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At 1:20, Sal verifies the calculator is in radian mode. I understand the difference between radians and degrees. How do I know which I should be using? What part of the problem tells me I should be using radians? | t7NvlTgMsO8 | If you are in Calculus, you should completely stop using degrees. You just cannot reasonably work with degrees at this level of math. As far as I know, no calculus is ever done in degrees. It is always radians. |
What's the 'range' thing at 2:50? | t7NvlTgMsO8 | basically the range of values for which you need to find x or y values that are in that range |
At 3:44, what is the purpose of the square in the formula for the hypotenuse, A square + B square = C square? | AA6RfgP-AHU | Thank you very much. :) |
At 5:03, can the 3(a) and the 4(b) be switched around? | AA6RfgP-AHU | sure a and b can be switched around but c has to be the longest side of right triangle from the formula c^2=a^2+b^2 |
At 6:53, can the side with the question mark be C? | AA6RfgP-AHU | You can call each side whatever you want. But then of course you would have to change the formula accordingly. |
at5:14 what does he mean | AA6RfgP-AHU | his example was 4^2 + 3^2 = c^2 this is the same as 16 + 9 = c^2 and 16 + 9 = 25 the you d just have to find the cube root of 25 and you have the answer. did that help at all? |
How come at 10:00 Sal put the last factor 3 as its own separate self and not together with the other factors? | AA6RfgP-AHU | What he is doing to simplify the radical is to find perfect squares so he can remove them from under the radical. He factors 108 and finds that it equals 2*2*3*3*3 so there are two 2s and three 3s. If you take 2x2x3x3 you get 4*9=36, a perfect square (sqrt=6). The remaining 3 must stay under the radical because it cannot be simplified any further. |
At 5:39, what is a principle root? | AA6RfgP-AHU | The principle root referenced at 5:39 means the main root of a square. For example, square roots of 81 could be both -9 and 9. This is because 9^2 = 81 and (-9)^2 = 81. However, the principle root refers to the positive one, which is 9. |
At 6:45, is this example a special case of the 30-60-90 triangle? | AA6RfgP-AHU | Yes, it is. In a 30-60-90 triangle, the sides have a ratio of x : sqrt(3) times x : 2x. So since the triangle s sides do have this ratio, it s a 30-60-90 triangle. |
At 10:15 how does Sal come up with sqr 36 and then 6 sqr 3? I'm confused. | AA6RfgP-AHU | Hello, well first you have to find the square root of 36. That is 6. Then because the square root of 36 is being multiplied by root 3 you would find the square of 36 (6) and then multiply it by root 3. Since six is simplified and has no root attached to it it ends up multiplying to 6 root 3 |
At 1:26, Do you ALWAYS need to know at least two sides of the right triangle to put the Pythagorean Theorem into effect? If not how do you find the length of the hypotenuse or the missing leg? If so how do you do it? | AA6RfgP-AHU | In order to use the Pythagorean theorem, you will need to be given 2 sides or at least the information to find the values for 2 sides. |
At 10:41 Sal says the square root of 108 would be a little bit larger than 6, but wouldn't the square root of 108 be a little more than 10, not a little more than 6, because 10 x 10 = 100, so the square root of 108 must be around 10. | AA6RfgP-AHU | Yes, you are correct! The square root of 108 is 10.4 to three significant figures which is indeed a bit larger than 10 rather than 6. â108 can be simplified to â36x3 or â36 x â3 and then becomes 6 x â3 which is simply written as 6â3 in surd form. That s probably why Sal said 6 instead at 10:41. |
8:18 I've noticed that Sal seems to have a bunch of shortcuts for arithmetic problems up his sleeve. I paused and solved that subtraction problem systematically from right to left, but he just sort of used intuition. Are there certain arithmetic tricks I can learn to speed things up? | AA6RfgP-AHU | yes there are I can help you |
At 3:41, I learnt that in the Pythagorean Theorem, a right triangle's hypotenuse, equals the sum of a and b squared and divided by 2. Why do we calculate it as 'squared'? | AA6RfgP-AHU | That is because you don t get the right answer if you don t square them because â(a+b) is NOT equal to âa + âb. Thus c² = a² + b² We solve for c by square rooting: c = â(a²+b²) This IS NOT equal to c = (âa²) + (âb²) = a + b For example â(3² + 4²) = â25 = 5 But, â3² + â4² = 3 + 4 = 7 |
Wait a second, so at 10:30 he said you can just leave the answer as the square root of 108. Does that mean you don't need to simplify to 6 times the square root of three? | AA6RfgP-AHU | Yes you can just leave it unsimplified. However, it s more common for it to be simplified. On a test teachers usually ask to simplify it, even though it s essentially the same answer. |
At 1:50, is the hypotenuse the longest side of the right triangle, or the side opposite of the right angle? Or is the longest side always opposite of the right angle? Or does the hypotenuse needs to be both the longest side, and the side opposite of the right angle? | AA6RfgP-AHU | The hypotenuse is always the side opposite the right angle. It is the longest side IF the triangle is a right triangle. |
In the last question he showed (solving for B squared (6squared + Bsquared = 12squared)) at 8:44, the square root of 108 is, on your calculator, 10.39230485. He says it's 6 square root 3.
