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at 2:21 to the end of video i was lost plz someone explain | LohXZt7QzCM | Sal moves the decimal point two spaces to the left because he is dividing by 100. |
At 3:50 I don´t understand why 1,098 turns into 1098. The decimal just gets lost. Can someone explain this to me ? | LohXZt7QzCM | Hello Daniel! Sal only removed the comma, which makes it 1098. The decimal isn t lost, it s behind 8. since ur supposed to divide 1,098 by 100 u would move the decimal two spaces to the left which gives u the decimal 10.98 does that make sense? |
I am confused where the plane intersects the 3D cone, in the hyperbola. (9:45 in the video) | 0A7RR0oy2ho | In order to picture a hyperbola you have to imagine there being two cones, one on top of the other, touching at their points (sort of like this |><| ). If you then slice this double-cone with a vertical plane you ll end up with a hyperbola. Does that help? |
At 00:24 (about) Sal was writing down the names of the conic sections, could anybody please tell me the reasons for those particular names???
Thanks | 0A7RR0oy2ho | circle ellipse parabola and hyperbola ha ha |
On 3:20, Sal drew asympototes, aren't they suppose to be drawn in dotted lines? | 0A7RR0oy2ho | My teacher always instructs to draw them in dotted lines, because otherwise you might misinterpret them as the axes of the coordinate plane (which are drawn as continuous lines). Though there is no official rule about this. I guess it boils down to personal preference or the preference of your maths teacher. |
06:00 That is also a Minkowskiy space, isn't it? | 0A7RR0oy2ho | Yes, it is a Minkowski space. |
Is there a way to find when (what angle measure) a plane must be tilted to to "skew an ellipse until it pops and turns into a parabola" (8:55)? | 0A7RR0oy2ho | Yes. The angle, t (theta) = s , of the side of a cone with the horizontal. Then if s < t < 90 it s still a parabola, and 0 < t < s it s an ellipse. |
At 3:21 what is an Asymptote if you were to explain it to someone? | 0A7RR0oy2ho | A line in which no points rest and cannot rest depending if holes exist (Entirely different topic so I won t get into detail). Asymptotes can be crossed in some situations. |
At 3:21 Sal mentions asymptotes. What are they used for? | 0A7RR0oy2ho | Asymptotes help you think about the limit of where a curve is headed. You can look at a parabola and say, I see that it is curving, but because of where the asymptote is, I can tell that it will never get past this particular line. |
around 4:00, is the graph of y=tan(x) hyperbola? | 0A7RR0oy2ho | No, y=tan(x) is a tangent function. |
Hey i couldn't see his yellow drawing at top left @ 10:11 | 0A7RR0oy2ho | It s OK. It was pretty messy.What part of it could you not see? |
what does he mean it pops (9:06 - 9:16)? | 0A7RR0oy2ho | that it s no longer shown as a circle, it s just an open U shape |
at 3:27 what are the blue lines? | 0A7RR0oy2ho | The blue lines are the asymptotes. As x approaches negative infinity or positive infinity the hyperbola will come closer and closer to these asymptotes but never reach them. |
At 3:41, what is the exact term for a "vertical hyperbola" | 0A7RR0oy2ho | vertical hyperbola dum dum |
Is the mathematical definition of a cone what is drawn in the video at 4:45, with 2 openings? Or is this just a useful construction for showing the difference between a hyperbola and a parabola? | 0A7RR0oy2ho | Technically it s a double cone, but it s just referred to as a cone. |
at 10:05, there is a verticle plane. so, the circle will be ... (yellow one). why it becomes like that shape? | 0A7RR0oy2ho | Because it intersects both cones, you are left with a shape called a hyperbola. It expands in two separate directions becuase the cones it intersects are also expanding in both directions. |
At 8:50, how can there be a parabola when the cone is infinite? | 0A7RR0oy2ho | The cone is infinite, and so is the plane and so is the parabola. The key to the parabola is that the plane has to be exactly parallel to a side of the cone. Tilt one way and you get an ellipse, and the other way you get a hyperbola. |
