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At 4:54 what if there are only 3 numbers on the left and right what would I do? | qLYYHWYr8xI | If you have only 3 numbers on each side, then you still choose the middle number on each side to be the median number. |
At 0:48 he he says it is important what you do the order of multiplying in but if its multiplying the order shouldn't matter right? Doesn't 1 x 2= 2 and 2 x 1= 2? | iUQR0enP7RQ | In matrix multiplication, order does matter because the dimensions have to be ordered correctly. For example, you can multiply a 3x3 matrix with a 3x2 matrix because the center numbers- the number of columns in the first matrix and the number of rows in the second matrix-(3 and 3) are the same. However, you can t multiply a 3x2 matrix by a 3x3 matrix because the center numbers (3 and 2) are not the same. |
what is that sign that sal uses at 0:53 | iUQR0enP7RQ | Are you referring to the equal sign (=) that has an extraneous mark on it? I think this was just a writing mistake: it s not easy to write things out using the program that Sal is using. So: this is just the equal sign. It s unfortunate that Sal happened to make the same mistake on both symbols, here :-( |
How to come up with this matrix at "7:03"? What's the relation with matrix A? | iUQR0enP7RQ | Sal doesn t go into it in this video, but there is a way to get the inverse without memorizing the formula. The idea is to set up an augmented matrix [A|I] and then use reducing to get to [I|A^-1]. Try checking out the videos on Reduced Row Echelon Form (that s where I d start at least) and then try it yourself with the generic matrix he gives here to see how to get this formula. |
shouldnt it be -15/7??? at 12:00+ | iUQR0enP7RQ | No, the first part of what he is doing is he is multiplying the first object from Matrix A -- in this case, 5/7 -- by the first object in Matrix B -- in this case, 3 -- and since both values are positive, the answer is positive. If one of these values negative, then the 5/7 would be negative; however this is not the case. |
At 3:34, Sal mentioned column vectors. So, each column in a matrix is a vector? | iUQR0enP7RQ | Yes, a matrix made up of only one column is called a column vector while a matrix made up of one row is called a row vector. Therefore you can consider a single column in a matrix as a vector. |
At 2:18 he says that an identity matrix is zeros with ones along the diagonal. Could you put the ones anywhere so long as you had one one in each column and row?
for example, would this work?
[0010]
|1000|
|0100|
[0001] | iUQR0enP7RQ | No. They must be in this (diagonal order). He proves it at 2:20 by showing you why it works. :) |
at 1:05 why less than or equal to? | 17a443nL7Qw | You typically preserve the equality (in this case, the less than or equal to) from the original problem statement. |
At 0:45 he says that x is less than or equal to negative 2, but he didn't switch the sign. Why did he not do that? Help plz!!! | 17a443nL7Qw | He did not divide or multiply by a negative #,only then do you switch the sign. |
at 1:13, why is the dot filled? | 17a443nL7Qw | The little line under ⥠means or equal to . Let s say, for example, xâ¥3.That would mean x is greater than or equal to 3. So to say or equal to, you would have to fill in the dot so that it doesn t look like x>3, with the empty dot. Get my point? |
at 1:24 what does Sal mean by "all the nubers lower that -2"?
i mean it could go all the way to -1,000,000,000,000 (etc). | 17a443nL7Qw | Yes it can,we don t know what the number is |
by the way in the last part at 7:12 grant missed the transpose of the (x-x0) i believe correct me if i am wrong | ClFrIg0PpnM | You re correct :) |
at 1:45, why did he put a 2 at the end of the number line when he didn't even use it | Kt7Dwr7BftE | It also lets you see how big some numbers are in comparison to other numbers. |
At 8:59, who invented Khan Academy | Kt7Dwr7BftE | The person who teaches you in the KA videos is the creator of Khan Academy. He is Salman Khan(Sal for short) |
At 0:45 isn't X 4 less than 9. Maybe I'm just not understanding . . .
