q": "I think Sal make a mistake on (vid @ 5:11) when he write the greater than sign! it should be Less than", + "A": "No, Sal is correct. If he had: i sqrt(x) where X<0, then X is negative. Backup thru Sal steps. If X is negative * (-1) = +X. And he would have started with sqrt(x), not sqrt(-x). He is also trying to highlight that if you had something like: sqrt(12), you would not make this into i sqrt(-12). The imaginary number is not needed if the radical contains a positive number to start with.", + "video_name": "rYG1D5lUE4I" + }, + { + "Q": "Does the rule at 2:32 apply if, for example, a is positive and b is negative?", + "A": "Bobo, \u00e2\u0088\u009aa*\u00e2\u0088\u009ab = \u00e2\u0088\u009a(a*b) applies if both a and b are positive or it either a or b are negative. It does not apply if both a and b are negative.", + "video_name": "rYG1D5lUE4I" + }, + { + "Q": "At , 3:03 Sal says that the people who say that\ni\nisn't the principal square root of -1 are wrong. Is this just Sal's personal thinking, or is it a thing that mathematicians have decided upon? Basically, is it official that\ni\nisn't the principal square root of -1?", + "A": "It honestly depends on who you ask. However, i is, in fact, widely believed to be rad(-1). However, NOT considering i to be such a thing prevents you from solving ( or even understanding ) many problems where using complex numbers is necessary, a lot of which are applicable to real life. But really, like with everything else, it s up to each individual person to decide what they think.", + "video_name": "rYG1D5lUE4I" + }, + { + "Q": "At 6:41 how can it only apply when x is greater or equal to zero, given that it is a negative number?", + "A": "When the number is positive, it applies as a normal (square) root. For example, the square root of 4 is 2, but the square root of -4 could be seen as 2i, because i=-1. Therefore, x must be greater than or equal to zero in order to have that negative number, and in turn, contain i. Like he says at 5:58, the two negative numbers are where it goes wrong. x cannot be negative.", + "video_name": "rYG1D5lUE4I" + }, + { + "Q": "At 14:21 Sal points out that S = {[x1, x2] \u00e2\u0088\u0088 R2 | x1 \u00e2\u0089\u00a5 0} is not a subspace because it is not closed under multiplication. Then, at 18:07 he says that the span of any set of vectors is a valid subspace. However, I thought that since the definition of Span is the set of all linear combinations of a set of vectors, there must be a Span ([x1, x2] \u00e2\u0088\u0088 R2 | x1 \u00e2\u0089\u00a5 0). So, there seems to be a contradiction.", + "A": "From what I understand, it must be able to span all R2 vectors in order to be consider a valid subspace of R2 but with the given requirement which is x1\u00e2\u0089\u00a5 0, that is not possible with negative scalar. Thus it is not a span of R2. Am I correct?", + "video_name": "pMFv6liWK4M" + }, + { + "Q": "At about 5:30 he was talking about the unit circle. How did he come up with 2pi/3 instead of 2pi?", + "A": "Instead of having cos(x), the problem involved cos(3x). In other words, there were 3 repetitions within the usual period of 2\u00cf\u0080. Therefore, each of those periods was of length 2\u00cf\u0080/3.", + "video_name": "SBqnRja4CW4" + }, + { + "Q": "At 5:36 , how did you plot g inverse (x) on the graph, and how did slope come in there ?", + "A": "Well, because y = -x/2 - 1/2 is a linear function, you only need two points to draw it. You can use the y-intercept (x=0): y = - 0/2 - 1/2 = - 1/2. That s the first point. Secondly, you can write -x/2 = -(1*x)/2 = -1/2 x, so -1/2 is the slope of the function. with any x your getting your second point (e.g. x=1 -> y = -1/2 - 1/2 = -1). Draw a line and you re finished.", + "video_name": "wSiamij_i_k" + }, + { + "Q": "At 1:30 Sal says that f^-1(x)= -x+4, but in the start f(x) is also equal to -x+4. How can it be the same?\n\nThis may seem silly but i am confused about this question!", + "A": "okay, if we have y=-x + 4, then x = -y +4, that s why the inverse function is same. Another example can be if y=x, then x=y, so the inverse function is same as the function.", + "video_name": "wSiamij_i_k" + }, + { + "Q": "At 2:41, what does Sal mean by \" And notice, both of these numbers are exactly 10 away from the number 5?\" Why are the numbers 10 units away from 5? Why isn't it 10 away from 0?", + "A": "To be 10 away from zero, the problem would need to be: |x| = 10. Notice the original equation: |x - 5| = 10. You need to take into account the -5 inside the absolute value. That s where the 5 comes from. Hope this helps.", + "video_name": "u6zDpUL5RkU" + }, + { + "Q": "At about 5:30, Could you write that as -4 1/2? Or is that not allowed?", + "A": "That is allowed, but it just makes it easier to write it like -9/2.", + "video_name": "u6zDpUL5RkU" + }, + { + "Q": "At 1:39, Sal said that 0 to the zeroth power is undefined. Why?", + "A": "Well, any number to the zeroth power is 1 right? So 0 to the zeroth power would be 1. But zero to any power is 0. So 0 to the zeroth power would be 0. Which is it? It can t be both, so it is undefined.", + "video_name": "NEaLgGi4Vh4" + }, + { + "Q": "At 1:58 why is 0 to the 0 power undefined?", + "A": "it is 1 any number to the power of 0 has to be one", + "video_name": "NEaLgGi4Vh4" + }, + { + "Q": "At 1:17 Sal said \"anything to the zeroth power is equal to 1. What if the number is a negative?\nWouldn't that be -1?", + "A": "It depends on how it s written. If it is expressed as -x^0, or negative x to the power of 0, then it is still equal to 1. If there is a negative sign outside of the term, such as 5 - x^0, you do the exponent first and get 5 - 1.", + "video_name": "NEaLgGi4Vh4" + }, + { + "Q": "I don't understand. At 0:51, Sal says 1/0 - 1/0 is undefined. And then, at 3:11, he says it's indeterminate. Are undefined and indeterminate supposed to be equal to each other? Because the function's the same but it seems to be equaling two different things.", + "A": "This came up in our Calc II class today - undefined and indeterminate are not the same. For example, 1/0 is undefined, however with these limit problems, we know there is a limit (most of the time) even if the Initial Form of the problem is something like 0/0. My understanding is we call this the indeterminate form because with a little manipulation (as Sal demonstrates) there actually is an answer - we just don t see it in the initial form, hence it is indeterminate.", + "video_name": "MeVFZjT-ABM" + }, + { + "Q": "At 9:00, I am not sure but why didn't Sal solve those 2 equations using matrices? I mean before these vector videos, he was using matrices to solve these kinds of equations. Or is it that these equations can not be solved through matrices? Thanks In Advance.", + "A": "If he used a matrix, it would remove the C constants and sort of defeat the purpose for doing what he was doing. He just wanted to keep the constants intact so you could see what was happening.", + "video_name": "Alhcv5d_XOs" + }, + { + "Q": "Why do you subtract the green equation from the red one? at 9:17 min", + "A": "That is a good question! This is a system of linear equations having 2 unknown variables and 2 equations with the variables. In order to solve this linear system of equations, we need to eliminate one variable to get an answer for the other variable. So, at 9:17, Sal subtracts the green equation from the red one to eliminate the variable C1 to get the value of C2. After getting C2, you can substitute the value of C2 in any equation to get the value of C1. Sal does this at 9:30. Hope this helped.", + "video_name": "Alhcv5d_XOs" + }, + { + "Q": "For the final example 13:00:00-end, why does Sal assign a random number for vector c3? How would you solve this to determine dependence without knowing the value(s) of a vector?", + "A": "That s the nice thing about free variables like c3. We get to choose whatever number we want for c3, and no matter what we choose, it will still satisfy the equations. To determine dependence without making a choice for our free variables, all you need to know is that there are free variables. If there are free variables, then the set is linearly dependent.", + "video_name": "Alhcv5d_XOs" + }, + { + "Q": "Hey guys I was just wondering about why, at 13:41, can he just pick random values for C3?", + "A": "Because he KNOWS that the vectors are linearly dependent. This is because you only need 2 linearly independent vectors to span R2. Any additional vector MUST be a linear combination of the other two by the very definition of spanning R2.", + "video_name": "Alhcv5d_XOs" + }, + { + "Q": "At 10:44 shouldn't there be a +c for the integration constant?", + "A": "It s a definite integral, so there doesn t need to be a constant of integration.", + "video_name": "AFF8FXxt5os" + }, + { + "Q": "At 1:11, Sal says that the figure he is drawing is a rectangular pyramid. Isn't that a square pyramid?\nThe base side lengths seem equivalent...", + "A": "Rishi@ a rectangle can look like a square because some rectangles are usually very similar looking to them", + "video_name": "ZACf9EecFrY" + }, + { + "Q": "At 20:00, why does a derivative of 0 mean a maximum/minimum? I get why, but I thought y=x^2 has only one minimum at x=0.", + "A": "Yes and if you let d/dx x^2 = 2x =0, you get x = 0 (and y = 0).", + "video_name": "viaPc8zDcRI" + }, + { + "Q": "I think there's a mistake right 12:56 when he starts out factoring, or fastforward to 13:46.\nHe's just factoring the equation inside the square root. 1/4xo^2 + (2+4xo^2); o being sub 0, so xo is x sub 0.\nHe factors out 4/xo^2 and gets 4/xo^2(xo^4 + 1/2xo^2 + 1/16)\n\nIn the first part, 4/xo^2 and 1/4xo^2, the 4's cancel and we should be left with 1/xo^4 or xo^-4. Sal just put it as a positive x^4. I might be nitpicking, but I'm just making sure I'm right as there are no annotations correcting this.", + "A": "Yes I do, thank you! It s always the algebra that can be confusing.", + "video_name": "viaPc8zDcRI" + }, + { + "Q": "at 13:20 how did you decide to factor out 4/x^2. It seems like a wild goose chase to me.", + "A": "If you notice that a polynomial has degrees such as -2, then 0, then 2, and you want to turn it into 0, 2, and 4 to make it easier to factor, you can multiply by the second degree, but must make sure to also divide by the second degree to keep it equivalent. Dividing by the second degree is the same as factoring out the reciprocal of the second degree. Example, a = (1/1)a = (n/n)a = (1/n)(n)a = (1/n)(na). I don t know if this helps.", + "video_name": "viaPc8zDcRI" + }, + { + "Q": "At 18:45 How does khan figure out that when derivative of -x_0-1/2x_0 is equal to 0 is actually minimum or maximum of the function?", + "A": "derivative = 0 ==> (implies) a maximum or minimum", + "video_name": "viaPc8zDcRI" + }, + { + "Q": "At 14:03, I don't understand what Sal does to get the expression 4/x0(x0^4+1/2(x0^2)+1/16) under the squareroot. It seems to me that he divides the whole expression by 4, but I still can't make sense out of it...", + "A": "He s factoring out 4/(x0)^2 from the three terms. Unfortunately, he turns around the expression so that in the factored form the first and third terms are exchanged, which might be contributing to your confusion (I did a double take as well!). If you try factoring out 4/(x0)^2 from the three terms but keep them in the same order, you end up with: 4/(x0)^2 [1/16 + (1/2)(x0)^2 + (x0)^4]. You can see it s the same as what he has. Hope that helps!", + "video_name": "viaPc8zDcRI" + }, + { + "Q": "At 13:00 Sal begins to factor the expression under the radical sign. This factorization would not have occurred to me. Can anyone comment on the insight that leads to this?", + "A": "First put everything over a common denominator- 4xo^2. I think it becomes much clearer if you do this intermediary step. Impressive nevertheless!", + "video_name": "viaPc8zDcRI" + }, + { + "Q": "In the end part of the video, at 7:02, can the -90 degrees be written as 270 degrees? or should it really be -90 degrees?", + "A": "In most cases, they are equivalent. -90 degrees = 270 degrees. There are some contexts when they may not be equivalent. E.g., suppose you are flying a plane, heading North. A -90 degree turn might correspond to a 90 degree LEFT turn (counter-clockwise), to the West. A 270 degree turn might correspond to a 270 degree RIGHT turn (clockwise). You still end up facing the same direction (due West), but you ve taken two very different actions to get there.", + "video_name": "z8vj8tUCkxY" + }, + { + "Q": "How come at 9:45 he says that if you integrate it you get the same answer? Wouldn't you really get u(x)=x+C not u(x)=x? What happened to the constant of integration?", + "A": "You are allowed to add a constant, but given a constant you have infinitely many solutions so in general we simply take 0 as the constant. And 0 you can easily leave out.", + "video_name": "j511hg7Hlbg" + }, + { + "Q": "@ 1:25 how do you get 9^2", + "A": "Sal gets the 9^2 because he originally has 9^(t/2 +2) Using the exponent rule: x^a *x^b =X^ab so you get 9^t/2 * 9^2", + "video_name": "Y6wNiYcuCoE" + }, + { + "Q": "I like the parentheses at 1:12 rather than multiplying through by -1. Suppose some people might prefer to multiply, though? Seems messier than necessary.", + "A": "It s kind of the same thing.", + "video_name": "8Wxw9bpKEGQ" + }, + { + "Q": "At 0:21, you mention \"Fibonacci numbers\"; 1,1,2,5,8,13,21,34,...; what are those? And why are they called that?", + "A": "In 1175 A.D., the man who invented the Fibonacci Numbers, Fibonacci, was born. Throughout his life he encountered many circumstances where these numbers appear (like in the spirals of a pineapple or pinecone). This pattern frequently shows up in nature and is extremely fun to find out where it exactly fits in.", + "video_name": "gBxeju8dMho" + }, + { + "Q": "At 1:30, he said that you would multiply 1 by one half if multiplying by a negative exponent. Am I correct in the sense that if 3^3 is 27, 3^-3 power would be 1/27? Thank you!\n\n-KoKo", + "A": "Yes... 3^(-3) = 1/27. Great job!", + "video_name": "JnpqlXN9Whw" + }, + { + "Q": "At 2:04, could you multiply with a decimal? I mean, fractions and decimals are the same things, right?", + "A": "I don t understand your question properly but let say (5.5)^-1 = 1 / 5.5 let say (1/1.3)^-1 = 1.3", + "video_name": "JnpqlXN9Whw" + }, + { + "Q": "At 6:25, why was 1/(25/64) changed to it's reciprocal, 64/25?", + "A": "You actually don t have to change the fraction 5/8 to 1/(25/64) or 64/25. Sal states you could just change 5/8 to 8/5 and raise the negative exponent to a positive one. He did this to get the right answer.", + "video_name": "JnpqlXN9Whw" + }, + { + "Q": "at 6:41, why does he switch 25/64 to 64/25 ?", + "A": "Multiplication is the inverse operation of division. Instead of dividing by 25/64, you can multiply by 64/25. It is easier to multiply fractions.", + "video_name": "JnpqlXN9Whw" + }, + { + "Q": "Did he mis-speak at 0:45-48 seconds? He said to view the top example as multiplying 2 by \"negative 1\"", + "A": "Yes that was a mistake. He meant times 1. :)", + "video_name": "JnpqlXN9Whw" + }, + { + "Q": "At 6:24, how did we get 64/25?", + "A": "Sal has: 1 divided by 25/64 Do the division -- change division to multiply by using the reciprocal 1 * 64/25 = 64/25 Hope this helps.", + "video_name": "JnpqlXN9Whw" + }, + { + "Q": "At 4:51 why does it change to a positive 3?", + "A": "Because x^-y =1/(x^y). If you don t understand the logic behind that, I can give a more detailed explanation.", + "video_name": "JnpqlXN9Whw" + }, + { + "Q": "Why are vectors represented as column form and not row form ? For eg. at 4:00 of this video why wasn't vector V represented as [5,0] in row form.", + "A": "It is simply a convention that most people agree upon, many authors of books write row vectors instead of column vectors. The advantage of the column vector is that it is easy to see how to do matrix multiplication. Further on in linear algebra, one learns about the transpose map and it s relation to functions that operate on vectors to give scalars (linear functionals). Then it becomes a bigger deal whether or not your vector is column or row. For now try not to worry about it too much.", + "video_name": "br7tS1t2SFE" + }, + { + "Q": "5:47 if the magnitude called \"scalar\" on its own, what is the direction on its own?", + "A": "Scalar has no direction.", + "video_name": "br7tS1t2SFE" + }, + { + "Q": "Hi at 1:04 you indicated that speed and direction is velocity, but isn't velocity = change in speed regardless of direction?", + "A": "Velocity is the change in position with regard to direction, Speed is the change in position without regard to direction. A change in either speed or velocity is acceleration.", + "video_name": "br7tS1t2SFE" + }, + { + "Q": "On 0:04 seconds why does he say number A instead of letter A?", + "A": "In algebra, a letter is a variable that represents a number. When Sal says letter a , a is representing its place on the number line. Hope it helps!", + "video_name": "29P6bar7nHc" + }, + { + "Q": "at 9:25, why would there be a negative sign?", + "A": "he put a negative sign there because he was trying to subtract the two equations. to do that one of the equations had to be negative. so he multiplied the second equation by -1 to make that possible. so the equation went from:::: 3x+y= 1.79 to:::: -3x-y= -1/79 Hope This Helps You Undertsand", + "video_name": "vA-55wZtLeE" + }, + { + "Q": "At 9:04, Sal multiplies the bottom equation by -1. He could have divided by -1, right?", + "A": "Same thing, dividing or multiplying by -1 will give you same equation.", + "video_name": "vA-55wZtLeE" + }, + { + "Q": "I have trouble following Sal's explanation from ca. 4:00 to ca. 5:30. d/dx theta = sec^2 theta, but what's the logic behind d(theta)/dt? Did I miss a video demonstrating (or exercises testing how to) differentiate both sides w/ respect to \"something else\". Also, there is no detailed discussion of how/why it is permissible to cancel out terms (i.e. the d(theta)s in this example). Additional chain-rule exercises leading up to these problems would be appreciated.", + "A": "it is not d/dx(theta) it is d(tan theta)/dt = d(tan theta)/d(theta) * d(theta)/dt =sec^2 theta*d(theta)/dt that is how you get the final expression in terms of sec^2theta", + "video_name": "_kbd6troMgA" + }, + { + "Q": "At 5:20, you take the derivative of h/500. Aren't you supposed to use the quotient rule for that?", + "A": "You don t have a variable in the denominator. That 500 m is a constant. So you would treat it as ( \u00c2\u00b9\u00e2\u0081\u0084\u00e2\u0082\u0085\u00e2\u0082\u0080\u00e2\u0082\u0080 ) h", + "video_name": "_kbd6troMgA" + }, + { + "Q": "At 4:48, when Sal was writing \"m=2, (-7,5)\" into an equation, why isn't it \"5-b = 2(-7-a)\"? why does Sal replace b with 5, not y with b?", + "A": "In Sal s format of point-slope, you swap out a for the x-value and b for the y-value. You will usually see these written as Xsub1 and Ysub1 where (Xsub1, Ysub1) is the ordered pair. Sal chose to use (a, b) for the ordered pair. The X and Y in the formula stay as X and Y. They become the variables in the equation.", + "video_name": "K_OI9LA54AA" + }, + { + "Q": "I've heard slope-intercept form is y=mx+b. At 6:05, how would that fit in?", + "A": "If you distribute across the parenthesis, and then add/subtract the term on the y side (from both), you should get an answer in slope-intercept form.", + "video_name": "K_OI9LA54AA" + }, + { + "Q": "At 1:00 in the video, what do the triangles mean when he is talking about what the slope equals?", + "A": "The triangles are supposed to mean The Change in , so it is The Change in Y/ The Change in X , also known as slope, or known as in Slope-intercept form, m.", + "video_name": "K_OI9LA54AA" + }, + { + "Q": "At 1:20 or so why does he use 2 instead of 1 as the smallest number", + "A": "Starting at 2:03, he notices that he missed the 1 s, and fixes it.", + "video_name": "09Cx7xuIXig" + }, + { + "Q": "At 1:52, why did Sal add 14 and 9? Shouldn't he subtract?", + "A": "He distributed the negative sign for the second polynominal so -9 become +9. If you don t distribute then you would have to do this way, 14 - (-9) which equals to 14+9", + "video_name": "5ZdxnFspyP8" + }, + { + "Q": "At 5:20, couldn't the cube root of a^2b^2 be simplified to a^2/3 b^5/3?", + "A": "Yes, you can use fractional notation as well, in fact I prefer fractional notation in these situations. Sal is just using a different approach. Both are correct. a^2/3 times b^2/3 is not more simplified than the cube root of a^2 times b^2, it is just different. I hope that helps!", + "video_name": "c-wtvEdEoVs" + }, + { + "Q": "I dont understand 1:20, why dont you make a^2 a*a and you make b^5, b^2 and b^3", + "A": "Because he explained that b^5 is not a perfect cube so he had to divide it, thats my explanation to it.", + "video_name": "c-wtvEdEoVs" + }, + { + "Q": "At 1:02 Do we have to do anything else to the numerators and the denominaters other than divide?", + "A": "No, you are only just meant to divide at that point.", + "video_name": "2dbasvm3iG0" + }, + { + "Q": "At 1:55, Sal says \"their greatest common factor is 3\" what does greatest common factor even mean?", + "A": "The Greatest Common Factor means when you take two numbers and find a factor that both these numbers have in common. For example: What is the greatest common factor of 6 and 9? Well, the first step is to list their factors: The factors for 6 are: 1, 2, 3, and 6. The factors for 9 are: 1, 3, 3, 9. Now what number is the same in both these factor lists? 3! So the Greatest Common Factor will be 3.", + "video_name": "Bt60JVZRVCI" + }, + { + "Q": "I'm confused at 2:10. Sal says that the sequence converges but I learned that when we calculate limits, if you have infinity over infinity, its called a \"indetermination\". Though, what Sal said makes perfectly sense...", + "A": "Recall when we want to find the horizontal asymptote, we take the limit as x approaches infinity. The method was to multiply the numerator and denominator by 1 over the highest term of x on the denominator. Similarly, we find the limit as n approaches infinity to find out if it diverges or converges. So if we multiply by 1/n\u00c2\u00b2 for both the top and bottom, it will converge to 1.", + "video_name": "muqyereWEh4" + }, + { + "Q": "Sal says at 2:00 he isn't 'rigorously proving' his answer, I'm curious, how would one go about rigorously proving the result?", + "A": "One way is to divide the numerator and denominator both by n^2, then take the limit of the result as n approaches infinity. If you haven t seen that process yet, you will soon!", + "video_name": "muqyereWEh4" + }, + { + "Q": "At 2:18 Sal says we should subtract 114 from both the sides.But Instead of that we could transpose it.It is quite easier by transposing", + "A": "Don t ask me why he didn t. It would be quicker.", + "video_name": "hmj3_zbz2eg" + }, + { + "Q": "At 3:40 when sal says that to get the last angle in a triangle you have to do (180- a- b) but shouldn't it rather be 180 -(a+b)? Pls clarify my doubt\u00f0\u009f\u0099\u008f\u00f0\u009f\u008f\u00bc", + "A": "Either way works, since the first way you would use GEMDAS (Grouping Symbols, Exponets, Multiplication/Division, and then Addition/Subtraction) and thus subtract a from 180 and then b from whatever is left. You could also see 180 -(a+b) as 180+ -1(a+b)", + "video_name": "hmj3_zbz2eg" + }, + { + "Q": "At 00:34, couldn't I just do 64+31+50+x=180?", + "A": "You sure can! There are many ways to figure out each of the angles.", + "video_name": "hmj3_zbz2eg" + }, + { + "Q": "Why do we use a question mark in the video at 0:55 seconds in the video?", + "A": "Th question mark represents the measure in degrees of the angle that the question is asking about. At 5:05 he labels the question mark z .", + "video_name": "hmj3_zbz2eg" + }, + { + "Q": "At 1:04 you drew a =D, which looks like a smiley face. What is it?", + "A": "It s just a sloppy arrow.", + "video_name": "T4JKO0OGjpQ" + }, + { + "Q": "At 3:00 they wrote two to the sixty third power. Couldn't you also write it as 2^63?", + "A": "Yes, the two symbols mean the same thing", + "video_name": "UCCNoXqCGZQ" + }, + { + "Q": "At 1:24 he said line uv and he wrote,it but when he wrote it couldn't he have done another letter because uv looked like w which would get heeps confusing right", + "A": "Most likely it was due that each line contained 2 points. A third letter was not needed. Furthermore, he made up a random problem with letters on each line in ABC order. Hope that sorts out the confusion. :)", + "video_name": "aq_XL6FrmGs" + }, + { + "Q": "At 4:10 why y-4=2x is equals to y/2-2=x? Sorry for my question. Hope somebody could help me with this thing.", + "A": "Sal just divided the entire equation by 2: y/2 - 4/2 =2x/2 Reduce each term and you get: y/2 - 2 = x Hope this helps.", + "video_name": "W84lObmOp8M" + }, + { + "Q": "At 4:23, isn't it suppose to be (y-4)/2, not y/2-2?", + "A": "(y-4)/2, and y/2 - 2 are equivalent. So either version will work.", + "video_name": "W84lObmOp8M" + }, + { + "Q": "At around 4:10, when Sla carries the 2 from 2x he divides. I understand that but why is it that he does (y/2) -2 instead of (y-4)/2? do either work or is the way Sal does it the only correct way and why?", + "A": "Since your fraction is already in simplest terms, it would also be an acceptable answer.", + "video_name": "W84lObmOp8M" + }, + { + "Q": "In 3:55, why couldn't you do the same method for the first example?", + "A": "Sal could have, he just skipped that step. We can apply the method like this: 2 is 2 * 1. 4x is 2 * 2x. We have a common factor here - 2. So we pull it out to get: 2 ( 1 + 2x).", + "video_name": "I6TBBzIvgB8" + }, + { + "Q": "So with the 6x + 30 I paused the video and did it. His answer was 6( x + 5) I came up with the answer 2( 3x + 15). Math can be done many ways so I was thinking can both our answers be right. Or does this specific thing have to be done a certain way? This was at 4:00 minute", + "A": "Sal s answer is more simplified because you can factor the 3 out of your answer. Usually math problems ask for the most simplified answer.", + "video_name": "I6TBBzIvgB8" + }, + { + "Q": "At 1:03, for the prime factors of 12, instead of saying 2 x 2 x 3, could you instead say\n2^2 x 3? Would it still be okay?", + "A": "Yes that is another way of writing it, just simplified. Though I am not so sure if the question will allow it. If the question says about anything to simplify, then simplify, if not then don t. ( But in real life, YOU SHOOULD ALWAYS for CLASS unless not allowed for some reason)", + "video_name": "I6TBBzIvgB8" + }, + { + "Q": "At 1:55 How did Sal get 2(1+2x) instead of 2(1+3x) or 2(2+2x)? ;)", + "A": "You might have wanted to add the terms inside the parentheses but remember that you cannot add 1+3x or 2+2x ...etc because they are not like terms. you multiply them by their common factor separately. thats why the 2(1+2x). try to multiply the 2 by both terms and see what you get.", + "video_name": "I6TBBzIvgB8" + }, + { + "Q": "At 2:20, He could have continued that lin and made 2(1+[2 {1x}])", + "A": "True, but it is less complicated to do 2(1*2x).", + "video_name": "I6TBBzIvgB8" + }, + { + "Q": "At 4:48 couldn't you just have figured that angle DBE was 45 because it is the half of 90? I mean if I do it always with that logic can it go wrong?", + "A": "Always prove everything..proving is better.", + "video_name": "7FTNWE7RTfQ" + }, + { + "Q": "At 1:19- 1:24 the video says that the ft would cancel out. I don't see how they cancel out. In class I'm doing this and my teacher says use a chart to do this, but how do i get things to cancel out. i really want to pass the 9th eoct.", + "A": "It is known as simplifying the equation . Suppose you are given 9/3*27/6. You could simplify it and you will get 3/1*9/2, that is 27/2. If you do it the long way you will the same answer. Sal did the same thing.", + "video_name": "F0LLR7bs7Qo" + }, + { + "Q": "At 0:30, what are the indices of a sequence?", + "A": "The index is the counting number n (or k, or i or whatever). What he says is that we often view a sequence as a function of the indices. In other words, for each value of n, there is a specified value of the sequence based on the definition in terms of n. If the index is n, and the sequence is defined as starting at n= 0 or n = 1, then for every value of n, we can generate a new term of the sequence. If the sequence is (-1)\u00e2\u0081\u00bf\u00e2\u0081\u00ba\u00c2\u00b9 \u00e2\u0088\u0099 1/n\u00c2\u00b2 when the index = 2, the term is -\u00c2\u00bc Hope that helps", + "video_name": "wzw9ll80Zbc" + }, + { + "Q": "what does mean looking at the frequency of scores at 4:42 and 4:43", + "A": "Frequency means how many times it occurs. So the frequency of scores means how many times each score occurred.", + "video_name": "0ZKtsUkrgFQ" + }, + { + "Q": "I dont understand what ur saying at 5:30", + "A": "at 5:30, he is combining like terms to make the equation simpler and easier to work with.", + "video_name": "cNlwi6lUCEM" + }, + { + "Q": "Can you explain a little more on why ln(x) + c (@ 1:10) has to be greater than 0?", + "A": "The input for logarithmic equation has to be greater than 0. This is because y=ln(x) <==> e^y=x , but e^y is never 0 or negative. So x>0", + "video_name": "sPPjk4aXzmQ" + }, + { + "Q": "5:61 Is there something wrong here?", + "A": "if you are writing in decimals it is a decimal dot (looks like a period) not a colon. If it is time, the time is impossible because there can be only 60 minutes per hour actually 59 before the next hour. Good Question! Keep it Up!", + "video_name": "AGFO-ROxH_I" + }, + { + "Q": "On 7:34, it says the first number to the right is the ones place. How about decimal numbers?", + "A": "Decimal numbers have place values below the ones place.", + "video_name": "wx2gI8iwMCA" + }, + { + "Q": "At 1:00 how did he know to put t-5 into parentheses instead of 210t-5=41790?", + "A": "t represents the number of trees. t is the x , or independent, or domain variable. The y variable in this problem is the # of oranges (the range, or the dependent variable) When the dude cut down 5 trees, he messed with the domain, t. Since he only messed with the domain, and not with the range (the number of oranges), we want to isolate that -5 stuff with the t. If he didn t put the parentheses, it would be like subtracting 5 oranges, not subtracting 5 trees.", + "video_name": "xKH1Evwu150" + }, + { + "Q": "At 2:10, Why you place 210 on the other side instead of distributing? Isn't it distribution next then you eliminate and carry over to the other side?", + "A": "You can do it both ways. Whether you divide both sides by 210 first or distribute the 210 across the (t-5), you get the same results.", + "video_name": "xKH1Evwu150" + }, + { + "Q": "I watched the videos on the binomial theorem but they didn't show what he is doing here... I can't follow his thinking process at around 2:00 when he keeps expanding the binomial. Any help for me? I wouldn't be able to write out the whole thing by myself is what I mean.", + "A": "The expansion for (a + b)^n always starts with a^n and always ends with b^n. The stuff in the middle comes from the binomial expansion. Check it out in the precalc section! It is most excellent. :)", + "video_name": "dZnc3PtNaN4" + }, + { + "Q": "Since C can be negative (when pi/2 < theta < pi) how do we know the value in the radical at 4:45 will remain positive?