At 8:12 wouldn't the parabola have a bottom edge so therefore it wouldn't be a parabola? | 0A7RR0oy2ho | It has an edge, but it is on the top part of it. Parabolas don t necessarily have their inflection (I don t recall the right term, but I think that s the one) on their bottom part. What differentiates this parabola (the inflection is at the top) is that if it was plotted on a plane, it would probably has a formula like this: y = -a*(x^2) + b*x + c, with a>0 (a being a real number), and b and c any real numbers. |
At 4:44 Sal says that 2 * pi/2 is pi, so why does he then take the cosine of pi/2? Is that a mistake, or am I misunderstanding something? | IReD6c_njOY | Hi, He takes 3cos(2*Ï/2) = 3cos(Ï) = 3*(-1) = -3. |
You said cos(pi/2) is minus 1 at 4:48 when you should have said cos(pi) is minus 1. | IReD6c_njOY | Hi said 2 times Ï/2 equal Ï, so cos(Ï) = -1 |
At about 9:50 in your video did you mean that it has to be in the form:
x = 3 cos(anything*t)
y = 2 sin(anything*t)
Because you said:
x = 3 cos(anything*t)
y = 2 sin(anything*t)
Cheers Stefan | IReD6c_njOY | He definitely meant y = 2 sin {anything}t. Otherwise, this parametric equation would follow the path of a circle, not an ellipse. |
Couldn't you take a normal equation and turn it into a parametric equation if you were given the coefficient of t, kinda like you can find the specific antiderivative with an initial condition? (see 10:00) | IReD6c_njOY | You are correct. Notice Sal says just with this information when he says you can t. |
at around 9:50, i believe there is a mistake -- shouldn't it be 3 Cos of anything *t
and 3 SIN of anything *t | IReD6c_njOY | I think it should be 2 sin of anything *t not 3 sin of anything *t, Cobyswat. |
At 3:00, how can you put any number before t in the equation sin^2t + cos^2t = 1? For instance, if you put a 2 (as Sal does in this problem), wouldn't you have to multiply 1 by 2 as well? If not, how come? | IReD6c_njOY | So, is the reason why you can plug in any number because if sin^2t + cos^2t =1, then it is almost like they are canceling each other out. And this means that whatever number you plug in to multiply by, as long as it s the same number for sin and cos, they would still cancel each other out? Can someone provide an example? |
At around 5:30, how would I know which direction the graph is moving if the point jumps from (3,0) to (-3,0)? | IReD6c_njOY | Good question. You don t. Since the equations were basically the same in the video except the second set were based on 2t rather than 2 then Sal knew that the second graph was going in the same direction as the first but just twice as fast |
Around 07:30, how can you see which direction the ellipse is going when you go one half circle at a time? If you only have those coordinates, it might aswell go the other way couldn't it? | IReD6c_njOY | You are right in thinking the direction cannot be determined from what Sal has said. Rather, in this case, we know from the previous example that the path is anticlockwise. If he hadn t done that example first (the one with 3cos(t) and 2sin(t)) then we couldn t know the direction at all. Instead we would have to plot a point based on another t value, like pi/4. |
I'm a bit confused at what Sal is doing at 1:48. Why does he bracket a single 2 with both 6 and 8? | lxjmR4pYIVU | Because three 2s are the same as 8 and one 2 and one 3 is the same as 6 if you multiply them. |
At 2:11, I can't understand, I mean, I now know the prime factorization of eight, but I can't understand 'to be divisible by eight, you have to have at least three 2's in the prime factorization.' What does that mean? Why do you need at least three 2's to be divisible by eight? How does all of this work? | lxjmR4pYIVU | The prime factors of 8 = 2*2*2. So if you find the prime factors of another number, and it also has prime factors of 2*2*2, you know you can divide by 8 (because 2*2*2 IS 8, just in a different form). For example, prime factors of 72 = 2*2*2*3*3. The factors of 2*2*2 = 8, so 72 can be divided evenly by 8. 72 / 8 = 9. Notice, the 9 is the 3*3 in the prime factors. Hope this helps. |
at 4:36, how do you add the fractions? won't it become a improper fraction? | lxjmR4pYIVU | If it becomes an improper fraction, you can simply make it a mixed fraction later. Remember that when adding or subtracting fractions, the denominators need to be the same. 1/7 + 14/7 = 15/7 which is 2 1/7. Hope this helped! |
Does 3/3 really equal EXACTLY 1?