Thanks | j5xis6Hlnds | Point A is 5 less than 9 as Sal said at 0:50. A is at the point (4, -3), and the centre of dilation is at (9, -9). Therefore, A is 5 away from 9, as 9 - 4 = 5. Maybe you were confused because one of A s coordinates is 4. |
Why does he say he messed it up at 0:34, when he counted right? | -Zlq5tNl94M | He skipped the second rectangle at first :) |
At 5:00 in the night how is it so dark? | xCIHAjsZCE0 | its in alaska |
At 7:12 why did Sal say Each child drank 2 cups instead of eating 2 Cupcakes? | xCIHAjsZCE0 | I think it was by accident... Either that, or what the previous answers were saying. Good job noticing it! :) |
At 6:58, why does he take 200c - 300c? | xCIHAjsZCE0 | This is because he is subtracting the second equation from the first equation. Here is the breakdown of what he did: 500a + 200c = 2900 500a + 300c = 3100 500a - 500a = 0 200c - 300c = -100 2900 - 3100 = -200 It was necessary to take 200c - 300c in order to find out what c is equal to. After that, take the value of c and back substitute to figure out what a is equal to. |
At 7:11 Kal says that each child drinks two cups. Which is it, are we drinking cups or eating cupcakes? Ha!. | xCIHAjsZCE0 | Daryl, It another example that shows Sal is human and imperfect and can make mistakes just like most of us. I just wish I made as few mistakes as Sal does. |
at 4:00 I started to wonder
how does elimination help me?
also, what if you are doing something with the formula d+tr (or whatever it is) how to you get it to y=mx+b?
thanks <3 | xCIHAjsZCE0 | If you are presented with an equation in the form ax + by = c if is usually easier to solve the system using elimination rather than converting to slope intercept form and trying to work with fractional coefficients. |
at 0:44, how does the king know how many cupcakes both kids and adults eat? | xCIHAjsZCE0 | I don t know. Maybe he keeps track? |
at 6:25, why do you subract the two equations and not add them? | xCIHAjsZCE0 | The goal is to eliminate one of the variables, in this case it was a . Sal subtracted the two equations to cancel out the a s . If he added the equations, the result would still have two variables. I hope that helps |
at 2:27 do you add or subtract to get the answer for both of the equations? | xCIHAjsZCE0 | For this equation he subtracted, but he subtracted to get rid of both the 500a s so he could solve for c. Hope this makes sense. |
4:38, divisor (x-a) is 0, dividing 0 is not in the definition of division. | NIazpCER9oM | x-a is not in the denominator anywhere in the theorem. Because division by 0 is undefined, there is a removable discontinuity in q(x) at x=a; but since in the remainder theorem q(x) is multiplied by x-a, the reason for a discontinuity no longer exists. |
At 1:21, why isn't the remainder placed over the divisor as it is in other videos? Is there a difference between the two answers or the way they're are written? Such as having added (6/(3x-1)) or having added 6. | NIazpCER9oM | It s because if you move (x - 1) from the right side of the formula to the left by dividing, you also have to divide 6 by that monomial. The equation then changes to: (3x^2 - 4x + 7)/(x - 1) = (3x - 1) + 6/(x - 1) |
At 0:14 he says the angle makes a complete line. Is there a special name for this type of angle or is it just called a line? | 2mzuFKCuDg4 | a straight angle |
At 3:55, he makes an equation that says (x + 3)(x + 7) = x to the second power + 10x. Why is the x also following the 10? It's already been expressed in the x to the second power. | SjN3_xCJamA | we are multiplying two binomials. so we can express it as x(x+7) + 3(x+7) = x^2 +7x + 3x + 21 = x^2 +10x +21 |