\n\nEdit: Nevermind, I see my error. C can never be less than -1 on the unit circle, so that radical will never be negative.", + "A": "you made a small mistake in your edit: if C<-1, the radical becomes more positive, as the formula has 1-C, not 1+C in it, so C would have to become larger than 1 for the radical to become negative.", + "video_name": "yV4Xa8Xtmrc" + }, + { + "Q": "At 3:00 isn't that called the Reflexive Property?", + "A": "In statement 3 (CA=CA) this is the reflexive property of congruency.", + "video_name": "fSu1LKnhM5Q" + }, + { + "Q": "at 0:33 thers a arc on the outer side what is that called?", + "A": "Even about the reflex angle, it doesn t even count as still an obtuse angle, so the reflex angle is 2/3 of a circle. \u00f0\u009f\u0099\u0082", + "video_name": "4ZyTVTGVPgE" + }, + { + "Q": "At 6:01\nWhat I don't understand is that if the sign is the same, why don't you add or subtract\nEX#1:\n-15+(-16)\nisn't that technically subtraction?", + "A": "It can be both. You can do it whatever way is easiest to you. That s why he is teaching you it! Hope this helps! :)", + "video_name": "Oo2vGhVkvDo" + }, + { + "Q": "at 3:37, he explains how absolute value is always positive. how come it can't be negative?", + "A": "The mathematical definition of absolute value says that it the magnitude of a real number without regard to its sign. Think about distance. You would use absolute value to calculate this because you can t have a negative distance.", + "video_name": "Oo2vGhVkvDo" + }, + { + "Q": "whats AA at 4:45", + "A": "AA is short for Angle-Angle similarity. This tells us that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. This also means the third angle of the first triangle is congruent with the third angle of the second triangle.", + "video_name": "7bO0TmJ6Ba4" + }, + { + "Q": "At around 7:53, I noticed Sal wrote XY/AB = k = BC/YZ. Shouldn't the \"BC/YZ\" be \"YZ/BC\" instead? As if XY/AB = k, then BC/YZ must equal to 1/k.", + "A": "Yes, nice catch! Sal only messes up once in a while. Just submit that in the Report a mistake In the video , and just say, at 7:53, Sal says XY/AB = k = BC/YZ, but should say BC/YZ be YZ/BC, if you are really worried about it that much!", + "video_name": "7bO0TmJ6Ba4" + }, + { + "Q": "At 11:00 and 11:19, when he was explaining with two non-similar triagles, why did he say \"unnecessarily similar\"?", + "A": "He said necessarily similar.", + "video_name": "7bO0TmJ6Ba4" + }, + { + "Q": "I'm at 2:45, I realized that you also could prove similarity if one angle and two sides are congruent, right ?", + "A": "I believe so, yes. Later on in the video, Sal describes that as another similarity theorem: The SAS (Side Angle Side) way of determining similar triangles.", + "video_name": "7bO0TmJ6Ba4" + }, + { + "Q": "So at 9:00, if you have log base 2 (32/sqrt 8), you're NOT supposed to simplify (32/sqrt 8) into (4*sqrt 8)?", + "A": "Yes, you could do that and still get to the same answer, but sal just skipped it", + "video_name": "TMmxKZaCqe0" + }, + { + "Q": "At 8:10, how is Log2 sqrt of 32/sqrt8 converted into Log2 (32/sqrt8)^1/2?", + "A": "The square root is the same thing as an exponent of 1/2. Likewise, the cube root is the same thing as an exponent of 1/3. So, this isn t even a computation or an operation, it is just a different way of writing exactly the same thing.", + "video_name": "TMmxKZaCqe0" + }, + { + "Q": "I don't get why he corrected from -1/2 to -1/4 in the very end (9:48)? Can someone please explain?", + "A": "He did not distribute the 1/2 to the -1/2 log\u00e2\u0082\u00828 term (he wrote -1/2 log\u00e2\u0082\u00828, which was unchanged from the original term), so he corrected it to -1/4 log\u00e2\u0082\u00828. Hope this helps!", + "video_name": "TMmxKZaCqe0" + }, + { + "Q": "At 8:25-8:38 why did he remove the exponent 1/2 and put it on the left so that it turns into 1/2_log(32/sqrt(8))? He mentioned a property but which one is it?", + "A": "Because, one of the property of logarithm is: log of a^b = b log a (log of a power b equals b log of a) in this video, log of some thing power to 1/2, then equals to 1/2 log of some thing. Hope it helps.", + "video_name": "TMmxKZaCqe0" + }, + { + "Q": "How does Sal cancel out the 2 a's at about 2:30?", + "A": "Remember that multiplying a number by 1 does not change it. So what Sal did was multiply the expression by (1/a*a)/(1/a*a).", + "video_name": "tvj42WdKlH4" + }, + { + "Q": "At 1:51 Where does the aa being a divisible of both come from? That was confusing, how would you even know to use that formula?", + "A": "This is basically factoring and cancelling but with letters instead of numbers. It s like saying what s 32/4? well, since the numerator is actually divisible by four (2*2) we can simplify by dividing the numerator and denominator by 4 giving us 8/1 or 8. (this is the same problem that Sal shows in the video but with the number 2 in place of a). Does that help?", + "video_name": "tvj42WdKlH4" + }, + { + "Q": "If you can have the same two terms, such as the time at 6:22, forever and ever in one sequence, can you have one term for a whole sequence? What would an example be?", + "A": "Yes, but it s not useful: a(1) = a1 a_i = a(i-1) + 0 (i > 1)", + "video_name": "Kjli0Gunkds" + }, + { + "Q": "At 2:11 did it have to be a fraction?", + "A": "Well, you could try to divide and write your answer as a decimal, but seeing as how the answer would probably be a decimal that stretches on for a really long time, using the fraction will be much easier.", + "video_name": "_ETPMszULXc" + }, + { + "Q": "i dont think the y-intercept is 4/5 at 1:58", + "A": "but that is the xintercept since the y is 0", + "video_name": "5fkh01mClLU" + }, + { + "Q": "At 2:00, shouldn't Sal add -4/5 to b and 0, resulting in our final answer being negative?", + "A": "Sal ha 0 = -4/5 + b He needs to move the -4/5 to the other side. Remember, we always use the opposite sign, or the opposite operation to move items to the other side of an equation. The 4/5 is negative. This means it is being subtracted from b . So, to move it, we do the opposite, we add 4/5 to both sides. -4/5 + 4/5 will cancel out like Sal shows in the video. If you did: -4/5 +(-4/5), you get -4/5 -4/5 = -9/5. So, the b would not be by itself. Hope this helps.", + "video_name": "5fkh01mClLU" + }, + { + "Q": "10:20 What is the purpose of functions in a practical real life scenario?", + "A": "Functions are used all the time. -- Computer programs are functions -- the cash register at a store uses functions to determine what you owe -- when you calculate the tip on a bill in a restaurant, you are using a function. Those a just a few. There are many more.", + "video_name": "5fkh01mClLU" + }, + { + "Q": "At 6:11, how come its 0-5 instead of 5-0? Is that crucial to get the correct answer or does it not matter, because you are still finding the change?", + "A": "(y2 - y1)/(x2-x1) works either way. Just make sure that whatever point you started with for the difference in y in the numerator is the same point you start with for the difference of x in the denominator.", + "video_name": "5fkh01mClLU" + }, + { + "Q": "at 2:49 how does x squared divided by x equal x?", + "A": "x squared is the same as x * x. If you divide x * x by x you get x.", + "video_name": "FXgV9ySNusc" + }, + { + "Q": "At 3:00, why did Sal put the answer to x^2 divided by x above the 3x? Why not above the x^2?", + "A": "I agree with you at 3:00. It would be better and less confused, if Sal put the x right on top of x^2 , even though it is not a require. In fact, x can be put any where within the line.", + "video_name": "FXgV9ySNusc" + }, + { + "Q": "At around 8:00, you need to restrict x=-4 to be equal to the first expression. So if your long division works out with no remainder, you have to make restrictions for your original denominator, or am I missing something?", + "A": "You are correct. The original expression is undefined at x = -4, so the correct answer would be: (x\u00c2\u00b2 +5x + 4) / (x + 4) = x + 1; x \u00e2\u0089\u00a0 -4", + "video_name": "FXgV9ySNusc" + }, + { + "Q": "It seems like around 8:24 or so, something important got lost. The original formula was undefined when x was -4, because at that x-value the denominator was 0. The new formula of simply x + 1 is defined everywhere. What happened there?", + "A": "The new formula is x + 1, x =/= -4, so the expressions are equivalent. Sal just forgot to mention that.", + "video_name": "FXgV9ySNusc" + }, + { + "Q": "At 3:30 minutes into the video it says a histogram is really a plot, kind of bar graph... How is a histogram related to a bar graph in anyway?", + "A": "It has the same formation.", + "video_name": "4eLJGG2Ad30" + }, + { + "Q": "I dont understand the time 2:50", + "A": "He added the 5 just to go in order, the 5 shows up 0 times.", + "video_name": "4eLJGG2Ad30" + }, + { + "Q": "What are the \"buckets' Sal talks about at 3:41?", + "A": "He uses the term bucket to represent a range of data. The example that he uses, he lists all numbers 0,1,2,3,4,5. You might not have a lot of numbers, so you might want to clump, say 0-1, 2-3, 4-5. So you have 3 buckets.", + "video_name": "4eLJGG2Ad30" + }, + { + "Q": "about 04:00, does this mean that every sum of normal distributed, independent, and squared variables will have the chi-square distribuition?", + "A": "Indeed it does. This is mainly because the sum of normally-distributed, independent, and squared random variables is the very definition of the chi-square distribution.", + "video_name": "dXB3cUGnaxQ" + }, + { + "Q": "At 6:59, how does Sal make the logical leap that the top angle is also Y, given that he has a 90 degree angle and an angle of 90-y?", + "A": "The two acute angles in an right triangle must add up to 90. Therefore, if one value is being subtracted from 90 to represent an angle, that value must represent the other angle. When you add them up, they will add up to 90 (90 - y + y = 90).", + "video_name": "R0EQg9vgbQw" + }, + { + "Q": "So at 2:05, Sal put -2y after the -6x^2. But when I was doing the problem myself, I put 8xy first and then -2y. Is the way I ordered the expression wrong and if it is...why? This was my answer:\n( 6x^2y - 6x^2 + 8xy - 2y +4 ) This was Sal's answer:\n( 6x^2y - 6x^2 - 2y + 8xy +4 )", + "A": "Hey Tushar Gaddi!, it does not matter in what order you put it in as long as you dont change any of the negative( - ) or posiive( + ) signs. the way you wrote it was just fine. for problems like this this is why the Order Of Operations comes into play. no matter what order you put it in you will get the same answer. Hope This Helps! Good Luck and Have Fun! :)", + "video_name": "jroamh6SIo0" + }, + { + "Q": "At 1:11 you go through this really calculated sum but you could just find 25% of 66 and that would be your answer 66!", + "A": "You cant just do 25% of 66 because you didn t know the 66. The only 2 numbers that you know are that you have $50 and the sale is going to take 25% off. you are calculating the $66. Hope this helps.", + "video_name": "4oeoIOan_h4" + }, + { + "Q": "in 5:31 Sal says mathleat what is that???", + "A": "An athlete is someone who does physical activity and is good at it. A mathlete is some who performs math and is good at it, usually competing against other people.", + "video_name": "xO_1bYgoQvA" + }, + { + "Q": "At 3:35, how is x to the a over x to the b equal to x to the a-b? I know he explains it, but it still doesn't make that much sense.", + "A": "Try a numeric example: x^5 / x^2 This is a fraction and must be reduced. Cancel out the x^2 and you get x^3. So, what happened to the exponents? They were subtracted. x^5 / x^2 = x^(5-2) = x^3 Sal did the same exact thing, except he has variables instead of numeric exponents. Hope this helps.", + "video_name": "0z-yIFzpunM" + }, + { + "Q": "What was the point in him specifying what the f vetor was at 5:40? He never used it to solve his problem.", + "A": "He uses it to remind us where he gets his P(x,y) and Q(x,y). This have been explained through many of the previous videos, so i just a remainder, and not a explanation.", + "video_name": "gGXnILbrhsM" + }, + { + "Q": "At 5:20, shouldn't the da be a dx?", + "A": "Yes. He writes that originally but the step after that he rewrites it as dx.", + "video_name": "gGXnILbrhsM" + }, + { + "Q": "At 4:15 of the movie above suddenly you drop the unit vectors(i,j,k) from the result of bxc. Is it ok to do that? If it is ok, then I want to know why is it possible to do that.", + "A": "i, j, and k are (1, 0, 0), (0. 1, 0), and (0, 0, 1). a = (a1, a2, a3) = a1i + a2j + a3k (the resultant of the components of a).", + "video_name": "b7JTVLc_aMk" + }, + { + "Q": "When Sal says multiply b and c by the dot products of a and c and a and b at 13:31 (b(a dot c) - c(a dot b)) what does he mean by multiply?", + "A": "Scalar multiplication of the vector b with the scalar (a dot c) and so on", + "video_name": "b7JTVLc_aMk" + }, + { + "Q": "Doesn't he mean cross product at 2:00?", + "A": "Yes, he meant cross product.", + "video_name": "b7JTVLc_aMk" + }, + { + "Q": "At 20:00 couldn't the graph left of zero be the right half of upward concavity ( / )?", + "A": "No, because slope is zero at 0. Isn t it?", + "video_name": "hIgnece9ins" + }, + { + "Q": "I don't understand why at 8:45 we started looking at x > 2/3.", + "A": "He was attempting to determine concavity. x=2/3 is a point of inflection. It is where the graph changes concavity. You need to determine the sign of the 2nd derivative at points both less than and greater than your point of inflection to determine the concavity of the function along those intervals.", + "video_name": "hIgnece9ins" + }, + { + "Q": "I'm wondering about the result at the end of the video (8:07) : x^3y+1/2(x^2y^2) = c\nIf that were a diffrential equation describing a physic phenomenon, how would you turn this solution into a function you can actually use to describe the physical system you took the diffrential equation from ?\nAnother way of saying this would be : How do you turn x^3y+1/2(x^2y^2) into\ny = some x business ?", + "A": "I believe you can use the quadratic formula to get the explicit solution in terms of y. Just move the c to the left side so you have ay^2 + ay + c = 0 ps I thought you were talking about psychic phenomena for a minute.", + "video_name": "0NyeDUhKwBE" + }, + { + "Q": "At 0:44, he said it would have been a function of y that is integrating factor. i tried u(y) instead of u(x) but I can't solve for u(y). I just curious that is it possible to use u(y) for this question too? And how do we know which one would we use? u(x) or u(y), judging for what or trial and error?", + "A": "I have not tried to solve for the integrating factor of u(y) but i do know that there may or may not be an integrating factor for u(y). Like you said it is kind of trial and error. All of these exact equations that need an integrating factor COULD have a u(x), u(y), u(x,y) or any combination of them but it will be up to you to figure out which one it has.", + "video_name": "0NyeDUhKwBE" + }, + { + "Q": "At 7:05, he begins to explain a simpler way to find the value of cesium-137 in the sample after 150 days. Though, because 150 is divisible by 30, isn't there an even simpler way? You could essentially just divide 8 in half 5 times and reach the same answer of .25. Is this valid?", + "A": "yes, that is how I learned it in science class. Just don t forget to include year 0!!", + "video_name": "polop-89aIA" + }, + { + "Q": "hello there its your friendly neighborhood precal student here again\n\ni have a synthetic division question in my summer homework (yipee!)\nthe denominator is 3x-2\nwould i still put positive 2 at the same place where Sal puts the 3 at 2:00 in the video\nor does the 3x affect this?\n\nThanks for your help :)", + "A": "It depends on the question. You look for the highest polynomial which you want to subtract away. If you re dividing the same polynomial, but now by 3x-2, yes, you would still put a 2 down there, but note that you multiplied it by 3/2. Remember to upvote good questions and helpful answers", + "video_name": "3Ee_huKclEQ" + }, + { + "Q": "Wait at 4:57, Sal doesn't put the x^5 term. He puts the highest degree as x^4. Am I missing something? I thought that 487 would be the constant and that perhaps that meant the equation was even or something. What happened to the x^5 term?", + "A": "Remember, when you are dividing with terms containing variables that instead of adding the exponents (i.e., like you do when you re multiplying them), you subtract the exponents. So in the example (e.g., 2x^5/x), the exponent subtraction would be 5-1=4 or your x^4 term, just as in the next term : x^3/x would yield your 3-1=2 or x^2 term, etc. Hope this helps.", + "video_name": "3Ee_huKclEQ" + }, + { + "Q": "At 4:07 why is it h over two? I am still confused on how he exactly got that.", + "A": "The area of a circle is \u00e1\u00b4\u00a8r\u00c2\u00b2, where r is the radius, right? We are told the diameter of the circle in this problems is h, right? What is the relationship between the radius and diameter of a circle? 2r=D, here D=h so 2r=h which means that, the radius r = h/2. You may want to review similar triangles.", + "video_name": "Xe6YlrCgkIo" + }, + { + "Q": "At 5:20, what is he talking about when he says \"This business\"?", + "A": "Occasionally in these videos Sal saves a little time by using the words this business as a way to refer to some expression he s manipulating on the screen. In this video, as he says that, Sal is putting brackets around the expression \u00cf\u0080h^3/12, so that s what he means here by this business.", + "video_name": "Xe6YlrCgkIo" + }, + { + "Q": "At 5:50 how did he get the derivative to be just pi/12?", + "A": "That s not what happened here. For convenience, Sal moved the constant (pi/12) outside the derivative. He had the derivative of (pi*h^3)/12, which is the same as (pi/12)*h^3, and he rewrote it as (pi/12) times the derivative of h^3.", + "video_name": "Xe6YlrCgkIo" + }, + { + "Q": "what is the meaning of 'inx' at 1:31.", + "A": "That is an l, not an i. The ln stands for the natural logarithm, or the logarithm with base e. The number e is called Euler s number (pronounced oiler ), or the natural base. It is the base of an exponential that is its own derivative, which is a handy thing in calculus and differential equations.", + "video_name": "OkFdDqW9xxM" + }, + { + "Q": "At 6:08 in the video, why does the \"log a\" become \"log x\"?\nAlso, why is the \"a\" taken away from the subscript of the log?", + "A": "It is not taken away, but the log form is re-written into exponential form, where a is the base and the exponent is written in superscript. log a does not become log x Sal takes the log base x of both sides (of the exponential equation a^c=b) because it is essentially the same thing by comparison and he is not changing the value of the equation.", + "video_name": "OkFdDqW9xxM" + }, + { + "Q": "At 0:49, he says x is an arbitory base. What is that?", + "A": "I m assuming that he means that x is just a letter. Your variable could be almost any letter of the alphabet and it still means the same thing.", + "video_name": "OkFdDqW9xxM" + }, + { + "Q": "At 0:16, what is theoretical probability?", + "A": "Theoretical probability is basically calculating a probability for something without doing the actual experiment. It is what should happen in theory, thus theoretical probability.", + "video_name": "RdehfQJ8i_0" + }, + { + "Q": "At 3:20, why is it 1/15", + "A": "To change 16/15 into a mixed number, you divide. 15 goes into 16 once (that s the whole number) Subtract 16 - 15 = 1. We have a remainder of 1 that becomes the new numerator Thus, you get 1 1/15 Hope this helps.", + "video_name": "bcCLKACsYJ0" + }, + { + "Q": "At 9:22 How do you know to put the number before the decimal, or at 5:06 the zero?", + "A": "It depends if the denominator divides before the decimal point or after. For instance, if you had 31/15, it would come out to 2.1. I hope that this was helpful! :)", + "video_name": "Gn2pdkvdbGQ" + }, + { + "Q": "In 1:40 how come we don't multiply by -1 to make -3p a positive and flip the inequality? I've seen it in other problems before.", + "A": "You can either multiply with -1, divide by -3, or just swap the numbers (the left goes to the right and vice versa), do as you like.", + "video_name": "0YErxSShF0A" + }, + { + "Q": "at 1:48, i didnt under stand why -32/-3 was crossed out can some one\nexplain it to me", + "A": "Watch the video more carefully. It was not -32/-3, it was -3*z/-3 since you have a -3 on the numerator and denominator they cancel out, so that just leaves you with z.", + "video_name": "0YErxSShF0A" + }, + { + "Q": "At 2:21, could you explain how to determine the greatest integer between an interval for example [0,1]?", + "A": "firstly, integers are all positive and negative whole numbers including 0: ...-3,-2,-1,0,1,2,3... so what are the integers between the interval [0,1]? 0 and 1 which is greater 0 or 1? 1 So the answer to your question is 1.", + "video_name": "CZdziIlYIfI" + }, + { + "Q": "At 7:24, I still do not quite understand why the integral of f(x) between 0 and 1 is the same as the integral of f(x) between 1 and 2? I mean I can kind of visualise it, but how can I prove this is true? Thanks a lot:)", + "A": "That is the case because of symmetry. The area between 0 and 1 is the mirror image (along y = 1) of the area between 1 and 2. The easiest way to prove it is to calculate both integrals and see that the result is the same. Int from 0 to 1 (1-x)*cos(pi*x) = Int from 1 to 2 (x-1)*cos(pi*x) = 2/pi^2", + "video_name": "CZdziIlYIfI" + }, + { + "Q": "at 10:50 it says du is equal to dx. why he doesn't write 1? and at 12:02 it write again dx, instead of 1.\nCould anyone make some sense of this?\nI guess it is related to the dx at the end of the \"\u00e2\u008c\u00a0f(x) dx \" formula, but still not sure what that dx represent, and why it is supposed to be 1 here... i'm confused", + "A": "1 is there but it is noted implicitly. In calculus, 1 is unusually implied in problems. Dx less us to do the substitution and it essentially means(in that context) that we are differentiating. When I do these kinds of problems, I don t really think about the formal definition of dx.", + "video_name": "CZdziIlYIfI" + }, + { + "Q": "At about 1:49 Sal is explaining that if x=1 than [x]=0, because it is the largest integer, but it says that [x] must be lesser or EQUAL to x! Why is that?", + "A": "In real life, you can t deal, in decimal number, with how many siblings do you have. Anyway, the greatest integral function is, just, a function to create, only, an integer value. So, why does define as must be lesser or equal to x is because when you evaluate x = 0.7, you notice that 0.7 is not completing any integer number, therefore, it is f([0.7]) = 0. This f(x)= [x] looks, graphically, for the greatest integer function of [x], like stairs. Take off the decimal of any x, make it an integer.", + "video_name": "CZdziIlYIfI" + }, + { + "Q": "In 1:03 can a radius come from outside of the circle also?", + "A": "A radius is a line from the center of a circle to the circumference.", + "video_name": "04N79tItPEA" + }, + { + "Q": "At 5:34, how did Sal Khan get a rise over run of -5/6 if you're supposed to subtract the 5 from 5x + 6y = 30 and then divide 6y by 6? I thought you get a slope and y-intercept of 5/6 + 5.", + "A": "As you said... you subtract 5x . You do this on both sides of the equation. The 5x is now on the other side with a minus in front of it. Thus it is now -5x . Divide by 6 and you get: -5/6 (x).", + "video_name": "LNSB0N6esPU" + }, + { + "Q": "At 0:36, why would you add -3/4? Shouldn't it be subtracted?", + "A": "Adding a negative is equal to subtracting its positive! For example, 2-1 = 2+-1 =-1+2, and all of these are correct. I think the -3/4 was placed before -10/6 so that this equation can look like the previous equation dragged down. :)", + "video_name": "9tmtDBpqq9s" + }, + { + "Q": "At 0:14 how does he turn the seven-sixths to negative.", + "A": "Since there is a subtraction sign after the - 3/4, this could be viewed as adding negatives. Since 7/6 ad 3/6 have common denominators already there, we could block them up to solve the problem easier. -7/6 + -3/6 = -10/6 Then you can find the solution by scaling the numerator and denominators of -10/6 and -3/4 and then add the two together.", + "video_name": "9tmtDBpqq9s" + }, + { + "Q": "At 1:30, why does he say \"the negative direction\"?", + "A": "lim : Means you are inputting smaller negative values. x\u00e2\u0086\u00920- Relating the above limt to the example, ln(n \u00e2\u0089\u00a4 0) is undifined. Hence the given limit condition: lim x\u00e2\u0086\u00920+", + "video_name": "CDf_aE5yg3A" + }, + { + "Q": "At 4:30 he says there's no evidence that DC is equivalent to AC. Are we sure? How do we know DC is not AC? Is it bigger or smaller or what?", + "A": "We know DC is not equivalent to AC because if it was the case, then we would have an isosceles triangle. A theorem associated with isosceles triangles is that the two angles opposite the equal lengths must be equal. That is not the case, since 31 degrees is opposite to AC and 59 is opposite to DC.", + "video_name": "TugWqiUjOU4" + }, + { + "Q": "I'm a bit confused, I thought DC and EF were the same because both triangles are similar 3:30. Can someone explain?", + "A": "If the triangles are congruent, then corresponding parts of corresponding triangles are congruent, however, if triangles are similar (AA is one method to show this), then the corresponding sides are proportional ( a common scale factor to get from each side to its corresponding side on the other triangle).", + "video_name": "TugWqiUjOU4" + }, + { + "Q": "At 4:14 where did you get the plus sign from? Wouldn't you put a subtraction sign there? (because the previous color coded terms had a subtraction sign at the beginning?)", + "A": "At that point in the video, Sal is combining: -2x^2 + 3x^2. He does this by adding/subtracting the coefficients: -2 + 3 = +1, not a -1. So, once combined, the 2 terms creates +x^2. Hope this helps.", + "video_name": "FNnmseBlvaY" + }, + { + "Q": "at 0:48 isn't xy a 5 not a 6? just asking :D", + "A": "\u00f0\u009d\u0091\u00a5\u00f0\u009d\u0091\u00a6 = \u00f0\u009d\u0091\u00a5 \u00e2\u0088\u0099 \u00f0\u009d\u0091\u00a6 \u00f0\u009d\u0091\u00a5 = 3, \u00f0\u009d\u0091\u00a6 = 2 \u00e2\u0087\u0092 \u00f0\u009d\u0091\u00a5\u00f0\u009d\u0091\u00a6 = 3 \u00e2\u0088\u0099 2 = 6", + "video_name": "FNnmseBlvaY" + }, + { + "Q": "At 0:02, how is it possible to have a term like 4xy?", + "A": "If I square (2x + y)^2, then (2x+y)(2x+y) = 4x^2 + 4xy + y^2. We can combine variables, and this will we a term that could be combined with any other xy terms we might have.", + "video_name": "FNnmseBlvaY" + }, + { + "Q": "At approximately 8:59, why are we allowed to divide the \"outside bit\" by four, and multiply the \"inside bit\" by four?", + "A": "You can multiply both the outside and the inside because any number is itself multiplied by 1, and 1 = 4 * (1/4) You can hence multiply an expression by 4 * (1/4) while keeping its value. Using the property of multiplication m * (a * b) = (m * a) * b = a * (m * b) you can write that as 1/4 times the outside multiplied by 4 times the inside. I hope this helps. --Phi \u00cf\u0086", + "video_name": "64bH_27Ehoc" + }, + { + "Q": "When he starts factoring at 6:29, why doesn't the square (the 2 on the blue section) get factored out with the rest of the equation? Is it because it's not exactly s^2 like the original yellow equation?", + "A": "sqrt(3)\u00e2\u0080\u00a2s^2/4 + 3\u00e2\u0080\u00a2sqrt(3)\u00e2\u0080\u00a2(s/3)^2/4 + 12\u00e2\u0080\u00a2sqrt(3)\u00e2\u0080\u00a2(s/9)^2/4 + 48\u00e2\u0080\u00a2sqrt(3)\u00e2\u0080\u00a2(s/27)^2/4 ... sqrt(3)\u00e2\u0080\u00a2(s^2/4 + 3\u00e2\u0080\u00a2(s/3)^2/4 + 12\u00e2\u0080\u00a2(s/9)^2/4 + 48\u00e2\u0080\u00a2(s/27)^2/4 ...) sqrt(3)/4\u00e2\u0080\u00a2(s^2 + 3\u00e2\u0080\u00a2(s/3)^2 + 12\u00e2\u0080\u00a2(s/9)^2 + 48\u00e2\u0080\u00a2(s/27)^2 ...) sqrt(3)/4\u00e2\u0080\u00a2(s^2 + 3\u00e2\u0080\u00a2s^2\u00e2\u0080\u00a2(1/3)^2 + 12\u00e2\u0080\u00a2s^2\u00e2\u0080\u00a2(1/9)^2 + 48\u00e2\u0080\u00a2s^2\u00e2\u0080\u00a2(1/27)^2 ...) sqrt(3)\u00e2\u0080\u00a2s^2/4\u00e2\u0080\u00a2(1 + 3\u00e2\u0080\u00a2(1/3)^2 + 12\u00e2\u0080\u00a2(1/9)^2 + 48\u00e2\u0080\u00a2(1/27)^2 ...)", + "video_name": "64bH_27Ehoc" + }, + { + "Q": "I lost at 0:43 until the video is over. I didnt understand anything.. pls help", + "A": "What did you not understand? The video is about finding a Common Denominator. Is that the part you didn t understand or how he changed the 1/10 into 10/100?", + "video_name": "DR2DYe7PI74" + }, + { + "Q": "What does R^2 (at 0:59) mean?", + "A": "Basically, it s a coordinate space analogous to the xy plane that we all know and love from graphing functions in algebra 2.", + "video_name": "8QihetGj3pg" + }, + { + "Q": "what is that fancy bracket that Sal draws around the 2*3*5 at 1:18 called, if it is called anything other than a bracket?", + "A": "A bracket is [ or ] . A brace is { or } . I guess you can call it a squiggly line that connects the selected objects and relates them to something else in the part that sticks out in the middle.", + "video_name": "QUem_2dkB9I" + }, + { + "Q": "But at 4:35, why is it an x minus 2. He is shifting from g(x) to the LEFT, to the f(x). Shouldn't it be a PLUS sign, since he is going to the LEFT? Or is g(x) your end point, and f(x) is your starting point?", + "A": "Think of it this way: make an x/y table for your points. You plug in an x-value to the function and apply the operations to it to solve for the y value, correct? It s reverse order of operations when it is directly attached to the x. (Another way of imagining this would be to think about switching the -2 to the left side of the function: going over the equals sign would change the -2 to a positive number, 2)", + "video_name": "ENFNyNPYfZU" + }, + { + "Q": "at 4:00, how is it positive? I don't understand Sal's explanation. Can someone explain it please? and plz explain how square root of -1 exsists...", + "A": "\u00f0\u009d\u0091\u0096\u00e2\u0081\u00b4 = \u00f0\u009d\u0091\u0096\u00c2\u00b2 \u00e2\u0080\u00a2 \u00f0\u009d\u0091\u0096\u00c2\u00b2 = (-1)(-1) = 1 The principal square root of -1 is \u00f0\u009d\u0091\u0096 simply because we define it to be so. In other words, we define \u00f0\u009d\u0091\u0096\u00c2\u00b2 = -1. Mathematics doesn t bother with does or does not exist because it simply deals with logical extensions of definitions of axioms we set.", + "video_name": "ysVcAYo7UPI" + }, + { + "Q": "Isn't it supposed to be i=\u00c2\u00b1sqrt(-1) at \"0:56\"???", + "A": "But isn t (+sqrt(-1))^2=(-sqrt(-1))^2 or is it just defined and can t be changed???", + "video_name": "ysVcAYo7UPI" + }, + { + "Q": "At 3:15, Sal said that i^4=i*i^3 and resulted with positive 1. Could you just simply do i^4=i^2*i^2 and get -1*-1 just resulting with positive 1 as well. Is this right or it doesn't work all the time? Thanks for the video!", + "A": "Your technique works. Remember, we can regroup or multiply in any order due to the associative and commutative properties of multiplication.", + "video_name": "ysVcAYo7UPI" + }, + { + "Q": "A 1:13, how can the square of any no. be negative ? Given that i = under root -1 and square of i = -1 ?", + "A": "You are right. The square of any number either positive or negative, cannot be a negative. i is not any number, it is an imaginary number. You might wonder about the purpose of this. The purpose of i is to compensate for the fact that normal numbers cannot be negative when squared. and square root of -1 would make no sense.", + "video_name": "ysVcAYo7UPI" + }, + { + "Q": "At time 6:08 it says that even if a is less than 0 it is still going to be positive? So my question is how do you know what to go by ? A is less than 0 so it is negative or a to the 4rth power which indicates it is positive?", + "A": "You would go by the order of operations to figure out the sign (parenthesis, exponents, multiplication, division, addition, subtraction). So since -a^4/3 is the same as -1*(a^4/3) then you would resolve the exponent before multiplying by -1. The exponent is even which means that you will always get a positive number in the numerator giving you a positive fraction which you THEN multiply by -1 making it a negative number. Hope this helps! :)", + "video_name": "Pms4cBWwPSU" + }, + { + "Q": "At 0:40, why is the volume (4/3)*(pi)*(r^2)? Why is it 4/3? I'm in middle school, so I don't understand why it's 4/3.", + "A": "If you want to find out why it is 4/3 you can look up who created the equation for a sphere. It may explain how that particular person got the equation.", + "video_name": "IelS2vg7JO8" + }, + { + "Q": "Um I don't get \"7:20\"", + "A": "Given: n = l - m n = log_x (A/B) l = log_x (A) m = log_x (B) Therefore (plugging in to the first equation): log_x (A/B) = [log_x (A)] - [log_x (B)] Does that answer your question?", + "video_name": "yEAxG_D1HDw" + }, + { + "Q": "At 3:37 Sal says that the range of x values can be narrower than the maximum possible range. Does this mean that delta can vary?", + "A": "Yes. Delta will change depending on the epsilon chosen.", + "video_name": "w70af5Ou70M" + }, + { + "Q": "At 5:28 Sal made the mistake of not making the distance between x and c greater than 0. Is that the same case as with the distance between f(x) and the limit? I feel like because it's distance as well it would need to be greater than 0 too.", + "A": "Think about this. If you are at school (assuming you are not home schooled), the distance between you and your home is some positive number. If you are at home, then the distance between you and your home is zero.", + "video_name": "w70af5Ou70M" + }, + { + "Q": "At 7:30, is sss the only kind of way to find congruence in a triangle?", + "A": "The congruence postulates are: SSS, AAS, ASA, SAS. AAA shows similarity only, not necessarily congruence. SSA may or may not show congruence, depending on the details. But generally SSA does not show congruence by itself -- you need some other bit of information to establish congruence. For example, if the known angle is right or obtuse, then SSA proves congruence; but, if the known angle is acute, then you would still need more information to establish congruence.", + "video_name": "CJrVOf_3dN0" + }, + { + "Q": "can you write that congruency sign (at 1:39) on a keyboard?", + "A": "In Windows, like in Microsoft Word or Microsoft Excel, you can your font to Symbol. Then, that symbol is SHIFT+2 (or the @ key on your keyboard.). As a side note, with the Symbol font you get most of the Greek letters..alpha, beta, delta, pi, etc.", + "video_name": "CJrVOf_3dN0" + }, + { + "Q": "At 1:20 can you reflect a triangle also?", + "A": "yes. that is what flip means.", + "video_name": "CJrVOf_3dN0" + }, + { + "Q": "At 2:27, how are 1, 3, 9, and 27 [[\"\"positive\"\"]] divisors of 27,000", + "A": "They are all positive numbers that 27 000 can be equally divided into. 27 000/1=1, 27 000/3=9000, 27 000/9=3000, 27 000/27= 1000. These are actually all the positive divisors of 27. He knows that every single divisor of 27 would be a divisor of 27 000 =)", + "video_name": "17st-s5gg10" + }, + { + "Q": "At 0:56, when Sal is graphing y-k=x^2, he puts the vertex higher on the graph. I don't understand why it's higher on the graph if x^2 is k LESS than y. Shouldn't it be lower on the graph?", + "A": "Think of it this way: you would have to decrease the y value by k units to get down to x^2. That must mean that y is higher than it would be on the x^2 curve.", + "video_name": "99v51U3HSCU" + }, + { + "Q": "At 5:10, how did Sal come to know that (23/4) is (5 3/4) ?", + "A": "Divide it by 4; you have 20 as the nearest multiple so 3 remains giving 5 3/4 With division practice you become better", + "video_name": "w56Vuf9tHfA" + }, + { + "Q": "at 4:58 Sal got c=1 but why I get C=1/2 ?\nhere my solution\nx=-1/2y^-1 +c\nafter subst (1,-1)\nc= 1/2\nNOT: it seems like when I put C in x part like x+c=... and when I put it in y part like x= ....+c I get different values of C. So Do all of C's are correct?", + "A": "Yes, both Cs are correct, because they don t represent the same thing. In Sal s case, his C is on the x side of the equation (plus he swallowed the 2 into his C when he solved for y), and in your case, your C in on the y side of the equation. Still, if you use your value of C = 1/2 in your equation and solve for y, you get the exact same result that Sal did: x = -1/2 y\u00e2\u0081\u00bb\u00c2\u00b9 + C x = -1/2 y\u00e2\u0081\u00bb\u00c2\u00b9 + 1/2 x - 1/2 = -1/2 y\u00e2\u0081\u00bb\u00c2\u00b9 -2(x - 1/2) = y\u00e2\u0081\u00bb\u00c2\u00b9 -2x + 1 = y\u00e2\u0081\u00bb\u00c2\u00b9 y\u00e2\u0081\u00bb\u00c2\u00b9 = -2x + 1 y = 1/(-2x + 1)", + "video_name": "E444KhRcWSk" + }, + { + "Q": "At 1:45, how can we say that sample mean=p (i.e. the proportion of teachers who think computers is a good tool) ? Is there a rule or something to take that value which I've missed?\nBecause for a binomial distribution E(X)= np where n is the number of trials and p is the success proportion.", + "A": "Just use the same old formula (sum x(i))/250, with 108 of the x = 0, and 142 of them = 1. So the mean is 142/250 Now: How many teachers think computers are a good tool? How many teachers are there? What proportion think computers are a good tool?", + "video_name": "SeQeYVJZ2gE" + }, + { + "Q": "at 18:12, shouldn't it be \"take larger samples\" instead of MORE samples? 2 different things", + "A": "When he says take more samples , he means take larger samples or make more observations . People use the word sample ambiguously - as in: a sample of 100 samples , instead of a sample of 100 observations .", + "video_name": "SeQeYVJZ2gE" + }, + { + "Q": "At 11:01 you just end saying that it is .5 + .495 to get .995 to look up on the z table. Why .995? Just a few seconds before that you said the interval is symmetric about the mu and the right half was .495. Since that is .495 and .495 + .495 = .99 which is the confidence level we want, why do .5 + .495? That lost me.", + "A": "For z = 2.58, probability (area) is .9951. But this is the area from minus infinity to +2.58 SDs. We want the area from the 0 to 2.58 SDs (so we can double it), so we subtract .5. Then we have .4951*2 = .9902, approximately .99 = 99%", + "video_name": "SeQeYVJZ2gE" + }, + { + "Q": "But why wait to round it at 5:30", + "A": "Remember, mathematicians don t like to play with long numbers as shown in scientific notation. Besides, this is just an example, so we want to work the easy way, as long as his watchers understand.", + "video_name": "XJBwJjP2_hM" + }, + { + "Q": "At 4:30, couldn't I multiply 0.3979 and 10^5 BOTH by 10? Wouldn't the value be kept equivalent? Or no?", + "A": "No.It wouldn t since it ll make it 3.979*10^6=3979000 but the original answer is 39790. Hope that helps!", + "video_name": "XJBwJjP2_hM" + }, + { + "Q": "At 0:10, How come the inches in the water increase?", + "A": "the ring s volume is 1.5, so it displaces the water so it stays even, Because atoms cant go inside of each other...", + "video_name": "ViFLPsLTO1k" + }, + { + "Q": "at 0:55 what does sal mean by the leibniz notation", + "A": "Gottfried Wilhelm Leibniz, used the symbols dx and dy to represent infinitely small (or infinitesimal) increments of x and y. So f (x)= dy/dx, this was named in honor of Leibniz.", + "video_name": "6o7b9yyhH7k" + }, + { + "Q": "At 6:53 Why did Sal say that second deravative of why is also same as the first one ?", + "A": "If y = e^x, then the first derivative y is also equal to e^x (e^x is its own derivative). The derivative of the first derivative, known as the second derivative y , is therefore also equal to e^x. Thus, the first derivative of y is equal to the second derivative of y. Also why is how we pronounce the letter y.", + "video_name": "6o7b9yyhH7k" + }, + { + "Q": "At 13:01, Sal says that any non-zero number is equal to 1. Why is zero not included?", + "A": "0^0 is 1 in certain contexts and indeterminate in other contexts.", + "video_name": "zM_p7tfWvLU" + }, + { + "Q": "At 12:57, Sal says that 1^0 = 1. Why is that? Why isn't it undefined?