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At 8:15 I was completely lost: why/how he did that?
Who ever respond to this, thank you very much! | Ihws0d-WLzU | Well, it s a little odd how he did that, but he s just subtracting one number from another, and setting up the borrowing ahead of time. It s just: 3254 -2997 ------ 257 So he sees the first subtraction is 7 from 4, so he has to borrow, and that reduces the 5 in the tens place to a 4, and so on. |
Why at 2:04 did he subtract "x" one time? what is the point? Help! | Ihws0d-WLzU | Here we have two equations. The first one (100x=36.363636...) was made by multiplying x=0,363636... by 100 so we can get rid of fractional part after subtracting lower equation from upper one. We can do it cuz this way we subtract THE SAME QUANTITY (since x = 0,363636.. ) from the both sides of upper equation, which is valid step to do. This way we lose one x one the left side and all the fractional part on the right hand side. Hope it helps! |
At 2:20, I didn't understand how he got 101 tenths. | dNnItWLuHH4 | Imagine you wanted to buy some candy and the shop keeper had no change. The candy costs $20.10 (twenty dollars and ten cents) and you have a twenty dollar note and a dime. You go to the bank and they give you: a 10 dollar note 100 ten cent coins (dimes) plus you already have your original ten cents Now you can buy your candy with 101 dimes! |
at 1:10 how is it 2500? when the question is20.1? | dNnItWLuHH4 | The question was 0.25 and it s 25 hundredths. |
i was lost at 6:46. When solving the quadratic is 1/4 and 4 the only answer? what does he mean both of the constrains has to have the same sign?
How did he get 1/4 and 4 > 0, then 1/4 and 4 < 0? | GDppV18XDCs | Both (p-1/4) and (p-4) must be the same sign so when you multiply them together it will be a positive number (aka > 0). He breaks it into two scenarios: if they re both + or both -. If both (p-1/4) and (p-4) are positive they will be >0 and if they are both negative they ll be <0. Then he just makes sure the variable is alone on the one side and uses logic to deduce that the answer is less than 1/4 |
Around 8:34 in the video, Sal says that the equation can be simplified to p>4 because if something is greater than 4 it must be greater than 1/4. Wouldn't the equation be simplified to p>1/4 because if it is p>4 than p cannot be 2/4 which is greater than 1/4 but not greater than 4. | GDppV18XDCs | No, that part of the solution cannot be simplified to p > ¼ You want a summary statement that works all the time, and the solutions must satisfy both p > ¼ and p > 4 There are two parts of the constraint he has to consider: the positive case where the raw solutions are p > ¼ and p > 4 Using your 2/4, that cannot be a solution because it is not greater than 4. Giving p > ¼ as the summary solution would say that you could have 2/4 as a solution. |
At 7:54 why is it for both negative you need to flip the inequality sign? | GDppV18XDCs | Because a negative times a negative will always be positive, which fill in (p-0.25)(p-4)>0. |
At around 4:14 when you are taking away 2 1/4 p from both sides and you also move some of the parts of the left, why didnt you keep the squared on the one, on the left side of the greater than sign. | GDppV18XDCs | The reason is that 1² means you want to square the 1, in other words that you will multiply 1 x 1 ---and that result is just 1 There wasn t any reason to keep it as 1² when its value is so simple. |
At 3:38, where does he get -2p from for the inequality?? | GDppV18XDCs | Sal was taking the product of two binomials ( 1 - p ) * ( 1 - p ). The -2p came from the sum of the products of the 2 inner terms and the 2 outer terms. |
At 3:31, where did he get the -2p from? | GDppV18XDCs | Recall FOIL for multiplying binomials. (1 - p)² can be written as (1 - p)(1 - p), now use FOIL F, 1 times 1 = 1 O, 1 times -p = -p I, -p times 1 = -p L, -p times -p = p² Now we have 1 - p - p + p² Combine like terms: 1 - p - p + p² = 1 - (p + p) + p² = 1 - p(1 + 1) + p² = 1 - p(2) + p² = 1 -2p + p². |