At 5:18 Sal Says that you cannot add or subtract matrices with different dimensions. Why can't you just put a zero in all the missing places and then add all the others? | WR9qCSXJlyY | That s a very interesting idea! If it hasn t already been done, you could create this new operation on matrices. Who knows? It might turn out to be of great use, in some new branch of mathematics. My first question would be: Where would you put the missing places? There would be different ways of making two matrices conform, so the result of this new kind of addition would depend on the chosen method of padding (so to speak) with zeros. |
From 4:08-4:20. how do you properly understand how the negative (-) and positive (+) work in adding and subtracting? | WR9qCSXJlyY | You simply add negative numbers instead of positive numbers(in the second matrix) |
At 4:20, why do you put negative for some of the numbers and not all? | WR9qCSXJlyY | The (-1) is multiplied by all the numbers in the second matrix: 0 + (-1)(-1) = 1, 1 + (-1)(3) = -2 3 + (-1)(0) = 3, 2 + (-1)(5) = -3 And the answer matches the first method he used. |
3:27-3:28 Did Sal said negative one too many times? | WR9qCSXJlyY | He just repeated negative one. No biggie. |
At about 2:10, Sal said that you can't just put a matrix in any order when multiplying and dividing. I understand why you wouldn't be able to put the matrices in any order while dividing, but since multiplying is simply repeated addition, wouldn't the order of two matrices not matter? | WR9qCSXJlyY | Actually, repeated addition of a matrix would be called scalar multiplication. For example, adding a matrix to itself 5 times would be the same as multiplying each element by 5. On the other hand, multiplying one matrix by another matrix is not the same as simply multiplying the corresponding elements. Check out the video on matrix multiplication. Indeed, matrix multiplication is not commutative. |
On 0:17, is borrowing the same as regrouping? | OJ-wajo6oa4 | ues, in subtraction they are the same...... |
At 2:10, why are you allowed to arbitrarily set (2/3)x^2 equal to sin^2(theta)? | n4EK92CSuBE | Sal has noticed that 1-(2/3)x^2 looks like 1-sin^2(θ). So, in order to see if that can help him solve the problem, he sets them equal to each other. Here he skips a few steps. This appears to be what confused you. 1 - (2/3)x^2 = 1 - sin^2(θ) - set them equal -(2/3)x^2 = -sin^2(θ) - subtract one from both sides (2/3)x^2 = sin^2(θ) - multiply both sides by -1, and now we re caught up to where Sal started. I hope this helps! |
At 0:54, is there a reason Sal chooses to use 1-sinθ instead of 1-cosθ? | n4EK92CSuBE | Sometimes it is a matter of preference. However, the existence of a negative sign can make one easier than the other. Remember that your sine and cosine derivatives are related, but they cycle a negative around. That also happens in integration. |
At around 2:10 why would we set sin^2(theta) equal to (2/3)x^2? | n4EK92CSuBE | Sal wants to see if he can use the Pythagorean identity to help him substitute and solve the problem. He skips a few steps that show this, but he originally sets 1-(2/3)x^2 equal to 1-sin^2(x). |
At 2:52, he solved for theta and found that it equaled arcsin times the sqrt of 2/ sqrt of 3 x. Where does the arcsin come from and how do I know to think of that? | n4EK92CSuBE | arcsin is the inverse of sine therefore, sin(arcsin( anything ))= anything |
how does he get the sin squared in his equation at 2:12 | n4EK92CSuBE | He s using trig substitution to solve the problem. By using algebra to make the the equation look like the trig identity and then substituting sin in for the x term to get 1-sin^theta |
So, in the video at about 6:14, Khan takes the constant term 1/sqrt(2) out of the integral. What if he wanted to, say, rationalize that fraction with the integral? By multiplying in a sqrt(2)/sqrt(2)? The inside of the integral read as sqrt(2)*d(theta), but what would the outside look like? | n4EK92CSuBE | For a â â: d/dx(aâ¢x^n) â aâ¢d/dx(x^n) â aâ¢nâ¢x^(n - 1) â«(aâ¢x^n)dx â aâ¢â«(x^n)dx â aâ¢1/(n + 1)â¢x^(n + 1) |
At 2:07, Sal takes (2/3)x^2 = sin^2(theta).