\n\nAlso, why is any number to the 0th power 1?", + "A": "lets take an exponent series of x x^0 x^1 x^2 x^3 Now lets write what we know: x^0 = ? x^1 = x x^2 = x * x x^3 = x * x * x Now to get to x^3 to x^2 what do we do? We divide x^3 by x: x^3/x = x^2 because x * x * x/x = x * x = x^2 This logic works for getting from x^2 to x^1 x * x/x = x = x^1 Now extrapolating backwards, wouldn t going from x^1 to x^0 be the same as just x^1 divided by x? So: x^1/x = x^0 = x/x = 1 So any number to the zeroth power is equal to 1, except for 0 itself.", + "video_name": "zM_p7tfWvLU" + }, + { + "Q": "At 3:13, how does 3x^2 equal 27x^2? They seem like two different numbers.", + "A": "it was actually cubed not squared. On the video it says: 3x . 3x . 3x = (3 . 3 . 3)(x . x . x) (3x)^3 = 27x^3 you can test it by substituting say a 2 for the x value, then you would get 216 = 216", + "video_name": "zM_p7tfWvLU" + }, + { + "Q": "Is there a test anywhere with questions similar to 10:08? I enjoyed simplifying the expression but I want more challenges like that to see if I can do it again.\n\nThe test \"Practice Multiply Powers\" only has simple questions", + "A": "Keep working thru this section. There are later exercise sets that combine 2 or more of the exponent properties which makes them more challenging.", + "video_name": "zM_p7tfWvLU" + }, + { + "Q": "at 11:12, Sal is rearranging the problem. He begins with 2x3. Where is the 3 coming from? Please enlighten me on this.", + "A": "The 3 is coming from that last term in parentheses (3x^2y^2). First he multiplied all the numbers together (the middle term didn t have a number), then the letters.........", + "video_name": "zM_p7tfWvLU" + }, + { + "Q": "On the second problem (7:23), why is '8' divisible by both '9' and '24'? I honestly don't get it because I'm thinking of it as '9/8' or something. I get the part of 2.2.2, though.\nCould somebody please point out what's wrong here? thanks in advance.", + "A": "The point is that any number divisible by 9 and 24, is also divisible by 8. Why?! because the prime factorization of 9 and 24 contains the prime factorization of 8. by the way, at first that confuse me :)", + "video_name": "zWcfVC-oCNw" + }, + { + "Q": "4:05 12 is a number that is in the problem!\n\nAll numbers divisible by both 12 and 20 are also divisible by 12?", + "A": "Yup, and all numbers divisible by both 12 and 20 are also divisible by 20.", + "video_name": "zWcfVC-oCNw" + }, + { + "Q": "At 1:18, he says that in order to be divisible by both a number has to have 2 2s, a 3 etc... but why 2 2s and just 1 3?", + "A": "12 needed 2 2s and one 3 and 20 needed a 5 and 2 2s but the 2s were thare and he use prime numbers and 2, 3, and 5s are prime", + "video_name": "zWcfVC-oCNw" + }, + { + "Q": "at 2:42, to isolate the -2, why did you have to divide and not subtract?", + "A": "be careful with leading negative numbers. Try to think of this as a negative number, not subtraction. The negative two is being multiplied by the absolute value. In order to cancel this number we do the opposite of multiplying by -2 which is dividing by -2.", + "video_name": "15s6B7K9paA" + }, + { + "Q": "At 6:10 can it be y=k/x since it is y=k*1/x", + "A": "Certainly! That is what inverse variations generally look like. People don t usually write y = 8 * 1/x, they usually write it as y = 8/x.", + "video_name": "92U67CUy9Gc" + }, + { + "Q": "At 4:20,how can we assume it is an isosceles pyramid? We don't know for sure,do we? That question might have been a trick question.", + "A": "I guess because we are using the actual Great Pyramid of Giza for the problem, and it is in real life isosceles, we can assume this.", + "video_name": "Z5EnuVJawmY" + }, + { + "Q": "At 1:42 Sal says to move the 0 degrees on the protractor to one side of the angle. How do you know which side to use?", + "A": "One side is in the angle, if the angle is right or acute, than use the side that flows into the actual angle, obtuse angles can vary.", + "video_name": "wJ37GJyViU8" + }, + { + "Q": "at 1:30 \u00c2\u00a8\u00c3\u00aft would be embarrasing if i didnt\u00c2\u00a8 no sal it would be kinda histerical (is that how you spell it?). and show your human", + "A": "*hysterical, that s how it s spelt :) And seeing as angle measuring is quite simple for a mathematician, it would be pretty embarrassing for him.", + "video_name": "wJ37GJyViU8" + }, + { + "Q": "i am confused:\nat 3:20 how does Sal go from =44 to 00000000+000", + "A": "Well he took the commutative property and broke it down. 4*8+4*3 4*8 is equal to 32. 4*3 = 12. I ll break the equation cause it s just how i work out problems. (4^2+4)+(8*3). 4 times itself is a product of 16.16+4 equals 20. 8*3 =24. 24+20=44.", + "video_name": "gl_-E6iVAg4" + }, + { + "Q": "At 1:22 in the video do you do four times eleven?", + "A": "Yep! 4(11) = 44", + "video_name": "gl_-E6iVAg4" + }, + { + "Q": "At 1:56 how did you get x = 4.? And one ore thing I am still not getting what does this theorem states?", + "A": "The theorem says that the third side of a triangle has to be LESS than the sum of the other two sides AND MORE than the rest of the two sides. So when you subtract 6 from 10 you get 4.", + "video_name": "KlKYvbigBqs" + }, + { + "Q": "I don't understand, at around 8:00 when Sal is explaining vector [c1 c2 0 c4 0] he said that c1,c2,c4 must be zero showing linear independence, now aren't the third and fifth term also zero? If c1 c2 c4 are zero then the solution would be [0 0 0 0 0], doesn't that imply all column vectors to be linearly independent?", + "A": "He says that the 1st, 2nd and 4th c must be 0 for the result to be the 0 vector, and hence are linearly independent. Whereas, the 3rd and 5th just happen to be zero.. but since these vectors can be made from the other vectors, you would also be able to find a way to get back to 0 even if these happened not to be. (He mentions showing this in the next video).", + "video_name": "BfVjTOjvI30" + }, + { + "Q": "At 8:16, when you have the area of 324 pi. Why can't you substitute pi with 3 because 3.14 rounded is 3 and multiply 3 by 324?", + "A": "The answer will not be accurate", + "video_name": "mLE-SlOZToc" + }, + { + "Q": "At 5:15 , what is a circumference ?", + "A": "The circumference of a circle is the length of the perimeter of the circle, or the distance all the way around. It is equal to pi times the diameter of the circle or pi times 2 times the radius.", + "video_name": "mLE-SlOZToc" + }, + { + "Q": "Before the time of 3:04, shouldn't the non green marbles be 11/14?", + "A": "No, we are trying to find the probability of picking a NON-BLUE marble. There are 14 marbles total, two of which are blue. Thus the number of non-blue marbles is 12/14, which simplifies down to 6/7.", + "video_name": "mLE-SlOZToc" + }, + { + "Q": "At 1:31, isn't there an easier way of solving?", + "A": "I m sure there is! But Sal is not trying to show us the easiest way, here: he s trying to explain the principles of probabilities and choice. Understanding and explaining these principles is far more important for Sal than showing us the easiest way to find a solution.", + "video_name": "mLE-SlOZToc" + }, + { + "Q": "at 5:30 sal says area of a circle. however,circles dont have area,circles have circumfrence", + "A": "All two-dimensional shapes have a perimeter and an area. Perimeter is a distance, the length of the bounding line(s). Area is ... well ... an area. It measures the amount of a flat surface that is contained within the perimeter. For circles, the perimeter is called the circumference.", + "video_name": "mLE-SlOZToc" + }, + { + "Q": "At around 2:15 , why does (1-cos(2x))\u00c2\u00b2 turn into 1-2cos(2x)+cos\u00c2\u00b2(2x) ? Where does the 2cos(2x) come from ?", + "A": "Sal was simply expanding the expression (1/2 (1-cos2x))^2. 1/2 squared is 1/4 and (1-cos2x) squared is (1-cos2x) times (1-cos2x). If you recall from Algebra that (a-b)(a-b) = a^2 -2ab + b^2, then let a = 1 and let b = cos2x and multiply it out. a^2 = (1)(1) = 1, -2ab = -2(1)(cos2x) = -2cos2x. b^2 = (cos2x)(cos2x) = cos^2 2x. Hope this helps. Good luck.", + "video_name": "n34jx1FIN8M" + }, + { + "Q": "towards the end of the video at 10:45 sal says that the cut off for staticians is 5% or less. why is it 5% and less and not 5% and more. can i please have an example as well as to why it is less than 5%", + "A": "We start with an assumption (null hypothesis), and calculate the probability of the observed result if that assumption is actually true. Hence, small probability will make us say Hmm, these results don t match up with our assumption very well, the assumption is probably wrong. Large probability does not make us question our assumption: it says the data are fairly compatible with the assumption, so it might be okay.", + "video_name": "W3C07uH-b9o" + }, + { + "Q": "is there a way to convert the remainder into a decimal on 2:06", + "A": "There sure is. Think of 15/4 (15 divided by 4) as how many groups of 4 can 15 be divided into. The answer of 3r3 means 3 full groups of 4 and a partially completed group, the remained, of 3. That partially completed group holds 4 but only has 3 in it. We call this 3/4. So we can rewrite 3r3 as 3 3/4. We can do our division on 3/4 and convert it into a decimal, which equals 0.75. So 15/4 = 3r3 = 3 3/4 = 3.75", + "video_name": "BIGX05Mp5nw" + }, + { + "Q": "At 1:28 Sal says that we must divide both the sides with 5 but instead of that we can transpose 5.It is much easier that way!", + "A": "fair enough, but I think that dividing both the sides by 5 is good for beginners because the fundamental belief of algebra, that if you do the same thing to both the sides of an equation,you won t change anything seems much more prominent in dividing both sides by 5 than in transposing.", + "video_name": "c6-FJRda_Vc" + }, + { + "Q": "I calculated M by subtracting the first formula [(mx^2)+bx=xy] from the second (y=mx+b). Which is the opposite of what sal does @0:50. I get a different formula for M, is this OK? I can't equate the two formulas. Here is the formula I get (all the x and y should have the mean sign. M= [(xy/x)-y]/[(x^2/x)-x)", + "A": "Multiply both top and bottom by -1, and the result is [(-xy/x)+y]/[(-x^2/x)+x] where all the x, x^2, and y should have the mean sign. This is equivalent to [y-(xy/x)]/[x-(x^2/x)] simply by switching the order of the terms in the numerator and denominator, respectively. This is Sal s answer.", + "video_name": "8RSTQl0bQuw" + }, + { + "Q": "So, I now understand that you can multiply a real number (or scalar, which was defined at 0:30) by a matrix, but can you multiply a Matrix by another Matrix? Wouldn't it be just like adding or subtracting, except you multiply instead?\nFor example:\n\n[1 8 3] * [2 9 4] = [2 72 12]\n\nWould that be correct?", + "A": "No and it is more complicated than that. You can watch Dr. Khan s video on this but I ll give you the quick version. For 2 matrices to be multiplied, the number of rows in the first matrix must be equal to the number of columns in the second matrix (remember matrix multiplication isn t always commutative as AB isn t necessarily BA). In your case, those two matrices cannot be multiplied.", + "video_name": "TbaltFbJ3wE" + }, + { + "Q": "at 2:20 I have no idea whats going on", + "A": "He is reversing the multiplication he did to make it a whole number so that the decimal would be in the correct place.", + "video_name": "D5fmcpNygQk" + }, + { + "Q": "Can someone explain to me how he got the 6i in (9+6i-1) at 5:50? Thanks!", + "A": "Shivanie, He was multiplying (3+i)(3+i) Using FOIL you get First 3*3 = 9 Outside 3*i = 3i Inside i*3 = 3i Last i*i = -1 So you get 9+3i+3i-1 And the 3i+3i = 6i so you get 9+6i-1 I hope that is of help to you.", + "video_name": "dnjK4DPqh0k" + }, + { + "Q": "Can someone explain to me what Sal is doing at 5:29 onwards?", + "A": "Sal is using the same FOIL technique except now there are complex numbers. ((3 + i) / 2)^2 can also be written as ((3 + i)*(3 + i)) / (2*2). By using FOIL the numerator will become... F: 3*3 = 9 O: 3*i = 3i I: 3*i = 3i L: i*i = -1 (3 + i)(3 + i) ----> 9 + 3i + 3i - 1 ----> 8 + 6i 2(8 + 6i) / 4 ----> 4(4 + 3i) / 4 ----> 4 + 3i I hope this helps", + "video_name": "dnjK4DPqh0k" + }, + { + "Q": "At 2:34 Sal says that any percent is that percent over 100. But however what if your number was greater than 100 say like 109%?", + "A": "109% is 109/100, which is 1.09.", + "video_name": "-gB1y-PMWfs" + }, + { + "Q": "he lost me at 2:32, what is he saying. Please help", + "A": "(anything)%=(anything)/100 I hope you understand now!", + "video_name": "-gB1y-PMWfs" + }, + { + "Q": "How did Sal decide how big the blue circles were at 1:00 to 1:10", + "A": "The first circle needs to be at least half the diameter of the circle win the problem. Then, with the second circle, Sal simply placed the midpoint of the new compass on the midpoint of the first circle, made the circles the same size by adjusting the new compass, and then placed the new circle s midpoint on the opposite side of the circle in the problem. Hope this helps :)", + "video_name": "-gWtl6mdpeY" + }, + { + "Q": "so should i have studied quadratic equations before i got to this? it looks like that's a later topic in the algebra play list. and where do i find the vertex form/formula?\n\nfor instance at 5:02 sal says \"this is in vertex form\" referring to y = 2 (x-4)^2 + 3 \"where x = 4 and y = 3\"... and then he plots that point. i don't knw what that means or where i can look for it in the playlist.\n\nat 5:57 i think this might be completing the square?", + "A": "Yes, you need to know quadratics before doing these videos -- they seem to have been put too early on this list. It is possible to do some simple non-linear equations before mastering quadratics, but I would not recommend it. Try going to the Functions videos and then coming back to these videos once you re completely done with quadratics.", + "video_name": "FksgVpM_iXs" + }, + { + "Q": "What does Sal mean @16:38 when he said usually they are the negative of each other?", + "A": "You normally see vector fields pointing to decreasing the scalar, not increasing the scalar. For example, the force on a particle at a certain point is equivalent to the negative of the gradient of the potential energy at that point.", + "video_name": "K_fgnCJOI8I" + }, + { + "Q": "What does he mean at 3:52", + "A": "He means that to determine whether a point is on a line or not you can input the coordinates into the given equation and if the equation is true, than the point is on the line, but if the equation false, than the point isn t on the line.", + "video_name": "SSNA9gaAOVc" + }, + { + "Q": "at 1:14 what is the operation?", + "A": "He just multiplies 5 and 3 and adds it to 2 multiplied by -4", + "video_name": "SSNA9gaAOVc" + }, + { + "Q": "Around 5:50, wouldn't you also divide by 2x1 to remove the repeats for tails? Or would that cancel out because tails was not included in the total probability in the first place?", + "A": "I think tails don t factor in because our question didn t address them as something to calculate. If, say, we were asking what the probability would be of getting 3 heads and 2 tails exactly in six flips (assuming that, in this scenario, it is possible to get a coin on its side), then, yes, we would have to factor in tails. Also, tails were included in our total probability (all possible sequences of heads and tails), but again, their chance of occurring wasn t asked for in the question; so we ignore them.", + "video_name": "udG9KhNMKJw" + }, + { + "Q": "At about 1:17, he showed that he was converting the decimals to whole numbers. That method really confuses me. Can somebody please show me a way to solve the problem while keeping the decimals and solving it that way? would it be possible to instead of changing the decimals, keep the decimals and work out the problem with the decimals?", + "A": "You can do 0.6 / 1.2 But, the 1st step in decimal division, is to change the 1.2 into a whole number. Shift the decimal places one place to right 6 / 12. Then, do the long division. You will get c = 0.5", + "video_name": "a3acutLstF8" + }, + { + "Q": "At 1:00 Sal tells us about parallel lines. Are they related in any way", + "A": "Yes. They never intersect. If you have 2 unparalleled lines, then somewhere they will intersect and they are therefore not parallel.", + "video_name": "V0xounKGEXs" + }, + { + "Q": "I still don't understand how does the computer program calculate the \"pseudo-sample variance\" @4:10 if we don't know mu's value. Can someone please explain?", + "A": "In real life we generally don t know the value of \u00ce\u00bc. However, in a simulation, we are making up the data, and we do in fact know \u00ce\u00bc. What were doing is: 1. Set \u00ce\u00bc and create some data from a distribution with that mean. 2. Pretend that we don t know \u00ce\u00bc, and calculate the mean and standard deviation. 3. Remember that we know \u00ce\u00bc, and perform the calculations shown in the video.", + "video_name": "F2mfEldxsPI" + }, + { + "Q": "Shouldn't the unit vector i go into the other direction of the x-axis? (Minute 12:44) Otherwise we set up a left-handed coordinate system, didn't we?", + "A": "Yes, Sal decided to change the sign of the x coordinate on minute 9:58, turning the system into a left-handed coordinate system.", + "video_name": "bJ_09eoCmag" + }, + { + "Q": "at 0:03, some people find it offensive to have people ask their ages. and at 0:34, how can you throw ages into a bucket? They aren't physical objects.", + "A": "It is metaphoric. He is putting the ages into categories. The categories are being compared to buckets. They are not actually buckets. Also, due to the scenario, probably no one was offended about the ages, and Sal never asked anyone. He said if you were to go and ask the people at the restaurant, this is what you would get.", + "video_name": "gSEYtAjuZ-Y" + }, + { + "Q": "At 2:46, how can one list the factors of \"a\" if it has already been declared prime?", + "A": "It hasn t been declared prime. a/b is reduced to lowest terms. 27/32 is reduced to lowest terms. It s (3*3*3)/(2*2*2*2*2).", + "video_name": "W-Nio466Ek4" + }, + { + "Q": "At 4:53, i don't understand why f2=p, because a^2=p.b^2 so p is a factor of a^2 so i think p=f2.f2 not p=f2. Can you please explain? Thank you", + "A": "We know that P is a factor of a^2, because a^2 = P*b^2. P is a prime number, so it can t be the product f2*f2. P has to be one of the prime factors of a^2. These prime factors come in pairs, as they do in all perfect squares (as Sal shows in the video). Sal picked f2 as a possible example.", + "video_name": "W-Nio466Ek4" + }, + { + "Q": "At 3:20, why does Sal write -10, is this because the ball is going down to the ground according to physics or he just make typo?", + "A": "It depends how you want to formulate your series. In the video Sal starts the series at n = 0. What is 20 * (1/2)^0? It is 20. However, the first bounce is only 10m, not 20m! Therefore, we need to deduct 10. In other words, after the ball has been dropped (i.e., the 0th bounce) it has travelled a distance of: -10 + 20(1/2)^0 = 10m", + "video_name": "tqTJZEglrvc" + }, + { + "Q": "At 1:08, when sal divides both sides of 24x/24x wouldn't you be left with 1x? so then you move the variables to one side making 1x-1x making it 0x. ahh i think i just answered my own question. 0xanything is 0. right?", + "A": "he s not dividing though, he s subtracting", + "video_name": "zKotuhQWIRg" + }, + { + "Q": "in 5:31 whats that division symbol really sorry if it a silly doubt", + "A": "At 3:46 he explains what that symbol is. It is a subtraction sign. A division sign is the opposite, like / .", + "video_name": "2B4EBvVvf9w" + }, + { + "Q": "(about 3:30 minutes into the video) Why is f(c) greater than or equal to f(x)?\nThe few seconds after that are also not quite clear to me. Help please!", + "A": "Essentially, f(c) is a random point representing a relative max. f(x) represents the rest of the graph within the domain (c-h,c+h). So, if f(c), the point, is higher than the rest of the graph,f(x) in the selected interval, then it must be a relative max. Hopefully that helped.", + "video_name": "Hoyv3-BMAGc" + }, + { + "Q": "3:25 why bigger or equal to? if it's equal how can it be a maximum?", + "A": "The maximum value a function gets is still the largest value whether the function reaches it one times, five times, or infinitely many times. For a local min that is not a global min, you would typically only have the equal scenario come up if there is a horizontal region in the function.", + "video_name": "Hoyv3-BMAGc" + }, + { + "Q": "At 4:06 he says that the denominator is zero but isn't the square root of 0 + 1 just equal one. would the graph be different?", + "A": "Yes, but he was finding the limit of 0/(sqrt(0+1)), which is 0.", + "video_name": "xks4cETlN58" + }, + { + "Q": "At 9:23 pm, how do you factor problems when the coefficient does not share a common factor with the other numbers?\nFor example:\n2x2 - 3x + 2", + "A": "Your example you gave here riverav is not factorable. To answer your question, however, you do the regular factoring polynomials method sal taught us to get your answer, or if you have exhausted all factors, the problem is not factorable.", + "video_name": "GMoqg_s4Dl4" + }, + { + "Q": "At 2:54, why did you add 3k and -3k? I can't understand why and extra coefficient was added.", + "A": "was the k squared? because that might be why...", + "video_name": "GMoqg_s4Dl4" + }, + { + "Q": "Wait, at 0:37 Sal says that for the first flip there's 2 possibilities, same on the second and the third. So 2 and 2 and 2 should be 6, right?", + "A": "The 2 s should be multiplied instead of added together. This should be seen in layers like this: There are 2 possibility for the first flip. For every possibility of the first flip, there are 2 possibility for the second flip. So there are a total of 2 * 2 possibilities for the first two flips. For every possibility of the first two flips, there are 2 possibility for the third flip. So there are a total of (2 * 2) * 2 possibilities for the three flips.", + "video_name": "mkyZ45KQYi4" + }, + { + "Q": "At 6:33, can we also write:\n= 1 - ( 1 / ( 2 ^ 20 ) )\n?", + "A": "No, not quite. There are only 10 2s, so it would be 1 - ( 1 / ( 2 ^ 10 ) ).", + "video_name": "mkyZ45KQYi4" + }, + { + "Q": "At 2:03, how do you add 7 + 1/100?", + "A": "He isn t. He s multiplying them. But if you want to add them, you d get 7 1/100 (seven and one hundredth).", + "video_name": "he4kcTujy30" + }, + { + "Q": "At 3:44, how did we get cos^2(theta) \u00e2\u0080\u0093 sin^2(theta) to equal to 1 \u00e2\u0080\u0093 2 sin^2(theta) and to 2cos^2(theta) \u00e2\u0080\u0093 1. Thank you!", + "A": "First, cos^2 (theta) = 1 - sin^2 (theta). This is from the Pythagorean identity sin^2 (x) + cos^2 (x) = 1. Therefore, cos^2 (theta) - sin^2 (theta) = 1 - sin^2 (theta) - sin^2 (theta) = 1 - 2 sin^2 (theta). Second, we flip the Pythagorean identity around and replace sin^2 (theta) with 1 - cos^2 (theta). We get 1 - 2(1 - cos^2 (theta)) = 1 - 2 + 2 cos^2 (theta) = 2 cos^2 (theta) - 1.", + "video_name": "lXShNH1G6Pk" + }, + { + "Q": "at 1:49, why don't we plug in 8 for x^2?", + "A": "we only plug 8 into x^2 to get h (height) at that instant. To get dh/dt we have to differentiate x^2+h^2=10^2 to get relation between dx/dt, dh/dt, x(for that instant) and h(for that instant). Now we will solve dh/dt using simple algebra by putting known values into it.", + "video_name": "kBVDSu7v8os" + }, + { + "Q": "at ~13:20, sal is writing out 3rd/final term of the 3x3 determinant |A|...but shouldn't it be \"-f(ah-bg)\" vs \"-f(dh-eg)\" ?", + "A": "Yes. Transcription error from a few minutes in. [I m writing words to pass the comment screener.]", + "video_name": "32rdijPB-rA" + }, + { + "Q": "at 0:49 isnt it the other way because it would be 1.5 in real life problem", + "A": "Do you mean 1*5? 1.5 is a decimal number for 1 1/2. Any dot used for multiplication must be raised. Anyway... I think Sal is using the bar under each number to separate the digit from its place value. I don t believe he is using it for division if that is what you were thinking.", + "video_name": "BItpeFXC4vA" + }, + { + "Q": "in 4:24 why he drew a point outside the parabola? that point is undefined according to y=x^2, the function f(x)=x^2 but its f(x)=3 when x=2:- this is a wrong statement. And what is the meaning of limit? the limit going to tell u the defined function like in parabola x^2=4 when x=2. what is the meaning of limits?? :S", + "A": "The function he used in this example is a piecewise function which forces the value of f(x) to equal 3 when x=2. A limit is used to describe the value of f(x) as it starts to approach a number. This becomes a key component in many aspects of calculus.", + "video_name": "W0VWO4asgmk" + }, + { + "Q": "Could someone explain how Sal solved 21 times 2/3 in his head so quickly? It happened around 2:57 in the video. I would like to understand his method.", + "A": "Its called cross products or cross multiplication.", + "video_name": "XOIhNVeLfWs" + }, + { + "Q": "at 0:12 what is o-blood", + "A": "There are different types of bloods, that is just one of them", + "video_name": "qrVvpYt3Vl0" + }, + { + "Q": "Instead of using his \"aside\" with the triangle beginning at 1:49, I did something similar but using x/3 instead of 'S'. In other words, I said:\nUsing the Pythagorean Theorem: ((x/3)/2)^2+h^2 = (x/3)^2\nh^2 = (x/3)^2-(x/6)^2\nh = x/3-x/6\nh=x/6\n\nObviously this differs from Sal's answer but I can't figure out why?", + "A": "Your mistake was when you square rooted, \u00e2\u0088\u009a(a\u00c2\u00b2+b\u00c2\u00b2) is NOT \u00e2\u0088\u009aa\u00c2\u00b2 + \u00e2\u0088\u009ab\u00c2\u00b2 and is not a+b Here is the correct way to do it: h\u00c2\u00b2 = (\u00e2\u0085\u0093x)\u00c2\u00b2- (\u00e2\u0085\u0099x)\u00c2\u00b2 h\u00c2\u00b2 = \u00c2\u00b9\u00e2\u0081\u0084\u00e2\u0082\u0089 x\u00c2\u00b2 - \u00c2\u00b9\u00e2\u0081\u0084\u00e2\u0082\u0083\u00e2\u0082\u0086 x\u00c2\u00b2 h\u00c2\u00b2 = \u00c2\u00b9\u00e2\u0081\u0084\u00e2\u0082\u0081\u00e2\u0082\u0082 x\u00c2\u00b2 h = x / \u00e2\u0088\u009a12 h = x / (2\u00e2\u0088\u009a3) h = \u00e2\u0085\u0099 x\u00e2\u0088\u009a3", + "video_name": "IFU7Go6Qg6E" + }, + { + "Q": "At 4:38 Sal says the word reciprocal.\nWhat is a reciprocal?", + "A": "The easiest way to find the reciprocal of a number is to think what should I multiply this number with to make it equal 1? That s basically all there is to reciprocals.", + "video_name": "a_Wi-6SRBTc" + }, + { + "Q": "At 1:18, Sal mentions \"interval notation\". I watched all the videos in order in \"Creating and solving linear equations\" but did not see anything about interval notation. Is there a video for this?", + "A": "At 1:18 Sal is introducing interval notation in this video.", + "video_name": "xOxvyeSl0uA" + }, + { + "Q": "At 5:00, how does 8x-5 turn into 8x-20x??", + "A": "8x - 5(4x + 1) Is the right side of the inequality. So, to simplify the right hand side of the inequality, Sal distributes the -5 to (4x + 1), which is -5(4x) + -5(1) = -20x -5. So, it is 8x - 20x - 5. Hope this helped!", + "video_name": "xOxvyeSl0uA" + }, + { + "Q": "at 1:19, if x can be from negative infinity to -1, but not including negative 1, so why does he include -1 in the partenthases", + "A": "The symbols \u00e2\u0080\u0098(\u00e2\u0080\u0098 and \u00e2\u0080\u0098)\u00e2\u0080\u0099 indicate exclusive values, whereas the symbols \u00e2\u0080\u0098[\u00e2\u0080\u0098 and \u00e2\u0080\u0098]\u00e2\u0080\u0099 indicate inclusive values. In the example x<-1 which is represented as (-\u00e2\u0088\u009e,-1) because -1 is not inclusive. If the example had been x\u00e2\u0089\u00a4-1 then -1 would have been included and could be represented as (-\u00e2\u0088\u009e,-1]", + "video_name": "xOxvyeSl0uA" + }, + { + "Q": "At 4:28, what is a basis?", + "A": "At 4:28, A basis is a System which consist of the MINIMAL amount of VECTORS which are needed to define a room (space, coordinate system). All VECTORS in from a BASIS must be liear dependant from eachother.", + "video_name": "C2PC9185gIw" + }, + { + "Q": "At 4:15 is there an easier way to find that number that if given the certain exponent (5) makes it into the 32? (how did he know it was a 2?)", + "A": "With enough practices you ll be able to recognize certain numbers or quickly calculate in your head. Also he was using it as an example so he would pick something he already knows and easy for us to recognize.", + "video_name": "lZfXc4nHooo" + }, + { + "Q": "Isn't a line segment that has no length a point? Refering to 4:50", + "A": "Yes. A point really has no size, and since lines have no width, if a line also had no length, it would not be a line, it would be a point.", + "video_name": "Oc8sWN_jNF4" + }, + { + "Q": "At 5:00, Vi mentions a line that has no length. Wouldn't that be resembling a point? A point has no length whatsoever, or width, hence only trapped in 1st dimension. So does a potential line with no length. So... that means it's a case of a=b and b=c so a=c, right?", + "A": "A point is zero-D it has no length", + "video_name": "Oc8sWN_jNF4" + }, + { + "Q": "At 2:29 why does Vi draw a man with 3 \u00f0\u009f\u0091\u0080", + "A": "That man lives in 4 dimensional space, meaning that a person needs three eyes to see properly.", + "video_name": "Oc8sWN_jNF4" + }, + { + "Q": "At 5:17, how did you get those numbers if young are adding 2, then, then 6.", + "A": "Each number is 2 more than the previous number. If x is the first number, then the 2nd number is x+2. The third number is 2 more than the previous number, which is the 2nd number, which also is x+2. So the 3rd number is (x+2)+2 = x+3. The 4th number is the 3rd + 2, which is (x+4)+2 = x+6", + "video_name": "8CJ6Qdcoxsc" + }, + { + "Q": "at 4:45 why is the second derivative negative? i thought if it is going up, than it is positive both below and above the x axis?", + "A": "The second derivative is negative wherever the first derivative is decreasing.", + "video_name": "LcEqOzNov4E" + }, + { + "Q": "Question about 8:37 onwards: so, what if the critical points are undefined for f(x)? i.e.: the \"maximum\" point of the downward concave area doesn't have a value, is discontinuous -- is this point still considered a maximum, even though there's no value for the point, or do maximum and minimum points only apply if the interval is continuous?", + "A": "We can check the function, however, discontinuities in the derivative sometimes result in discontinuities in the original function (such as the derivatives of tanx, 1/x, and 1/x\u00e2\u0081\u00bf).", + "video_name": "LcEqOzNov4E" + }, + { + "Q": "at 7:36 you said slope is increasing. Does that mean slope is becoming more positive?", + "A": "Increasing slope can mean one of two things: more positive or less negative. Whichever situation you have, increasing slope always implies concave up.", + "video_name": "LcEqOzNov4E" + }, + { + "Q": "At 5:40, why is it true that if the first derivative/slope of the line is increasing, then the second derivative must be positive? (and vice versa for decreasing/negative)", + "A": "Consider that when the original function f(x) is increasing/decreasing, then the first derivative f (x) is positive/negative. Similarly, when f (x) is increasing/decreasing, then its derivative f (x) is positive/negative. However, the main idea of this video is to help illustrate that when the second derivative is positive/negative, then the original function is concave up/down. The second derivative is useful for classifying extrema and for identifying concavity of a function.", + "video_name": "LcEqOzNov4E" + }, + { + "Q": "So there is the (1:00):\nf(g(x)) = sqrt( g(x)^2 - 1 )\nI was recently watching video series on complex numbers and I am just curious why can't we rewrite that thing as\ng(x) * sqrt(-1)\nand so\ng(x)*sqrt(i^2)\nto\ng(x)*i hence state the solution in terms of complex numbers? I know it is a boo-boo *but why?