At 7:05, what does he mean by both positive, and what does he mean by both negative? | GDppV18XDCs | Listen again carefully from about 6:30 to 6:45. Sal explains that if the product of the two factors is greater than zero (in other words, positive), then the only way that can happen is if both are positive or both are negative. |
At 1:53, what is a "gelatinous cranberry cylinder"? Dose anyone know how she made it? | 4tsjCND2ZfM | You can buy a can of cranberry in the store. Personally, I don t like it but thats beside the point. When she refers to it as a gelatinous cranberry cylinder , she is just giving it a fancy, mathematical name. Hope that helps! Ben Doucette |
did anyone see on 2:02 the pi and the tau? | 4tsjCND2ZfM | Yes. The pi was half ot the tau . |
At 0:44, shouldn't she say "inseparably" instead of "in-separately?" It's not in my Web browser's dictionary unless I add the hyphen (which I did)? The video is AWESOME, like all Vi Hart videos are, but I just noticed that. | 4tsjCND2ZfM | Vi-isms are in a dictionary class all by themselves. snakesnakesnakesnake star flakes mathemusician matherole Christmath etc. Prediction: Some day you will see Vi-isms in your browser s dictionary. A word we use today Chortle was made up by Lewis Caroll by combing Chuckle and Snort. |
Who is the other person at 0:13? | 4tsjCND2ZfM | A French person. Apparently a cook of some sort. Vi Hart lives in Canada, and many French live there too, so I m not surprised that she could get a French cook to help her. |
at 0:55 it says they can be made in the fourth dememsion but can they be made in the fifth dememsion. | 4tsjCND2ZfM | You only need 4 dimensions. Any extra dimensions have no effect. |
i got confused on the part 2:30 | iivtjjdSu9I | Yep you are right izaac |
At 0:57 Sal says, "And instead of the decimal we'll write and." Do you always have to say "and" for a decimal when writing it out or saying it? | AuD2TX-90Cc | Without the and , one hundred sixty seven hundredths could mean 160.07 or 100.67 or 1.67 That s one hundred (and) sixty and seven hundredths or one hundred, and sixty-seven hundredths, or one hundred and sixty-seven hundredths. The extra (and) is the way it is said in English English. |
So at 0:03 to 0.06
what did it mean that you would give away the answer ? How would you give away the answer if you haven't even write it in word from yet?> | AuD2TX-90Cc | He would give it away by saying it in WORDS. |
At 6:17, Sal did CB/CA=CD/CE, but can you do CB/BA=CD/DE? | R-6CAr_zEEk | Yes you can, the reflexive property dictates as such. |
At 6:02, Sal starts talking about the ratios and their equivalents. Does this change for right triangles? | R-6CAr_zEEk | Sal used ratios and equivalents to calculate DE,the triangles in this video are similar triangles,which means their angles are the same.It also holds for right triangles . |
Throughout the video(like at 6:15), you use the fractions and cross multiplication to find the unknown. I have trouble knowing what goes where in those. I know how to cross-multiply after that. I just have trouble with the first step. Any advice? | R-6CAr_zEEk | When Sal puts down a fraction, say for example bc/dc, the letters are referring to line segments inside of the diagram. You have to find which sides correspond (are on the same side of the triangle) to each other and form a fraction or formula. Then you take a side you don t know and place the corresponding side on top of it. replace the segments with the lengths you do know, and begin cross multiplying. The answer will give you the missing length. |
Around 0:10 Sal said tranversals. What are tranversals? | R-6CAr_zEEk | A transversal is any line that passes through two other lines on the same plane. |
At 7:30 you say that 6 2/5ths MINUS 4 2/25ths = 2 2/5ths. Did you mean to say that 6 2/5ths MINUS 4 = 2 2/5? Because 6 2/5 MINUS 4 2/5 = 32/5 MINUS 22/5 equals 10/5. Simplified 10/5 equals 2. | R-6CAr_zEEk | no he said it the right way |
My question refers to the second example, at 6:15.
Instead of the ratio CB/CA = CD/CE, I used CB/CD = CA/CE and came up with the same answer.