But shouldn't it be (2/3)x^2 = m.sin^2(theta) where m is any arbitrary constant?
The range of the sine function is only from -1 to 1.
In case our x is greater than, say, 3, take 6 for example, then (2/3)x^2 cannot equal sin^2(theta), since sin^2(theta) can never equal 24, since it can equal 1 at max.
This where the constant 'm' will come in handy.
Why is it okay just to use sin(theta) ? | n4EK92CSuBE | You are wrong that the sine maps only to the range [-1,1]. While its true if you are dealing with the real numbers, it is not true if you are dealing with complex numbers. For example, sin(pi/2-i ln(2+sqrt(3)))=2 |
at 5:43 when Sal takes the square root of cos^2(x) why does he only take the positive form of it and not the +- form | n4EK92CSuBE | Good question. The ± really comes from â(x²) = |x|. So, to answer your question, I m gonna ask it a different way: why doesn t it simplify to cos θ/|cos θ|? For us to use arcsine at all, we have to assume theta is be -Ï/2 < θ < Ï/2, that s the domain of arcsine. (We can t use -Ï/2 or Ï/2 because then you ll have a division by zero problem) Graph cosine and look at what happens for θ in that interval. |
how do you solve for theta like sal did in 2:46 ? | n4EK92CSuBE | inverse trigonometric functions sin (arcsin(x))=x cos (arccos(x))=x tan(arctan(x))=x csc(arccsc(x))=x sec(arcsec(x))=x cot(arccot(x))=x |
At 3:29 isn't it supposed to be â(3/2)*-cosÎ, or I somehow missed something out? Isn't dx/dÎ sinÎ = -cosÎ and vice-versa?? | n4EK92CSuBE | d/dx[sin(x)] = cos(x) d/dx[cos(x)] = -sin(x) |
at 2:45, how does he know that theta equals that value? Like what are the steps he used to solve for theta, I don't understand. | n4EK92CSuBE | He took the inverse sine of both sides. You take arcsin to get rid of the sine just like you would square to get rid of a root. |
I can't help but notice that the time of this video is 3:14 (pi). Did Vi Hart do this on purpose? Does anyone else notice this? Thanks in advance. | z6lL83wl31E | Vi supports Tau and dislikes Pi, so I doubt it was intentional. It is a funny coincidence! |
In 0:55, why do you evaluate something in the parentheses before you tackle the exponents? | GiSpzFKI5_w | its just the order of operations. You will get it wrong if you don t do it that way. |
At 2:00, How Would You Know When To Use The Parantheses Of 5 And 4 For Multiplication Instead Of Just Using Them Normally? How Would You Know Which Parantheses To Do First? I Would Appreciate If You Reply Back To Me. Thanks! | GiSpzFKI5_w | If there are parenthses, then you do all the parenthesis at once, then solve for the rest. For example, 5 x (3 + 2) + 1 x (9 - 1) , you would first do the parenthesis, which would look like this: 5 x 5 + 1 x 8. Then use order of operations to get: 25 + 8, which equals 33. |
at 2:35 where does the 5x4 go in the order of operations? It's not technically multiplication | GiSpzFKI5_w | It is multplication. These are the different ways of writing a multiplication expression: 1.a x 2 2.a2 3.a(2) 4.(a)(2) 5.a * 2 these methods work for both numbers and variables, except we rarely use method 2 for variables. |
At 1:17 Sal mentions multiplication and division. For multiplication and division and also addition and subtraction, does it matter which order you multiply or divide? Do you multiply before you divide? Do you add before you subtract? | GiSpzFKI5_w | The order is from left to right, but it doesn t really matter. |
At 4:04, why did Sal subtract 28 - 11 first instead of adding 11 + 44 first? I thought the order of operations says to do addition before subtraction? | GiSpzFKI5_w | you can do either one first he just chose to subbtract first. |