*", + "A": "Sorry, your method doesn t work. You changed subtraction: sqrt( g(x)^2 - 1 ) into multiplication: g(x) * sqrt(-1). This is not a valid operation. Also, there is no property of square roots that lets you split the square root by terms (items being added/subtracted). You can only split square roots by factors (items being multiplied/divided). Hope this helps.", + "video_name": "_b-2rZpX5z4" + }, + { + "Q": "I don't understand what he says at 6:09, please explain!", + "A": "The length of one cycle of the standard cosine function is 2pi. So we need to ask ourselves: How does 2pi compare to the length of one cycle in the problem? That s why we set up the ratio of 2pi to 365, or written in fractional terms, 2pi/365.", + "video_name": "mVlCXkht6hg" + }, + { + "Q": "At 2:28 why does -24x become -25x when you subtract x", + "A": "Because a negative minus a positive is basically adding a negative to a negative.", + "video_name": "711pdW8TbbY" + }, + { + "Q": "At 5:40 Sal says that the square root of 2.25 could be 1.5 or -1.5. At 5:57, Sal says that 1.5 \u00e2\u0089\u00a0 -1.5. However, at 5:52, couldn't he have as easily used -1.5 as the square root of 2.25 instead of 1.5? If he had used -1.5, the solution 2.25 would have been valid. Is it because you can only principal square roots? If so, why?", + "A": "No. all square roots, even non-perfect squares will always have a positive or negative value, even square root of is +2 or -2. Why? If you might have forgotten; two negatives, when multiplied together, will always become positive. However, cube roots only have a positive root if the value inside the cube root sign is positive and negative if negative. And yes, 1.5 is not equal to -1.5 but their square is equal.", + "video_name": "711pdW8TbbY" + }, + { + "Q": "At 1:34, you did some factoring in your head...hard to follow to get the 24x. Could you expound upon that? I know - watch the factoring videos - but that one lost me. It wasn't quite clear WHY you multiply the 2x and the 6 to get the 24.", + "A": "Because the square factor form is as following: (ax-b)^2 ax-b x ax-b _________ ax^2 -abx -bax +b^2 Focus in the part (-abx -bax), since multiplication scalar is commutative, they are twice themselves. Rewrite them in order, (-abx -abx), which is equal to 2(-abx). If a = 2 and b = 6, representing them in the expression 2(-2*6x), 2(-12x) that is equal to -24x.", + "video_name": "711pdW8TbbY" + }, + { + "Q": "Ok, I know what PEMDAS is, what do you do if you get, say, 3*6:9? M and D are on the same level!", + "A": "work from left to right!", + "video_name": "0uCslW40VHQ" + }, + { + "Q": "At 0:43, the speaker explains PEMDAS . Is there another way to solve expressions?", + "A": "Not in my knowledge. to me, PEMDAS is the best way to do order of operations.", + "video_name": "0uCslW40VHQ" + }, + { + "Q": "Around 4:50 when Sal is subtracting \"all of this business\", i.e. -e^xcosx+Se^x cosx dx, why does the plus sign become a minus sign? Its e^x sinx - -e^xcosx... so that becomes plus. But why does the plus sign before the antiderivative become a minus sign??", + "A": "When he was taking e^x(sin(x)) - \u00e2\u0088\u00ab e^x(sin(x))dx, the minus sign acts as a negative sign so it would end up something like this in his thinking: e^x(sin(x)) + [-( \u00e2\u0088\u00ab e^x(sin(x))dx)]. You would take the integral of e^x(sin(x))dx to get -e^xcos(x) + \u00e2\u0088\u00ab (e^xcos(x))dx and factor the negative into the whole equation to get: e^x(sin(x)) + e^xcos(x) - \u00e2\u0088\u00ab (e^xcos(x))dx", + "video_name": "LJqNdG6Y2cM" + }, + { + "Q": "Around 2:00 I don't understand what he is saying about the point in the middle being an equidistant away from each angle. Please explain.", + "A": "He was referencing a video about perpendicular bisectors. Basically, Sal is saying that if you have one point that is equidistant from two other points on a line, but said point ISNT on that line, then it lies on the perpendicular bisector of that line. so since the distance from I is the same distance from AB, and I ISNT on AB, then I is on the perpendicular bisector of AB. Sorry if Im not much help, watch the video!", + "video_name": "21vbBiCVijE" + }, + { + "Q": "at 3:27,a part of the equation does not show up. why is that?", + "A": "you know how sometimes he slides the screen down I think its cause his screen is bigger than whatever were watching it on.", + "video_name": "CLrImGKeuEI" + }, + { + "Q": "Starting at about 3:35, Sal write the equation for L(x). Where does he get f(4) from? Also, is L(x) just the tangent line to f(x) at x = 4?", + "A": "Yes, L(x) is the tangent line to f(x) at x=4. Sal uses f(4) because he is writing the equation of the line tangent to f(x) at the point (4, f(4)) (if the x-value is 4, then the y-value is f(4), right?). You might be more used to always writing y = mx +b, where you put in the slope (which in this case would be f (4)), and then plug in a point to find b, but Sal s method is faster and easier. Basically, he is using the point-slope form instead of the slope-intercept form.", + "video_name": "u7dhn-hBHzQ" + }, + { + "Q": "At 0:36 when did \"Deca-\" prefix become \"Deka-\"?", + "A": "Both deka- and deca- are used alternatively and mean the exact same thing. I always used deca-, but apparently many people use the alternative deka-. Doing a web search indicated deca- was used about three times as often as deka-. But using deka- would probably result in less people misreading it as deci-. If I was King, I would declare deka- should always be used instead of deca-.", + "video_name": "SYkmadc2wOI" + }, + { + "Q": "At 2:10 could't you just do 17-5 and then get 12 and x=4", + "A": "he should of clarified it simpler", + "video_name": "XoEn1LfVoTo" + }, + { + "Q": "at 4:16 why dose it not excist any more?", + "A": "Hah that s a bit funny to read. It still exists but Sal removed it because it was subtracted", + "video_name": "XoEn1LfVoTo" + }, + { + "Q": "Why didn't Sal explain why -8/7 is the same that -(8/7) at 8:30. It isn't so simple to understand.", + "A": "just think about it. -8/7 is equal to 8/-7 and also equal to the negative value of 8/7. so -8/7 = 8/-7 = -(8/7)", + "video_name": "XoEn1LfVoTo" + }, + { + "Q": "at 7:41 you were saying -10 + 2 does not = -12. i have an easy way to understand it. imagine you are paying a debt of 10 bucks. then, you win 2 bucks in a competition. so when you give the person you owe your 2 bucks,you would only owe 8 bucks, as -10 + 2=8. all those who think my method is practical can answer this.", + "A": "sorry i was supposed to type -8 but i accidentally typed8", + "video_name": "XoEn1LfVoTo" + }, + { + "Q": "At 4:14, EX1. y/2-8=10;", + "A": "y/2 - 8 = 10 Add 8 to both sides y/2 = 18 Multiply both sides by 2 y = 36", + "video_name": "XoEn1LfVoTo" + }, + { + "Q": "in 1:20-1:25 i dont get it how can 3x+5=17", + "A": "Put, x = 4 and see. The equation holds!", + "video_name": "XoEn1LfVoTo" + }, + { + "Q": "At 0:41, is 5. (1) not the same as 5 x x 1 ?", + "A": "If another operation is before the parentheses, then you don t multiply. If you have something like 3- (-3), you just subtract the -3. If yo have 4*(5), you only multiply once.", + "video_name": "AJNDeVt9UOo" + }, + { + "Q": "where does he get 104 at 1:26? 80-24? where does he even get that.", + "A": "to add or subtract the fractions like 85/13 and 8/1 are we take the common denominators of both of the fractions and to maintain the equality the changes which we make in the denominator like to make the denominator of fraction 8/1 we multiplied the denominator by 13 so we do the same thing in the numerator thats how sal got 104", + "video_name": "KV_XLL4K2Fw" + }, + { + "Q": "Why is it (1+ the square root of 5,-2)[at 12:48]", + "A": "adding x coordinate of center point with focal distance y coordinate stays the same", + "video_name": "QR2vxfwiHAU" + }, + { + "Q": "At 0:35, how can Sal draw the ellipse if he doesn't know A and B?", + "A": "At the beginning of the video, Sal isn t trying to measure a specific ellipse. Rather, he s trying to deduce information about ellipsis in general. He could have drawn any size of ellipse and the conclusions he came to would have been the same. So he could draw the ellipse without knowing A and B because ANY ellipse with ANY size A and B would work.", + "video_name": "QR2vxfwiHAU" + }, + { + "Q": "Around 9:50 he mentions that v3 is a linear combination because it is v1 and v2 added together which gives a vector in between the angle of the two. If I took v1 - v2 is it still a linear combination because it is outside the angle? Or is it still a linear combination as it is in R^2", + "A": "It is a linear combination: the constant you multiplied v2 by was -1.", + "video_name": "CrV1xCWdY-g" + }, + { + "Q": "At 7:45 when Sal asks if the vectors are dependent or independent, don't we know that they can't be independent solely based on the fact that they are 3 vectors that are only written in two dimensions (a 2x1 matrix)?", + "A": "Yes, you can say that. But Sal hasn t proved that that is the case yet, and he is just trying to introduce linear dependence right now.", + "video_name": "CrV1xCWdY-g" + }, + { + "Q": "At 3:33, it says \"if I draw a vertical line\". Is it the same with a horizontal line?", + "A": "No, you can t-do that with a horizontal line. A function can have multiple x s leading to 1 y, but a function can t have 1 x going to several y s. For that reason, you must have horizontal lines", + "video_name": "qGmJ4F3b5W8" + }, + { + "Q": "I'm confused with these factorials (!) In the problem around 6:12 how does 5!/4!=5?", + "A": "5! = 5\u00e2\u0080\u00a24\u00e2\u0080\u00a23\u00e2\u0080\u00a22\u00e2\u0080\u00a21 4! = 4\u00e2\u0080\u00a23\u00e2\u0080\u00a22\u00e2\u0080\u00a21 5! 5\u00e2\u0080\u00a24\u00e2\u0080\u00a23\u00e2\u0080\u00a22\u00e2\u0080\u00a21 \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\u00e2\u0094\u0080\u00e2\u0094\u0080 4! 4\u00e2\u0080\u00a23\u00e2\u0080\u00a22\u00e2\u0080\u00a21 5! \u00e2\u0094\u0080\u00e2\u0094\u0080 = 5 4!", + "video_name": "WWv0RUxDfbs" + }, + { + "Q": "@0:34\n\nI understand that it doesn't produce the correct answer, in fact it seems to produce the reciprocal of the correct answer, but why doesn't it work to multiply the left and right sides by the fraction x/x (which would be equal to 1) which would leave us with 10x on the left and 15x on the right?\n\nI'm sure that I'm missing something simple, as usual.", + "A": "If you multiply both sides by x/x, here s what you would get: 7x/x - 10x/x^2 = 2x/x + 15x/x^2 This just gives you a much more complicated equation to try and solve. You need to multiply by x to eliminate the fractions and get the variable into the numerator.", + "video_name": "Z7C69xP08d8" + }, + { + "Q": "At 2:30, Sal crossed out -10 & +10. He said \"these negate each other\". What does negate mean?", + "A": "It means they cancel each other out to make 0.", + "video_name": "Z7C69xP08d8" + }, + { + "Q": "at 3:24 he started say that they are both independent. It was not clear to me if the first choice was dependent or not? Maybe I missed it.", + "A": "Yes, that is correct!", + "video_name": "VjLEoo3hIoM" + }, + { + "Q": "What is that weird N-shaped symbol that Sal drew at 2:32?\nI assume it's some sort of symbol meaning and.", + "A": "The \u00e2\u0088\u00a9 symbol Sal wrote in 2:34 stands for intersection, which you have probably encountered in basic statistics. For example, if you let X and Y be arbitrary sets, X \u00e2\u0088\u00a9 Y would be classified as the set containing the elements that are in Set X AND Set Y.", + "video_name": "VjLEoo3hIoM" + }, + { + "Q": "At 1:43, when he says that the {Ak} equation means that k=1 from the first to the last term, does that mean if he had 5 numbers that the \"4\" at the top of the equation would be a \"5\" instead?", + "A": "You are correct. That s why in the infinite equation, the value at the top (AKA the value the sequence goes to) is infinity.", + "video_name": "KRFiAlo7t1E" + }, + { + "Q": "At 1:49, Sal stops at \"a sub-4\". In this finite sequence, is it possible to have an \"a sub-5\"?", + "A": "Hi shanzi11, In that specific sequence no. This is because he states that it is from term 1 to 4 and therefore in this sequence only, subs greater than 4 do not exist. Hope that helps! - JK", + "video_name": "KRFiAlo7t1E" + }, + { + "Q": "I can't understand the part where he creates the function for the first sequence at around 2:50. How did he come up with 1+3(k-1)", + "A": "k a_k 1 + 3\u00e2\u0080\u00a2(k - 1) 1 1 1 + 3\u00e2\u0080\u00a2(1 - 1) = 1 + 3\u00e2\u0080\u00a20 = 1 + 0 = 1 2 4 1 + 3\u00e2\u0080\u00a2(2 - 1) = 1 + 3\u00e2\u0080\u00a21 = 1 + 3 = 4 3 7 1 + 3\u00e2\u0080\u00a2(3 - 1) = 1 + 3\u00e2\u0080\u00a22 = 1 + 6 = 7 4 10 1 + 3\u00e2\u0080\u00a2(4 - 1) = 1 + 3\u00e2\u0080\u00a23 = 1 + 9 = 10", + "video_name": "KRFiAlo7t1E" + }, + { + "Q": "Around 7:09. As a recursive function, Sal said that A sub 2 is:\n\nA(2-1)+3 Which is 1+3 which the answer is 4.\nBut why doesn't it work for A sub 3?\n\nA(3-1)+3 --> 2+3 --> 5\n\nI think I'm making a mistake but I don't know where the mistake is. Please help! Thanks!", + "A": "A(3-1) is not 2, its A(n) when n=2, its the second element\\member of the sequence, indexed at 2, and in this case A(2) = 4, and not 2. the fact that A(1) = 1 is sheer coincidence i m afraid :)", + "video_name": "KRFiAlo7t1E" + }, + { + "Q": "@ 2:56 what does this man mean by we added 3 times one less than the k term times? I don't understand", + "A": "Hey ISAIAH, This man is trying to show that a(k) = 1 + 3(k-1) Since the k term is what term it is (1,2, etc.) It could be referred to as how many times. That is what this man is referring to as the k term times . Hope that helps! - JK", + "video_name": "KRFiAlo7t1E" + }, + { + "Q": "Having trouble understanding how to explicitly define a sequence. Can anyone clarify what Sal means at 4:56 when he says \"we are adding 4, one less time\"?", + "A": "Sal is talking us though his calculations, and so he isn t being as clear as he could be, here. One less time means that we do not add four to obtain the first term. That means that with term #2, we add one 4 to the first term, with term #3, we add two fours to the first term, and so forth: we add one less 4 than the number of the term. (Thanks for the time-stamp: they really help with a question like this :-)", + "video_name": "KRFiAlo7t1E" + }, + { + "Q": "at 3:14 why is the depth of the cylinder dy.", + "A": "dy is an extremely small change in y, it is infinitesimal. We set it as this so that we can use the sum of infinitely thin cylinders to take an integral. Imagine if y was a large number. There would be a large volume unaccounted for, and the integral would not be accurate.", + "video_name": "43AS7bPUORc" + }, + { + "Q": "When finding the length of the B side at approx 1:17 do you add 4^2 to 3^2?", + "A": "Yes, you add 4^2 to 3^2 and then taking the square root of this sum. Just pythagorean theorem. Hope this helps.", + "video_name": "2yjSAarzWF8" + }, + { + "Q": "At 0:50, why did we go 4 points above?", + "A": "It went 4 points above because the distance between point A and point P is 4, and as the problem states, it wants you to dilate from point P with a scale factor of 2. 2*4=8. And so point A2 is 8 points away from point P.", + "video_name": "2yjSAarzWF8" + }, + { + "Q": "At 6:29 I found that the line went the other way. Are u guys sure that is the way the line goes?", + "A": "How did you get it to go the other way? It has a negative slope, so it should go down from left to right (or someone could slide down the hill). With a slope of -1/2, this says go down 1(change in y is -1) and right 2 (change in y is 2). Figure out where you went wrong to get line to go other way.", + "video_name": "unSBFwK881s" + }, + { + "Q": "why did you go back 4 at time stamp 1:34?", + "A": "He didn t. You have the y-intercept graphed. From there you know that the slope is 4, so up 4 and right 1. But that will only let you graph to the right. To graph to the left, you need to go down 4 and left 1. The complete opposite.", + "video_name": "unSBFwK881s" + }, + { + "Q": "At 5:30 didn't he mean the equation would be y=-1/2x-6? He said it would be y=-1/2-6 and I was wonder where the variable would be. I'm not sure if I'm correct or not, please let me know.", + "A": "Yes, you re correct. Initially he forgot to add the x. About a minute afterwards, though, he saw his mistake and fixed it. :)", + "video_name": "unSBFwK881s" + }, + { + "Q": "At 1:31 Sal says that the point is here. Why cannot it be on the left hand side?", + "A": "because it isn t a negative 1 so it is a positive on the graph hope this helps u", + "video_name": "unSBFwK881s" + }, + { + "Q": "1:01 What are the other equation forms useful for?", + "A": "Standard form: Ax+By = C is used frequently when solving systems of equations. Point-Slope form: Y - y1 = m(X - x1) will accept the slope and any point from the line. So, it is easy to use to create the equation of a line. Slope-Intercept form: y = mx + b is used to quickly obtain info need to graph the line. It is also used to change a linear equation into function notation. And, it can be used to create the equation of the line. Hope this helps.", + "video_name": "IL3UCuXrUzE" + }, + { + "Q": "I have no idea how to simplified (y-5)=2(x-1) at 00:43", + "A": "the word simplify in this context means to remove the parentheses using the distributive property and then use the addition property of equality to combine the constant terms. thus you first get y - 5 = 2x - 2. Then adding 5 to both sides you get y=2x+3. This final form is unique for any given line and is called slope-intercept form. It is the function form of the line and it is usually the form that you need if you are going to use a calculator or other graphing software to graph your line.", + "video_name": "IL3UCuXrUzE" + }, + { + "Q": "At 7:42, Sal mentions that we could of taken the Absolute value of the difference between the measurements and the mean instead of squaring them. Why don't we do that, it seems easier?", + "A": "A few reasons. 1. The absolute value function is much harder to deal with mathematically, because the derivative isn t nearly so nice as that of the square function. 2a. Squaring works very well with the Normal distribution. 2b. The sample mean is a natural estimate of location/center, and the Sampling Distribution of the sample mean is Normal, so we d like to use that. Hence, item 2a.", + "video_name": "PWiWkqHmum0" + }, + { + "Q": "I wish Khan Academy had a video where Sal explains all the special symbols that are used in math and what they stand for. For example, at 1:02 Sal says \"We're going to use 'Mu'\" what's 'Mu'?", + "A": "Mu = \u00c2\u00b5 = population mean. Population symbols are always Greek.", + "video_name": "PWiWkqHmum0" + }, + { + "Q": "so does phi work for any ratio? even 7:1?", + "A": "No. It only works for the golden ratio.", + "video_name": "5zosU6XTgSY" + }, + { + "Q": "Isn't the number at 7:04 kind of like pi? It keeps on going forever but never repeats.", + "A": "Yes, the number(or Phi) is an irrational number like pi since the numbers or never terminating.", + "video_name": "5zosU6XTgSY" + }, + { + "Q": "At 3:57 how is phi always equal to only part of phi, shouldn't Phi=Sq. root of 1+Phi equal the square root of 1+Phi, if 1+Phi is Phi there SHOULD be no solution", + "A": "At 6:15 Sal talks about how the \u00e2\u0088\u009a5 is an irrational number and so repeats forever like \u00cf\u0080. An equation has no solutions when one side doesn t equal the other not when one sides repeats forever I think. I m twice your age and struggling with this so it s awesome you re on it already.", + "video_name": "5zosU6XTgSY" + }, + { + "Q": "At 3:20 he multiplied each side of the equation by phi, wouldnt that make it\nPhi^2=1+1", + "A": "(phi - 1 = 1/phi)phi phi^2 - phi = 1", + "video_name": "5zosU6XTgSY" + }, + { + "Q": "At 12:00, how did he get from (a-b)/b to (a/b)-1?", + "A": "(a-b)/b=(a/b)-(b/b)=(a/b)-1", + "video_name": "5zosU6XTgSY" + }, + { + "Q": "at 9:07 how did minus 8 by 24?", + "A": "Because it will go into the negatives.", + "video_name": "-rxUip6Ulnw" + }, + { + "Q": "At 2:11 I really got confused... Like what? I don't get what she means? Like how?", + "A": "9x10 is basically 9 ten times. You move nine to the tens place, and zero is in the ones place since there are no ones left. 9 times 10 is 9, 10 times or 10, 9 times", + "video_name": "Ehd3cgRBvl0" + }, + { + "Q": "At 2:32 , I don't understand how he got that (s-7). Could someone explain it?", + "A": "Ah I see your confusion. Here is what he did: It started as S(S+5) - 7(S+5) What if we look at it all in parenthesis? (S(S+5) - 7(S+5)) What could you factor out of this big mess? Both terms have (S+5) in common right? So pull out S+5 and you get: (S+5)(whatever is not yet factored out) But, the only terms remaining in the original parenthesis was an S-7. So there you go! The final terms are (S+5)(S+7)", + "video_name": "2ZzuZvz33X0" + }, + { + "Q": "in 1:17 how do you get 5+-7=-3", + "A": "He got 5 + (-7) = -2, not 5 + (-7) = -3 He also had the constraint that a \u00c3\u0097 b = -35, and 5 \u00c3\u0097 -7 = -35", + "video_name": "2ZzuZvz33X0" + }, + { + "Q": "At 1:59 how did Sal get s(s+5)?", + "A": "Arnav, At 1:59, Sal took the part of the expression (s\u00c2\u00b2 + 5s) and using the distribtive property in reverse, he factored out an s Like this (s\u00c2\u00b2 + 5s) is (s*s + 5*s) so factor out (undistribute) an s s*(s+5) and rewrite as s(s+5) And in case you still don t understand the reverse distributive property, just use the distributive property on the answer and see if that helps. s(s+5) dstribute the s s*s + 5*s and rewrite as s\u00c2\u00b2 + 5s I hope that helps make it click for you.", + "video_name": "2ZzuZvz33X0" + }, + { + "Q": "At 1:41, can you factor out the quadratic equation into 2 binomials? Does it affect the answer?", + "A": "That is exactly what Sal did. He factored the quadratic into the binomials: (s-7)(s+5)=0 So, I m sure what you mean by your questions. If you can clarify, I ll try to help.", + "video_name": "2ZzuZvz33X0" + }, + { + "Q": "where did the 35 go at 2:11?", + "A": "Sal just factored a -7 out of that part of the polynomial. He divided the two terms by -7 to get -7(s+5). Hope this helps! :D", + "video_name": "2ZzuZvz33X0" + }, + { + "Q": "At 2:50, how does s(s+5)-7(s+5)=0 factor to (s+5)(s-7)?", + "A": "s(s+5)-7(s+5) factors into (s+5)(s-7) because s has been factored out of (s^2+5s) and -7 has been factored out of (-7s-35) both of the factored out forms are (s+5) you combine what you factored out of both sides and you get (s-7) leaving you with the factored form (s+5)(s-7).", + "video_name": "2ZzuZvz33X0" + }, + { + "Q": "At 2:16, couldn't you do s^2-5s+7s-35? It would mean the same thing right?", + "A": "I don t think you can factor the equation in thay form, but mathematically it means the same thing.", + "video_name": "2ZzuZvz33X0" + }, + { + "Q": "When solving a quadratic equation by factoring, if both equations could equal zero how come this is not included in the answer? Sal mentions around 3:45 that both could equal zero. In the above example the answer is given as s=-5 or s=7 but not s=-5 and s=7. Why is this? In the equation it makes sense that both could equal 0 as 0x0=0 but how can the answer be s=-5 and s=7?\n\nThanks!", + "A": "s=-5 makes one factor 0. s= 7 makes the other factor 0. Those are two different solutions to making the equation 0. But we didn t know until we did the factoring that the two factors would lead to two different zeros. It could have some out, for example, like this: (s+5)(s+5)=0. Then s= -5 would make both factors zero, and that would be ok because 0*0 = 0.", + "video_name": "2ZzuZvz33X0" + }, + { + "Q": "Wouldn't the (s+5), in about 2:45, be squared because there is two of them? I didn't think that you could just get rid of it or ignore it..", + "A": "Emily, We had s(s+5) - 7(s+5) We are combining like terms. The second (s+5) doesn t just disappear it is just combined. Think of the s+5 as being apples . s apples - 7 apples = (s-7) apples. We can do the same thing with (s+5) instead of apples s (s+5) - 7 (s+5) = (s-7) (s+5) I hope that helps make it click for you.", + "video_name": "2ZzuZvz33X0" + }, + { + "Q": "At 2:51 Sal wrote the equation as (s+5)(s-7)=0. When factoring quadratics, how do you know which constants are supposed to come first, like, in this case, 5 is the first constant and -7 is the second constant? That usually gets me when solving quadratic equations by factoring.", + "A": "It doesn t matter which comes first. The commutative property of multiplication tells use that the order we multiply in doesn t matter. Example 2x3 = 3x2. Apply the same property to the factors: (s+5)(s-7) = (s-7)(s+5). The order of the factors does not matter. Hope this helps.", + "video_name": "2ZzuZvz33X0" + }, + { + "Q": "at 2:09 why does he put the plus or minus sign?", + "A": "When we multiply +9 x +9 we get 81 also when we multiply -9 x -9 we still get 81. so the square root can be + or - 9. therefore he writes + and - as the root can be either in + or -.", + "video_name": "tRHLEWSUjrQ" + }, + { + "Q": "at 5:46 how did he get b+6", + "A": "Because, the sum of a+b must equal -4 and the product of a*b must equal -60. He just brute force went thru all the combinations possible until finding that +6 and -10 satisfy this. (a+6)(a-10) = b^2-4b-60", + "video_name": "STcsaKuW-24" + }, + { + "Q": "i didnt get what it meant in 5:00 could someone explain it to me??", + "A": "He is saying that the b s are not the same he just used b and a instead of x and y", + "video_name": "STcsaKuW-24" + }, + { + "Q": "i notice at 0:29 sal factor the number with -1 ? why he do that? can someone explain me?", + "A": "If you factor a negative number, -1 is a factor. and then you can focus on factoring the rest which is now positive. Also, -1 is a perfect cube, so you can do the cuberoot (-1) = -1.", + "video_name": "drhoIgAhlQM" + }, + { + "Q": "At 0:31 he says something about finding what 0 is equal to.", + "A": "He s not finding what zero equals, he said setting your to zero to solve for x. It is mathematically equivalent to frame the equation as 0 = x as it is to state x = 0.", + "video_name": "6agzj3A9IgA" + }, + { + "Q": "1:53 what is the meaning of willy-nilly? without-worry?", + "A": "When I ve heard this used, it has always meant to do something in a random manner, haphazardly, without any method or planning, in any way you please without thinking.", + "video_name": "6agzj3A9IgA" + }, + { + "Q": "At around 5:15, Sal says that the t-distribution has fatter tails because the small sample size causes an underestimation of the standard deviation of the sampling distribution of the sample mean.\n\nWouldn't a smaller sample size make you overestimate the standard deviation? And that is what leads to fatter tails? Could someone clarify this for me? Thank you!", + "A": "Too large an SEM would give too large an interval; too small too small. Fatter tails means a larger percentage of the area (probability) at higher SD. So you would need more SDs to get the same probability. So it looks to me like the fatter tails would tend to compensate for underestimating SEM. Why do you think that smaller sample size would overestimate the SEM? It gives a larger SEM, yes (the smaller the sample, the less accurate the sample mean is likely to be). Is it enough larger?", + "video_name": "K4KDLWENXm0" + }, + { + "Q": "at 1:37, how could 10 hundreths and 7 hundreths make sense", + "A": "10 hundredths + 7 hundredths = 0.17 = 1 tenth + 7 hundredths. 1 hundredth = 0.01", + "video_name": "qSPwUDmpnJ4" + }, + { + "Q": "at 5:41 Sal mentions a \"rule of thumb\". I'm new to statistics, but I can't seem to find it in my books or these videos. What is the \"Rule of Thumb\" and is there a video I'm missing?", + "A": "Rule of thumb is just an expression, it means a good generalization or a simple way to remember something. There is no single Rule of Thumb. :P", + "video_name": "5ABpqVSx33I" + }, + { + "Q": "At 5:54, how did Sal already find the b for Slope-Intercept Form?", + "A": "He distributed the -2/3(x+3) in the point-slope form.", + "video_name": "-6Fu2T_RSGM" + }, + { + "Q": "7:01 if -2/3X was positive, would the answer be 2/3x-y=4? or 2/3x+y=4?", + "A": "yes.", + "video_name": "-6Fu2T_RSGM" + }, + { + "Q": "at 7:00, can there be a standard form without an A?", + "A": "There will always be an A, it s just a coefficient. It can be 0 though, in which case the term does not exist.", + "video_name": "-6Fu2T_RSGM" + }, + { + "Q": "at 2:24 how did you get the slope? that is what confused me because when i tried it it didnt work", + "A": "0-6 over 6+3 = -6 over 9 Simplify -2 over 3", + "video_name": "-6Fu2T_RSGM" + }, + { + "Q": "At 6:48 where did you get the 4 from?", + "A": "It is simply the same equation as the one underneath slope-intercept form, because -2+6=4.", + "video_name": "-6Fu2T_RSGM" + }, + { + "Q": "3:00 of the video; I thought 4 to the exponent of 3 times 5 to the exponent of 3 would give you a different answer then then 4x5 to the exponent of 3. So I do not understand the logic of this.", + "A": "(4x5) to the third is (4x5)x(4x5)x(4x5). Because it is multiplication, we can move the numbers around, getting 4x4x4x5x5x5. 4x4x4 is 4 to the third, and 5x5x5 is 5 to the third. So, (4x5)^3 = 4^3 x 5^3.", + "video_name": "rEtuPhl6930" + }, + { + "Q": "At the end of the video, when he gives the problem, he says at 5:45 that the problem can be written as (3^2 * (3^2)^8)^-2.... but, it couldn't be (3^2 * 3 * 3^8)^-2? It would be a different answer, but it is following the rules in the same way...how could this be? Someone please?", + "A": "In (3^2 * (3^2)^8)^-2 , the second 3^2 is the expanded form of 9... thus 9 becomes 3^2 (3^2)^8 is 9^8 3 * 3^8 is 3^1+8= 3^9 It is pretty clear here that 9^8 and 3^9 is not the same.. And I don t see what rule you re saying you re following..could you explain that part?", + "video_name": "rEtuPhl6930" + }, + { + "Q": "At 2:56, why isn't (2x9)^100 =18^100? why is it 2^100 x 9^100?", + "A": "They are the same thing. See the example at 3:00.", + "video_name": "rEtuPhl6930" + }, + { + "Q": "2:59 of the this video. Doesn't this break the \"order of operation\" because you do what is in the parenthesis first then work your way out?\n\nalso in ths video and the previous video before this one, the subtitle at the bottom seem to flash a lot or something.", + "A": "Because they are all multiplication, we can rearrange the numbers any way we want, using the distributive property.", + "video_name": "rEtuPhl6930" + }, + { + "Q": "at about 6:10, when Sal has (3x2x(3x2)to the 8th), why does he only multiply the 8th to the second 3x2, and not both, because they are all within the larger parentheses?", + "A": "First of all it is not multiplication, but power (3^2*(3^2)^8) Power always applies to item it is after. 3^2 means 3 in power 2. The second power applies to 3. The power of 8 is after the closing parentheses, so it only applies to items in parentheses. (3^2)^8 means 3 to the power of 2 and all of that is to the power of 8.", + "video_name": "rEtuPhl6930" + }, + { + "Q": "At 5:32 Sal expresses 9^8 as 3^16 to be able to calculate the product of two exponents with the same base. It looks like you could instead express 3^2 as 9^1 and come up with a final answer of 9^-18 instead of 3^-36. The numbers are equivalent but is one answer better by convention?", + "A": "You are absolutely correct. It just depends if you want your base to be a prime number. If that is your goal you will always come up with the same answer, which has some elegance.", + "video_name": "rEtuPhl6930" + }, + { + "Q": "What does si mean and theda.2:20", + "A": "Psi and theta are Greek letters that usually denote angles.", + "video_name": "MyzGVbCHh5M" + }, + { + "Q": "at 2:01 what does si has mean?", + "A": "Psi (not si) is a letter in Greek alphabet (\u00ce\u00a8). Mathematicians use Greek letters to write angles. They often use other letters : \u00ce\u00b1(alpha), \u00ce\u00b2(beta), \u00ce\u00b3(gamma), \u00ce\u00b8(theta)", + "video_name": "MyzGVbCHh5M" + }, + { + "Q": "how does he know psi 1 equal 1/2 theta 1 at 8:15 in the vidio? i didn't undrstand the proof. i don't think i saw a proof. like wise for scy 2 and thaita 2 at 8:20", + "A": "Sal wasnt really proving anything in particular. All he wanted to show was that the centre neednt be within the arc being subtended. And he just did that using stuff that he had taught before", + "video_name": "MyzGVbCHh5M" + }, + { + "Q": "At 0:32 what does transversal mean?", + "A": "A transversal is a line that intersects two other lines. A transversal can be useful in determining whether the two lines it intersects are parallel.", + "video_name": "LhrGS4-Dd9I" + }, + { + "Q": "At 2:12, if both are increasing then don't the negatives cancel out and become positive?", + "A": "You are comparing the slopes, not multiplying the slopes. Both lines are negative, so both lines slant down from left to right. The slope of line F is decreasing faster because its slope is more negative than the slope of line G. Hope this helps.", + "video_name": "fZO-JylMFqY" + }, + { + "Q": "At somewhere around 8:00 (it's hard to tell; for some reason this video doesn't show me the time) Sal adds a squared and b squared. I don't understand how he was able to do this. Wasn't he talking about two different triangles?", + "A": "both of the triangles add up to make the larger one; he s trying to get a math statement that applies to the larger one.", + "video_name": "LrS5_l-gk94" + }, + { + "Q": "how does he figure out for what n means at 6:20?? i am very confused too!!!", + "A": "Since he is trying to get n by itself, he multiplies 8/36 with 36/8. They cancel out, and you are left with n. What you do to one side you do to the other. 10 x 36/8=360/8. There is one n left, so n=360/8. That s your answer.", + "video_name": "GO5ajwbFqVQ" + }, + { + "Q": "Couldn't Sal have just converted 5/4 into 1.25 at 0:60 instead of going through all of the 36*5/4 stuff?", + "A": "5/4 = 1.25 and 1.25 * 36 = ?? it is difficult to calculate However if we solve (5/4) * 36 it is equal to (36/4) * 5 = 8 * 5 = 40.Thus we neednt get answer in decimals if it can be cut. This method is fast and easy and removes converting into decimal part.", + "video_name": "GO5ajwbFqVQ" + }, + { + "Q": "The point of the video is to Multiply and Divide Scientific Notation, right? So how come at 2:19 you add? Is it something about exponent rules? If so, can someone please explain it, and, if not, can someone please tell me how? Thanks. And also, why do you have to change the number at 4:01? Thanks in advance for the help.", + "A": "Its an exponent rule. 10^2 x 10^3 is equal to 10^(2+3) because (10 x 10)x(10 x 10 x 10)= 10^5", + "video_name": "xxAFh-qHPPA" + }, + { + "Q": "At 5:17 what does adjacent mean? I forget. Thanks", + "A": "Adjacent means next to .", + "video_name": "TgDk06Qayxw" + }, + { + "Q": "at 5:57 does khan mean 0, cos(2x)>1 this is how it works: as x>o; cos(2*0)=cos(0)=1 cos(0)=1 so it is 8*1 which is 8 hope that helped", + "video_name": "BiVOC3WocXs" + }, + { + "Q": "@12:25, when Sal multiplied 10^17 by 10^-1, by the rules of multiplication, shouldn't the answer have been 10^-16, rather than 10^16? Thanks, whoever answers.", + "A": "The rules of exponents state that x^a * x^b = x^(a+b) we are adding, not multiplying, so the exponent in Sal s case stays positive as 17 > 1.", + "video_name": "0Dd-y_apbRw" + }, + { + "Q": "At 6:25 for the partial derivative with respect to (x) he did:\n(x^2).2+sin2\n= (2x).2+0\n= (4x)+0\nand I'm ok so far;\nthen he derived (4x) as equal to (4) - yes because (x) becomes 1.. But I thought we already derived x^2 as 2x :-/\nWhat i'm missing?", + "A": "The last line from 4x+0 to 4 is not a derivation, he just replaces x with its value, which is one ^^", + "video_name": "AXqhWeUEtQU" + }, + { + "Q": "at 1:30, how did you come up with 50 divided by 4 when you said 50 times 25?", + "A": "True. Sal said 50 times 25 percent. 25% is equivalent to 1/4. So that s why he divided 50 by 4.", + "video_name": "OBVGQt1Eeug" + }, + { + "Q": "At 7:53, how is -5 the square root of -\u00e2\u0088\u009a25? I understand that -5*-5 is equal to 25, since the negatives cancel out.\n*Note: I inserted the square root symbol by holding down on ALT and then typing 251 on the keypad.", + "A": "Since the negative sign is out of the parenthesis, it is negative, like if you learned what absolute value is, you ll know -I-5I is -5, since the negative is out of the absolute value signs, but if you are talking about the square root of negative 25, the answer is 5i, which you ll learn about later", + "video_name": "-QHff5pRdM8" + }, + { + "Q": "At 4:20, Sal said 22/7 is a rational number. However, 22/7 is a irrational number, it keeps on repeating. Please help me understand.", + "A": "22/7 is definitely a rational number. As you can see it is the ratio of two integers - and that s the definition of rational. You re right though its decimal expansion does go on forever, but the crucial point is that it does repeat. 