Would this method work on all similar problems? Or did I just get lucky? | R-6CAr_zEEk | That will work on similar problems due to the interchange means property of proportions (if a/b=c/d then a/c=b/d) . There are a lot of different ways to write proportions. |
At 4:14, how come Khan didn't convert the fraction into a decimal? | R-6CAr_zEEk | Its probably simpler to have as a fraction. |
At 6:45, should Sal have said & written +/- a sub1n times the DETERMINANT of A sub 1n instead of just a sub1n times A sub1n ? | H9BWRYJNIv4 | It should indeed be the determinant of A_1n, not just A_1n, since the formula would make any sense that way (It wouldn t be a pure number in the end) |
Why did u make the ex. matrix have at 9:44 have straight lines like | | rather than the matrix border like [ ]? | H9BWRYJNIv4 | He s trying to find the determinant of the matrix, which is written with the || lines instead of the [] brackets for the matrix. If you go back to the video on the determinants of 2x2 matrices, Sal talks about the various notations used for the determinant. |
How does the formula beginning at 5:03 translate into the formula for computing determinants for a 2*2 matrix given there are no submatrices? | H9BWRYJNIv4 | All recursive formulas require a base case, where the problem has become simple enough to solve without performing any more recursion. In this situation, the base case is the 2x2 determinant, which we have defined previously. |
9:18 Do you stop at a_1ndet(A_1n), or do you do the same for the rest of the rows? | H9BWRYJNIv4 | You only need to do this for one of the rows. |
At 4:35, why does Sal multiply the matrices this way? I thought you could multiply them straight across. Can you? | 3cnIa0fYJkY | No, you don t multiply matrices entry-by-entry. You add matrices entry-by-entry. Check the section on matrix multiplication for the exact process. |
Can you divide a matrix by a matrix? If so, and if it follows standard division, than Matrix I has to be equal to 1. Is this correct? at 3:17? | 3cnIa0fYJkY | Matrix arithmetic doesn t have division, but it has inverses, which is really the same thing. A matrix multiplied by its inverse (if it has one) gives an identity matrix. |
So, what's the identity matrix of a non square matrix i.e. :
| 1 2 |
| 3 4 |
| 5 6 |
at 6:53 | 3cnIa0fYJkY | They do have an identity matrix (two in fact) and it is square. It needs to have 1s going diagonally, 0s in all other positions, and obey such dimensions that multiplication is possible (is defined). In your case: [ 1 0 0 ] [ 0 1 0 ] x [ Your 3x2 Matrix ] [ 0 0 1 ] ...or: [Your 3x2 Matrix] x [ 1 0 ] [ 0 1 ] |
At 3:28 why do you multiply by P(B)? | 6xPkG2pA-TU | We can use the formula P(A I B) = P( A intersect B) / P(B) and then transpose for P( A intersect B) |
At 3:00, what is a principle ( or principal?) root? I have dealt with square roots many times, but is there a difference between a principle root and a square root? Thanks! | apkT6rVE8qo | The root that matches the radicand in sign(+or-). |
At 0:35, what does Sal mean by "one's place?" | mKsKU0BAiRM | The one s place is the position a digit has in a number. For example, in the number 493, the digit 3 is in the ones place. the digit 9 is in the tens place, and the digit 4 is in the hundreds place. Think about it as in the number 493, you have 4 groups of 100, 9 groups of 10, and 3 groups of 1 (100+100+100+100+10+10+10+10+10+10+10+10+10+10+1+1+1) = 493 |
Around 2:43 when he references line AB I was wondering if it can also be written as BA or does it have to stay as AB? | yiH6GoscimY | It can also be written as BA |
At 2:35, Sal said that an acute triangle is a triangle with all sides less than 90 degrees. When it came to explaining the right and obtuse triangle, he said ONE of the angles was 90 degrees (in the right triangle's case) and ONE of the angles was over 90 degrees (in the obtuse case). Is this true for the triangles, or did he mean only ONE angle is less than 90 degrees for the acute? | D5lZ3thuEeA | A triangle can have 2 or 3 acute angles. But, if it had 2or3 right or obtuse angles. it would not be a triangle at all! |
Can a triangle be 90 degrees? In 10:32 p.m | D5lZ3thuEeA | actually you can. watch in the next post |
at 3:14 the acute triangle looks like a equilateral | D5lZ3thuEeA | an acute triangle can be equelatitial |
At 2:37, Sal says "all of the angles are less than 90 degrees". Later, at 3:21 he says "notice they all add up to 180 degrees". So just to make sure that I understand this concept... In order for a triangle to be classified as Acute, it must meet 2 criteria. 1: The lengths are less than 90 degrees and 2: All add up to 180 degrees. | D5lZ3thuEeA | Only 1. All add up to 180 degrees has nothing to do with acute angles - that s true for any triangle. Ever. Isosceles, equilateral, scalene, acute, obtuse, right; the angles will always add up to 180 degrees. Try it with any triangle anywhere. |