( 3:48 ) and how about 9/9 because I heard It was .99999999999999999.... on and on for â! | lxjmR4pYIVU | yah, cause 3 out of 3 would equal a whole. |
at 3:45 how is 3 over 3 one? | lxjmR4pYIVU | 3/3 is 3 thirds, which is the same as 1 imagine cutting a cake into three pieces (thirds). now, eat the three pieces. how much cake did you eat? 3 * 1/3 or 3/3 or 1 cake. hope this helps |
I realize that I still have some difficulties in understanding the meaning of position vectors.
Starting at 15:30 Sal explains that the vector [3 0] - r ("the pink vector") is a member of N(A) although it is lying on the solution set of Ax = b ("that pink vector is not in standard position but it is going to be a member in our null space).
Does this mean that every vector is part of both the solution set and the null space? And would this mean that the solution set and the null space are equal? | qdf2CuMGdKs | The pink vector is still part of the null space because shifting a vector from standard position does not change it at all. You could also think of it like this: The solution set to Ax=0 is contained as a subsection to the solution set of Ax=b. I hope this cleared things up for you. |
At 14:37, Sal defines r as a member of the column space. Isn't that a mistake - did he not mean that r is a member of the row space? | qdf2CuMGdKs | yea he did, he misspoke, he never actually graphed the column space which in this case would be 3 6 |
Can you do the dot product on two column vectors? (See 16:56) Shouldn't Sal be using a transpose of one of them or something? | qdf2CuMGdKs | The dot product can be used on any vectors, as long as they are of complementary sizes. |
At 9:03, Sal says that that the arch of the graph will never touch the y axis. So would would y axis be called an asymptote? I mean, in hyperbolas and such we have asymptotes that can't ever touch certain lines. So i was just wondering if logs used the same terminology.
Thanks. Sylvia | DuYgVVU_BwY | Yes, it is an asymptote. Logs all have the y-axis as an asymptote unless translated. However, there is no limit to the range; there are no horizontal asymptotes in log functions. |
I want to graph the function f(x)= -1/2 log2 (x+3)
I am having trouble figuring out points to plot, x and y coordinates, so I can graph it. Like he begins to do at 2:38.
Please help show the mathematical steps in determining coordinates for this more complex logarithmic function.
Thanks! | DuYgVVU_BwY | x+3 tells you where the function lies on the x axis. in this case, 3 units to the left at 3 .. the -1/2 tells you the vertical stretch of the line ( i.e 2 means the line is steaper( like a V, 1/2 would be wider like a U. (but only one half of it ..) |
At 6:35 , sal says that the domain : x > 0 , but here we are putting the value of y and then finding the value for x , so how the domain is x > 0 ?
Domain should be in the form of y i guess .