22/7 = 3.142857 142857 ... Repeating decimals can always be converted back to a fraction. 22/7 is often used as an approximation to \u00cf\u0080, but \u00cf\u0080 is irrational and its decimal expansion never ends and never repeats.", + "video_name": "-QHff5pRdM8" + }, + { + "Q": "From 3:53 to 4:23 you said that 22/7 is rational number but, from 6:54 to 6:58 you said that pi is irrational. But, pi=22/7 and 22/7 is not an irrational number. So, how can you say that pi is irrational?", + "A": "22/7 does not = Pi. It is only an approximation for Pi, just like 3.14 is an approximation of Pi. Compare the numbers: Pi = 3.141592653589793238462643383... 22/7 = 3.142857142857142857142857... This is a repeating decimal, the digits 142857 repeat. The decimal values in Pi never repeat and never terminate. So, Pi is an irrational number. 22/7 is the ratio of 2 integers, so it is a rational number. Hope this helps.", + "video_name": "-QHff5pRdM8" + }, + { + "Q": "At 4:51, how would do solve a system of equation using substitution with 3 variables and it is a fraction?\nexample: x/3+y/4-z/2=24\nx/2+y/3+z/4=20\nx/4+y/2+z/3=25 ( these are made up equations)", + "A": "Really, nothing has changed. You just solve for a variable and substitute it into another equation. If you have trouble with it, I recommend you look at easier examples of a system with 3 equations, and look into rational expressions. I m afraid I m too lazy to solve the example problem for you since it s quite a pain to simplify fractions that many times.", + "video_name": "u5dPUHjagSI" + }, + { + "Q": "I don't get the part @ 1:15. Can someone explain", + "A": "The problem is x-4y=-18, -x+3y=11.At 1:15, they are just combining like terms from both equations.They re adding x and -x and which the x and the -x cancel out because it s 1x and -1x. They re adding -4y and 3y and they get -y.They add -18 and 11 and get -7. -y=-7 Divide both sides by -1 and get y=7 -7=-7 Then substitute the y values into the equations.x-4(7)=-18, - x+3(7)=11 x-28=-18 Add 28 to both sides and get x=10 -x+21=11 Subract 21 from both sides -x=-10 Divide both sides by -1 and get x=10 x=10,y=7", + "video_name": "NPXTkj75-AM" + }, + { + "Q": "i dont get the part at 0:44 . how does he know what those little lines are if there not labled?", + "A": "It s okay @supergirlygamer he knows about those because no s are written at the interval of 5 and there are 4 little lines between those intervals therefore, every little line represents 1 unit for e.g. -5 | | | | 0 | | | | 5 above there are 4 lines between the interval so, filling those gaps -5 -4 -3 -2 -1 0 1 2 3 4 5 I hope this clears your doubt :)", + "video_name": "Ddvw2wEBfpc" + }, + { + "Q": "At around 2:55 in the video, is Sal essential combining the operations of -1R2 and R2 + 2R1? That confused me at first...", + "A": "He s doing 2R1 - R2. Your suggestion that he s combining the operations of -1R2 and R2 + 2R1 doesn t look right because the R2s would cancel out leaving 2R1. I might be reading your question wrong though...", + "video_name": "_uTAdf_AsfQ" + }, + { + "Q": "At 1:11 Sal said the word \" trend\". What does trend mean?", + "A": "trend means pattern basicly", + "video_name": "mFftY8Y_pyY" + }, + { + "Q": "At 2:10, is Sal explaining the Triangle Inequality Theorem from geometry?", + "A": "Well, sort of. Maybe the opposite, because he is explaining WHY the sum of two vectors can t be greater than the sum of their magnitudes, using that Theorem, not trying to prove it.", + "video_name": "0t8W4JFpP2M" + }, + { + "Q": "Can we write that A is a subset of B? This is at 2:25 in the video.", + "A": "No. A has more elements than set B. This is denoted by other term called Superset . A is a superset of B.", + "video_name": "1wsF9GpGd00" + }, + { + "Q": "At 3:36, Sal said (x-2)^2 is \"always positive\" but I think it could be zero too. So shouldn't it be always non-negative?", + "A": "Yes, it should be always non-negative .", + "video_name": "dfoXtodyiIA" + }, + { + "Q": "At 2:45 how was x^2-4x+4 equal to (x-2)^2? Please answer. Thanks.", + "A": "To factor the quadratic, you need to find 2 factors of +4 (the last term) that also add to -4. The 2 factors are: -2 (-2) This creates the factors of (x-2)(x-2) or (x-2)^2 If this doesn t make any sense, then I recommend you go to Algebra 1 and review the section of lessons on Polynomial Factoring. Hope this helps.", + "video_name": "dfoXtodyiIA" + }, + { + "Q": "At about 4:52, why does he use a fraction and a number for r?", + "A": "When you multiply same bases, you add exponents, so 4/3 + (4)1/2 = 10/3 which is an improper fraction, but to make it a proper fraction, we get 3 1/3. So 3 sets of 3 rs come out of the cubed root and one r stays in which he does not get to until the very end of the video. He does the same thing with s when he gets 8.5 which is the same as 8 1/2.", + "video_name": "4F6cFLnAAFc" + }, + { + "Q": "At 1:20, why does sal use theta instead of a, b, c, etc?", + "A": "We use theta for angles in math. It is not so important now, but when you take trigonometry, you will use it all the time.", + "video_name": "b0U1NxbRU4w" + }, + { + "Q": "at 3:48 how did he get ninety out of 180-2 theta? im confused!!", + "A": "thank you! that just made it alot easier! :)", + "video_name": "b0U1NxbRU4w" + }, + { + "Q": "0:52 why do you factor", + "A": "So that we can manipulate all the other variables in an equation to find the value of a missing variable.", + "video_name": "NuccqpiUHrk" + }, + { + "Q": "At around 12:00 , Sal said that the functions are the inverse of each other. I understand what inverses are, since I've learned it in Algebra videos, but how can I tell that they're inverses? Is there any way to prove it? Thanks.", + "A": "We define arcsin, arccos, and arctan (also known as sin\u00e2\u0081\u00bb\u00c2\u00b9, cos\u00e2\u0081\u00bb\u00c2\u00b9, and tan\u00e2\u0081\u00bb\u00c2\u00b9) to be the inverses of sine, cosine, and tangent functions respectively. There is no proof for this as it is something we defined. It s like asking for a proof that a square has 4 sides.", + "video_name": "G-T_6hCdMQc" + }, + { + "Q": "At 2:04 cant 12/45 also be divided by 2?", + "A": "No. 45 is a odd number, therefore if you did 45/2 you would get 22 with a remainder of 1", + "video_name": "_btQus9HV_I" + }, + { + "Q": "At 2:25 , 8-3=5. How is it negative? Is it because we're moving towards left and conventionally, it is negative. I need a conceptual clarity there. Thank you :)", + "A": "Yes, it is because in order to move from 8 to 3 on the x-axis, you have to go backwards on the coordinate plane, which means that it will be negative.", + "video_name": "v_W-aaB1irs" + }, + { + "Q": "In 4:06 Khan draws his graph from the bottom to the top. Wouldn't it make more sense if he were to draw it from the positive region to the negative region? Considering the fact that Theta is greater than -3pi/2 and has a less obtuse angle measurement than -pi. Meaning if you draw Theta counterclockwise, wouldn't this be a more reasonable array?", + "A": "Since the angle is negative, it makes sense to me to go in the negative direction, clockwise. There is no negative region , but an angle can be in a negative or positive direction, regardless of where it is on the unit circle.", + "video_name": "soIt2TwV6Xk" + }, + { + "Q": "Can someone explain what \"sin\" is at around 9:40 -- ish?\nIs there a video on \"sin\"? If there isn't it would be helpful\nto add one. Thanks!", + "A": "sin stands for the sine function, which is an elementary trigonometric function. It s sort of hard to explain here, but basically: Given a right triangle with one of the acute angles as a , sin(a) would be the ratio of the side opposite to a over the hypotenuse. There are several videos on trigonometry, I think.", + "video_name": "UmiZK6Hgm6c" + }, + { + "Q": "At 7:50 how can you know that it is a right triangle? How do you know that the bisector of the obtuse angle is perpendicular to the base?", + "A": "Starting from the 60-60-60 triangle, when you bisect one of the angles, you end up with two 30-60-90 triangles because you created the 30 and the 60 stays the same which means the other has to be 90. In the case that he uses, he has bisected two of the sixty degree angles to create a 30-30-120 angle. When you bisect the 120 degree angle, you end up with two 60 degree angle, and the 30 degree angle does not change, so you still end up with a 30-60-90 triangle.", + "video_name": "UmiZK6Hgm6c" + }, + { + "Q": "at 6:55, Sal says that when it biomes pi/2, the slope becomes infinity. But, tan(\u00ce\u00b8) is always one, since its on the unit circle. so even if it does reach pi/2 or beyond that, wouldn't it still be equal to one? I don't understand why the graph does not look like a regular sine or cosine graph. Does that mean a tangent graph cannot go beyond pi/2? What does he mean by reaching infinity?", + "A": "tan(\u00ce\u00b8) is equal to sin(\u00ce\u00b8)/cos(\u00ce\u00b8), when the angle approaches \u00cf\u0080/2: - sin(\u00ce\u00b8) starts to approach 1. - cos(\u00ce\u00b8) starts to approach zero. Since the denominator goes to zero, the function goes to infinity. The tangent line is 1 (i.e., equal to the radius of the unit circle) just when sin(\u00ce\u00b8) and cos(\u00ce\u00b8) have the same magnitude (the sides of the triangle have the same length). That happens at \u00ce\u00b8 = \u00cf\u0080/4. At \u00ce\u00b8 = \u00cf\u0080/2 it s undefined (because it never reaches infinity) and so at \u00ce\u00b8 = -\u00cf\u0080/2, when it goes to negative infinity.", + "video_name": "FK6-tZ5D7xM" + }, + { + "Q": "in 0:10 what if the denominators were not the same? could that even happen?", + "A": "Later you will learn to make denominators that are not the same the same. You will multiply the fractions to make them equal in order to subtract. For example: 3/4 - 1/2 The denominators are not the same, so you must make them equal by multiplying 1/2 by 2/2 to end up with: 3/4 - 2/4 And now you can subtract and get: 1/4", + "video_name": "UbUdyE1_b9g" + }, + { + "Q": "At 2:46, what are those two arrows doing on the lines?Also, how come the shape isn't a irregular quadrilateral?", + "A": "Hi Jonathan! The arrows signify that the two lines that Sal drew are parallel. The figure drawn has 1 pair of parallel sides, therefore it is a trapezoid. Yes, it is irregular, because the sides and angles are not all equal.", + "video_name": "-nufZ41Kg5c" + }, + { + "Q": "at 4:55 it gets cofusing what does he meen?", + "A": "If you look on the right hand side you ll see that he has written 291 x 6 = 1746 So if 291 x 6 = 1746 Then just add a zero to both sides, and you get 261 x 60 = 17460 and then...add another zero to both sides and it becomes 291 x 600 = 174600", + "video_name": "omFelSZvaJc" + }, + { + "Q": "2:30 what is the difference that the brackets made does it mean anything", + "A": "The brackets basically mean that you other parentheses inside of them, and so you solve whats inside of them. They are the same thing as parentheses, they just look different, so when you are solving the equation you don t get all of the parentheses mixed up. A case to use brackets would be here: a((-b+c)(d-e)(f+g)) Instead you would have: a[(-b+c)(d-e)(f+g)]", + "video_name": "gjrGd9TjjnY" + }, + { + "Q": "At 4:24, isnt -3-24 just negative three beside negative twenty-four?", + "A": "-3-24 can be rewritten as -3 + (-24).", + "video_name": "gjrGd9TjjnY" + }, + { + "Q": "At 6:55 he missed a traingle", + "A": "He figured it out, just keep watching.", + "video_name": "qG3HnRccrQU" + }, + { + "Q": "sooo at 3:13 does the mean that the sum of interior angles are just how many triangles are in the polygon or hexagon?", + "A": "Yes, the sum of the interior angles is = 180 * (number of triangles polygon is divided into)", + "video_name": "qG3HnRccrQU" + }, + { + "Q": "At 0:03, how could there be negative degrees?", + "A": "Instead of the degrees going counter-clockwise (for positive), the degrees go clockwise from 0 degrees to get negative degrees (i.e reverse from positive).", + "video_name": "O3jvUZ8wvZs" + }, + { + "Q": "I don't get what he starts doing at 1:05, can someone explain please?", + "A": "The 1, the 3 and the 9 are all digits in the tens column. They are actually counting tens. 1 ten is 10, 3 tens are 30 and 9 tens are 90. He is just explaining what the numbers are actually representing. Comment again if this doesn t make it clearer for you.", + "video_name": "Wm0zq-NqEFs" + }, + { + "Q": "Adding three digit numbers like Sall (0:01) is simple, but is there a trick to adding faster in your mind? Thanks.", + "A": "Watch the videos for Regrouping.", + "video_name": "Wm0zq-NqEFs" + }, + { + "Q": "What does carry mean, at 0:16?", + "A": "When you add, you carry by putting numbers more than 10 to the top so it can be easier to solve.", + "video_name": "Wm0zq-NqEFs" + }, + { + "Q": "I'm sorry, I still don't get how Sal solved the problem around 5:00.\nThey are \"fundamentally different ratios\"...what does that mean?", + "A": "He s comparing the 5 to 1 and 4 to 1 ratios of y to x, and saying that they have different slopes. Therefore, the two lines must intersect somewhere at one point. If you ve watched enough videos on here, you ll notice that Sal frequently (over)uses the word fundamentally, to just mean certainly or definitely. He didn t mean anything special by the use of the word fundamentally here.", + "video_name": "SuB1gkto9LU" + }, + { + "Q": "As stupid as this question might sound, I don't exactly understand why at 1:54 Sal says that the angle is theta as well. Like how? (I understand the parts after that, but I can't seem to figure out why we are taking it as theta. Forgive me, if I've missed something and hence have the doubt; I like thorough explanations of even the simplest things because I tend to get muddled up quite often). Thanks!", + "A": "The yellow ray is the reflection of the green ray over the \u00f0\u009d\u0091\u00a6-axis, which means that if the green ray forms the angle \u00f0\u009d\u009c\u0083 with the positive \u00f0\u009d\u0091\u00a5-axis, then the yellow ray forms the angle \u00f0\u009d\u009c\u0083 with the negative \u00f0\u009d\u0091\u00a5-axis.", + "video_name": "tzQ7arA917E" + }, + { + "Q": "At 3:56 why isn't the (x,y ) coordinates are (cos theta, sin theta)? Why is the angle taken as (pi - theta) ?", + "A": "You are almost right. Where the yellow ray hits the circle, the ( x, y ) co-ordinates could either be labelled as Sal does or as ( - cos theta, sin theta). Since the x-co-ordinate is in a negative direction, cosine theta has to be negative. This gives us two of the many trig identities : cos ( pi - theta ) = - cos theta sin ( pi - theta ) = sin theta", + "video_name": "tzQ7arA917E" + }, + { + "Q": "At 4:34, is there no horizontal asymptote in this expression? Can anyone explain why? I thought a rational expression must have an asymptote.", + "A": "Why would a rational expression have to have an asymptote? Do you have a reason for thinking this? Let s say x=a, a being any possible real number. What s (x+1)/(x+1)? Try to get the answer to this by yourself. (x+1)/(x+1) is always = 1 for any possible x, so it can t have a vertical asymptote. Does it have a horizontal one? Well, it always = 1, but that s not an asymptote, because the graph doesn t approach f(x) = 1, because it s already 1 everywhere.", + "video_name": "ReEMqdZEEX0" + }, + { + "Q": "how did sal get rid of the cube root and the ^3? do they cancel each other out? 4:27\nis there a video explaining ^^^?", + "A": "The cube root of a number is another number that, when you multiply it by itself three times, gives you the original number. For example: The cube root of 27 is 3, because 3*3*3 = 27 if a\u00c2\u00b3 = x, then \u00e2\u0088\u009bx = a If we substitute, we have \u00e2\u0088\u009ba\u00c2\u00b3, which is just a. Sal s example had \u00e2\u0088\u009b7\u00c2\u00b3 which is just 7 (the number he used in the next step of the problem).", + "video_name": "8y7xP4zz0UY" + }, + { + "Q": "why does he say at 2:06 that 343 isn't divisible by 2 when the sum of 3+4+3 is 10 which is divisible by 2?", + "A": "adding the digits is only a test for divisibility for 3 and 9", + "video_name": "8y7xP4zz0UY" + }, + { + "Q": "at 1:01 why are the fours at the bottom of the denominator not negative I am confused :/", + "A": "a negative exponent is not applied to the coefficient, it just flips the exponential with a negative exponent to the other side of the divide line and thus makes the exponent positive. It is not (-4)^-3 power which would have three negative fours.", + "video_name": "CZ5ne_mX5_I" + }, + { + "Q": "( 3:37 ) Could (12^-7) / (12^-5) be written as (12^5) / (12^7) ?", + "A": "Yes it could because the exponents are negative. Correct!", + "video_name": "CZ5ne_mX5_I" + }, + { + "Q": "In 1:35 how does he get 8 1/3?", + "A": "He divided 100 by 12, which is 8 with a remainder of 4. The remainder can be written as 4/12, which can be reduced to 1/3, so 8 1/3", + "video_name": "jOZ98FDyl2E" + }, + { + "Q": "at 0:41 he's dividing them but couldn't you just write out the problem in long division too?", + "A": "Sal is working with ratios and rates which are types of fractions. This is why he is writing them initially as fractions. If you wrote the long division form first, it would work provided you got to the answers Sal has written out.", + "video_name": "jOZ98FDyl2E" + }, + { + "Q": "At 1:00, where does the formula come from?", + "A": "One place it comes from is after deriving the quadratic formula, you end up with (-b \u00c2\u00b1 \u00e2\u0088\u009a(b^2-4ac))/(2a), so the -b/2a where the line of symmetry is and thus the x coordinate of the vertex and the (\u00c2\u00b1 \u00e2\u0088\u009a(b^2-4ac))/2a is the distance away from the line of symmetry of the zeroes.", + "video_name": "IbI-l7mbKO4" + }, + { + "Q": "At 2:00, what is Sal doing? I don't get how or why he adds 16...", + "A": "Sal is using a method called Completing the square . it involves an equation (M*1/2x)^2. in his example if you take M which is the Middle term(8) and divide by 2 you would get 4. then squar it and you get 16. so that is why he adds and subtracts 16. this wont change the answer at all because +16-16=0. so your adding a fancy way of saying +0", + "video_name": "IbI-l7mbKO4" + }, + { + "Q": "At 6:50, he says that a light bulb is on if it has an odd number of factors, so if the bulb number is prime, is it always off(except for 1)?", + "A": "Yes, every prime number, by definition, has exactly two factors, meaning that it will always be off.", + "video_name": "WNhxkpmVQYw" + }, + { + "Q": "8:00 is the answer all square numbers will be on?", + "A": "Yes pretty much the square numbers that are smaller than 100.", + "video_name": "WNhxkpmVQYw" + }, + { + "Q": "At 8:11, what is a hypersphere?", + "A": "Hypersphere is a generalization for any sphere that is more than 3D. Normally we define a sphere in 3D as x\u00c2\u00b2+y\u00c2\u00b2+z\u00c2\u00b2=1. But you can generalize this to as many dimensions as you want. You could have a 4D sphere or a 500D sphere, but in general, they are referred to as hyperspheres.", + "video_name": "iDQ1foxYf0o" + }, + { + "Q": "At 0:32, how does one know when to write x/y and when to write y/x?", + "A": "its just another way to write division 4/2=2/4 and here sal is just saying 14/2 =/= 2/14 so in proportions you need bigger number on top...", + "video_name": "qcz1Cm_-l50" + }, + { + "Q": "at 2:05, does the table of values always has to start with 0 ?", + "A": "No, sometimes the value of x and never even be 0. However, it s often easier for to start at zero if x can indeed be 0 because that way you can find the y-intercept.", + "video_name": "86NwKBcOlow" + }, + { + "Q": "0:15 why he multiple for 6?? not for 3 i got confused.", + "A": "least common multiple of x/3 and 1/6 is 6. *if you want to add to x/3 and 1/6 you need the denominator be the same.", + "video_name": "CJyVct57-9s" + }, + { + "Q": "At 7:31 he did 10^200 divided by 10^50. How did he get 150 if 200 + 50 gives you 250.", + "A": "10^200/10^50 the exponent is subtracted 200-50, only multiplication is it added 200+50.", + "video_name": "kITJ6qH7jS0" + }, + { + "Q": "4:16 of the video to 5:00. How does 2 with the exponent of 8 + 2 with the exponent of 8 eventually get broken down into 2 with the exponent of 9; it doesn't seem to make any since because they both would have different equations?", + "A": "this happens as 2^8 + 2^8 = 2 * 2^8 which can be simplified as 2^9", + "video_name": "kITJ6qH7jS0" + }, + { + "Q": "At 1:35, why does Sal put parentasis around the 6?", + "A": "He puts parenthesis around the 6 because that mean multiplication or simply a form of it", + "video_name": "Rcb7ZUTOQ1I" + }, + { + "Q": "At 6:30 Sal write dt, but I cant see where he get that from. Anyone can help? Thanks", + "A": "dt is the differential, you put it at the end of the integration expression. If you re wondering why its dt and not dx ; its because it parametric, so your functions are functions of t - f(t) - and not like the usual functions of x - f(x). Hope i could help!", + "video_name": "99pD1-6ZpuM" + }, + { + "Q": "At around 3:19, doesn't point D also have a y value of 6?", + "A": "If you look carefully, point D is slightly below 6 and probably has a y-value of 5.5. This is later mentioned at 5:44.", + "video_name": "P3IlneCNm8A" + }, + { + "Q": "on the 30:60:90 triangle why do you square root it by three? thats the only part that lost me (:\n\nThanks,\nAshley", + "A": "It s a right triangle, so we can apply Pythagoras (a\u00c2\u00b2 + b\u00c2\u00b2 = c\u00c2\u00b2). The hypotenuse is c = 2, a = 1, and b = \u00e2\u0088\u009a3: a\u00c2\u00b2 + b\u00c2\u00b2 = c\u00c2\u00b2 1\u00c2\u00b2 + (\u00e2\u0088\u009a3)\u00c2\u00b2 = 2\u00c2\u00b2 1 + 3 = 4", + "video_name": "UKQ65tiIQ6o" + }, + { + "Q": "What do you mean of function of s in 0:16?", + "A": "He means that we will find the area of a triangle that has a side length of s, not of a specific triangle, like one with sides of length 4 or 7 or something. Working this way, the equation he finds will work for any equilateral triangle, and you just have to substitute the value of s (side length) into the equation to get the area.", + "video_name": "UKQ65tiIQ6o" + }, + { + "Q": "I am really puzzeled about the 7:26-7:35 portion of the video where Sal goes from a^2 =1/2 to\na = 1/sqrt 2....how did he do that?", + "A": "2a^2=1 --------- 2 ......2 The first 2 s cancel out and your left with: a^2 =1/2", + "video_name": "fp9DZYmiSC4" + }, + { + "Q": "At 03:36 isnt he marking wrong? He is marking cosine on the Y axis, but on the begining of the video he said cosine of data is the X, axis! And sine was the Y axis! Now im really confused!", + "A": "I understand the confusion. When he said cosine of theta is the x-axis, he was basically saying Instead of the x-axis and integers (i.e. -2, -1, 0, 1, 2 ect...) we are going to call it the theta-axis and use radians. Also, instead of saying cos(theta) = y-axis he mixed up the measurement for the two axis. One axis has been turned into radians (theta, cis(theta)), the other has been left in integer number form. (x/y form).", + "video_name": "fp9DZYmiSC4" + }, + { + "Q": "At 0:25 is one fourth just like a quarter?", + "A": "Think of one whole as 100. If you think of money, one dollar is 100 cents. One quarter is 25 cents out of the whole 100 cents. So a quarter is one fourth(a quarter) of a dollar(a whole).", + "video_name": "gEE6yIObbmg" + }, + { + "Q": "At 7:27, Sal said that if r= -1, then the values would keep on oscillating. However, if you actually work it out, the series would converge to a/2. If we say that the series, is S, than S= a-a+a-a+a-a+a-a+a... . Also, a-S would equal a-a+a-a+a-a+a... . This is equal to the original series S. So, we can say a-S=S. Then we get a= 2S. Therefore, S=a/2. Is there something I am doing I am not disregarding in my calculuations?", + "A": "Your logic seems plausible but fails the epsilon-delta test, which is the ultimate test for whether a series converges. There is no delta for which larger values of n will produce S values closer than, say, a/4 (a possible epsilon). We know this because it s clear that there is no point beyond which the sum stops oscillating between a and 0. Your result of a/2 is the average of the two values between which the sum oscillates, not the value to which the sum converges.", + "video_name": "wqnpSzEzq1w" + }, + { + "Q": "At 7:50 Sal said that the boundaries are -1 < r < 1 ,but why not between 0 < r < 1 ?", + "A": "The problem is that using 0 sign into a < sign or when to leave it the way it is? can someone explain? at 2:58 on the video...", + "A": "You change the sign whenever you divide or multiply by a negative number. And only that condition, anything else you keep the sign as it was.", + "video_name": "y7QLay8wrW8" + }, + { + "Q": "At 0:52 when he multiplied 3 by both sides, that same number has to correspond to the denominator for example if the dominator was -3, you multiply by -3 yes?", + "A": "Correct. This is because we need to get rid of the denominator. Does that make sense? And most don t know why you switch the sign, but I believe you do - otherwise you would have asked to know. I hope I helped!", + "video_name": "y7QLay8wrW8" + }, + { + "Q": "2:50, why do you swap numbers?", + "A": "He doesn t swap, he flips the inequality around because you are dividing by a negative number.", + "video_name": "y7QLay8wrW8" + }, + { + "Q": "At 1:28, Sal simplifies 2/3 by multiplying it by three(because he's doing that to the other side of the inequality sign). He then crosses out both threes and leaves the two. Why? How does that work? It's probably really obvious, but can someone answer this?", + "A": "Sure!, A fraction is just a number divided by another number, therefore to undo the division you multiply. Sal crossed them out because they cancel out each other. For example, if you have 6/3 that will equal 2. then multiply by three to get 6. But you should just multiply by the denominator and cancel out everything at the beginning to get 6! Hope this helps!", + "video_name": "y7QLay8wrW8" + }, + { + "Q": "At 2:47, I'm a little confused .. Why the limit isn't (7) as we are approaching point (8) as it's part of the function at this point? &if so how is the limit exist as we are approaching different points? Please somebody enlightens me!", + "A": "You can say that f (8) = 7 but that s not the limit. The limit is concerned with the value NEAR a point but not AT the point. And notice that between 2:50 and around 3:15 or so Sal checks the values on both sides of 8 and finds the limit to be 1. It s ok that the limit (1) does not match the value of f (8) = 7. It just shows that curve is discontinuous at that point.", + "video_name": "_bBAiZhfH_4" + }, + { + "Q": "at 4:24 -- what makes Sal determine it's t2/2? Is this a formula?", + "A": "Well, I think the deduction of this equation comes out here: d=Va*t, where d is the distance,and Va means the average velocity. while Va=(Vf+Vi)/2, where Vf is the final velocity and Vi is the initial velocity (in this case Vi=0). In addition,we know that the difference of velocity Vdelta=Vf-Vi=g*t. So,Vf=g*t+Vi,since Vi=0, so Vf=g*t+Vi=g*t+0=g*t. Now replace Vf by g*t: d=Va*t=(Vf+Vi)/2*t=(g*t+Vi)/2*t=(g*t+0)/2*t=g*t/2*t=g*t^2/2.", + "video_name": "m6c6dlmUT1c" + }, + { + "Q": "on 4:18 Hilbert who?", + "A": "David Hilbert. He was one of the leading number theorists of his time.", + "video_name": "ik2CZqsAw28" + }, + { + "Q": "At 5:15 what did she use to make the squiggle?", + "A": "She uses a Pipe Cleaner to make the squiggle. The brand is Dill s", + "video_name": "ik2CZqsAw28" + }, + { + "Q": "at 0:46 to 0:53 he said 9 is > or = to 5 i don't get that", + "A": "With rounding if the number is 5 or more than 5 than you round it up. For example you have 1.5, you d round it up to 2.", + "video_name": "tx2Niw7aJJ8" + }, + { + "Q": "At 09:39 in the video I thought there were 16 different scenarios.(Is it possible?)", + "A": "is what possible? It s written in red at the top of the video: 6/16 = 3/8 .. 6 scenarios for 2 heads are possible and there are 16 different total scenarios for heads or tails.", + "video_name": "8TIben0bJpU" + }, + { + "Q": "at 4:04 he sal listed outcomes for exactly one head... I think he forgot to list [TTTH]. Am I right?", + "A": "He accidentally wrote TTHT twice in his equation, however [TTTH} is in row 3, column 4 of his table.", + "video_name": "8TIben0bJpU" + }, + { + "Q": "I'm baffled as to why we keep using our original sample standard deviations as estimates for the population SDs (c. 6:50) once we're assuming the null hypothesis. If (and I might be barking up the wrong tree here) the hypothesis is that there's no meaningful difference whatsoever in weight loss effect between the two diets, why should their SDs remain distinct when imagined across the whole population? If the two groups' data are basically identical when viewed globally, shouldn't their SDs be identical too?", + "A": "because it would lead to same answer. if you sample twice from the same population then the best variance estimator is ((n1-1)var(x1) + (n2-1)var(x2))/(n1+n2-2) ... i know you understand which symbol means what here .. now calculate for variance of difference of means of two iid samples from this population using the just calculated estimate of variance. It is the same thing as what sal does", + "video_name": "N984XGLjQfs" + }, + { + "Q": "Whats a \"reciprocal\"? (4:07)", + "A": "For any fraction, its reciprocal is created by flipping the fraction. Example: 3/4: its reciprocal is 4/3 -5/2: its reciprocal is -2/5 6: Note 6 as a fraction is 6/1. Its reciprocal = 1/6 In the video, Sal is using the reciprocal of (5x^4)/4, which would be 4/(5x^4). Hope this helps.", + "video_name": "6nALFmvvgds" + }, + { + "Q": "at 1:10 Vi say says twogons. instead of twogons could you use biagons or bigons?", + "A": "Yes, you could use biagons, but that sounds ridiculous, so most people just stick with 2-gons.", + "video_name": "CfJzrmS9UfY" + }, + { + "Q": "In the video, at 00:40 she says 'you can draw a four pointed star, but that's not really a star by the way you're defining your stars' -why not?", + "A": "Well, later on in the video she explains the whole star game. You can t really use that method with four points.", + "video_name": "CfJzrmS9UfY" + }, + { + "Q": "at about 3:25 why does it bother you that a 25 pointed star a square star?", + "A": "It doesn t bother her that a 25 pointed star is a square star. What bothers her is the method by which the 25 pointed star is made. If it is made from 5 pentagons, then that is clearly a square star. But what if it is made from 5 5 pointed stars? Then, although P=25 still, Q=10 instead of 5.", + "video_name": "CfJzrmS9UfY" + }, + { + "Q": "at 1:25 why is 9x^2 not equal to 3x^2 ?", + "A": "We have 9x^2. We want to make it into (ax)^2. 3x^2 does NOT equal 9x^2. However, (3x)^2 does equal 9x^2. Why? When we have (3x)^2 the exponent distributes to both terms (the 3 and the x) so we have: (3x)^2 = 3^2x^2 = 9x^2.", + "video_name": "jmbg-DKWuc4" + }, + { + "Q": "At 5:25, You said that the median is the middle number, but at 2:25 you said that that average is the typical or the middle as well, but my teachers say to associate average with mean, so are there many averages or if not, whats the deal?", + "A": "Yes, there are many averages. The mean is the most common average, so it s often used as a synonym even though it properly should not be.", + "video_name": "h8EYEJ32oQ8" + }, + { + "Q": "Isn't the part in (3:53) where he finds the arithmetic mean, when he says to add and find the sum then divide, that also I think is one way how to find the average, right?", + "A": "to find Mean: add up all of the numbers and then divide by how many numbers there are Median: The middle number. if there are two in the middle, add them up and divide by two to find the middle of those two numbers Mode: Whatever number is the most common (there can t be two modes. The number has to be repeated the MOST. There cant be two highest repeated numbers.)", + "video_name": "h8EYEJ32oQ8" + }, + { + "Q": "At 2:08 Sal started explaining average. Are average and mean the same thing, because Sal never said anything about mean", + "A": "Yes! Average and mean are synonyms. They both involve the total sum of a set of numbers and dividing it by how many numbers given.", + "video_name": "h8EYEJ32oQ8" + }, + { + "Q": "If 6 5/x = 14, what does x equal to?\nFor Example:\n6 multiplied by x = 6x\n6x + 5= 8.75/x\n8.75/x = 14\non 7:38", + "A": "x = 0.625", + "video_name": "9IUEk9fn2Vs" + }, + { + "Q": "At 2:49, why is it 7x + 7 ?", + "A": "With the distributive property, you have to multiply each term in the brackets by the 7, so multiply 7 by x, and 7 by 1 to give you 7x + 7.", + "video_name": "9IUEk9fn2Vs" + }, + { + "Q": "i dont understand anything, in 3:29 how did -7x+x+2 = 7x+7-7x turn into -6x+2=7?\nhow did -7x turn into -6x? it seems impossible to me", + "A": "-7x+x=-6x", + "video_name": "9IUEk9fn2Vs" + }, + { + "Q": "In 1:16 where where doe's the speaker get 1/5 from ? And do I have to watch all of the pre-algebra videos before I understand where 1/5 comes from ?", + "A": "Thanx, then I ll have to watch all of the pre-al videos.", + "video_name": "9IUEk9fn2Vs" + }, + { + "Q": "At 2:53, how was Sal able to tell whether it was sin or cosine?", + "A": "When x is 0, the value of the cosine equation would be 1, and (0, 1) is not a point on the graph. When x is 0, the value of the sine equation would be -2, and (0, -2) is a valid point on the graph. Thus, the cosine equation can be eliminated.", + "video_name": "yHo0CcDVHsk" + }, + { + "Q": "At 0:24 why did the problem say the time when you don't need it? And why did it say how many wheels?", + "A": "Because the skill this video is trying to teach is how to look at a word problem and find the information that you need. So Sal said the time and how many wheels so you could find out what was the important part of the problem.", + "video_name": "6QZCj4O9sk0" + }, + { + "Q": "At 2:13, why is 3^2 not the same as 2^3?", + "A": "It doesn t work that way. 3*2 may be the same as 2*3, but exponentiation does NOT have the same property. Think about it. 2^3 implies 2*2*2, which we can calculate to be 8. 