Since when does 60/2=8? 2:50 | GiSpzFKI5_w | He said 16, not 60. You can see on the board 6 + 10 : 2. If you do addition first you ll get 6 + 10 = 16 and if you do division after you ll get 16 / 2 = 8. Sal said 16 . He also said that it is wrong. Order of operation tell us to do division first 10 / 2 = 5 and than do addition 6 + 5 = 11 8 is wrong answer. 11 is right. |
4:09 there first minus is there 28-11+44 as per pemdas first want to do addition then subraction but u did first 28-11 then u done adition tell me sir reply | GiSpzFKI5_w | Addition and Subtraction are actually on the same level. When you get problems like these, evaluate from left to right. |
at 1:14 why do we need parenthesis | GiSpzFKI5_w | There are 3 sets of parentheses in the problem -- which ones are you referring to? The 1st 2 sets are used to show multiplication. The 3rd set is used to group a set of work that must be done 1st. |
At 4:07, Why did Sal do 28 - 11? As in the order of operation (BODMAS), Addition should come first, right? | GiSpzFKI5_w | Addition and subtraction are done in the order you find them from left to right. The same goes for multiplication and division. Example 5 - 3 + 2 = 4 |
at 1:57 i realized that the (5)(4) is 5X4. is that another why? or what? | GiSpzFKI5_w | Yes, they both mean the same thing. You will see it a lot in the future. |
At 2:22, Sal said that we multiply 5 and 4. But why do we multiply them even though they're in different parentheses?
Any thoughts? | GiSpzFKI5_w | When there are two parentheses that are right next to each other, and already simplified as well as possible, (i.e. (5)(4) ) we can take away the parentheses, because there is nothing else to do inside of them, and we get 5 x 4. Since there is nothing in front of 5x4 that is higher up in PEMDAS we can multiply them, and get 20! Hope that helped :) |
Hi, in school I learned a trick called PEMDAS , so at 4:09 wouldn't it be 28-55 instead of 28-11+44 whereas you could've just used PEMDAS to solve the expression. Thanks | GiSpzFKI5_w | It s the same thing, so it doesn t matter. It doesn t matter which way round you do the addition and subtraction because you will get the same answer. As long as you do brackets then powers first, then multiplying and dividing, then adding and subtracting, it doesn t matter which order. You can switch multiplying and dividing and it should still work (in the UK we re taught to divide then multiply) or switch adding and subtracting. |
At 3:30 what does it mean when it says to simplify | GiSpzFKI5_w | it means to make a fraction such so it does the top number and the bottom number do not share a factor. for example, take the fraction 2/4. both the top and the bottom share the factor of 2, so if we divide the top and the bottom by two, you end up with the fraction 1/2, which is equal to 2/4 but is simplified. |
at 2:00 where did he get the one | L70UJVjc-bc | It s part of the exponential growth equation: y=a(1+r)^t |
At 4:26, did he intend to change the domain of the x-integral from [0,2] to [0,3]? If so, by what reasoning did he do so? | vxQvL_WhBGU | The domain for x was always [0,3]. That was what was stated at the very beginning. |
on 2:54 Sal does dz first. What happens if you do dx first rather than dz first for triple integral? would I still get the same result? | vxQvL_WhBGU | yes because changing the order of integration doesn t affect the final result. It is a matter of convenience as to which order you choose to integrate in. Hope this helps |
At 7:47-7:49 why didn't Pythagoras run right through the bean field? True he was scared of beans but he was going to get killed. | X1E7I7_r3Cw | As he proclaimed, he was more afraid of beans than death. |
Does this "irrationality D:" attitude of Pythagoras at 6:57 remind anyone of this?
A long long time ago
Long before the Superbowl
And things liiike lemonade
The Hellenic Republic was full of smarts
And a question resting on the Grecian hearts was
What is the circumference of a circle?