Please help me with this . | DuYgVVU_BwY | The domain is always the values of x - that is literally the definition of domain. The range is the values of Y |
at 3:58
Does anything to the 0th power equal 1 or 0. Some people say 1...some say 0. | DuYgVVU_BwY | Anything to the zero power always equals 1. |
At 5:01 how do you use a calculator? Like if the problem was log2(x)=y then how can I find out what power to raise 2 to for a result of 3? | DuYgVVU_BwY | Some calculators let you choose a base, but most don t. You would have to learn how to convert from one base to another. Sal has vids on that. |
At 6:33, what does Sal mean by that the domain has to be "x>0?"? | DuYgVVU_BwY | He means that the value you input into the equation cannot be 0 or negative. This is because there will be no solution (no possible y value) for those values of x. |
At 6:21 it is said that there is no value of y for which we get a negative x.Is this applicable to all logarithmic functions? | DuYgVVU_BwY | Yes. If you have any function which looks like y = log (x) then x > 0, otherwise you get imaginary numbers. |
At 1:25, there was a mistake, the question said:The bar graph shows how may( SUPPOSED TO BE many)! just telling you guys! Have a great day! | OmLl6pkvV-I | At 1:25, that was probably a typo. When people do the question, they ll probably know it s many and not may. |
At about 1:00, can there be an orthogonal version of a single vector? Doesn't a vector have to be orthogonal to something? ... or have I misunderstood the concept? | ZRRG386v6DI | The dot product can t be 0 if there s no dot product. |
0:50, the question "is4792 divisible by three"i wanted to ask if it is possible to just add up the last two numbers and check if they are divisible by three e.g. 9+2=11.And we know that 11 is not divisible by three . I'm really beginning to think that it also works that way. | NehkLV77ITk | On 0:57-1:20, they explain how to do that test |
At 4:17, Sal said, "If you add two things that are divisible by 3, then the whole thing (sum) is going to be divisible by 3." If that confused anyone, here is is the proof:
if numbers A and B are divisible by 3, then we need to prove (A + B) is divisible by 3.
Rewrite A = 3 * A'
Rewrite B = 3 * A'
Therefore, A + B = 3 * A' + 3 * B'
= 3 * (A' + B')
3 * (A' + B') is clearly divisible by 3, so (A + B) is divisible by 3. | NehkLV77ITk | edit: Rewrite B = 3 * B |
I'm confused at 2:11 | NehkLV77ITk | The 4 in the hundreds place is equal to 400. so that 4 equals 4 x (1 + 99). 400 = 4(100) = 4(1 + 99). |
sal says is 4792 divisible by 3 this is an emergencey! at 0:06 why say that? | NehkLV77ITk | For a number to be divisible by 3, the sum of the digits must be divisible by 3. Notice that the sum of the digits of 4792 is 4+7+9+2 which equals 22. However, 22 is not divisible by 3. So 4792 is not divisible by 3. |
Is there really someone wholl come up to you and ask you- I dunno, could 3488 be divided by 3( Its mentioned at 00:10) | NehkLV77ITk | Not very likely to happen. But best to be prepared. BTW this was also mentioned at the very start from 0:01 but with a different number. (4792) And how do you write in code?! |
At 2:53, why is it just plus 8? Why doesn't Sal write something like 5+3 or 9-1? Three and nine are divisible by 3. | NehkLV77ITk | here goes my first answer, he could actually do the same for 8, it would have been: 8[1+0]. get it 4[1+99]=4*100=400 9[1+9] =9*10 =90 8[1+0] =8*1 =8 =498 |
At 1:00 Sal says that in order to find out if 386,802 is divisible by 3, you add 3+8+6+8+0+2. On a math test, is it necessary to write the zero in your work? | NehkLV77ITk | Not really, because 0 plus what ever equals the number. It doesn t really change anything. |
At 2:10 Sal says 400 equals 4(1+99), but why can't you just write it as 4(2+98)or 4(3+97). And the video doesn't prove that it works because he's just writing it as 1+99, but you could also write it as 2+98. Why is that? | NehkLV77ITk | Because 99/3=33, thus 99 is a perfect example of a number divisible by 3. |
At 0:44, she mentioned one tenth, is there such a thing as an "oneth place" in decimals? | qb0QSP7Sfz4 | There isn t really a word oneth but lets start by thinking what a oneth would represent. Well, if a tenth is one divided by ten or 1/10 and a hundredth is one divided by one hundred or 1/100, then a oneth would be one divided by one or 1/1. Since 1/1 is equivalent to 1 then a oneth is equivalent to a one. So, to answer your question, there isn t a oneth place because oneths are equivalent to ones. |
At 0:08 Sal says he likes to have the bigger number on top, but you can have them the other way round can't you. | k68CPfcehTE | You can, but you end up with an extra step if you do it that way . |
0:10 why write 32 again? | k68CPfcehTE | he does this because he is writing the numbers in a different arrangement. This has two purposes: first, this is easier for some people to visualize, second (and more importantly) because this is the way to do long multiplication on paper. Hope this helps! |
If you compare the "How many department stores have exactly 7 watches" (2:08) to the tiger question at 2:31 i think Khal messed up.