3^2 implies 3*3 which we can calculate to be 9. Obviously, 9 does not equal 8. This hold true for all exponents. In general, a^b does not equal b^a. (There are exceptions. One that I know is 2^4 does equal 4^2. Both are 16. This is only one instance. Otherwise, they usually are not the same.)", + "video_name": "XZRQhkii0h0" + }, + { + "Q": "I really do not get this one. At 4:00 he points at a and says this is the heighth of the parallelogram. The parallelogram first starts with two sides of A and two sides of C. After comparing them he says the area is A^2 , this insinuates that Side A and Side C are the same length and that is just not true?", + "A": "Actually it is true. As he notes at 3:52 and repeats twice is that the height of the paralllelogram is a also which is shown in the triangle on the left. area of a parallelogram is base times height, so it is a \u00e2\u0080\u00a2 a or a^2. It does not have anything to do with the sides being the same length, and with the drawing, they cannot be the same length because c forms the hypotenuse of the right triangle which by definition must be longer than either leg.", + "video_name": "rcBaqkGp7CA" + }, + { + "Q": "At 0:15, what does F(x) mean?", + "A": "F(x) is just a notation to express a function in terms of x. It is the same as y = function, but that tends to be used in lower-level mathematics.", + "video_name": "1LxhXqD3_CE" + }, + { + "Q": "The only thing I don't understand is the (x-c) part at 3:15, why put the c and not simply use x, x^2, x^3 and so on, like on the Mclaurin series?", + "A": "It s a shift. It s like shifting the parabola function, y = x^2, three places to the left. You d write it as y = (x+3)^2. To shift it c to the left, you d use (x-c)^2. Or,in the case of the Taylor expansion, multiply the derivative(s) by (x-c).", + "video_name": "1LxhXqD3_CE" + }, + { + "Q": "At 7:42 can someone explain how he got x+sqrt of 2=0 and the same for x-sqrt2= 0?", + "A": "Sal recognised that the binomial x^2 - 2 could be viewed as the difference of two squares, so he factored it into sum and difference of the two numbers being squared, ( x and \u00e2\u0088\u009a2 ).", + "video_name": "x9lb_frpkH0" + }, + { + "Q": "at approximately 14:20, how would you write\n-1 (x^2 + 5x - 24) as a two parentheses group? like this? ---------> -1 (x-3)(x+8)\nor, do you leave it as is?", + "A": "Yes, you can write it the way you suggested: -1 (x-3)(x+8) Exactly how you would write it depends on what you need to do to reach the final answer. You can also use the distributive property to distribute the -1 into ONE (not both) of the factors: -1 (x-3)(x+8) = (3-x)(x+8) however, doing this is rather unusual.", + "video_name": "eF6zYNzlZKQ" + }, + { + "Q": "At 0:57, does he use the FOIL method?", + "A": "Yep! First Outside Inside Last", + "video_name": "eF6zYNzlZKQ" + }, + { + "Q": "at 14:46 we do not have to multiply negative 1 to both (x-3)(x+8) ?", + "A": "No, because -x*-x would equal positive x\u00c2\u00b2. The goal is to get -x\u00c2\u00b2. So, -x*x = -x\u00c2\u00b2 Hope this helps!", + "video_name": "eF6zYNzlZKQ" + }, + { + "Q": "At 13:55 it says that we turn 24 into 1 and 24,and then that if it is negative 1 and 24 it would be positive 23. Can you explain this?", + "A": "(a+b)^2 = a^2 + 2ab + b^2 Sal meant that 2ab would = positive 23 if a and b were -1 and +24", + "video_name": "eF6zYNzlZKQ" + }, + { + "Q": "I instantly went from getting it to COMPLETELY LOST.\n\nAt 2:14 he says, \"But we have i times i, or i squared, which is negative one.\" He lost me right there. I have no idea how he can say i squared is negative one. Can anyone explain this to me?", + "A": "The definition of i is the number whose square is -1. What he said was completely valid. You should watch the videos on i.", + "video_name": "Z8j5RDOibV4" + }, + { + "Q": "At 1:18 sal says 0/0 is undefined why?", + "A": "Division by zero is an operation for which you cannot find an answer, so it is disallowed. You can understand why if you think about how division and multiplication are related. 12 divided by 6 is 2 because: 6 times 2 is 12 Now image 12/0: 12 divided by 0 is x would mean that: 0 times x = 12 But no value would work for x because 0 times any number is 0. So division by zero doesn t work.", + "video_name": "Z8j5RDOibV4" + }, + { + "Q": "1:50 i still dont understand what the difference is between midrange and range? help?", + "A": "The midrange is an attempt to show in a single number how well or bad a class is doing, so it s pretty similar to the average and the median. The range is only used to show how big the difference is between the best and the worst student. It can t be used to judge how well or bad a class is doing. Only if all of the students are on a similar level or if there are huge differences between the students.", + "video_name": "DGZNaKnbQo0" + }, + { + "Q": "At 3:49, how is the abs(-x^2/3) the same as abs(x^2/3) ? Wouldn't the negative sign have to be like this: abs{(-x^2)/3}, for the negative sign to disappear since -x times -x is positive x^2? I know this is very basic, but it's confusing me...", + "A": "Let s solve it in the normal way: |-x\u00c2\u00b2/3| < 1 \u00e2\u0086\u0094 -1 < -x\u00c2\u00b2/3 < 1 \u00e2\u0086\u0094 -3 < -x\u00c2\u00b2 < 3 \u00e2\u0086\u0094 3 > x\u00c2\u00b2 > -3 Because x\u00c2\u00b2 >= 0 > -3 for every x so we just need to take care x\u00c2\u00b2 < 3 \u00e2\u0086\u0094 -\u00e2\u0088\u009a3 < x < \u00e2\u0088\u009a3.", + "video_name": "aiwy2fNF_ZQ" + }, + { + "Q": "How come 13/10. At 2:40?", + "A": "A one above a zero is is 10/10 s where are the 0.3 is 3/10 s. If you add 3/10 s to 10/10 s you will get 13/10 s.", + "video_name": "3szFVS5p_7A" + }, + { + "Q": "If you did not simplified 2xh+x*/h and you are finding the limit of h as it get closer to 0, doesn't the question become undefined number since it is dividing by zero. I tried it with a function of x+2 and it gave me h/h after all the simplifying. Did I do something wrong? Video(5:22 - 8:28)", + "A": "The limit takes care of that issue, we are not dividing by 0, but by a number that approaches 0. The slope of the function x+2 is 1, so it makes sense you ended with the answer of h/h since the Limit as h approaches 0 of the function h/h = 1", + "video_name": "IePCHjMeFkE" + }, + { + "Q": "At 7:46 how does he get 6 from 6+delta(x)??", + "A": "Basically we re asking what happens as the \u00ce\u0094x approaches zero. So pretend that \u00ce\u0094x is actually zero and then you have 6 + 0 and 6 + 0 = 6.", + "video_name": "IePCHjMeFkE" + }, + { + "Q": "At 1:20, why do you have to move left, why can't you move right. Is it because the place values get lower when you go to the eftl", + "A": "Exactly. If you go to the left, the place value gets 20 times greater. For example, there is the ones place, the tens place, hundreds place, thousands place, ten thousands place, hundred thousands place, millions place, ten millions place, and you get the idea. But, if you go to the right side, the place value gets 1/10 smaller.", + "video_name": "iK0y39rjBgQ" + }, + { + "Q": "Okay... he lost me at 0:14. I have no idea what's going on, can someone help me?", + "A": "a difference of square is a binomial in which both the terms are perfect squares and they are subtracted a2-b2 if you have a difference of squares expression here is how you would factor it a2-b2=(a+b)(a-b) in this case it is x2-49y2 a=x b=7y x2-49y2=(x+7y)(x-7y)", + "video_name": "tvnOWIoeeaU" + }, + { + "Q": "When, at 1:09 he shows what happens as a perfect square for A and B (that b is 7y, because 49 is a perfect square) would that work for say, 5, where for example it might be b=sqrt(5)? Or am I jumping to conclusions?", + "A": "it wouldn t be a perfect square, so no.", + "video_name": "tvnOWIoeeaU" + }, + { + "Q": "At 1:29, Sal says that 0.1 is bigger than 0.070. How is that possible when 0.070 has more digits than 0.1", + "A": "One of the easiest ways to compare decimals, it to give them the same number of decimal digits. Adding zeros on the right of the decimal does not change the original value of the number. Change 0.1 into 0.100 You are now comparing 0.100 to 0.070 100 is bigger than 70. Thus, 0.1 is larger then 0.070 Another way to look at this is the the further to the right the number is following the decimal point, the smaller the number. The 1 in 0.1 = 1/10. The 7 in 0.070 = 7/100 7/100 is much smaller than 1/10 Hope this helps.", + "video_name": "gAV9kwvoD6s" + }, + { + "Q": "at 4:52 he says over 2 does that apply all the time or just for this instance?", + "A": "The midpoint formula is ((x1+x2)/2,(y1+y2)/2). This applies all the time.", + "video_name": "Efoeqb6tC88" + }, + { + "Q": "At 4:06, What do you mean by rotating the plane in infinite directions?", + "A": "the plane could be facing any direction but you don t know by the representation.", + "video_name": "J2Qz-7ZWDAE" + }, + { + "Q": "at 3:26 Sal said that 49+9 is 57 but it is 58 right?", + "A": "Yes. This is a known error in the video. And, a box does pop up and tell you the error and correct info.", + "video_name": "-U53eHKCLcg" + }, + { + "Q": "At 3:33 the value would be square root of 58.", + "A": "Hello Soham, Correct, this is a know problem based on the number of comment it has received... Regards, APD", + "video_name": "-U53eHKCLcg" + }, + { + "Q": "at about 1:50, how do you get 2y=y+3? also, when you subtract y from both sides, you still need to divide by the 2, so wouldn't y be equal to 1 and 1/2? sorry if this is a stupid question but I could really use the help!:)", + "A": "To answer the first part of your question, we just get the +3 by combining -4 and +7. As for the second part, when you subtract y from 2y, you just end up with y, so you don t have any number you need to divide the 3 by. Hope that helped!", + "video_name": "uzyd_mIJaoc" + }, + { + "Q": "at 1:10 couldn't \"a\" be a different value", + "A": "Yes, it can. A variable can be any number you choose it to be. For example, X is the most used variable but, in the video Sal used a as the variable. This has no effect in the equation.", + "video_name": "P6_sK8hRWCA" + }, + { + "Q": "This might seem like a pretty arbitrary question, but at 1:37 Sal uses the \"/\" symbol to signify x(a+3-b) over (a+3-b). I've been seeing that \"over than\" symbol a lot in algebra and I was wondering if there was any difference between the over than symbol, \"/\", and the division symbol I'm used to seeing, \"\u00c3\u00b7\"?", + "A": "They mean the same thing. I m honestly not sure why, but once you get past pre-algebra, you stop seeing the \u00c3\u00b7 symbol.", + "video_name": "adPgapI-h3g" + }, + { + "Q": "At 4:06, Sal multiplies the numbers by -1. Do you have to do this?", + "A": "If you didn t do it, you would get: x = (-8-5a)/((-a-b) This fraction is not fully reduced. You would need to factor out a -1 from both the numerator and denominator to reduce the fraction.", + "video_name": "adPgapI-h3g" + }, + { + "Q": "At 1:21 , why does it matter where p is?", + "A": "because the P is the variable for the pizzas. It is with the 8.5 because each pizza is 8.50. If it were with the 42.5, that would mean we are saying the cost of the pizza is 42.50 apiece.", + "video_name": "2REbsY4-S70" + }, + { + "Q": "Around 1:30, he explains that we need to use the pythagorean theory to find the radius r. But can't we just estimate the no. of units from the centre (point -1, 1) to the point (7.5, 1), which also lies on the circumference?", + "A": "sometimes you will need precision in your answers. Pythagorean Theorem will give you as much precision as you need", + "video_name": "iX5UgArMyiI" + }, + { + "Q": "Is obtuse larger than acute?\n\nI LIKE KHAN ACADAMEY!\nAT 5:04", + "A": "Yes, an obtuse angle has one side of the triangle larger than 90*. An acute angle is an angle that is 89* or less. A right angle is exactly 90*.", + "video_name": "ALhv3Rlydig" + }, + { + "Q": "did sal make a mistake by telling indefinite integrals at 0:31 or have I misunderstood ?\n\nAnd one more, how can you just get what dx is ? I mean , I know how to take d/dx but dx ? Please explain succinctly.", + "A": "If either of the bounds of an integral are + or - infinity, then the integral is improper. The video show how to use limits to solve such improper integrals. dx represents an infinitesimal change in x. If you can measure the change in x, the change is not infinitesimal and the change is called \u00ce\u0094x. If you CANNOT measure the change in x, the change IS infinitesimal, and is called dx.", + "video_name": "9JX2s90_RNQ" + }, + { + "Q": "At 5:03, Sal said \"6.5 divided by 450\". Did he make a mistake? Can someone explain this?", + "A": "Yes he made a mistake, and I did not see a correction box, It appears that he should have said 675 divided by 450", + "video_name": "EtefJ85R1OQ" + }, + { + "Q": "0:44 Sal said exponential function f(t) = a . r ^t, is it always necessary, i mean can't exponential function f(t) = a - r^t or\nf(t) a + r^t ?\nWhat is exact definition of exponential function ?", + "A": "The a term doesn t vary exponentially (or at all).", + "video_name": "EtefJ85R1OQ" + }, + { + "Q": "At 1:39, why can't we use product rule or the quotient rule to find the derivative of (1/lnb)(lnx) or lnx/lnb?", + "A": "The KEY thing to notice in this problem is that 1 / ln (b) is just a constant value. And so this problem is not much different than say 5 * ln x. You can pull the constant value out of the expression and just differentiate ln x just like Sal does. This will make the problem simpler.", + "video_name": "ssz6TElXEOM" + }, + { + "Q": "how does he evaluate sin(at) at infinity? at 4:51 he doesn't take that into account", + "A": "sin(at) is a periodic function and it oscillates between -1 and 1. The same thing is for cos(at). So the expression in parentheses is always confined between some two numbers no matter how big t is. This expression is multiplied by e^(-st). When t goes to infinity, e^(-st) goes to zero. Zero times some finite number is still zero. Hope it helps!", + "video_name": "-cApVwKR1Ps" + }, + { + "Q": "At 1:40 why does Sal factor out -e^(-st) and not (-e^(-st))/s? Isn't it possible to factor that out as well?", + "A": "Yes, but it helps better with the evaluation later on since you d end up with something weird like 1/infinity/infinity or something like that.", + "video_name": "-cApVwKR1Ps" + }, + { + "Q": "At 3:59, shouldn't Sal get 62__ something?\n\nA confuzzled child.", + "A": "No, he got the right answer but he made his 0 look like a 6. I also got confused but saw his mistake.", + "video_name": "TvSKeTFsaj4" + }, + { + "Q": "at 1:52 ,why did (x+5)^2 became (x- -5)^2 ? I'm doomedddd", + "A": "Sal wrote it that way to get it into the form of the equation for a circle, which is (x - h)^2 + (y - k)^2 = r^2. In other words, the center of the circle is at (h,k), where h and k are the numbers being SUBTRACTED from x and y. Hope this saves you from being doomedddd!", + "video_name": "thDrJvWNI8M" + }, + { + "Q": "At around 3:36 Sal said that at 0 hours there were 550 pages left to read. Couldn't of Naoya also read in minutes? So there aren't really exactly 550 pages in the book right?", + "A": "Merely changing to minutes would not change the y-intercept because the rate would be equivalent (55 pages/hour = 55/60 or 11/12 pages/minute). So after 240 minutes (4*60), Naoya still had 330 pages to read. so 240 * 11/12 = 220 pages. Think about what is happening, you are changing pages/hour by dividing by 60 then you are multiplying by 60 to convert to minutes, the two 60s cancel each other out so 55/60 * 4 * 60 is the same as 55 * 4.", + "video_name": "W3flX500w5g" + }, + { + "Q": "At 2:23, Sal talks about using ratios of the sides to find the area of the equilateral triangle. Could you use the pythagorean theorem to find the height of the equilateral triangle and then calculate the area that way?", + "A": "yes, you could do that.", + "video_name": "QVxqgxVtKbs" + }, + { + "Q": "At 3:20, how is 5 tenths equal to 500 thousandths?", + "A": "Because the zeros after the decimal point don t carry any information if no other number follows them. For instance, 5 is equal to 5.0 or 5.00 or 5.000 and so on. But if there is a number after the zeros, then they are significant and can t be removed. Like this: 5.00002 is NOT equal to 5.2. That s why, in your example, 0.5 = 0.500. Since no other number comes after the final zeros, they are not important and can as well be removed.", + "video_name": "G7QiIkYfeME" + }, + { + "Q": "at 2:20 Sal says that a 1cm x 1cm x 1cm cube is 1 milliliter...why wouldn't this be 1 centimeter?", + "A": "The cube is equal to 1 cubic centimetre. A cubic centimetre is equal to 1 milliliter .", + "video_name": "LhMEqsL_M5o" + }, + { + "Q": "At 1:10, where did you get -66?", + "A": "He s factoring by grouping . He starts by taking a (the coefficient of f^2) and multiplies it by b (the coefficient of f). Hope this helps :)", + "video_name": "d-2Lcp0QKfI" + }, + { + "Q": "At 1:27, How did he get 9?", + "A": "Ah, 45 - 36 = 9", + "video_name": "EFVrAk61xjE" + }, + { + "Q": "At 1:24 sal writes the fraction 9/13. Why did he put a nine instead of four? Can someone please help me??", + "A": "because it is 9 away from the first root over the total amount of numbers in between", + "video_name": "EFVrAk61xjE" + }, + { + "Q": "How do you know which numbers are a and b in the equation? At 13:21 he says that a=3 and b=4 (because he took the square roots) but how do you know that a isn't 4 and b isn't 3? For ellipses you know that a is the bigger number, but what do you know for hyperbolas? Thanks!", + "A": "a is 3 so 3 squared gives u nine and b is 4 so 4 squared gives u 16.", + "video_name": "S0Fd2Tg2v7M" + }, + { + "Q": "at 2:43 sal said standard but wrote slandard why", + "A": "He probably made a mistake...you should report it is the tag named report a mistake ....", + "video_name": "ZgFXL6SEUiI" + }, + { + "Q": "At 2:50 why did Sal call the binomial a second degree polynomial? Didn't he say that it was not a polynomial", + "A": "We reserve the word polynomial for expressions in which all the terms have positive, non-fractional exponents. When Sal earlier said some expressions did not qualify as polynomials, he was excluding one that included a square root (which is a fractional exponent of 1/2) and also excluding one that had a negative exponent. He wasn t excluding ordinary binomials, which are included in the definition of polynomial.", + "video_name": "ZgFXL6SEUiI" + }, + { + "Q": "at around 14:40, wouldn't the width of the green square be 1/2b ?", + "A": "You can t assume that it is half of b from the picture. Never trust the picture. This is why Sal denoted it as c.", + "video_name": "ZgFXL6SEUiI" + }, + { + "Q": "At about 6:08 you talked about descending order, what would the degree of a term without an exponent be?", + "A": "If the term is something like 2x, then there is an exponent on that variable. If one is not written, it s implied that it is to the 1st power. If there is no variable at all, like in 4, you would say that it is degree 0. The only other weird case is that a term of 0 is said to have no degree.", + "video_name": "ZgFXL6SEUiI" + }, + { + "Q": "At about 3:40, Sal says that 5 is the highest exponent on a variable. Does this mean that a degree can only come from the highest exponent on a variable, or can it be on a normal number as well?", + "A": "The degree of a polynomial is by definition the largest exponent of the variable. So, yes we only consider the exponent of the the variable. So, x\u00c2\u00b2 + 50\u00c2\u00b3\u00c2\u00b9\u00e2\u0081\u00b7 would still be a second degree polynomial.", + "video_name": "ZgFXL6SEUiI" + }, + { + "Q": "At around 2:07 Sal said that the degree of the polynomial is the value of the largest exponent, whereas my algebra teacher says it is the sum of the exponent values. Who is wrong? Thanks.", + "A": "The both are! When working with polynomials of 1 variable, what Sal said is correct, assuming the polynomial is in canonical form, that is, you don t have terms like (x^3)(x^4), which in canonical form would be written x^7. When you have polynomials of more than one variable, you need to sum the exponents of each term, for example, (x^4)(y) has degree 5 and (x^2)(y^2)(z^2) has degree 6.", + "video_name": "ZgFXL6SEUiI" + }, + { + "Q": "9:43 Why is is a^2(x^2-2xf+f^2+y^2)? Why is the \"a\" outside of the parentheses? In other words, why isn't it just a^2x^2-2xf+f^2+y^2? Why are there parentheses?", + "A": "Because without the parentheses, the a^2 will not be distributed to the equation that was inside the square root. Without it you just get a^2 times x^2. With them you have to multiply each factor by a^2.", + "video_name": "HPRFmu7JsKU" + }, + { + "Q": "At 2:00 how did he get 36x?", + "A": "When Sal was doing the distributive property 9x(x+4) 9x times x is 9x squared and 9x times 4 is 36x.", + "video_name": "vl9o9XEfXtw" + }, + { + "Q": "at 4:05 how did he get -16?", + "A": "exponents with negitive bases", + "video_name": "vEZea0EThus" + }, + { + "Q": "Around 1:00, Sal mentioned \"functions that are not equations.\" Could anyone help clarify how there are some functions that are not equations?", + "A": "Functions aren t equations. They re mappings between sets. Here s a function: f: \u00e2\u0084\u009d \u00e2\u0086\u0092 \u00e2\u0084\u009d, x \u00e2\u0086\u00a6 2x + 1 It s a function from the set of real numbers to the set of real numbers, and a real number x is sent to the real number 2x + 1. A function may be represented with an equation. For example: f(x) = 2x + 1 defines (mostly) the same function as above. (It doesn t explicitly define the domain and range of the function.)", + "video_name": "l3iXON1xEC4" + }, + { + "Q": "hey at 1:40 doesn't 3 ^1 equal zero?", + "A": "Anything to the first power is equal to that anything. Take 3^2, that s 3 * 3, right? So 3^1 = 3. And note that 3^0 = 1, not 0.", + "video_name": "6WMZ7J0wwMI" + }, + { + "Q": "At 6:32, Sal says function is undefined at x2. He meant is non-differentiable, because it is defined right?", + "A": "I definitely think that Sal is trying to say where the DERIVATIVE is undefined. Because when the function is undefined at a point, we will not have a critical point because this point does not exist: ie, it is not defined", + "video_name": "lDY9JcFaRd4" + }, + { + "Q": "7:12 We can create tangent lines at a point that crosses the function?", + "A": "Yes, a line can be tangent at one point on a curve but then cross it later when the curve takes a U-turn later on down the road.", + "video_name": "lDY9JcFaRd4" + }, + { + "Q": "At 4:50, why don't the endpoints count as maxima/minima?", + "A": "They can be maxima/minima on a closed interval (but not always), but in the video, we are not interested in them because we only want to show point (non-endpoint) that is min/max will have f (a)= 0 or undefined. Endpoints are max/min but they don t necessarily have f (a)=0 or undefined. Hope that helps.", + "video_name": "lDY9JcFaRd4" + }, + { + "Q": "This is a bit confusing. At 2:24 he said that we don't have more than one local minimum but at the far right of the graph of the function shouldn't the part of the graph that fall under the x-axis count as a local minima, or am I just not paying attention", + "A": "A local minimum has higher points at both sides. This point only has higher one one of the sides so it is not a minimum.", + "video_name": "lDY9JcFaRd4" + }, + { + "Q": "I don't understand how the three becomes negative. I thought it was just a subtraction sign? 2:11", + "A": "it s because it s part of the number. If it has a negative sign in front of it it s because the number is negative ex. 4 - 3 = 1 the 3 is a negative.", + "video_name": "xMsG9hvqzbY" + }, + { + "Q": "In the second problem at 3:37, why does he write 6z + 2, instead of 6z + 1, when it's written 1 in the equation?", + "A": "Well, that s BECAUSE IT s 2(3z+1)=2(3z)+2(1) IT s SO SIMPLE!", + "video_name": "xMsG9hvqzbY" + }, + { + "Q": "At 5:45 shouldn't \"a sub n\" equal a*n!", + "A": "Yes, but a equals 1. a sub n is not a. I hope this clarifies the video!", + "video_name": "dIGLhLMsy2U" + }, + { + "Q": "There may be a mistake at 5:47. You say it is equal to n!, when it is equal to n!a.", + "A": "No mistake. Here a = 1. And just like how we don t write 1x\u00c2\u00b2 + 1x - 2, but rather x\u00c2\u00b2 + x - 2 we don t write n! as 1n! Does that make sense? (If a was not equal to 1, then we would need to include it)", + "video_name": "dIGLhLMsy2U" + }, + { + "Q": "On problem 51. or (2:55)\n\nCan you prove to me why all the four right triangles are congruent? I know they are... but why? D:", + "A": "The shape in the middle is a square, so all four sides are equal. When it is placed inside another square, the triangles that it creates (4), are all congruent, because the four side lengths of a square are equivalent. If the shape in the middle were a rectangle that is not a square, there would be two congruent triangles, and another two congruent triangles, which are different from the first two. So, because they are both squares, the triangles are congruent.", + "video_name": "6EY0E3z-hsU" + }, + { + "Q": "At 1:16, how is a a^2 + b^2 equal to a^2 + 2ab +b^2?", + "A": "You misunderstood. It says that (a+b)^2=a^2+2ab+b^2. => (a+b)^2=(a+b)(a+b) Distribute => a*a+a*b+b*a+b*b => a^2+ab+ab+b^2 => a^2+2ab+b^2.", + "video_name": "6EY0E3z-hsU" + }, + { + "Q": "What does he mean at 5:39. \"But if I just cancelled these two things out, the new function would be defined when x = -8\". Why -8?", + "A": "Because when x= -8, the denominator is 0, so the function is undefined. But if we cancel the factors (x+8), then we could plug in x= -8 without dividing by 0, so the function would defined. So since one is defined at x= -8, and the other is not, cancelling the (x+8) changes the function, which we don t want.", + "video_name": "u9v_bakOIcU" + }, + { + "Q": "@ 2:16 where does -16 come from?", + "A": "Ok, so he s trying to factor the trinomial (ax^2+ bx + c). This method is what I learned as the long method. He is just finding the LCM of a and c so he can split bx so it is easier to factor it out. It is just finding or converting numbers into more factor able numbers and group them. This is what Sal calls factoring by grouping. I hope this helps.", + "video_name": "u9v_bakOIcU" + }, + { + "Q": "At 6:06 Khan is explaining why x can't be -8, but he didn't say that it can't be -2. So, does this mean that x can be -2? This will also give you a 0 in the denominator.", + "A": "No, x cannot be -2 either, but it is not necessary to specify it because x - 2 is still in the simplified expression. You have to put the x does not equal -8 because the term that would have made that clear has vanished.", + "video_name": "u9v_bakOIcU" + }, + { + "Q": "at 2:19 why has he divided 1* 10^4 upon 7*10^5 when it is written in the question 7*10^5 than 1*10^4?", + "A": "To find the quotient of exponents you subtract the exponents from the other. If you need more help, you can look at some other of Sal s Exponents videos.", + "video_name": "DaoJmvqU3FI" + }, + { + "Q": "Quick Question at 5:55 he writes cos^2 and theta and sin^2 theta now based on how he wrote it I am wondering if it is cos^(2 theta) or cos^(2) Theta?", + "A": "cos^2(\u00ce\u00b8) is the trig representation for (cos(\u00ce\u00b8))^2.", + "video_name": "n0DLSIOYBsQ" + }, + { + "Q": "at 6:30 Sal mentions break even\nwhat does that mean?", + "A": "Break even is the point when revenue equals expenses and so there is no profit or loss incurred. If the expense amounts to $25 then the break even point is when revenue is $25 also. At this point there will be no loss or profit as 25-25 = 0", + "video_name": "5EdbPz1ZVn0" + }, + { + "Q": "like sal said in 5:36 are all sums of 3 angles 180", + "A": "No, not all angles will sum to 180. Ex: three angles could be 10, 20 and 30. They don t sum to 180. Only three angles of a triangle will always sum to 180.", + "video_name": "BTnAlNSgNsY" + }, + { + "Q": "At 2:30 Sal describes the term 'Complementary Angle\" and states that if two angles add up to 90 degrees then they are complementary. Do the two angles that add up to 90 degrees have to be adjacent?", + "A": "No. (Complementary simply means that, if put next to each other, they would create an angle of 90 degrees; they don t actually have to be next to each other.) The same applies to supplementary angles.", + "video_name": "BTnAlNSgNsY" + }, + { + "Q": "I thought you can't divide by variable 7:00\nor am I missing something here?", + "A": "You can divide by a variable, so long as the variable is not 0 (ie b does not equal k).", + "video_name": "okXVhDMuGFg" + }, + { + "Q": "At 2:30, when he says that the absolute value could also work in ensuring that the value is positive, can someone explain to me why the absolute value isn't used in the equation?", + "A": "In the video, Sal does some algebraic manipulation to achieve the formula of the parabola. It is much easier to derive the parabola if he were to square the expression and take the square root than to take the absolute value of the expression. Both methods yield the same value of the expression; however, the latter method (squaring then taking the square root) allows for more easier manipulation. Hope this helps!", + "video_name": "okXVhDMuGFg" + }, + { + "Q": "In practice sessions video (using hint), of unit vectors at around 2:28 ,he said that we should divide 3 by 5 and also 4 by 5...why should we divide 3 by 5 and 4 by 5?", + "A": "(Note that this question actually refers to the next video.) The problem asked us to find the UNIT vector. In other words, a vector of length 1 unit. We re given a vector of length 5 units (which is 5 times what we want), so we have to scale it down by dividing each of its components by 5.", + "video_name": "9ylUcCOTH8Y" + }, + { + "Q": "at 2:58 Sal says that any real number is greater or equal to 0 but isn't that a whole number?\nisn't a real number greater than 0?", + "A": "Natural numbers: 1, 2, 3... Whole numbers: 0, 1, 2, 3... Integers: ...-3, -2, -1, 0, 1, 2, 3... Real: Includes all positive and negative numbers including the decimals and fractional values.", + "video_name": "qFFhdLlX220" + }, + { + "Q": "Why does Sal keep saying \"the principal root of...\" as opposed to \"the square root of...\"? At 1:30 I heard him say \"the square root of, or the principal root of...\" so does that mean they're the same thing? Because it appears as if he sort of corrected himself.", + "A": "Each square root actually has 2 roots. Consider: 5^2 = 25, but if you square (-5), it is also 25. So, 5^2 = 25 and (-5)^2 = 25. Now, consider square root of 25. Is it 5 or is it -5? We need to know what value to use. So, when you see sqrt(25) , it is understood that the answer should be the principal root or the positive root = 5. If you see - sqrt(25) , the minus sign in front of the radical tells you that your answer should be the negative root = -5. Hope this helps.", + "video_name": "qFFhdLlX220" + }, + { + "Q": "Wait- at 2:37, is tau 2 pi?", + "A": "Yes, tau is equivalent to twice pi.", + "video_name": "FtxmFlMLYRI" + }, + { + "Q": "Sorry, I don't get 0:48-0:52.\nWhy do you need a distance and to pick a point?", + "A": "the distance is the radius and the point is the center", + "video_name": "FtxmFlMLYRI" + }, + { + "Q": "at 1:19 what is a 4 dimensional object", + "A": "Actually, Steven Hawking has speculated that all objects have 4-dimensions, and the fourth dimension is time. Like, as an object grows older, the volume (or whatever you d call it) of it s fourth dimension would increase.", + "video_name": "FtxmFlMLYRI" + }, + { + "Q": "At 00:50,...is multiplying out the Binomial the only way to get rid of the bracket. If we can distribute the exponent in for example (2r)^2 to be 4r^2.....why can't we just distribute the exponent through (x+9)^2 ?", + "A": "Because (a + b)^2 isn t the same thing as a^2 + b^2. Example: (2 + 2)^2 = 4^2 = 16 =/= 2^2 + 2^2 = 4 + 4 = 8 Multiplying the binomial is the correct way.", + "video_name": "bFtjG45-Udk" + }, + { + "Q": "At 4:57, why does Khan use a^2+2ab+b^2 for (a-b)^2 instead of a^2-2ab+b^2? Am I wrong? Why? Thank you!", + "A": "no, he doesn t. he s got it all right", + "video_name": "bFtjG45-Udk" + }, + { + "Q": "Why did Sal distribute the 4x^2 at 6:25 instead of just writing (4x^2+y^2)(4x^2+y^2) like he did for the previous questions?", + "A": "It s more detailed that way.", + "video_name": "bFtjG45-Udk" + }, + { + "Q": "At 1:46 why can Sal simplify any further. Cant he take the square root", + "A": "We don t know the value of x and you can t apply the square root individually like sqrt(4x^2/9+4) =2x/3+2 , it is wrong, so you can t simplify any further from there.", + "video_name": "hl58vTCqVIY" + }, + { + "Q": "So at 6:34, are (0, 2) and (0, -2) the foci of the hyperbola?", + "A": "Those are the vertices of the hyperbola.", + "video_name": "hl58vTCqVIY" + }, + { + "Q": "I don't get it at 3:30. If I type in (40)sin40/30 into my calculator I get approx 0.93. If I type 4/3sin40 I get approx 0.86.", + "A": "It should be 40 sin (40) /30 = .86. Be careful with where parentheses go. What you actually did was 40 sin (40/30) to get .93.", + "video_name": "IJySBMtFlnQ" + }, + { + "Q": "At 3:07, is that \"theta\" like a variable?", + "A": "Yes. Theta can be used like x. But it is usually used for angles so you will see it quite a bit in trigonometry.", + "video_name": "IJySBMtFlnQ" + }, + { + "Q": "I'm lost. 3:42 shows Sal making sin go to the other side by using sin-1. I know it's a cofunction, but is it like a reciprocal? Can someone explain how sin becomes sine-1 when moved to the other side? (Ex: 3x=2, you divide 3 on both sides to leave x, to make x= 2/3)", + "A": "1. Sin(a) \u00c3\u00b7 A = sin(b) \u00c3\u00b7 B 2. Sin(a) = sin(b) \u00c3\u00b7 B * A 3. a = arcsin( sin(b) \u00c3\u00b7 B * A) Since the problem is asking for a specific angle, you have to pull the arcsin to get the specfic angle in this equation. This works for cos, tan, and sin: Sin(x) = y and arcsin(y) = x", + "video_name": "IJySBMtFlnQ" + }, + { + "Q": "At 10:00 the right hand rule , what happens when i change the letters from\na to b and b to a , where is the explanation that\na cross b = b cross a , is true or not ?", + "A": "Compute (a1, a2, a3) x (b1, b2, b3) = a x b and (b1, b2, b3) x (a1, a2, a3) = b x a. Are they the same? How do they compare?", + "video_name": "pJzmiywagfY" + }, + { + "Q": "in the video at 3:25 I want 2 know how to make a hexaflexagon, but it goes to fast. Can you make a slow video on how to make a hexaflexagon?", + "A": "Hleyendecker 2020, the major predicament of alacritous motion in the video can be eradicated! Because Vi shows numerous ways of construction on the hexaflexagon, at 3:22-3:27, a reasonably stagnant-paced clip is displayed to contrive a hexaflexagon in a rare moment of slowness.", + "video_name": "VIVIegSt81k" + }, + { + "Q": "How do we actually fold a hexaflexagon at 0:34? She moves and talks too fast.", + "A": "If you go to the bottom right corner of the video and click on the cog icon (settings), and click on the speed option, you can slow the video down with the options that come up. Hope that helps!", + "video_name": "VIVIegSt81k" + }, + { + "Q": "(6:27) what sal says is wrong. it is less likely for the next toss to be heads if you look at is as a whole. lets say you toss the coin 100 times and you get 90 heads and 10 tails. it is more likely to get that then 90 heads and then 10 tails because there is only combination so theoretically, it is less likely to get a head is less likely in the next toss.", + "A": "True, but nonetheless the more times you flip the more you approach 50/50 results. This person just assumed that there was some underlying force that pulled everything together into theoretical accuracy. But the only way you approach this truth is through sheer quantity of data, there is no invisible force that makes anything more likely.", + "video_name": "VpuN8vCQ--M" + }, + { + "Q": "Why at 4:53 in the video Sal puts down four squared raised to the seventh power equal to four to the seventh power", + "A": "its an error. (4^2)^7 is actually 4^14 he corrected himself at 5:23", + "video_name": "dC1ojsMi1yU" + }, + { + "Q": "At 3:25, Sal says \"...the magnitude or absolute value of Z1...