Is the right scalene triangle Sal mentioned at 5:34 an example of a Pythagorean triple? | D5lZ3thuEeA | Yes, it is because 3 squared plus 4 squared equals 5 squared. |
at about 4:28, Sal says that obtuse triangles only have one angle, is that always true? | D5lZ3thuEeA | Yes if Sal says it it is right |
At 1:59, Salman Khan said that Equilateral Triangles can be Isosceles Triangles. Is he correct? | D5lZ3thuEeA | Yes, an Isosceles triangle has to have 2 equal sides and the angles opposite the equal sides must also be equal. Every equilateral triangle meets this definition since all the sides and angles are equal. However not all isosceles triangles are equilateral. Hope this helps |
At 5:50, Salman Khan said Equilateral Triangles can be Acute Triangles. Is he correct? | D5lZ3thuEeA | Yes! A triangle s angles have to add up to 180 degrees. An acute triangle s angles all have to be less then 90. So for an acute triangle to be equilateral all the angles would have to be equal, less than 90, and add up to 180. The example of this is a triangle with 60 degree angles since it is less than 90, equal to each other (making it equilateral), and add up to 180 (60+60+60=180). This triangle would be both equilateral and acute. |
At 4:10, why can't the interval be within -infinity < x < 0 and 0 < x < 5/2? | KblYjo1Ijws | Careful with the word and, it implies that both are simultaneously true. The statement you gave says any real number less than 5/2 excluding 0. If the word or is used, it would read x is either less than 0 or x is between 0 and 5/2, but not both. You might have to say this out loud to grasp the concept I m getting at, but it is very helpful to understand when watching the video. |
At 0:55, why does he try to find the excluded values when there is only one answer to the equation? | bRwJ-QCz9XU | In general when you see an equation like this, it s not always easy to see what the solution is, but it is relatively straight-forward to find the values for which the fractions are undefined by having a zero in the denominator. This step is necessary because if you proceeded to solve this type of equation and the solution was indeed one of the excluded values, then this equation doesn t have a solution because the equation is undefined at this specific value. |
at 0:55,why did he not exclude 0? | bRwJ-QCz9XU | Since we cannot divide by 0, we exclude values for p that would cause the denominator on either side to become 0. For the left, we say that p cannot equal 1, and for the right we exclude -3. We don t exclude a value of 0 for p, since the resulting denominators are non-zero, but in working through the problem we see that the solution is something else anyway. |
At 3:13 I Have no idea how you got (-1 ). The guy in the video please answer and what is you name please. If anybody knows please tell. | bRwJ-QCz9XU | Once he gets to -p = -17 he needs to get rid of the negative sign, so he multiplies both sides by -1 to get p by itself. His name is Salman Amin Sal Khan. |
8:56 what 1 doing inside of a bracket. example: 1( 1 + 0.100/2)^2 | BKGx8GMVu88 | when you invest $1 at 10%, do you get back 0.10, or do you get back (1 + 0.1)? |
2:19 where did he get 75 percent from ? | BKGx8GMVu88 | Its not 75% . Its 0.75 . 50% of 1.5 is 0.75 (1.5*50)/100 =0.75 |
At 9:20, shouldn't the yearly computation be 365.25 to account for leap years? | BKGx8GMVu88 | Good question, it s small details like that which show a very bright mind! Leap years do affect the way interest is calculated and sometimes it is even explicitly addressed in a contract. To break it down logically it would work like this : non leap year = 365 days = 365 * i = $365 leap year = 366 days = 366 * i = $366 average long run = 365.25 |
1:02 - 1:35 how did he get 12 by multiplying 8 x 2 because it is 16, did he divide somewhere with the 1/2? how did he do that? | 7S1MLJOG-5A | Half of 8 is 4 4 times 3 is 12 |
In 1:12, I get the first part of the equation but cannot understand how he got the second part of the equation. Can anyone help me? | 7S1MLJOG-5A | The area of a triangle is given by the formula (1/2)bh and he explains why that makes sense. Yes, he does make a mistake, which he later corrects. h = 3 and not 4 like he initially has it. |
at 3:21 why and how do you switch the order and signs of the terms? | yAH3722GrP8 | -a+b is the same thing as b-a. Sal was simply moving the negative term to the right, turning an expression with a negative number into an easier to understand subtraction expression. |
At 5:56, can you simplify the square root of 2 x squared minus square roots of 6 x squared? | yAH3722GrP8 | You can t really simplify the sum of the radicals anymore, but you can write sqrt(2) * x^2 + sqrt(6) * x^2 as x^2(sqrt(2) + sqrt(6)), which is factorized. |