The answer should have been (on the tiger one) 3 because of 2,3, and 4 zoos having more than 24 tigers. How did Khal get 9? I do not get it, can someone explain that to me? | PXKHyT__B2k | You are counting only the rows, not the number of zoos in each row. Remember, each number on the right represents a zoo. Thus... The row labeled 2: has 3 zoos with 25, 28, and 29 tigers. The row labeled 3: has 5 zoos with 30, 31, 32, 38 and 38 tigers The row labeled 4: has 1 zoo with 40 tigers. If you count all these, there are 9 zoos with more than 24 tigers. Hope this helps. |
around 3:06, he says that the equation equals theta. does that mean the inverse tangent and normal tangent just cancel each other out??
thanks in advance for replying! | aHzd-u35LuA | tan(θ) = 324/54 Yes, inverse tangent does cancel out tangent, another way to think about it is that inverse tangent undoes tangent. To isolate the theta in the above equation, you undo the tangent with an inverse tangent, but remember, you have to do it to both sides. θ = tan^-1(324/54) |
At 4:17, it was 80.53 degrees | aHzd-u35LuA | The question required rounding off the answer to 2 decimal places. As the value the calculator gave was around 80.537, rounding off to 2 decimal places would give you 80.54 degrees |
At 8:37 pm. The test I just took today asked me this. "angle A is 30(degrees), using the link below (a trigonometric chart). What is the Cos of A?" Now on the chart I can see the sine, cosine, tangent, etc, as they relate to the degrees including 30 degrees. But the cosine that I see on the chart for 30 degrees is not the answer. Please help. | aHzd-u35LuA | cos 30° = ½â3 This can also be expressed as â¾ and (â3)/2 For reference, sin 30° = ½ tan 30° = â
â3 = 1/â3 |
But.. at 2:22 what is inverse tangent | aHzd-u35LuA | It is the inverse function of tangent. In other words, if you know the tangent of an angle, the inverse tangent would give you the angle. NOTE: Although inverse tangent is typically symbolized as tanâ»Â¹ x, it is NOT the reciprocal of tan x. The same goes for the inverse functions of the other trig functions. |
at 2:36 does sal multiply both sides by tan^-1 like we do in linear equations? | aHzd-u35LuA | Tan^(-1) is called inverse tangent or arc tangent (arctan). It does not mean and is not the same as 1/tan. When you take tan^-1 of tan(θ) they cancel out leaving you with θ alone. This is how you find the measurement of an angle in the right triangle using SOH CAH TOA. Similarly, there are sin^-1 (arcsin)and cos^-1 (arccos) for sine and cosine. |
Um, I don't want to be nit-pickey, but 4:18 in the video, Sal says 80.54, but the calculator said 80.53. Did I miss something? Did he say to round up? | aHzd-u35LuA | If you listen carefully in the video, he says that the problem asks us to round up. |
At 4:18, Sal says that theta is 80.54 degrees, but the calculator shows 80.53.. So was that a mistake or was there just a reason behind it? | aHzd-u35LuA | Sal s answer is correct. The problem asked for the answer to be rounded to 2 decimal places. The calculator has 80.537677792. The 3rd decimal place is above 5, so you need to round up. You didn t. You just truncation the number rather than rounded. Hope this clarifies things. |
At 3:41 Sal talks about using a random digit table. In his example, he took two consecutive digits and then moved to the next two consecutive digits to get 59, 83, 35, 59, 37, .... Would it have been legitimate to have just moved one digit at a time rather than two to get 59, 98, 83, 35, 59, 93, 37, ...? | acfjqWTwee0 | I had the same in mind. The answer is: You have to assign each of your cases a random number to pick that has the same number of digits than your largest case. Let s say we have 1, 2, 3 .. 25 cases, then we assign the following random numbers: 01, 02, 03, .. 24, 25. |