But they were set on rational numbers
And it ranks among their biggest blunders
They worked on it for yeeears
And confirmed one of their biggest fears
I don't know if they cried
When irrationality was reeealized | X1E7I7_r3Cw | ...But something deep inside them died the day, they discovered, Pi.... |
3:44 to 3:52 What the blocks is she playing with? | X1E7I7_r3Cw | Vi used the piece of her paper she cut while doing stopmotion |
3:37 does anyone know any other whole nunber thing that works other than 3,4,5? | X1E7I7_r3Cw | You re looking for Pythagorean triples . Three whole number sides that give you a right triangle, like 3,4,5 or 5,12,13 or 8,15,17. There are infinitely many. One easy way to generate them is to square any odd number (say 7 which gives you 49) and then the two consecutive numbers that add up to 49 (24 and 25 in this case) give you the other two sides. So, 7,24,25 is also a right triangle. |
In 4:47, b square is even. Why does that mean that b is even? | X1E7I7_r3Cw | Good question. An odd number squared is always odd. - 3*3=9 - 5*5=25 - 17*17=289 An even number squared is always even. - 2*2=4 - 4*4=16 - 24*24=576 You can reverse these two rules to say that the square of an even number (assuming it has a square) is even and the square of an odd number is odd |
at 6:46, why does someone keep saying " unless it doesnt exist" . | X1E7I7_r3Cw | That person has just proven that things wouldn t make sense unless the ratio of two whole numbers equalling â2 does not exist. |
At 4:21, aren't the ratios supposed to be the other way around?
sqrt(2) â 14:10 â 1414:1000 â 141,421,356:100,000,000 â .... | X1E7I7_r3Cw | Yes they are. |
6:32 but it can be odd because 6 is odd and so is 10. can somebody help? | X1E7I7_r3Cw | there are ratios modern ratios say 6:2 is the probability of say in baseball 6 points at inning 6 and 2 points at inning 2 now 6:2 is the probability of the 6 point team winning |
At 00:03 what does she mean by dirt on him? | X1E7I7_r3Cw | No no no! The interactive transcript said it turned out he was just too good. |
At 8:09 she says he might not have liked them metephorically. What does she mean by that? | X1E7I7_r3Cw | to abstain from beans meant not to vote because back then you voted by putting beans in a jar. |
At 0:16 Why was Pythoragras scared of beans ? | X1E7I7_r3Cw | Thanks WallAvi for the anwser i will look it up on the website |
At 11:53, we see that 4 choose 0 is equal to 4 choose 4, and 4 choose 1 equals 4 choose 3. Can we generalize this and say that n choose k equals n choose (n-k)? | iPwrDWQ7hPc | Yes we can. There are (at least) two ways to see this. n choose k = n!/(k!·(n-k)!), and n choose (n-k) = n!/((n-k)!·(n - (n-k))!) = n!/((n-k)!·k!), which is the same thing. Or we can note that Pascal s triangle is symmetrical and n choose k is given by the kth entry on the nth row. |
at 0:53 can we make (a+b) to the 2nd power be 2a+2b | iPwrDWQ7hPc | No. 2(a+b) will create 2a + 2b. The exponent of 2 on (a+b)^2 is not the same as doing 2(a+b). You need to use FOIL to multiply the 2 binomials. (a+b)(a+b) = a^2 + ab + ab + b^2 = a^2 + 2ab + b^2 |
Sal, can you explain more clearer how you got n/k!(n-k)!, I understand its a formula we must know to solve the binomial theorem but can you explain how for example at 9:56 you did the n/k!(n-k)!. want to know how did you get 4x3x2x1 ? | iPwrDWQ7hPc | the product of n natural numbers from 1 to n is denoted n! and is read as n factorial. So n!=1x2x3x4.......(n-1).n. therefore 4! = nx(n-1)x(n-2)x(n-3). => 4 x 3 x 2 x 1. |