In 1:33 of the Addition and Subtraction of Polynomials video Sal mentions that a Polynomial cannot have fractional or negative exponents in it. Yet, in this video, they have. Which one is it? Or is it a binomial that different from a polynomial? Finally, is it that important to know these terms further into Math or are they just fancy words to showoff at parties? | yAH3722GrP8 | This is just a matter of what you call things. If a function has only positive integer exponents of x and only real coefficients of x, then it is a polynomial. Otherwise, it is some other kind of function. So, it isn t that you cannot have fractional or negative exponents in a function, it is just that the name polynomial cannot be used to describe the function if you have fractional or negative exponents of x. |
At 1:34, Sal talks about an exponential model. What is that? | 2EwTHdg-xgw | Exponential function, in this case, is a function that y-values are decreasing but never touches x-axis. It keeps decreasing but NEVER touches x-axis. |
Im confused at 4:27 please help:) | wbAxarp_Ug4 | Sal is saying that when the denominator is smaller you divide the whole into bigger pieces and when the denominator of the fraction is bigger you divide the whole into smaller pieces. So take Sal s example of 3/4 and 3/9. Draw a square and divide it into 4 pieces and then draw another square the same size and divide it into 9 pieces. Now see. Is 3 pieces of the 4 bigger or 3 pieces of 9? 3 pieces of 4 is bigger. |
At 3:59, Why does Sal put a dot on the smaller fraction? Wouldn't you just make the sign point to the bigger number? | wbAxarp_Ug4 | I guess he would rather make a dot. But yes, I think the other way might work better. |
At 3:14 he says it would make a trapazoid, but i dont get how if your cutting from the top down, you get a trapeziod | hoa1RBk4dTo | It just where the knife meets the rectangular pyramid. The way it meets,it turns into a 2-Dimensional figure,a trapezoid. |
At 8:52,how is high school geometry way different from elementary geometry?Shouldn't they be the same? | hoa1RBk4dTo | High school geometry builds on a lot of the topics that you learned in elementary school in order to be able to solve more complex problems. In high school, you will often learn proofs of topics that you studied throughout middle school and elementary school, as well as more trigonometry topics dealing with cosine, sine and tangent. |
At 0:58, can n be imaginary? | bRZmfc1YFsQ | Yes, it can. But, of course, working with complex exponents is a bit difficult, although the power rule still applies. Thus, d/dx 5x^(3i) = 15ðx^(-1+3ð) |
In 4:31 of this video he said that he has a candy bar and divides into 25 equal parts. So why 25 equal parts? Why not 2 equal parts? | kZzoVCmUyKg | It s an example. Besides, 25 parts is a lot more possibilities than 2. |
at 7:28, how do you divide fractions? | kZzoVCmUyKg | Dividing and multiplying fractions is really easy, Ex: 4/10 divided by 2/5 Two 10ths = one 5th so if we have four 10ths it would equal two 5ths another way to say it is 1/2 ----- this is just a basic problem |
9:35, how do you do fractions without the pictures? | kZzoVCmUyKg | Do you mean like 1, 1/2, 1/3, 1/4, 1/5 and so on? |
How can you use the fruits as a whole, because the fruits are not equal and he said at 4:41ish that the whole point is to be equal when dividing a fraction. | kZzoVCmUyKg | Sal assigned each fruit as 1 whole instead of using their mass. He tried to simplify it a bit. Think of it this way. If we used only apples and each apple counted as 1 whole; ho many wholes do we have if we have 5 apples? We would consider that 5 wholes. But in reality each apple is not exacly the same size and shape as the others. We consider each one a whole to make it simpler to understand. |
In 3:40 of this video he ask : "what fraction of my fruit is yellow"? why not ask : "What fraction of my fruit is blue"? | kZzoVCmUyKg | because otherwise it would be 1/5 and that s boring |
8:00 How many times more intense than the smallest detectable earthquake is an earthquake measuring 5 on the Richter Scale in Columbia in 1906? | RFn-IGlayAg | So I would say the Columbia Earthquake is 2.5 times more intense |
At 7:27, why is the base 10? if base was greater, the differences between two earthquakes would be different right? | RFn-IGlayAg | Correct, the differences would be greater with a larger base. I believe that the Richter scale and most logarithmic scales use base 10 for sake of simplicity, since multiplying numbers by ten or powers of ten is much easier. |
At 0:29, doesn't Sal mean the middle not between? If the point is ONLY between, then it could be anywhere from the maximum to the minimum. | s4cLM0l1gd4 | He could have been more specific and said middle or half-way between, since otherwise between could mean anywhere from the maximum to the minimum (as you said). I guess he assumed we would understand what he meant. |
I'm not sure that Sal's definition of "period" at 3:11 is sufficient. After all, there are periodic functions (more complex ones than sine and cosine) in which you could return to the same y value and the same slope and still not have completed the cycle. An example would be a wave that alternates two short oscillations with one long one.