At 3:32, How is choosing people with numbers assigned from 01 to 80 random? The person which is assigned the number 80 will have the least chance of being chosen because there are so many other 70's, 60's.... Shouldn't a random sample have everything in it equally likely? | acfjqWTwee0 | it is equal because the person who is number 76 has the same amount of chance as being chosen with a person who has number 80. They are just numerical place holders to facilitate the generating process. |
At 5:40 why does he say that 0*12=0 when before in one of the last couple videos he says it is undefined. | d8lP5tR2R3Q | Oh now I understand. |
at 1:43 you talk about properties what are those?? | d8lP5tR2R3Q | In your standard algebra a*b would always equal b*a for all numbers a and b. This follows from the commutative property . However, it is also possible to create other number systems where this is not the case. |
at 0:55 sal said that a negetive number times a negetive number makes a positive number i don't get that. | d8lP5tR2R3Q | i guess its like the opposite of adding is multiply so yeah |
at 1:40, Sal guesses Transitive and Commutative Properties. Isn't it the Associative Property? | d8lP5tR2R3Q | It is the commutative property. |
from 1:54 to 2:54 what does he mean | d8lP5tR2R3Q | He was explaining the rules of multiplying and dividing negative numbers:D |
(on 1:05 ) how do you know the amount you can borrow from the other number? | LSaaKau63Gg | Always borrow one from that digit. That is borrow one 10, or one 100 or one of whatever the place value is. |
At 1:10, Sal says that angle SIE is a supplementary angle. How did Sal know that LE was a diameter? | pCLGpRaJfJ8 | LE isn t a diameter... It s just a straight line segment and <SIE and <LIS add up to 180 degrees which makes them supplementary. A segment doesn t have to be the diameter to be straight. A diameter has to pass through the center of the circle to be a diameter. In this case that means that to be a diameter a line segment would have to pass through point O. |
@ :10:10 Can someone give a Actual Real Life example of that.?? of Mutally exclusive thank you | QE2uR6Z-NcU | When you flip a coin, heads and tails are mutually exclusive. |
anyone noticed the error @ 7:00 (12+13)/29-5 !=20/29! | QE2uR6Z-NcU | If I know what you mean, I believe it was actually (12 + 13 - 5)/29 = 20/29. :) |
At 5:00 the question P(Y or cube) was asked could you subtract the green spheres and get the same answer | QE2uR6Z-NcU | Yes. P(not green sphere) = P(yellow or cube) |
At 2:39 why the negative sign in: [ - ( x - 3 )^2 - 8 ] was distributed to the -8 too? Because I learned that for example 2(x+1)(x+2) = 2x+2 + x+2. Which means only distributing the first number to the first expression without the second. | 4Bx06GFyhUA | The expression you wrote above is not the same as the one that Sal wrote. Sal s blue parentheses enclose 2 terms : (x-3)^2 and -8. The negative sign is outside of those blue parentheses and is therefore distributed to each of the terms inside. Your expression has moved the negative sign inside the parentheses (brackets) so that, as written above, the negative sign will only affect the first term. [ By the way, 2(x+1)(x+2) = (2x+2) times (x+2), not plus. } |
At 1:00 Sal begins using completing the square method in order to find the lowest maximum value.
Can I use X= -b/2a where X gives the lowest maximum value and b and a are the coefficients of x and x^2 respectively.
Thanks.