At around 6:00 Sal writes the formula. Isn't the sum of numbers between 0 and n if n=4 infinite? This would make the answer be infinite every time n>0. Enlighten me please. | iPwrDWQ7hPc | That notation simply means that the equation he wrote right to sigma, gets added to itself when k varies from 0 to 4. So first time in that equation we are gonna write 0 in place of k and then add the same equation but this time we use 1 in place of k and this continues till k reaches the given number, that is 4 in this case. |
at 1:20 why is it ab+ab how did it come to that | iPwrDWQ7hPc | FOIL method. (a+b)*(a+b)= a*(a+b)+b*(a+b)= a^2 +ab+ba+b^2 and ab=ba so it is a^2+2ab+b^2 |
What is the value of e at 4:07? | mXsn-YYUN4Y | e is an irrational number like Ï (meaning it cannot be written as the ratio of 2 integers and thus in its decimal form it will go on forever without any pattern). The first few digits of e are: e â 2.718 |
At 2:05 Sal uses his calculator and chooses "e" and raises that to a power of 2.1. What is "e" and where did that irrational come from? | mXsn-YYUN4Y | e is a constant, just like PI is a constant. e is something like: 2.71828.... e is the base of natural logarithm. I believe that e stands for Euler s number. |
7:44 The solution is not 2.06 because the values we got are 7.8 and 7.6, so they're in distance of 0.2 apart. He should have been more precise, it's probably 2.055 that would have gotten a more precise answer that would get the solution to be 0.01 apart (I'm guessing, we'd have to verity). | mXsn-YYUN4Y | It s x, not y, to the nearest 100th. 2.06 is the closest in hundredths for x. Do you think it s closer to 2.07? 2.05? (The closest I got was 2.05855, with the difference in y s about 3 thousandths) |
At 6:48, Sal says that 2.06 is definitely going to work. How does he know right off the bat that that will be the estimate? Because that is the closest value hundredths away, does that mean that that is how he can estimate it? To get the 2 answers within .01 of each other, how do we know that the answer is not going to be 2.065, or 2.062354, or anything really? It seems too precise for that to be the answer... | mXsn-YYUN4Y | He knows that 2.05 is too small and that 2.07 is too large, and that 2.06 is much closer than either. So he has a reason to think that 2.06 is as close as he can get in hundredths. |
At 2:57, grant said red vectors are super long but they should be super small right ? | ZTbTYEMvo10 | I agree, I think the colors are wrong - the ones near the origin should be blue / small vectors. |
at 2:10 can the circle area be less than the area of the sector? | u8JFdwmBvvQ | think about this: a circle is a pizza sliced into piece(s). The piece(s) largest area can only be the pizza. That s like what a sector is : a slice of a pizza |
In 0:56, where did he get 360? | u8JFdwmBvvQ | That is how many degrees there are in a circle. |
@13:00 Sal is talking about the existance of more than one inverse functions. So for f(x) there exists f-1(y) and g-1(y) that will get us back to x (if that makes sense). But aren't f-1 and g-1 the same functions, something like "y= x - 2" and "x - 1 - 1"? Or are there 'really' different functions that map every value of x to the same value of y? | -eAzhBZgq28 | He only assumes that there are two distinct inverses in order to show that that leads to the conclusion that they re the same (a contradiction), and thus proves that really there s only one inverse for any function. |
i dont get it, you read the composition thing from right to left or what? 14:00if you were to read it normally then he is wrong isnt he?for example the composition of f with g should be Ix and not Iy, because we first do X -> Y then Y -> X it's Ix right?