So my question is, what is the technical definition of a period? | s4cLM0l1gd4 | A period is the length of the smallest interval that contains exactly ONE copy of the repeating pattern of a periodic function (any function that repeats its values in regular intervals, or periods ). A period can start anywhere and end anywhere, but the length is always the same. |
At 2:41 he says 1 - 3 = -1, its -2. | s4cLM0l1gd4 | This is a known error in the video. At 2:43 in the video, a box pops up and tells you that Sal meant to say -2 rather than -1. |
At 4:07, Sal starts explaining what the period is, and he says that it is 2, but isn't the period of this graph 2pi? | s4cLM0l1gd4 | No, the period of this particular graph is just 2. It takes 2 units for the function to go through a full cycle, so the period is 2. |
@3:00pm does value of period ,amplitude and midline have units? | s4cLM0l1gd4 | There was no indication of units on the x or y axis, nor did Sal mention what exactly the graph was intended to represent, so I do not think so. |
at 6:25 Sal said I encourage you to test it out on the original equation. what did he meant by that. How can I test the solution on the original equation ? | utQi1ZhF__Q | I think that he meant solving it as separable equation. |
In the first example of this video (when he started solving at about 1:00), the differential equation is a separable differential equation. So, how is the name of this equation, should I say 'separable' or 'exact'?
Thank you!! | utQi1ZhF__Q | You say, that this is an exact equation, because My=Nx, and separable, because you can algebraically sweep x and y to different sides of the equation. Two different definitions of two properties, and both match. |
At 1:10, why is 6 to the eighth power not equal 6 times 8? | mJ1P4A-KA8k | the exponent, or power, indicates how many times you multiply a number by itself. So 6 to the 8th is really 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6. ... 6 multiplied by itself 8 times. Hope that helps. |
At 2:26 why one and five are combined while negative seven is separate? f(x)= 1,5 OR -7
Is there something between those two numbers in common? For example, why not to say just 1 or 5 or -7 instead of 1,5 or -7. | 4n7TIvRHuDs | Sal is just using a common list form used in English. When you write a list, you typically don t but the word and or or between every list item. You list the items separated by commas then us the the conjunction ahead of the last item in the list. The prior line is what the range looks like in math language. |
at 2:24 Sal said that "all the points on this circle are equidistant from c" and then later for point p as well but that doesn't seem to be correct because not all the points in a circle are equidistant from the centre only all the points on the CIRCUMFERENCE are. right? | g_dStt4st2I | Listen again carefully to the video at 2:24. Sal says that all the points on the BLUE circle are equidistant from C and that all the points on the YELLOW circle are equidistant from P. It s only the 2 points of intersection of the blue and yellow circles that are equidistant from both C and P (because the 2 circles have the same radius). |
In 3:48 what does circle centered mean? | g_dStt4st2I | He s referencing where the center of the circle is; it s centered at point (a, b), say. |
At 1:54 in the video, Sal makes the two circles (centered at the center of the original circle and at point P) big. Is there a specific size for the circles for that specific distance or does any size circle work for any distance? | g_dStt4st2I | The circle you use in this process does not have to have a definite circumference, however must be larger than the original circle in the diagram. |
so at 4:25 what's basically happening is that an angle at the center of the circle is double the angle made anywhere else on the circle, and conversely the angle anywhere else on the circle would be double the angle at the angle at the center. | 8vFhNhL-zm8 | Yes you are correct. It is a theorem, the inscribed angle is half of the central angle if and only if they are on the same arc. |
At 4:05, can you just skip the step in which Sal finds the measure of the arc and go straight to finding the solution? | 8vFhNhL-zm8 | Yes, you can. The important fact in the problem is to know that for any arc the inscribed angle is half the central angle. |