PS I did get the correct answer using this method. He showed it in finding the x coordinate of finding the vertex of a parabola. | 4Bx06GFyhUA | By completing the square, Sal finds a quadratic (x - something)^2 that is shifted up or down by some other thing. X=-b/2a does not take into consideration the c term or constant. The quadratic shows explicitly the min or max value of this function. |
What does Sal mean, from 1:07 to 1:17, about each of the four total parts not being exactly 25%? If I had a set of data, would the four parts vary in percentage depending on the number of data I have in a set? | oBREri10ZHk | Sal means that the areas in the box plot aren t exactly looking like 25%, although he should have said that instead. |
At 1:25, what are the 2nd and 4th quartiles? | oBREri10ZHk | The second quartile is 10, and the fourth is 16 |
Regarding the last statement at 6:32, can we say that if this statement is true (exactly half are older than 13 (the median)), then we know for sure that there is an even number of students. Otherwise (if the statement is false), then we know that there is an odd number of students. Right? | oBREri10ZHk | That sums it up good. |
As a general rule, is it better to use decimals or fractions when doing problems like this? My personal preference is fractions, but could someone please point out the merits of using decimals? For example, if you look at 1:52, that table gets a bit messy. Is it better to use fractions in general or are there some cases where decimals are good? | zFksanIexHI | It s sometimes hard to immediately see the value of a fraction, where decimals show you very clearly the magnitude of the number, so decimals will be more useful in the real world in situations where you need to know what exactly a number is. I find fractions easier to deal with when manipulating expressions, though, and you always know you ll have the exact value when dealing with fractions where decimals sometimes have repeating numbers and so forth. Basically, it really depends on what you re trying to do. |
At 2:18 Sal says, "Now to find the median of the seven number". What do you do when the upper and lower half are even? | oajrmwCALmc | You take the average of the two middle numbers. For example if the numbers were: 1,2,3, 5, 6, 7. The median would be the average of 3 and 5 which is 4. (3+5)/2 If the numbers were 1, 2, 3, 4, 5, 6, the median would be the average of 3 and 4 which is 3.5 or 3 1/2 (3+4)/2 Hope this helps. |
At 3:09, why can't Sal use the fact that the antiderivative of (cosx)^2 = 1/2(x+sinx*cosx)? I worked the problem out this way initially, and unless I made some unrelated mistake, the two answers aren't the same. I got 2pi as the final answer. | -cR6FzM1zNE | (cos(x))^2 = 1/2(x+sin(x)*cos(x)) should yield the same answer, as sin(x)*cos(x)=(1/2)sin(2x) |
At 3:25, Sal gives the formula for calculating the vertex of a parabola,
-b/a.2
Is this formula -b/a.2 or -b/a.c since in the example c = 2. | za0QJRZ-yQ4 | -b/2a not -b/ac |
In 1:39-1:42, Sal says that a quadratic has a parabolic shape. I have been learning about quadratics lately and I wonder: why do they have a parabolic shape? I just started to learn about parabolas in physics two weeks ago (so I know a little about them), but I can't seem to understand how the two connect. | za0QJRZ-yQ4 | The parabolic curve derives from the 2nd degree term inside of the quadratic. Polynomials with different degrees have even more curves!! And as for seeing the parabola in physics, did the equation/formula used to get the parabola have a 2nd-degree term in it? Gargamel |
At 2:39 why does Sal select the numbers -2,-1,0,1 for his x values? I have often seen these numbers selected for use when needing to input values for x. Is it for simplicity? | za0QJRZ-yQ4 | Those are convenient numbers. They are relatively small, with some positive and some negative. |
Somewhere around 3:04, why isn't the equation 3x+6x-2. Why is the equation 3-6-2? | za0QJRZ-yQ4 | You are solving f(x) for a particular value of x, so this isn t the equation in general, just what it equals at a particular value of x. f(x) = 3x² + 6x - 2 f(-1) = 3(-1)² + 6(-1) -2 f(-1) = 3(1) + (-6) - 2 f(-1) = 3 - 6 - 2 = -5 |
At 0:53, Mr. Khan mentions about imaginary and complex numbers. What are some examples of imaginary and complex numbers, and how are they used in equations and in everyday life? In addition, in what aspect of mathematics are these numbers covered? | za0QJRZ-yQ4 | Very little mathematics beyond arithmetic is used in everyday life if you don t work in a field involving mathematics. Imaginary and complex numbers have a lot of applications in physics, like electrical engineering. They are introduced algebra 2 or precalculus. |
At 7:30, Sal says the domain is all real numbers >= -5. But why is this? The parabola keeps going on to the left with more negative numbers? Don't those numbers count as well?