\". He denotes it like |Z1|. Why doesn't he denote it as ||Z1||?", + "A": "Notations are subject to a bit of flexibility. I had a physics teacher in college that consistently referred to the absolute values of vectors. In fact, absolute value is a type of magnitude. So you could legitimately denote it |*| or ||*||. But here, I think Sal opted for the simpler and more familiar notation.", + "video_name": "FwuPXchH2rA" + }, + { + "Q": "13:04 I've tried to make a non-congruent triangle that complies with SSA in CAD and I haven\u00c2\u00b4t being able to do so. Was Sal wrong or there are so few possible triangles that are non-congruent and SSA that I can't find them by trial and error? In any case, many triangles that are SSA are also congruent.", + "A": "Well, the answer was in the More on why SSA is not a postulate video... :S. I should be more careful when asking questions from now on. Equally thanks for your reply.", + "video_name": "8Ld8Csu4sEs" + }, + { + "Q": "When Sal talks the definition of similar (at 2:36) , he says that in geometry similar things have same shape. However, I still wonder if he meant just having same type of form (like triangle, pentagon or rectangle) or if the angles of the figure also have to be the same so two figure can be similar geometrically?", + "A": "Two shapes are similar if:the corresponding sides are proportional and the angles are congruent. The proportionality constant can be one, in which case the sides are the same length, but the definition of similar is the first statement.", + "video_name": "8Ld8Csu4sEs" + }, + { + "Q": "at about 3:15 in the video. Can someone explain the difference between direct and joint? thanks", + "A": "i believe that the difference is that in the direct variation you are dealing with only TWO variables (x and y) and one constant number (k); in the joint variation you are dealing with THREE variables, like Sal said, the example would be the area (A) of a rectangle, which is the width (w) times the length (l), so if you had to insert these into a table, you would have to have THREE columns.", + "video_name": "v-k5L0BPOmc" + }, + { + "Q": "at 3:46 , Can you really just square the 1/3 and then plug it into the radical? I have never seen that before.", + "A": "Yes as you re not changing the equation in any way. You re basically squaring a positive multiple then when you place it inside the radical you re square rooting it again so it s exactly the same multiple. (1/3)^2 = 1/9 sqrt(1/9) = 1/3", + "video_name": "WAoaBTWKLoI" + }, + { + "Q": "is it me or, It appears that at 5:20 sal gave the final answer as if it was (-u^5/5+u^3/3) instead of ( u^5/5-u^3/3) after unwinding the trig and u substitution. please correct me if I'm wrong.\nRegards", + "A": "I don t see any problems with the final answer.", + "video_name": "WAoaBTWKLoI" + }, + { + "Q": "At around 7:30, when he is discussing the trig. ratios, is there any particular reason why, for example, we use adj/hyp instead of hyp/adj? If we used the reciprocal of any of these ratios would it matter?", + "A": "For each of the main trig functions, sine, cosine and tangent, there is another trig function that is its reciprocal: secant is 1/cosine, cosecant is 1/sine, and cotangent is 1/tangent. For an acute angle in a right triangle, adj/hyp is cosine. You can t use hyp/adj for cosine because that s something entirely different (secant) with a graph that looks nothing like the graph of cosine.", + "video_name": "QuZMXVJNLCo" + }, + { + "Q": "where did Sal get the number 7 1/2 from at 1:44?", + "A": "7 1/2 is half of 15", + "video_name": "h0FFEBHBufo" + }, + { + "Q": "At 05:40: \"So a note and the note with twice the frequency, totally are like the same note, am I right?\" Can anybody explain this statement to me, please?", + "A": "The first note is a note on a keyboard (or whatever she was playing at the time) then the second note is twice the frequency, or 1 octave up. so technically, they are the same note, even though they are not pitch. one 8(how many notes in a octave) x 2 (doubling the frequency) = 16(twice the frequency, or 1 octave up from the first note.", + "video_name": "i_0DXxNeaQ0" + }, + { + "Q": "at 1:56 Vi says cochlea, what does the cochlea do?", + "A": "Sound goes into your ear, past your ear drum, past the bones in your ear , into your cochlea and through the nerve to the brain. The cochlea basically processes the sound so you can understand it.", + "video_name": "i_0DXxNeaQ0" + }, + { + "Q": "Hey guys, did you notice that at 1:05 Sal said tenths when he ment thousandths!", + "A": "No! I didn t thanks for letting me know! ;P ;) :)", + "video_name": "BINElq3DFkg" + }, + { + "Q": "How do you know when to leave the circle open or closed on the number line at 3:59", + "A": "You leave the circle open when you need to exclude it from your inequality (less than or greater than inequalities). You shade it in when it is included in the inequality (commonly known as less than or equal to OR greater than or equal).", + "video_name": "FZ2APP6-grU" + }, + { + "Q": "How did Sal just throw in the factor of dx at 3:45? The volume of a real shell is not the area of its outer surface times the depth of the shell, so why should that be the volume when the shell is infinitesimally thin?", + "A": "The volume of the shell, as stated in previous videos, is the circumference times the height of the shell times the width. Here, the width is dx. However, it does not really matter in the end, because you are just taking the definite integral to find the area. Hope that helps!", + "video_name": "SfWrVNyP9E8" + }, + { + "Q": "3:10 Why would you subtract 90 degrees from that equation? I haven't exactly figured that out.", + "A": "Sal subtracted 90 degrees from both sides of the equation to simplify the equation. What I would do instead (personally) is add 90 and 32 to get 122, and then subtract 122 from both sides. 180-122= 58, so either way, you get the same answer. Hope that helps you!", + "video_name": "iqeGTtyzQ1I" + }, + { + "Q": "@2:56 how does it simplify to 1, not the best at algebra", + "A": "1/x * x = 1/x * x/1 = (1*x)/(x*1) = x/x = 1 We multiply 1/x with x, so there s one x at the numerator and denominator.", + "video_name": "iw5eLJV0Sj4" + }, + { + "Q": "at 5:21 i understand that A to the B+C power equals A to the B power times A to the C power but what about if it was negative, as in A to the B-C power. would that make it A to the B power divided by A to the C power or would that just make C negative?", + "A": "Yes, you are correct. A to the B-C power would give you A to the B power divided by A to the C power. Sal actually explains this property at 7:19. Another way of doing this is: A^(B-C) = A^B x A^-C and since A^-C = 1/A^C we can rewrite this as A^B/A^C (A to the B power divided by A to the C power).", + "video_name": "vSijVSL3ChU" + }, + { + "Q": "I dont understand the way Sal's doing these. I paused at 0:06 and factored it by grouping, because it seemed like the obvious way to go. Like this:\n30x^2 + 11xy + y^2\n30x^2 + 5xy + 6xy + y^2\n5x(6x+y) + y(6x+y)\n=(5x+y)(6x+y)\nMultiplying it out, i get back to the beginning.\nI did the problem in the previous video the same way. Is this correct? Or am i doing it wrong and getting the right answers just by accident?", + "A": "I did it the same way you did.", + "video_name": "0xrvRKHoO2g" + }, + { + "Q": "At 2:55, what is meant by derivative of something \"with respect to\" something else?", + "A": "With respect to is generally used to describe the term you are talking about. For example, say you have: f(x) = (x^2)/3 with respect to x, the function is the same, (x^2)/3 BUT with respect to x^2, the function is x/3 Taking the derivative of a function with respect to something basically means you are determining what the derivative function is doing to the term that you re talking about. Hope that helps!", + "video_name": "Mci8Cuik_Gw" + }, + { + "Q": "at 2:17, we could just treat e^(ln 2)^x as a function and use the chain rule to differentiate it, couldn't we?\nbut the ans is different", + "A": "Sal has been solving e^(ln2*x) not e^(ln2)^x. I have hope it is a typo.", + "video_name": "Mci8Cuik_Gw" + }, + { + "Q": "At 3:30 and onwards, how come the 1 in \"anti-deriv: 1+sinx\" isnt accounted for? shouldn't its anti-derivative be x?", + "A": "It s not 1+sin(x), it s 1*sin(x). Which equals sin(x). Or 1*1*1*1*1*1*1*1*sin(x), depending on weather.", + "video_name": "bZ8YAHDTFJ8" + }, + { + "Q": "At 1:52 Sal writes g'(x) = cosx and g(x) = sinx and not {sinx+C}. Can someone explain?", + "A": "Sal chose a convenient antiderivative. Any choice for an antiderivative would yield the same final result. Try the same process choosing a nonzero number for the constant. See what result you get.", + "video_name": "bZ8YAHDTFJ8" + }, + { + "Q": "At 3:40, why isn't the anti derivative of 1 added to -cos x..won't it be x times -cos x?", + "A": "Hmm, are you trying to apply the product rule ? That is only for derivatives. In this case, we are doing the anti-derivative (integral). So when he wants to do the anti-derivative: \u00e2\u0088\u00ab1\u00e2\u008b\u0085sin(x)dx = \u00e2\u0088\u00absin(x)dx = -cos(x) + C the 1 times inside the integral has no effect, since 1\u00e2\u008b\u0085sin(x) = sin(x). Or maybe you had some other reason in mind?", + "video_name": "bZ8YAHDTFJ8" + }, + { + "Q": "At 6:26 Sal Khan says \"... our variance is essentially the probability of success times the probability of failure.\" Mathematically I understand this (Khan walks us through the derivation) but conceptually I don't. If variance is some measure of the spread of values around the mean, how does the product of the probably of success and failure describe the variance?", + "A": "To me, p(1-p) seems like an algebraic simplification without a conceptual component to it. Sometimes algebraic simplifications lead to more conceptual insight, but this one really doesn t.", + "video_name": "ry81_iSHt6E" + }, + { + "Q": "at around 5:37, Sal divided the 2 and the 12, but, don't you have to divide the 27 too or am I just forgetting a rule?", + "A": "(27*12)/2 = (3*3*3*2*2*3)/2 now you can cancel out factors", + "video_name": "8C5kAIKLcZo" + }, + { + "Q": "In 0:26 what does compute mean", + "A": "Compute means to calculate, find, or figure out. He will show how to find the answer.", + "video_name": "twMdew4Zs8Q" + }, + { + "Q": "why at around 3:00 is the x2 put inside of the square root symbol would it not be in the front like the 8", + "A": "You are not seeing it correctly. The x2 is not inside the radical.", + "video_name": "Z3db5itCIiQ" + }, + { + "Q": "At 2:05 Sal puts in the -9y^2x at the end of the simplified polynomial equation. Could he have put -9y^2x at the beginning? Why did he put the -9y^2x where he did?", + "A": "The terms in the polynomial can be listed in any order. For example - these are all the same: 4x^2y - 10xy + 45 - 9y^2x (this is Sal s version) 4x^2y - 10xy - 9y^2x + 45 45 - 9y^2x - 10xy + 4x^2y - 9y^2x + 45 + + 4x^2y - 10xy etc.", + "video_name": "AqMT_zB9rP8" + }, + { + "Q": "At 2:50, why not just keep it (a+2)(a-2) and then cancel out (a+2) from the top and bottom? Why does this not work to simplify?", + "A": "I see. So (sorry if this is worded wrong) you have to combine the -(a-3) before simplifying for the same reason you can t cancel out the two a s in (a + b)/a ?", + "video_name": "IKsi-DQU2zo" + }, + { + "Q": "at 4:37, a^2-a is just a. I don't understand why the answer isn't just a-1. I guess that is another one of those \"algebra\" rules that people are just supposed to magically know?", + "A": "You cannot subtract a^2 and a. Because they are not like terms. Powers are related to mutliplication, and will not be affected using addition and subtraction. And no, you are not supposed to magically know this - lol - but you should have learned about combining like terms before you started working on rational expressions. If you missed that in one of your previous courses, you can certainly go back and review this skill. It should be listed under the Algebra I content.", + "video_name": "IKsi-DQU2zo" + }, + { + "Q": "what is a real number 1:54\nis there such a thing as a fake number", + "A": "Imaginary numbers exist, and they exist because sometimes one needs to express the square root of a negative number, which doesn t exist. i is the central imaginary number, and it stands for the square root of negative one.", + "video_name": "IKsi-DQU2zo" + }, + { + "Q": "6:09 .... did Vi just say \"damn\"?", + "A": "No she said Bam!", + "video_name": "EdyociU35u8" + }, + { + "Q": "What does Vi mean at 0:19?", + "A": "Pi is not infinite. A number is infinite, by definition, if it is greater than all positive integers. Pi is less than 4, so pi is not infinite.", + "video_name": "5iUh_CSjaSw" + }, + { + "Q": "Isn't the triangle person from 4:00 Wind from wind and mr. ug?", + "A": "No, the triangle is actually Vi s symbol for herself. And, as you probably know, Vi loves triangles.", + "video_name": "5iUh_CSjaSw" + }, + { + "Q": "At 4:54, how does this equation with all the ones = (x=(x+x)/1)?", + "A": "Since the fractal fraction is infinitely big, you can say that since infinity minus 1 is still infinity,", + "video_name": "a5z-OEIfw3s" + }, + { + "Q": "How come at 5:00 Vi says 2 = 1?", + "A": "no, the equation is x=2x. so you bring x on the right side to the left side to get x/x=2. Then, any number divided by that number is always 1. So, 1=2", + "video_name": "a5z-OEIfw3s" + }, + { + "Q": "At 4:47, I'm a little confused why he multiplied each side by 2... I keep rewatching it and trying to understand but it's just not clicking with me", + "A": "He s trying to relate the inequality to the definition of f(x). Since f(x)=2x in the region of interest, and the inequality only has a x, he is multiplying the inequality by 2 in order to get the definition of f(x) in the inequality.", + "video_name": "0sCttufU-jQ" + }, + { + "Q": "At 2:50, why does he go from 9 down to 1 to solve for the denominator. In other problems I thought you would continue from (in this case) 28, 27 ........3,2,1. Why is this different?\nSorry if this is confusing!", + "A": "The problem is different since there are 9 cards in a hand and to fill each slot it will be 9! which is 9 down to 1", + "video_name": "SbpoyXTpC84" + }, + { + "Q": "At 6:16 why did he subtract (36-9)!?", + "A": "36! means 36*35*34*33*32*31*30*29*28*27*26*25*24*23*22....*1 But since we want it to stop at 28, we have to cancel the rest out by dividing with 27!(27*26*25*24*23*22*21*20*19*18*17....*1)", + "video_name": "SbpoyXTpC84" + }, + { + "Q": "At time5:14 min, shouldn't the answer be 362880...i think u shud verify...u mistakenly pressed smth on ur calculator..i calculated it to be 36880", + "A": "9! = 362880. That is how many ways there are to arrange 9 objects. But Sal is calculating the number of 9-card hands, so he needs to start with 36 objects. He is dividing the number of permutations of 9 cards (from a set of 36), by the number of ways to arrange those 9 cards.", + "video_name": "SbpoyXTpC84" + }, + { + "Q": "At 10:09 How do you find the surface of a rectangle", + "A": "Surface area of a rectangle= its length multiply wide.", + "video_name": "I9eLKDbc8og" + }, + { + "Q": "At about 2:23, to figure out the 1.5 portion Sal says \"15 times 15 is 225\" and gets 2.25 that way. What is this process called?", + "A": "It s actually 1.50 times 1.50 and the answer is 2.25.", + "video_name": "I9eLKDbc8og" + }, + { + "Q": "At 2:01 what is that line over repeating decimals called ?", + "A": "The line over the repeating decimal can be called a vinculum . In a repeating decimal, the vinculum is used to indicate the group of repeating digits.", + "video_name": "d9pO2z2qvXU" + }, + { + "Q": "At 0:19, when Sal said 8/2 is not a perfect square, what's the difference between a perfect square and a non-perfect square?", + "A": "A perfect square is when a whole number is the square root of the number. like \u00e2\u0088\u009a49=7 But \u00e2\u0088\u009a74 is a non-perfect square.", + "video_name": "d9pO2z2qvXU" + }, + { + "Q": "At 0:15, Sal says:\nIf you take the square root of a number that is not a perfect square, it is going to be irrational.\n\nWhat about sqrt 2.25? Isn't that rational? Does the rule he stated only apply to integers?", + "A": "Sal is correct. The definition of perfect square is a number times itself is the square. Since 1.5*1.5=2.25, 1.5^2=2.25, therefore 1.5 is the number multiplied by itself, so 2.25 is the perfect square 1.5. So in this case it works. The hope is that the perfect square will be the nice and easy whole numbers.", + "video_name": "d9pO2z2qvXU" + }, + { + "Q": "At 5:17 why do you have to times everything with -2?", + "A": "Because by doing so, we can get 200m in one equation and -200m in the other, which allows us to solve using elimination. We can add the two equations and be left with only one variable, w.", + "video_name": "VuJEidLhY1E" + }, + { + "Q": "During the video, specifically 1:00, Sal does not explain WHAT a line of best fit/line of fit is. My question: How does one find a line of best fit, and how do you know that it is true?", + "A": "Well, a line of best fit is sort of like an estimate. Nobody can truly find the line of best fit (unless all the points are on the same line). Usually, the line of best fit, assuming the points follow a pattern, is the equation of the line connecting the first point and the last point.", + "video_name": "ioieTr41L24" + }, + { + "Q": "At 1:16 i lost you... why do we regroup? I need another example to kinda clarify it.", + "A": "Because you don t have enough in the tens place, so you need 1 from the hundred place to add to the tens place.", + "video_name": "X3JqIZR1XcY" + }, + { + "Q": "At 1:50, why does Sal square the denominator?", + "A": "because it was originally 2c in the denominator INSIDE the big parentheses with the squared exponent. In order to move the 2c outside of the parentheses the operation around those parentheses must operate on the 2c. Since the exponent says square everything inside these parentheses you must square the 2c to eliminate those parentheses around the denominator. Notice after the 2c is squared, the parentheses with the squared exponent still surrounds the numerator, but no longer surrounds the denominator.", + "video_name": "nZu7IZLhJRI" + }, + { + "Q": "at 2:50 suppose the question was log10(16)+log10(2) would you than multiply 16*2 or would you still divided it?", + "A": "log (a) + log (b) = log (ab), provided that both a and b are positive. log (a) - log (b) = log (a/b), provided that both a and b are positive. Thus, log (16) + log (2) = log(16*2) = log (32)", + "video_name": "Kv2iHde7Xgw" + }, + { + "Q": "at 2:41, could i cut the log's base and get 3x= 16-2, simplifying more early than the exposed in video or is it mandatory to use the properties explained?\nMost things in mathematics can be simplified before to reach resolution.\nThis will be the first out rule.", + "A": "No, you cannot the simplify the log base at log 3x = log 16 - log 2 Simplifying the log base should be done after the two logs on the right are combined. If you finish the work on your question you will find that you get 14/3 and not the correct answer of 8/3.", + "video_name": "Kv2iHde7Xgw" + }, + { + "Q": "why did you subtracted the -3 with the 4x in 6:10? pls help.", + "A": "(x + 7)(4x - 3) is equal to 4x(x + 7) - 3(x + 7). You just distributed it. They re still the same and it s appropriate to write it in that way.", + "video_name": "X7B_tH4O-_s" + }, + { + "Q": "At 8:40, why is it (x+1)(6x+1) instead of 7(x+1)?", + "A": "Multiply the factors... only the correct factors will create the original polynomial of 6x^2 + 7x + 1 7(x+1) = 7x + 7. This is not the original polynomial. So, these factors can not be correct. (x+1)(6x+1) = 6x^2 + x + 6x + 1 = 6x^2 + 7x + 1. This matches the original polynomial. so, these are the correct factor. Hope this helps.", + "video_name": "X7B_tH4O-_s" + }, + { + "Q": "At 0:40, Sal mentions that the technique of factoring by grouping becomes obsolete once you learn the quadratic formula. So, if I have a quadratic and I need to factor it (not just find the zeros, but actually know what it looks like factored, like if I'm trying to simplify a larger rational expression), is there any way to factor it with just the quadratic formula? Or would you have to use one of the factoring techniques?", + "A": "at 0:40 he is just saying the quadratic equation is easier than rooting.", + "video_name": "X7B_tH4O-_s" + }, + { + "Q": "At 1:20, wouldn't it be a*c instead of a*b? you said a*b but did 4*-21. It just confused me when I did a*b on my homework and it was incorrect", + "A": "Yes... You need to multiply A*C from the quadratic Ax^2 + Bx + C. Unfortunately, Sal chose the variables a and b to represent the numbers you are seeking to find after multiplying AC. His choice does make the video confusing because we refer to A, B and C as the coefficients in the trinomial. Call the 2 number m and n instead of a and b . You still need to find two numbers that multiply to = AC and also add to = the middle term B. Hope this helps.", + "video_name": "X7B_tH4O-_s" + }, + { + "Q": "At 4:00 Sal states that y=1/k and that this relationship is true for y' and makes a substitution. Would this relationship extend to second, third (etc.) derivatives? Could relationships like this be established for other equations and their derivatives? Feel free to give me a problem!", + "A": "y=f(x)=1/x. y=1/k for x=k only. You can use it for substitution for y in 2nd, 3rd or nth derivative as long as x=k then y=1/k. Let say you want to use x=2, then y is not 1/k anymore, but y=1/2.", + "video_name": "FJ7AMaR9miI" + }, + { + "Q": "At 2:13 he states that 90 x -1/3 = -30 . Can anyone please explain how he got that answer? I understand the finding the common ratio step, but what I don't understand is how whenever I find the common ratio my math doesn't add up. I think I'm multiplying my fractions wrong.", + "A": "a * (-(b/c)) = a*(-b)*(1/c) = -(ab)/c. 90*(-(1/3)) = 90*(-1)*(1/3) = -90/3", + "video_name": "pXo0bG4iAyg" + }, + { + "Q": "Sal, at 3:33 you said a series is a sum of a sequence, but could it also be a group of the sums from a sequence?", + "A": "Yeah, I guess those can be called sub-series of a sequence.", + "video_name": "pXo0bG4iAyg" + }, + { + "Q": "At 8:56, he says the formula to find the 12th bounce is (120)(0.6)^n. I thought it was (120)(0.6)^(n - 1). I am kind of confused about that...", + "A": "In the video, he counts the zero bounce so you can subtract 1 from both sides and then they cancel out. ex. Jumps: a^n=120(0.6)^n-1 Bounces: a^n-1=120(0.6)^n-1 the -1 s cancel so: a^n=120(0.6)^n", + "video_name": "pXo0bG4iAyg" + }, + { + "Q": "at 4:32 why do we have to multiply 50 by 1 hour? I thought all we needed to do was divide 3600 by 50 . Also i did not get whether it was 72 km per second or 1 km per 72 seconds. Although i had some questions this was a fantastic video that triggered a much needed Eureka! moment!! Would i need to multiply 50 by 2 hr if a question said 20/km per 2 hrs or is that not mathematically correct to use 2 hours as a unit", + "A": "its 1km per 72 seconds. 1/72", + "video_name": "d5lcGCbV5cM" + }, + { + "Q": "at 4:10 , just have a silly question: are addition and subtraction between a matrix and a scalar undefined?", + "A": "Yes, addition and subtraction between a scalar and a matrix (or even between matrices of different dimensions) is undefined. That is why previous to adding, the scalar is multiplied by the Identity Matrix, so that at the time of the addition, you are adding two matrices of the same size.", + "video_name": "rfm0wQObxjk" + }, + { + "Q": "it is 5:00 pm ET, why is the exponent 3/5 after you multiply 3 times 1/5 wouldn't you multiply the numerator and denominator of the exponent against the power of 3 and get 3/15 which can be reduced to 1/5, thouroughly confused over here!", + "A": "3 does not equal 3/3. 3 as a fraction = 3/1 Thus, 3 times 1/5 = 3/1 * 1/5 = 3/5 Hope this helps.", + "video_name": "Ht-YXje4R2g" + }, + { + "Q": "At 2:45: Can 6^11/10 be re-written as 6^1/10?\n10/10 = 1 Leaving 1/10\n6^1 = 6 so the remaining 1/10 is left over.", + "A": "Actually, we can t change the exponent from 11/10 to 1/10 by subtracting one from the exponent. We could do this however: 6^(11/10) 11/10=10/10+1/10=1+1/10. 6^1=6. 6^(11/10) 6^(10/10+1/10) 6^(1+1/10) 6^1*6^(1/10) 6*6^(1/10) I hope this helps!", + "video_name": "Ht-YXje4R2g" + }, + { + "Q": "ok so at 1:10 say got 4 but how did he get that out of 6?", + "A": "6 divided by 3 is 2, so 2 is 1/3 of 6. 4 is 2/3 of 6.", + "video_name": "6dyWKD_JPhI" + }, + { + "Q": "I entered this limit (as an equation) onto the Desmos graphing calculator, and it came out similar to the graph in the video at 3:31, with one exception: At x=0, there was a straight line going from 0,2 to 0,1. Is this due to something in this limit, or is it just a glitch in the calculator?", + "A": "I d guess that the calculator defines 0/0 as 1. As it evaluated the function at 0, it got 1 instead of 2. The calculator basically calculates the coordinates of a lot of points and then connects the dots, thus causing the downward spike. That s my guess of what s happening, anyways.", + "video_name": "t7NvlTgMsO8" + }, + { + "Q": "In 2:07 can the hypotenuse be the butom side if the triangle is fliped?", + "A": "Yes there can be a hypotenuse no matter which way the triangle is flipped. The only property is that there should be a 90 degree angle in the triangle. The side opposite to that will be the hypotenuse. :)", + "video_name": "AA6RfgP-AHU" + }, + { + "Q": "This doesn't have much to do with the video, but at 5:28, Sal says we take the positive square root of both sides. Is there a negative square root?", + "A": "Yes, for example, the positive square root of 25 is 5 and the negative square root is -5. When you square negative numbers, you get a positive answer, therefore the square root of a positive number will have both a positive and a negative.", + "video_name": "AA6RfgP-AHU" + }, + { + "Q": "10:09 instead of it being multiple perfect sqauares wouldnt yoiu just leave it alone and put n/a when finished because my teacher said that its no pyth. anymore unless it in a perfect square", + "A": "No you wouldn t. If it wasn t a perfect square, you would put it under the radical sign, and that would be your answer. Hope I helped! :)", + "video_name": "AA6RfgP-AHU" + }, + { + "Q": "At 10:35 did anyone else notice that that triangle wasn't a right triangle?", + "A": "No those are all right triangles, but are set at different angles.", + "video_name": "AA6RfgP-AHU" + }, + { + "Q": "At 5:25 Sal refers to the square root of 25 that is positive and calls it the principle root. Is that the name of the positive answer of a square root? Is there a name for the negative answer of the square root?", + "A": "The principle square root of a number is the positive square root. If you want to specify the negative answer of a square root its simply the negative square root You could also say the positive square root to identify the principle square root. The positive square root is used more often that the negative so it gets a special name", + "video_name": "AA6RfgP-AHU" + }, + { + "Q": "At the time of 5:40 he mentions the squre root. Can anyone explain what that is or show me a video of how to find the sqaure root", + "A": "A square root a number to the 1/2 power. like 25^1/2=5 because 5^2=25. (E.G. square root of 49 is 7 because 7^2 (7x7) is 49", + "video_name": "AA6RfgP-AHU" + }, + { + "Q": "so i stopped at 5:48 and i was wondering why each equation has to be like squared such as his example 4 squared + 3 squared = c squared, how come? please no long answers im in sixth grade", + "A": "If you put squares on each side of the right triangle, the sum of the smaller squares would equal the largest square. Because the area of a square is (side)^2, and we are looking for the side, we square the sides.", + "video_name": "AA6RfgP-AHU" + }, + { + "Q": "At 5:32, Sal says it could be negative five as well. But isn't it impossible for a length to equal a nonpositive number? Even though he said, that in this case, we only need the positive root, wouldn't that imply that it could be negative in other cases? Could he be speaking only of geometrical properties? Or is he just absent-mindedly pointing out the mathematical property of equality that a square root of a number can be both negative and positive?", + "A": "There are two numbers you can square to get 25. You can square 5: (5)^2=25 or -5: (-5)^2=25. So there are actually two answersfor the square root of 25: 5 AND -5. But as he pointed out, we re dealing with distances, so we know that the answer can t be -5. That s why he said we re taking the positive square root.", + "video_name": "AA6RfgP-AHU" + }, + { + "Q": "How is it possible that the hypotenuse is always opposite of the right angle? Also at 0:40 he says has to be right triangle, is it possible to do it with any other kinds of triangles?", + "A": "because hypotenuse is defined as the side which is opposite to the perpendicular! and it is a universal fact that it would be the largest side of a right angled triangle. No,you can t Pythagoras theorem is based on right triangles and is the base for trigonometry which is studied in higher classes", + "video_name": "AA6RfgP-AHU" + }, + { + "Q": "At 9:35 it says the term perfect square. What does that mean?", + "A": "By perfect square, you mean to say that if the square root of a number is taken the result would be a whole number. For example, 4,9,16 and 25 are perfect squares, since if you take the square root of those numbers, you would get 2,3,4 and 5, which are whole numbers. Hoped it helped! :)", + "video_name": "AA6RfgP-AHU" + }, + { + "Q": "At around the 10:00 minute mark he starts talking about principal roots and stuff. Can someone help explain that to me?", + "A": "Principle root simply means that the root is positive, not negative.", + "video_name": "AA6RfgP-AHU" + }, + { + "Q": "at 7:20 couldn't you just do a+b=c instead of A2+B2=C2.", + "A": "You can t just use a + b = c because you are trying to take the square root of both sides and just eliminate the squares. But the square root of both sides of a^2 + b^2 = c^2 gives you sqrt(a^2 + b^2) on the left and you have to do what s inside the parentheses first.", + "video_name": "AA6RfgP-AHU" + }, + { + "Q": "at 4:22, why does he cross out the 2s?", + "A": "Do u know why in the video he subtracted 2x and not 5x", + "video_name": "f15zA0PhSek" + }, + { + "Q": "At 1:16 what exactly does he mean by 7 away from 0, what if it was negative?", + "A": "The simplest way to explain absolute value is forget the sign . Thus, |-7| = |7| = 7", + "video_name": "hKkBlcnU9pw" + }, + { + "Q": "At ~8:25 Sal says that sin(x) reflected over the y-axis is equal to sin(-x). It looks to me that you could just as correctly said that sin(x) reflected over the x-axis is equal to sin(-x). Is this right?", + "A": "The sine function is a member of a special family of functions we call odd functions. If f(x) is odd, f(-x)=-f(x). You are right about your statement, because it is another property of odd functions.", + "video_name": "0zCcFSO8ouE" + }, + { + "Q": "At 1:27, Sal says that if you take away 2 x's from one side, that side will go up; it has less weight. But wouldn't that side go down if x was a negative number?", + "A": "Yeah, but you can t have negative mass.", + "video_name": "Ye13MIPv6n0" + }, + { + "Q": "At 6:25, why did he plug in 2 and 4 into the original equation to find the minimum?? Shouldn't he have just picked one number??", + "A": "The derivative is a second degree polynomial thus it is a parabola .......... when sal found its two roots at 1 and 3 ........ it is understood that the vertex of parabola will exactly be between them because the symmetry of parabola.... i.e. x=2 ....and for y value he plugged x=2 .....3(2)^2-12(2)+9.......3(4)-12(2)+9....", + "video_name": "SE1ltVuE5yM" + }, + { + "Q": "At 2:31, didn't Sal do the dot inaccurately?", + "A": "It is off by just a little, but this is just due to human error and the fact that he didn t have a grid to draw on. It is implied that the dot is at x = 9.585 s and y = 100 m.", + "video_name": "EKvHQc3QEow" + }, + { + "Q": "People say that we see math in our everyday lives -- and while I understand how this concept applies to beginning math, pre-algebra, algebra, and trig, how does this apply to calculus? At 1:01, Sal says that differential calculus is all about finding instantaneous rate of change, but is that the only \"everyday use\"? Or is calculus simply a concept that is used in other subjects, or even professions, like engineering?\n\nThanks!", + "A": "I think the best way to find a good answer to this question is to just keep watching the videos! If you attend college for any engineering discipline, you have to learn calculus before you even begin learning the specifics of your discipline (whether it be mechanical, electrical, civil, computer, computer science, etc...). The best way to understand what every day things calculus will enable you to do is to learn calculus and start doing incredible things every day :-)", + "video_name": "EKvHQc3QEow" + }, + { + "Q": "At 6:00 I am wondering what happened to miles/Meters/ they got confused in my mind. Which one is using?", + "A": "If you re asking about how he got from 10.4 m/s to 23.5 mi/hr, ... 