At 1:14. How did he figure out it was a right angle from it just being perpendicular? | 8vFhNhL-zm8 | All perpendicular line segments form 90° angles. It s the definition of perpendicular. |
Typically, on the AP Statistics exam, when they ask you to provide a 5-number summary of a set of data, can the minimum and maximum be outliers in your answer? So, at 8:03, would your 5 number summary be 6, (Q1), (Q2), (Q3), and 19? Or would it still be 1, (Q1), (Q2), (Q3), and 19? Which is better? | FRlTh5HQORA | It should say in the question. If it doesn t say anything then include the outliers. |
why does Sal, at 2:24, talk about the slope being positive one? isnt it rise over run, so that would make it 0/1=0? | 61ecnr8m04U | Yes, the slope of the BOTTOM curve is 1 but that s not what he s graphing. He s saying the slope of the TOP curve is 1 and that s reflected in the BOTTOM curve which has a constant value of 1 (for the interval he is talking about). |
At 0:48, why is d/dx being used to represent "the derivative of"? | 61ecnr8m04U | d stands for infinitesmally small change . dy/dx means the ratio of an infinitesmally small change in y to an infinitesmally small change in x. That s the definition of a derivative. |
At 3:00; instead of having an absolute value where the slope is 1 & -2 could you also have a parabola? | 61ecnr8m04U | First of all, in technicality, where the slope is 1 & -2, it is actually neither 1 nor -2 (indicated by the empty circles). Even if the slope were one and negative two, you could not use a parabola. Using a parabola would imply a changing slope. The function shown in the video had constant slopes of 1 and -2. When the derivative value is constant over a segment, that means that the slope of of the anti-derivative over the same segment is constant as well. tl;dr: no |
At 6:01, why does Khan use k? Wouldn't the diagram be
r => T (r) => k => H (k)
Why does Khan go from T (r) straight to H (k)? What happens to the K? Do we just ignore the K? Why??
Thanks. | pIMfRbznxKA | The k is not lost. It is just assigned the value of T(r). Sal 1st uses the function T(r). It has an input of r and its output is T(r). Remember, k is just a variable to represent the input to the function H(k). Sal then makes k = T(r) . The input value for function H(k) will be the output from function T(r). It s like saying find the value of function H(k) if k=2. You find H(2). But, Sal is finding H(T(r)). Hope this helps. |
On 7:00 they metion about the angles wouldnt the 70 degree and the angle right next to it have to equal 180 because then the whole thing wouldnt make sense right? | gRKZaojKeP0 | the 70 and 110 degrees are supplementary angles . when they are supplementary that means they add up to 180 . so 110 + 70 = 180. |
At 4:75 to 4:59 he says a lot of "thats" which that is the top yellow angle? | gRKZaojKeP0 | I meant 4:53 to 5:00. Oops :) |
4:40 What does he mean by congruent angles? | gRKZaojKeP0 | When he says congruent angles, that means that the angles are the same measurement. |
At 0:59, how can you tell which point is which when they're all so close together? | Jpbm5YgciqI | There is a shape to the dots...they are organized from lower left to upper right. |
At 1:25 what would be his score | Jpbm5YgciqI | Can you clarify what you mean about the score at the time @1:25? |
Can anybody really really descriptively explain what a linear function is ? I started to get confused at 0:14. Can any body help me ?? | Jpbm5YgciqI | A linear function is a function in degree 1, i.e. it has no term with x to the power of anything > 1. So linear functions can t have x^2, x^3, so on, types of terms. They can only have terms with x^1 or x^0. Also they cant have negative degree terms. |
At 4:01, how does that happen, it just DOES NOT MAKE SENSE? | PC_FoyewoIs | Calm down Think about it |
At 0:57, you have to enter x first, then y right? | PC_FoyewoIs | yes. The Z coordinate would be third on a 3-D plane. |
At 2:50 the constant x's power one meant the derivative was one, but I remember in one of the first videos covered that the derivative of any constant is zero. What made it one here? | j9FDoYNxZlw | The derivative of a constant is 0, but x is not a constant. It s a variable. So we apply power rule, which works for functions of the form x^n. |
from 2:11 on I am completely confused. And yes I have watched it multiple times. | 499MvHFrqUU | Factor the terms. The gcf, in this situation, is 10uv. You put all the rest in parentheses. Does that help? |