Thanks in advance! | za0QJRZ-yQ4 | It is the range, not the domain, that is f(x) ⥠â5. The domain is all real numbers (which is always the case for polynomials). |
How do you get the x values to put in the table, like you said -2. -1, 0, 1, 2 as x values? at 2:25 | za0QJRZ-yQ4 | You choose them at random. In most cases, it s favourable to use small numbers to make it easier on oneself. Of course, you should also choose negative AND positive numbers to be able to draw the parabola in both directions. However, the numbers you choose are your own choice. :) Hope this helped. |
At 1:05 Sal is talking about real numbers. Is "e" a real number? | za0QJRZ-yQ4 | No, e is not a real number. e is an imaginary number, like i . They do not belong to the number line. They have their own plane which is called the complex plane . |
At 3:14, I don't get how -5 is the vertex. For example, if you have -5 as x and insert it you would get:
3(-5)^ + 6(-5) - 2
3(-25) + -30 - 2
-75 - 30 - 2
-107
So that's why i'm confused. | za0QJRZ-yQ4 | -5 is the y-coordinate of the vertex. Also, your arithmetic is wrong here. (-5)^2 = 25, not -25. |
In the first video, Sal used different notations to state that the domain was all real numbers. Why didn't he at 0:40? Does it make a difference? | za0QJRZ-yQ4 | Nope! As long as other people understand the point you are trying to make, it doesn t really matter. This is perhaps the clearest way to express all real numbers , as its quite literally spelled out for you. |
do we regroup by taking away 1 from 17 0:33- 0:78 | r3M68V9Joac | This will help you regroup. Regrouping fractions means taking away 1 from the whole number and adding it to the fraction to make it an improper fraction helping you add or subtract. |
Around 1:25, Sal says "the power of three". What douse that mean? | tVDslyeLefU | The power of... term is meaning if you re multiplying something like 10x10x10 or 10 to the third power. It s simply saying you are multiplying this number by another number however many times. |
At 1:30 i don´t get what that means | tVDslyeLefU | At that point, it is the volume of 1 single cube with the side 1/4 ft. |
At 0:05 Sal says the unit cubes are "1/4 ft by 1/4 ft by 1/4 ft." But in previous videos he said a unit cube is "1 by 1 by 1." Which is it? | tVDslyeLefU | This video uses fractional cubes, (look at the title) regular unit cubes are 1 by 1 by 1. I may be wrong, but I think I am correct. :) |
At 1:45, Sal khan said 'For every two apples, we have five pieces of fruit.' What did he mean by that? I don't get it. | UK-_qEDtvYo | Sal wants to find the ratio of apples to fruit The number of apples = 4 Fruit in this case means the total of all apples and oranges (apples + oranges = 4+6 = 10 pieces of fruit). Thus, the ratio of apples to fruit = 4 / 10 Reduce the fraction, and you get: 2 / 5 Hope this helps. |
At 2:44, is a ratio is basically a fraction? | UK-_qEDtvYo | yes it is. It confused me to. |
So when we write the time we say something like 8:20. Is that the same as 8 hours for 20 minutes? | UK-_qEDtvYo | No, it means 8 hours and 20 minutes after noon if it says p.m., and 8 hours 20 minutes after midnight if it says a.m. |
Can you only use fractions in the problem used in the video which is 2:5. 2, representing the number of apples we have, and 5, representing the number of fruit. | UK-_qEDtvYo | Yup. Totally correct. |