Im starting to thin you read it like parenthesis? like f(x) etc? | -eAzhBZgq28 | (fog)(y) = f(g(y)). (gof)(x) = g(f(x)). So e.g. for fog you first do g(y), then f(x=g(y)). |
Also he says at 9:51 that y is a member of the set capital Y, what does he mean by the set? | -eAzhBZgq28 | Any collection of things {1, 2, 3} , or {you, me, Sal}. or whatever. |
What's the line on top of 36? On 0:27 | Ihws0d-WLzU | The line is just there to indicate that 36 repeats forever. That s why Sal wrote that 36 with the line over it equals 0.363636..... They mean the same thing just expressed differently. |
At 2:06 it says we divide both sides by 99, but they are leaving it as a fraction, Is it supposed to be left as a fraction or is it supposed to be divided? | Ihws0d-WLzU | Well, since the title of this video is Converting repeating decimals to fractions (part 2 of 2) you should probably leave it as a fraction. Besides, if you divided your answer, you would be left with the original decimal number that you were trying to convert into a fraction. For example, if you converted 0.3333333 to 1/3 and divided 1/3 then you would be left with 0.333333333. |
I don't get 5:45 | Ihws0d-WLzU | U |
i don't get 7:30 to the end of the video. Can someone explain to me what sal is doing in the last two minutes?
(He uses a different method.) | Ihws0d-WLzU | All Sal is doing in the last several minutes is converting the repeating decimal into a fraction. He shows that you can, instead of creating a infinitely long decimal, use long division to get a mixed number. That makes it a lot easier to use in many different things; multiplication, addition, subtraction, division, etc., etc. |
At around 5:18 in the video Sal multiplies the Numerator and Denominator by 10. Why is it that we can multiply the right side of the equations by 10 and not the left side but still get a valid equation? | Ihws0d-WLzU | Oh, haha, that makes sense. I appreciate the response Danielle. :) |
at 1:25 you multiply the 0.3636... by 100 which is 36.36....., but you don't multiply the x(0.36) by 10? | Ihws0d-WLzU | You would want to multiply by 10^2=100 instead of 10^1=10, because now the repeating group is 2 digits (the 36) instead of just 1 digit. If you are not convinced of this, try multiplying by 10 instead of 100, and you will see that when you subtract the value of x from the value of 10x in the next step, you will encounter a difficulty because the repeating parts of the decimals will fail to cancel out. Have a blessed, wonderful day! |
At 5:00, how does multiplying 70.7 times 10 make the fraction correct? This is might be stupid, but I just dont get it. | Ihws0d-WLzU | Miriam, 70.7/900 can t be a fraction because it contains a decimal, 70.7 By multiplying 70.7/99 by ten, it changes to 707/990, and since there s no decimal anymore, the fraction is acceptable. Hope that helps! |
At 4:09, how does 100x - x =99X? | Ihws0d-WLzU | If you have 100 of something (x in this case), then take away 1 of those x, you are left with 99 of x. |
At 3:55, wasn't he supposed to put 10x instead of x alone? | Ihws0d-WLzU | The repeating decimal has two repeating digits. In order to make the repeating portions of the decimal cancel each other out, he had to use 1x. If he used 10x, he would have had another repeating decimal on his hands, as 71.4141... - 7.1414... = 64.2727... Thus, 1x was the proper choice. |
2:55 Wait a second! If he says that in 0.714 only the 14 part is repeating, then why is he multiplying with a 100 instead of a 10? I don't get this part. From the looks of it you could even argue that the repetition starts from 0.714. Or am I wrong here? He would have got just 99x = 7.07 right?
Can someone please explain this to me? | Ihws0d-WLzU | The trick is to get the repeating pattern directly below itself. If you only multiply with 10 you get: 7.14141414... (positive 10x) 0.71414141... (minus 1x) 6.42727272... (10x-1x) Which is just another repeating pattern I am not sure what you mean by your last question about the 99x, but 99x=70.7 |
@3:45 isn't "14" the number that is mark to be infinitely repeating? why Sal left 41 after the decimal: 71.414141 instead of 7. 141414.... why? ;_; shouldn't the digits after the decimal point be identical? | Ihws0d-WLzU | He multiplied the decimal by 10 which we know from elementary school just shifts the decimal 1 place value to the right. |
At 3:18, what does Sal mean with 'the repeating pattern can be right under itself'? | Ihws0d-WLzU | i think it means that he is dividing the repeating decimal out |