10.4 meters / second, when converted to miles/hour, is roughly 23.5 miles/hour. Since most of us (in the USA) drive in cars that have speedometers reading out in miles/hours, it s easier for some to be able to relate to 23 miles per hour, versus 10.4 m/sec. However, they are equivalent speeds (velocities), just one uses metric (SI) units, and the other uses US units.", + "video_name": "EKvHQc3QEow" + }, + { + "Q": "At 2:04 shouldn't it be -1 x -4 = 4 and not 5?? so the real answer should be x^2+3 right?", + "A": "Correct. This is a known problem and as such has a pop-up box in the lower right-hand corner to say so. It appears on screen shortly after Sal s mistake.", + "video_name": "KvMyZY9upuA" + }, + { + "Q": "At 0:23 why did you put diffret divison structures?", + "A": "because if you don t know hat problem by heart before you do it its easier to put it into that structure", + "video_name": "AjYil74WrVo" + }, + { + "Q": "3:09 why is y zero?", + "A": "To find the two intercepts, you have to set x = 0 (to find the y intercept) and y = 0 (to find the x intercept). He is just finding the x intercept at this point.", + "video_name": "6CFE60iP2Ug" + }, + { + "Q": "The method at 7:29 is nice but I can't make it work for something like:\n(4x^2 + y^2)^2\n\nI end up with 16x^2 + 8x^2 * 2y^2 + y ^4 but it should be 16x^2 + 8x^2 * y^2 + y ^4", + "A": "_4x^2 + _______ + y^2 x 4x^2 + _______ + y^2 --------------------------------- _______4(x^2)(y^2) + y^4 + 16x^4 + 4(x^2)(y^2) ---------------------------------- 16x^4 + 8(x^2)(y^2) + y^4", + "video_name": "fGThIRpWEE4" + }, + { + "Q": "At 9:40 is it ok if you use the same technique for multiplying to binomials?", + "A": "It depends on what you are doing.", + "video_name": "fGThIRpWEE4" + }, + { + "Q": "At 2:50 Sal says this is a fifth degree polynomial. What is that?", + "A": "A 5th degree polynomial is a polynomial that has the 5th power as the highest exponent in one of its term. Ex: 2x^5 _+ 2 x^5 + x^4 + 3", + "video_name": "fGThIRpWEE4" + }, + { + "Q": "At around 4:48: Why do you subtract - 10x^2y dy/dx from both sides?", + "A": "When you solve an equation for a variable, you have to move all the terms with that variable to one side of the equation and all of the other terms to the opposite side. Then you can factor out the variable you re solving for and divide by the term in parenthesis: a simplified example would be: -2xy - 3 = 5y (to solve for y) -3 = 5y + 2xy -3 = y(5+2x) -3 / (5+2x) = y", + "video_name": "1DcsREjyoiM" + }, + { + "Q": "At 1:20, I just can't understand why the derivative,at the end of the application of the chain rule, is equal to ...2y*dy/dx. Why it's not just 2dy/dx??", + "A": "When you take a derivative, you bring down the power, and subtract one from the exponent. So derivative of y^3 would be 3y^2(dy/dx) and derivative of y^5 would be 5y^4(dy/dx). In your case, it was y^2, thus its derivative is 2y*(dy/dx)", + "video_name": "1DcsREjyoiM" + }, + { + "Q": "@2:40 is Sal making an assumption that AG is the longest part ?", + "A": "He may be eyeballing it, but you can also tell by the fact that line AG goes all the way past point F on its side, which is also the point that bisects line AE. That shows that AG is longer by proportion than line GD, or the longer part of the median if that made sense :)", + "video_name": "k45QTFCHSVs" + }, + { + "Q": "When you are multiplying a fraction with the matrix, is it necessary to simplify if allowed?\nRefer to 9:47...", + "A": "No, it is not necessary.", + "video_name": "iUQR0enP7RQ" + }, + { + "Q": "when he fins the determinant of B he says that it is 1/-7 and that is what he uses to multiply with. So why does he change it to -7 when he puts the B in absolute value signs over on the side (9:34) ?", + "A": "When dealing with matrices the absolute value sign actually means the determinant and does not mean to take the absolute of the number.", + "video_name": "iUQR0enP7RQ" + }, + { + "Q": "at 6:25, why do you subract the two equations and not add them?", + "A": "you can do either or as long as you are left one variable eliminated", + "video_name": "xCIHAjsZCE0" + }, + { + "Q": "at 5:00, why do you subtract 300 instead of 200?", + "A": "Because he is subtracting the blue/teal equation from the red/pink equation. Subtracting the red equation from itself would just get you 0=0, which is true, but not very useful.", + "video_name": "xCIHAjsZCE0" + }, + { + "Q": "At 7:50, Khan says \"one equation for one unknown.\"\nDoes this mean that if two equations for 2 unkowns and 1 equation for 1 unknown is possible to be solved, then for 3 unknowns you have to get 3 equations? And so on and so forth?", + "A": "That is exactly correct. Good job :-)", + "video_name": "xCIHAjsZCE0" + }, + { + "Q": "@ 5:09 why Sal is subtracting 500a and 300c from 500a + 200c?", + "A": "The whole point of solving systems of equations by elimination is to get rid of one variable by making it subtract to be 0, so if you have a positive 500 and a - 500, then the two add to be zero which gets rid of a, so when we add the coefficients of the c variable, we can find a value for c, then substitute it in to find a.", + "video_name": "xCIHAjsZCE0" + }, + { + "Q": "What is the angle between two hands of a clock at 4:30", + "A": "If the total clock face represents 360\u00c2\u00b0, then each number on the clock represents an angle of 30\u00c2\u00b0 and each minute, 6\u00c2\u00b0. So at 4:30 the minute hand is at 30*6\u00c2\u00b0 = 180\u00c2\u00b0 and the hour hand is at 4.5*30\u00c2\u00b0 = 135\u00c2\u00b0. Thus the angle between them is 180\u00c2\u00b0-135\u00c2\u00b0 = 45\u00c2\u00b0", + "video_name": "2mzuFKCuDg4" + }, + { + "Q": "At 3:51 where did he get 10x from? He seems to have pulled it out of thin air.", + "A": "The 10x is created from multiplying the 2 binomials (x+3)(x+7) Let s do the multiplication (use FOIL to multiply the binomials). (x+3)(x+7) = x^2 + 7x + 3x + 21 Combine the middle 2 terms... they create the 10x. x^2 + 7x + 3x + 21 = x^2 + 10x + 21 Hope this helps.", + "video_name": "SjN3_xCJamA" + }, + { + "Q": "At 3:59ish, Sal switches the subtraction to addition and adds -1. Do we always use 1? And why do we change the sign? What happens if you do not use a scaler?", + "A": "the jest of it is this ... a - b = a + (-1)b = a + -b", + "video_name": "WR9qCSXJlyY" + }, + { + "Q": "At 5:08 he says '0', but he writes '6' . Which one is he saying??", + "A": "It was a sloppy 0. The actual value is irrelevant since the two matrices have different dimensions.", + "video_name": "WR9qCSXJlyY" + }, + { + "Q": "Greetings from Venezuela...Very helpful explanation, thanks Sal! Just a question: at 3:28, Sal is taking the derivative of x with respect to theta. The derivative of sine of theta is the cosine of theta, agreed. But why is the sqrt(3)/sqrt(2) not derived?", + "A": "because sqrt(3)/sqrt(2) is a constant. Sorta like why you wouldnt derive pi, or any other number that isnt being multiplied by a variable such as X.", + "video_name": "n4EK92CSuBE" + }, + { + "Q": "At 0:58 he says you can use either sin^2 or cos^2, but won't that result in arccos at 7:05 instead of arcsin, which is a different answer? Or am I making a mistake?", + "A": "I didn t watch the video, but arccos and arcsin differ by a constant and a negative sign only. So you ll end up with, say, -arccos instead of arcsin, and the constant difference will be absorbed by your arbitrary constant. Both are equally fine antiderivatives.", + "video_name": "n4EK92CSuBE" + }, + { + "Q": "at 1:43 when it is like (5)(4) is that multiplication because that confused me because cant u just writ it like (5 times 4) or does it have to be like (5)(4)", + "A": "Yes, (5)(4) is just the same thing as 5 times 4 . This is just another way to write it, which you will see quite often in math. You can write it however you prefer, but you should get used to seeing it written this way as well, because it will show up often. I hope this helps.", + "video_name": "GiSpzFKI5_w" + }, + { + "Q": "At 3:00 what did he mean?", + "A": "First solve the problem of first bracket. Then solve the other problems.I think you got it,", + "video_name": "GiSpzFKI5_w" + }, + { + "Q": "At 04:09, if the hypotenuse is irrational does this mean that the hypotenuse is a multipal of \"root 2\" or can it also be another irrational number?", + "A": "root two", + "video_name": "X1E7I7_r3Cw" + }, + { + "Q": "refering to 2:00\n\nwas he actually that crazy, he meaning pathagros", + "A": "Mostly, but you have to remember that he was a mathematician, and mathematicians love elegance and simplicity. Adding irrationals to mathematics made it far more ugly. And nobody likes to find that what they had believed to be true to be wrong.", + "video_name": "X1E7I7_r3Cw" + }, + { + "Q": "At 8:00, was Pythagoras really scared of beans?", + "A": "There are several theories on why Pythagoras did not allow his followers to eat beans. One more likely theory states that he believed that beans contained the souls of humans, but we aren t sure.", + "video_name": "X1E7I7_r3Cw" + }, + { + "Q": "At 8:30, why does Sal keep expanding everything out? I do not understand it.", + "A": "he is using this as a complete example to show how it works. He is also using the sigma, which is a sum of all integers from the number on the bottom to n.", + "video_name": "iPwrDWQ7hPc" + }, + { + "Q": "At 4:39 point, when writing \"n choose k\" for the first time, you say, \"We'll review that in a second. This comes straight of out ?\" I didn't hear that part. It comes straight out of WHAT?", + "A": "There is a term called Combination,which states that each of the different groups or selection which can be made out by taking some or all of a number of things at a time.or simply Selection of r terms out of n terms....that part is derived from this very term.....selection of r terms out of n terms..... nCr = n!/r!(n-r)! ....", + "video_name": "iPwrDWQ7hPc" + }, + { + "Q": "Why 4! / 0!4! = 1? it's just ( 4 * 3 * 2* 1 ) / ( 0 * 4 * 3 * 2 * 1 ) = 24 / 0\nwhich is undefined. Why sal says it's equal to 1? at 9:37", + "A": "0 factorial does not equal zero. By definition it equals 1.", + "video_name": "iPwrDWQ7hPc" + }, + { + "Q": "At 4:21, what is the sideways W symbol, and what does it mean?", + "A": "The sideways W is a Greek letter known as a Sigma. It indicates a pattern.", + "video_name": "iPwrDWQ7hPc" + }, + { + "Q": "at 2:35, when looking to draw the vector [1,2], I don't understand why the x component should be 1 and the Y component should be 2. Isn't the desired output, based on y = 1 and x = 2?", + "A": "There s no mistake in there. The input coordinates are (2,1). And according to the partial derivative of the given function, the output is a vector field with x-component equal to the ordinate and y- component equal to the abscissa. So, the output vectors are given by = yi + xj , where i and j are the basis vectors for x and y axes. So the output for (2,1) will be 1i+2j", + "video_name": "ZTbTYEMvo10" + }, + { + "Q": "at 1:21 didnt understand the formulae", + "A": "The formula is showing there is a correlation between the angle of the sector and the area of the sector. If we know the angle and the area of the whole circle we can find the area of the sector, since they are similar. For more detail: 0:28", + "video_name": "u8JFdwmBvvQ" + }, + { + "Q": "At 1:40 where did he get nine times nine from? Also he divided the 350/360 by ten should he divide the other side by ten also?", + "A": "Hey Janet, 9*9 is the same thing as 81. With fractions, if you divide the numerator by 10, you divide the denominator by 10 as well. You don t need to divide the other side, it s just simplifying a fraction and still the same number after all.", + "video_name": "u8JFdwmBvvQ" + }, + { + "Q": "At 0:28, Mr. Khan mentions a ratio. What is that?", + "A": "He basically created a proportion using the values given in the circle.", + "video_name": "u8JFdwmBvvQ" + }, + { + "Q": "The result of the composition of Ix and g has to be the same as the result of the composition of h and f and g when one inputs a 'y' value and gets an 'x' value (at time marker 16:40). But how is showing that if the results are the same, then the functions are the same as well? (abstractly speaking)", + "A": "Speaking any kind of way (abstractly or otherwise), x = g(y) = I_X(g(y)) = h(f(g(y))) = h((I_Y)(y)) = h(y). So g(y) = h(y), and g = h. (I don t really understand this either yet.) : |", + "video_name": "-eAzhBZgq28" + }, + { + "Q": "3:41 OK really confused. why do the repeating numbers start at 4 and not 1. Sal writes 414141... but shouldnt it be 14141414...\ncan anyone explain this?", + "A": "x=.714141414... If you multiplied by x by 10, then that would move it one place to the right, or 7.14141414... and the 141414... would start immediately after the decimal point. Since you have to multiply by 100, however, you move it two places to the right and get: 7 1. 4 1 4 1 4 1 4. The numbers after the decimal must start with the 4 first since you moved it two places to the right. The 141414... pattern is still there. You re just starting at a different place.", + "video_name": "Ihws0d-WLzU" + }, + { + "Q": "This video was really helpful, I just have one question. How do you whether to use 10x or 100x or 1000x at 1:01 in the video?", + "A": "How many different numbers are repeating? If it is .333... , one repeating times 10, if it is ,232323... two repeating, so times 100, three repeating .234234234... times 1000. A zero for each repeating number.", + "video_name": "Ihws0d-WLzU" + }, + { + "Q": "At 4:04 can we multiply by 10?", + "A": "If we multiply by 10, the decimal point would only shift to the right one point. we need the point shifted over twice, so we multiply by 100.", + "video_name": "Ihws0d-WLzU" + }, + { + "Q": "At 9:22, how do you turn 0.00123 with the 3 repeating into a decimal?", + "A": "x = 0.001233... 100000x = 123.33... 10000x = 12.33... 90000x = 111 x = 111/90000 = 37/30000", + "video_name": "Ihws0d-WLzU" + }, + { + "Q": "at 4:00, he could have just multiplied it by ten. that would have been enough to get the seven on the other side of the decimal point. why'd he multiply it by 100?", + "A": "That s because you still want the decimal points and the repeating part (which was 141414...in this case) to line up.", + "video_name": "Ihws0d-WLzU" + }, + { + "Q": "at around 5:02, why didnt he multiply 4 into the number to the right of the greater than symbol? If you are making a change to one side wouldn't you have to do it to the other, because it would affect the end result?", + "A": "He did. He said, let s multiply both sides by 4 and he pointed to both sides of the inequality. 4 ( p\u00c2\u00b2 - 17/4 p+ 1 > 0 ) becomes 4 \u00e2\u0088\u0099 p\u00c2\u00b2 - 4 \u00e2\u0088\u0099 17/4 p + 4 \u00e2\u0088\u0099 1 > 4 \u00e2\u0088\u0099 0 which is 4p\u00c2\u00b2 - 17p + 4 > 0 because zero times anything is still zero He probably didn t mention zero times 4 is zero because he guessed we knew that by the time we are doing quadratic inequalities because we run into it so much when solving quadratics and other equations.", + "video_name": "GDppV18XDCs" + }, + { + "Q": "in 1:16, why did the voice changed?", + "A": "Yes, Vi did get farther from her mic, thats why her voice got deeper and quieter", + "video_name": "4tsjCND2ZfM" + }, + { + "Q": "At 2:37 What does beat a dead horse mean?", + "A": "It is an idiom, meaning it is not to be taken literally, and it means to waste time and/or energy repeating something in excess or doing something otherwise that will be non-helpful or productive.", + "video_name": "AuD2TX-90Cc" + }, + { + "Q": "At 4:14, how come he didn't turn the fraction into a decimal?", + "A": "Sal solves two problems where a missing side length is found by proving that triangles are similar and using this to find the measure.", + "video_name": "R-6CAr_zEEk" + }, + { + "Q": "At 2:51, how do you figure out which line segment to put together when you are trying to figure out the missing length?", + "A": "Since you are looking for the side CE, notice that it is the third letter to first letter of second triangle. With the congruency statement, the same two letters are CA, so they are one of three pair of congruent sides. Does this answer your question?", + "video_name": "R-6CAr_zEEk" + }, + { + "Q": "at 6:16, would it work if you wrote CA/CB = CE/CD instead of CB/CA=CD/CE? because I got pretty confused.", + "A": "yes it would work", + "video_name": "R-6CAr_zEEk" + }, + { + "Q": "At 2:20 Did When Sal said Sin 32, Does that also mean Sin A?", + "A": "at 2:20 when sal says sin32, yes that is equivalent to sinA", + "video_name": "yiH6GoscimY" + }, + { + "Q": "At 4:29 What is the exact difference between obtuse and acute triangles", + "A": "in the obtuse triangle, it has one obtuse angle (bigger than a right angle) and in an acute angle, all angles are smaller that right angle. Ex: acute:all angles 60 ( 60+60+60=180) Ex: obtuse: one angle 120 another 35 and another 25 Hope this helped! Please vote this", + "video_name": "D5lZ3thuEeA" + }, + { + "Q": "At 8:00, wouldn't you have to times the number of years and the rate the interest is compounded for raising everything?", + "A": "Yes, I suppose. But in this video the loan is only for one year.", + "video_name": "BKGx8GMVu88" + }, + { + "Q": "At 0:35 couldn't you just make the two triangles into one rectangle with a height of 3\" and a width of 5\"?", + "A": "No, but you could make the two triangles into a rectangle with a height of 3 and a width of 4 (the entire base of the pentagon is 8, so half of that would be 4)", + "video_name": "7S1MLJOG-5A" + }, + { + "Q": "At at 4:12 - 4:14, why did Sal write x^4 '+'... and not '-' ...?", + "A": "Addition does not change signs of the original values. If he had used a minus sign, it would need to be distributed across the term terms in the parentheses, which would result in those values having the wrong signs. Hope this helps.", + "video_name": "yAH3722GrP8" + }, + { + "Q": "Could someone please tell me why at 3:40 -x^2*sqrt6+x^2*sqrt2=(sqrt2-sqrt6)x^2?\n\nShouldn't it be -x^2*sqrt6+x^2*sqrt2=sqrt2-sqrt6 since one of the x^2 is negative while the other is positive? Shouldn't the x^2s cancel out then.\n\nI'm not sure if I've just made a careless error or am just missing something here, but I don't know why you get a negative x^2 or an x^2 at all. Please help explain this.", + "A": "So lets pretend for a minute that instead the expression was -6z + 2z We can rearrange them using the commutative property: = 2z - 6z And then factor out the z, using the distributive property: = z (2 - 6) Now we can replace z with x^2, and the numbers with their square roots and we can still do the same thing: -Sqrt(6)x^2 + Sqrt(2)x^2 = Sqrt(2)x^2 - Sqrt(6)x^2 = (Sqrt(2)-Sqrt(6))x^2", + "video_name": "yAH3722GrP8" + }, + { + "Q": "At 3:21 why is it sqrt2 - sqrt6 and not the other way around? Or would it still be the same either way?", + "A": "It s equivalent, sal choose to do it like that so you only have to use one operation symbol i.e. rather than: -sqrt6 + sqrt2 He choose: sqrt2 - sqrt6 But both are equivalent", + "video_name": "yAH3722GrP8" + }, + { + "Q": "At 2:10 he says that if r=1 denominator is 0, and we can't divide by zero. But, in that case numerator would also be 0, since a-a*(1)^n=0. Isn't lim 0/0=1?", + "A": "No, the limit of 0/0 is undefined, and since the limit is for the variable n and not for r, you cannot use any of the limit techniques to get rid of the 0/0.", + "video_name": "b-7kCymoUpg" + }, + { + "Q": "@9:52 I don't understand how a smaller denomater is bigger than a larger denmotor ?", + "A": "the larger the denominator the smaller the piece The smaller the denominator the larger the piece.", + "video_name": "wbAxarp_Ug4" + }, + { + "Q": "at 5:30 he Sal says 3 forth of the pizza has cheese, why does he put the number like that, one on top of the other, what does it mean and why not put the 4 on top instead of the 3?", + "A": "first i think you meant at 2:30. Sal s pizza had 1/4 with olives & 3/4 with cheese, right? now it makes sense 3 of the 4 slices of pizza are cheese while 1 slice is olives. now if it was 4 out of the 3 pieces have cheese that would mean you would have 3 slices of pizza with 4 of those 3 slices being cheese, that would make things a bit confusing.", + "video_name": "kZzoVCmUyKg" + }, + { + "Q": "I still don't understand, at 0:33, why did he make reference of the pizza as an example of fractions?", + "A": "the circle is the most simple to esplain fractions.", + "video_name": "kZzoVCmUyKg" + }, + { + "Q": "At 4:00 what if you were given only two points where the function intersects the midline twice? How do I find period with those two points?", + "A": "It depends on which two points you re given, but if you re referring to two consecutive points where the function intersects the midline, then the horizontal distance between them would be 1/2 of the period. Can you see it?", + "video_name": "s4cLM0l1gd4" + }, + { + "Q": "Why go through all the trouble described by Sal around 04:00 to find the period of a function if one can simply measure the distance between two consecutive maximums or two consecutive minimums?", + "A": "How would you go about measuring it precisely?", + "video_name": "s4cLM0l1gd4" + }, + { + "Q": "At 6:27, how did you get 110 degrees?", + "A": "180 degrees is a straight line and 70 degrees is an angle. Since the 70 degree angle and the other angle he is trying to find are supplementary it means that the angles must add up to 180 degrees. So 180 degrees minus 70 degrees is equal to 110 degrees.", + "video_name": "gRKZaojKeP0" + }, + { + "Q": "1:47 What is a nonlinear correlation?", + "A": "nonlinear correlation = non linear correlation linear correlation --> correlation assuming there is a line (straight). non --> not doing non-linear correlation --> correlation that assumes the line is not a straight line.", + "video_name": "Jpbm5YgciqI" + }, + { + "Q": "at 2:05 dose he mean negitive", + "A": "Sal said 4+7 to see how many blocks were in between the points. At 2:05 if he had done 4+(-7) he would have gotten -3 which is impossible. there can t be -3 blocks between her house and the mall. Hope this helped.", + "video_name": "PC_FoyewoIs" + }, + { + "Q": "@4:05 why didn't Sal write 20u^2v/10uv^2? why did we drop the exponent?", + "A": "That did confuse me a bit, but the reason why is because we have to put the GCF in the bottom for it to be the same as 10uv(2u-v). If we did 20u^2v/10uv^2 along with the other part, we would be left with our answer being 10uv(2u/v-1), which is not the same as 10uv(2u-v).", + "video_name": "499MvHFrqUU" + }, + { + "Q": "At 5:19, Sal draws a \"cone\", however it appears to be two cones on top of each other (tip to tip). Why is this?", + "A": "The correct term for the solid is double-napped cone . Essentially two congruent cones with the same axis and a common vertex. Sal just didn t use the formal name for the solid.", + "video_name": "0A7RR0oy2ho" + }, + { + "Q": "At 9:00, as in trigonometry equation, why don't we put negative sign in front of the coefficient instead of the..mm....unknown? Ex. x= -3 cos (t), instead of x= 3 cos (-t)", + "A": "Because trignometric functions are not commutative. a*cos(t) is not always the same as cos(a*t), even though sometimes it is.", + "video_name": "IReD6c_njOY" + }, + { + "Q": "Why at 2:44 does he write 2 dot 2 dot?", + "A": "he is trying to say that 2 multiply by 2 multiply by 2 multiply by 2", + "video_name": "lxjmR4pYIVU" + }, + { + "Q": "from 3:30 to 3:34 what was he saying can you please explain", + "A": "He was just saying... when he did 2/8 times 3 on the top and 3 on the bottom is the exact same as multiplying it by 3/3 :D Hope that helps =)", + "video_name": "lxjmR4pYIVU" + }, + { + "Q": "During 1:25-1:50, the LCD should be 0, shouldn't it?", + "A": "Not exactly.. the way you get LCD ( Lowest common Denominator ) is by factorizing the denominators of fractions until you get something common. Sal was just looking for something common. and if you noticed he stopped at 24. I hope this helps.", + "video_name": "lxjmR4pYIVU" + }, + { + "Q": "why does x have to be greater than zero in the domain?\n\nTime on the video: 6:39", + "A": "The log of 0 is undefined. The log of negative numbers involves rather difficult complex numbers, so it is usually treated as undefined at this stage of studying math.", + "video_name": "DuYgVVU_BwY" + }, + { + "Q": "At 11:30 or so, why do we ignore the normalization scalar that's being multiplied with the vectors? We can keep it aside until the end like that? Looks cool.", + "A": "The Gram-Schmidt method is a way to find an orthonormal basis. To do this it is useful to think of doing two things. Given a partially complete basis we first find any vector that is orthogonal to these. Second we normalize. Then we repeat these two steps until we have filled out our basis. There are formulas that you could write down where both steps are taken care of in a long computation but it is useful to understand the process as a multiple step procedure which is what Sal is doing.", + "video_name": "ZRRG386v6DI" + }, + { + "Q": "At 03:51, the last vector sal just wrote (0,0,1,1) is the vector v1, shouldn't it be the vector v2 instead (0,1,1,0)? Or is it the formula above that should be Y2=V2-Proj(V1)*u1 instead of v2 in the end?", + "A": "The projection of v2 on v1 is in the direction of v1, so it s magnitude is multiplied by u1 = v1/||v1||.", + "video_name": "ZRRG386v6DI" + }, + { + "Q": "I don't get it at 0:34 what does he mean?", + "A": "Compute means to calculate, find, or figure out. He will show how to find the answer.", + "video_name": "k68CPfcehTE" + }, + { + "Q": "why does he say minus is it not negative at around 5:20", + "A": "Any number minus another number is the same as saying that number plus the negative form of the other number. example: 7 - 5 is really the same as 7 + -5 Minus and negative are really just the same thing. I hope this helps you1 Unikitty <[:)]", + "video_name": "d8lP5tR2R3Q" + }, + { + "Q": "at 5:52, I'm a little confused about the way Sal explains how there are 7 cubes that are not yellow or something. What does that mean?", + "A": "It s easier to see from the table over on the left. When you want to count all the shapes that are either yellow or cubes, you add the seven yellow spheres, the five yellow cubes, and the eight green cubes.", + "video_name": "QE2uR6Z-NcU" + }, + { + "Q": "Why he needs to minus 5/29 at 7.25 at 7:24?", + "A": "He subtracted 5/29 so he wouldn t count the overlapping area twice.", + "video_name": "QE2uR6Z-NcU" + }, + { + "Q": "at 0:53 how is it 8:20,should it be 8:12", + "A": "In this video, Sal is asking for the ratio of Apples to Fruit. In other words, how many apples compared to how many pieces of fruit total. Since 8 out of the 20 pieces of fruit are apples, the answer for this question is 8:20. However, if the question was What is the ratio of Apples to Oranges? your answer of 8:12 would be correct since there are 8 apples to 12 oranges.", + "video_name": "UK-_qEDtvYo" + }, + { + "Q": "could you do the same with 5:2 as 5/2?", + "A": "Yes, they are equivalent ways of writing the same ratio.", + "video_name": "UK-_qEDtvYo" + }, + { + "Q": "there are 18 monkeys, 6 gorillas, and 15 apes what ratio is same to 5:13? Please someone help me i am having trouble", + "A": "The total number of animals is 18 + 6 + 15 = 39, and there are 15 apes. Note that 5:13 is equivalent to 15:39, from multiplying each number in this ratio by 3. So 5:13 is ratio of the number of apes to the total number of animals Have a blessed, wonderful day!", + "video_name": "UK-_qEDtvYo" + }, + { + "Q": "how did sal reduce the original number/ 8:20 to 2:5", + "A": "common factor of 8 and 20 is 4 and 8/4 = 2 and 20/4 = 5 so 2:5. does this help you?", + "video_name": "UK-_qEDtvYo" + }, + { + "Q": "he said for the first question that the fruit was 8:20 when it was 8:12. why did he say that? or was it a mistake?", + "A": "You are confusing fruit vs oranges . By fruit, Sal is referring to apples + oranges = 8+12 = 20 The ratio of apples to oranges = 8 : 12 The ratio of apples to fruit = 8 : 20 Hope this helps.", + "video_name": "UK-_qEDtvYo" + }, + { + "Q": "is 2:5 the same as 2/5?", + "A": "Yes, those are the same.", + "video_name": "UK-_qEDtvYo" + }, + { + "Q": "If ratios and fractions are technically the same then why do you use ratios or if you are thinking the other way around why do you use fractions? The only thing different I see if that fractions are used more often and they are written differently. ratios: 2:3 fractions: 2/3.", + "A": "You should think of ratios as a special usage of fractions. They are used to compare similar quantities. Fractions can be used for many more purposes.", + "video_name": "UK-_qEDtvYo" + }, + { + "Q": "At 1:21 why can he only measure length?", + "A": "He can only measure length because it is a line. A line is a one-dimensional object. A two dimensional objects allows you to measure width and length, and a three-dimensional object allows you to measure its height, width, and length", + "video_name": "xMz9WFvox9g" + }, + { + "Q": "At 2:36, what is a \"unit Square\"?", + "A": "Its the unit of the shape ( e.g. feet, inches ) squared. The square is the little 2 at the top. For example 56 ft squared.", + "video_name": "xMz9WFvox9g" + }, + { + "Q": "at 6:11 why did he only count the first cubes showing e forgot the back that you cannot see", + "A": "He didn t forget. He showed that there are two layers of 2 x 2 blocks. Each block is 1 unit^3 and there are 8 blocks so the volume is 8 units^3", + "video_name": "xMz9WFvox9g" + }, + { + "Q": "Let's say I was faced with a similar question to the one at 0:00. I used the vertical motion model and the quadratic formula to solve for the ball's time in motion. What would I do if both solutions of the equation are positive?", + "A": "The only way for your scenario could be true is if the y intercept were negative, so he would be shooting the ball from below ground level. The smaller number would be here the ball initially reaches ground level, and the second would be where the ball hits the ground. So you would have to have an equation such as f(x) = -16x^2 + 20t - 40. Even if you shot it off at ground level, one solution would be zero (from the origin). In either case, the time would be the highest x value.", + "video_name": "OZtqz_xw0SQ" + }, + { + "Q": "At 3:46, Sal gives a formula.... is that formula a generic one or is it restricted to n=7?", + "A": "It is generic . Sal chose 7 just for example purposes.", + "video_name": "LwhJVURumAA" + }, + { + "Q": "At about 1:11 Sal(?) says 1/2 times 1/2 = 1/4. Then at about 1:26 1/2 is added to 1/4 to get 3/4 chance of winning. Why is one added and the other multiplied?", + "A": "The first case requires Brit to win both of the two times, whereas the second case requires Sal to win either time.", + "video_name": "tDdtAF3WtIY" + }, + { + "Q": "At 0:32, they talk about adding more branches for each game. I wonder what would happen if they played 6 games instead of three?", + "A": "Exactly the same would happen, only the difference between chance of winnings would not be that much.", + "video_name": "tDdtAF3WtIY" + }, + { + "Q": "At about 1:20 he says, \"P = 0.25p equals to 1.25p\". How did it become \"1.25p\" from \"P = 0.25\"? Thanks!", + "A": "Sal is simplifying the expression: P + 0.25P. Remember P has a coefficient of 1. P and 1P are the same. Sal is just adding like terms: P + 0.25P = 1P + 0.25P. Add 1+0.25 and you get 1.25. Thus, 1P + 0.25P = 1.25P. Hope this helps.", + "video_name": "ao9cx8JlJIU" + }, + { + "Q": "Since we are dividing by 4 at 1:16 wouldn't we write 4 at the beginning of the equation like this 4(x^2+10x-75=0?", + "A": "If you use factoring, you would create your format: 4(x^2+10x-75) = 0 This is done sometimes, but it actually easier to complete the square if the 4 is gone completely. This can be done by dividing the entire equation by 4, which is the technique that Sal used. Hope this helps.", + "video_name": "TV5kDqiJ1Os" + }, + { + "Q": "At 5:35, Sal says that the radius will be smaller than it was before, but I'm confused because I thought that the radius of a unit sphere is always constant. Does he mean the z-coordinate or something like that instead of the radius?", + "A": "think in 3D... take another plane // to xy plane... and it intersects the sphere above the origin... it is going to form a smaller circle, and obviously its radius is going to be smaller than unity.", + "video_name": "E_Hwhp74Rhc" + }, + { + "Q": "At 1:00, why is the Celsius scale called the Celsius scale and why is the Fahrenheit scale called the Fahrenheit scale?", + "A": "The Celcius (or centigrade) scale is named for Anders Celsius (1701 - 1744) who created and defined a similar but upside down (0 was boiling water, 100 freezing water. The Fahrenheit Scale is named for Daniel Fahrenheit (1686-1736), based on one he first proposed in 1724.", + "video_name": "aASUZqJCHHA" + }, + { + "Q": "at 2:02, I tried to do that prob on my own, but i failed.", + "A": "It s trying to show you WHY multiplying fractions works the way it does. Let s move on to how to actually multiply with fractions. First, remember that every whole number can be rewritten as a fraction. 5 is the same thing as 5/1. So what is 10 x 1/2? Think of it as 10/1 x 1/2. Now, multiply the two numerators together. 10 x 1 = 10. Now multiply the two denominators: 1 x 2 = 2. Put them together... 10/2 and simplify if possible: 10/2 is the same as 5.", + "video_name": "hr_mTd-oJ-M" + }, + { + "Q": "(0:48) why in multiplying fractions it is taking away, not increasing?", + "A": "The reason is when you multiply fractions the number being multiplied gets smaller because a fraction is a part of a whole. When you multiply a number by one: 5x1 You get 5 the same number you multiplied. So, if you multiply a number by a fraction ,the product should be less then the number you multiplied since a fraction smaller than 1. Same with decimals (if less than 1) since fractions are decimals.", + "video_name": "hr_mTd-oJ-M" + }, + { + "Q": "from 0:19 to 2:14, isn't there another way ?", + "A": "To be honest, drawing fraction models are slower. You can just multiply the the two fractions (should be improper for both) and get the right answer. Ex) 1/2*1/2= 1*1/2*2 = 1/4", + "video_name": "hr_mTd-oJ-M" + }, + { + "Q": "Why didn't he just make the -6 a + 6 at 0:25? The way I am being taught right now is you take the first set of complex numbers leave them the same (2-3i stays the same) and then do the opposite of -(6-18) and this would be +6+18 when you remove the parentheses. The full equation should look something like this when the parentheses are removed: 2-3i+6+18. Why didn't he do it this way?", + "A": "That would be true if it were (-6-18i) but look where the parentheses fall: -(6-18i). The basic rules of algebra apply and you have to distribute: -6+18i, as Sal had.", + "video_name": "tvXRaZbIjO8" + }, + { + "Q": "I love this song but what does Tau mean 0:50", + "A": "Tau in this case means the ratio between the circumference of a circle and its radius.", + "video_name": "FtxmFlMLYRI" + }, + { + "Q": "1:14 - 1:20:\n\"Well, depending on the dimension, Because it's 1, 2, 3, There's 4 and even more.\"\nWhat is the fourth dimension?", + "A": "The 4th dimension is time. As far as we know, it is the biggest dimension perceivable by humans. You can t see time, but you can measure it, and tell the difference between long and short periods of time.", + "video_name": "FtxmFlMLYRI" + }, + { + "Q": "AT 0:07 sal say to \"massage the equation\", but what does that mean?", + "A": "It means manipulate the equation, converting it into an equivalent form that makes it easier to solve.", + "video_name": "wYrxKGt_bLg" + }, + { + "Q": "@ 10:26 in the video he says 5 is the same thing as 20/4 + 15/4. How is 5 the same as 20/4? Thanks.", + "A": "Think of a fraction as literally the numerator divided by the denominator. When 20 is in the numerator, it s the same as saying 20 divided by 4. 20/4= 5.", + "video_name": "wYrxKGt_bLg" + }, + { + "Q": "At 6:30 Sal makes the bottom equation negative and the top one positive. Would it make a difference if I made the top one negative and the bottom one positive.", + "A": "It doesn t matter. You want one equation to be negative and one equation to be positive so when you add them, one of the variables become 0 (eliminated). You could have both positives or both negatives and use subtraction. Subtraction is easier to mess up when subtracting negatives. So I recommend making one positive and one negative then use addition.", + "video_name": "wYrxKGt_bLg" + }, + { + "Q": "At \"10:32\" how does he get 7x= 35/4 ? Wouldn't the it be 7x=20/4 because 5+15/4=20/4.", + "A": "No 5 = 20/4. 15/4 + 20/4 = 35/4...", + "video_name": "wYrxKGt_bLg" + } +] \ No newline at end of file