I understand how he got that completely, but is 10.3923085 wrong? | AA6RfgP-AHU | Thank you very much. Your answer has helped me with some of my test prep. |
Why would you want to square root both sides? (minute: 5:42) | AA6RfgP-AHU | its because of the properties of equality, if you do something to one side, you do it to the other |
At 7:51, can I just take the positive root of both sides to solve for B? | AA6RfgP-AHU | Yes the negative root has no meaning for distance (cannot have a negative distance). |
At 3:45, Why is it important to square the variables? | AA6RfgP-AHU | Pythagoras actually found the property by noting that if you squared the two sides, then that is equal to the square of the third side Lets take a basic Pythagorean Triple 3-4-5 If we just add the sides, 3+4 does not equal 5 But if we square 3 (9) and 4(16) and then add 9+16 = 25 and we square 5 (25) we get the same value We can prove the theorem using Geometry and that allows us to apply it with problems, so the importance of the squares are because that is what the theorem states |
At 0:42, Sal said the triangle has to be a right triangle. Does this mean you cannot use the Pythagorean Theorem for other triangles? If so, why not? | AA6RfgP-AHU | The Pythagorean Theorem only works for right triangles. It is expanded later into the Law of Cosines (c^2=a^2+b^2-2abcos(C)) which works for any triangle. |
At the second question at 6:26, is the length of the unknown side sqrt108? I paused the video(you hear me saying that a lot). | AA6RfgP-AHU | You ve gotten these right 4 in a row! Good job! |
At 3:29 he writes side a as a squared, same thing with side b. Why did Sal do that? | AA6RfgP-AHU | The theorem states that if you multiply a*a and b*b will the theorem be valid. Take a right triangle with a=3 b=4 c=5 If you add 3+4=5, the point of the theorem is not proved If you square the numbers then add 9+16=25, the theorem is not valid |
At 9:58, why does Sal write the square root of the last 3? | AA6RfgP-AHU | When you are simplifying square roots, you look for pairs in the prime factorization of the radicand. In this case: â(2 * 2 * 3 * 3 * 3) Here we have one pair of 2s and one pair of 3s with a leftover 3. So: â(2 * 2 * 3 * 3 * 3) = [â(2 * 2 * 3 * 3)] * â3 The square root of 2 * 2 is just 2 and the square root of 3 * 3 is just 3, so the square root of 2 * 2 * 3 * 3 is 2 * 3 = 6 [â(2 * 2 * 3 * 3)] * â3 = 6â3 |
At 5:44, it says that the hypotenuse was 5, but could it have been negative? | AA6RfgP-AHU | No; the hypotenuse couldn t have a negative number because there is no such thing as a negative distance in this and similar situations. |
I need to find a perimeter of a rectangle that has a ratio of 4:3 respectively, and a diagonal of 20 cm. How can I find its perimeter using the Pythagorean Theorem? | AA6RfgP-AHU | 20^2=(4x)^2+(3x)^2 25x^2=400 x=4 The perimeter is 2(4x+3x) so 2*7*4=56 |
8:08
Why is it -36, and not just 36? | AA6RfgP-AHU | Sal is subtracting 36 from each side of the equation: 36+B^2=144 so as to get: B^2=144-36 which is B^2=108. That is why it is -36 (minus 36), not 36. Hope this helps! :) |
At 10:20 how do you simplify sqrt 36 sqrt 3 into sqrt 6 sqrt 3? | AA6RfgP-AHU | The square root of 36 is 6. |
at 10:2 why does he do square root of 2X2X3X3 and put the last 3 in a seperate square root? confused. | AA6RfgP-AHU | Square roots of perfect squares can come out of the square root sign (2â¢2 and 3â¢3), and numbers that do not match (3) have to stay in, so he separates it out into perfect squares and non-perfect squares. |
At 0:43, why does the triangle have to be a right triangle in order for the Pythagorean Theorem to work? | AA6RfgP-AHU | That is how Pythagoras devised his theorem to work. It is actually a specific case of a more general result called the Law of Cosines, which you might learn later. The Law of Cosines works for any type of triangle. |
At 3:31, why are the three sides squared. please explain? | AA6RfgP-AHU | Because that is how Pythagorean theorem works. The are always squared when your talking about Pythagorean theorem. |
If the resulted number, such as 108 in 8:41, doesn't have a root or anything that makes it up? | AA6RfgP-AHU | If it wasn t a perfect square, you would put it under the radical sign, and that would be your answer. And if you could, you would simplify your answer. Hope I helped! :) |
At 7:50, instead of doing what Sal did, couldn't you just do:
12² - 6² = B²?
Does that work? | AA6RfgP-AHU | Yes...you re omitting a couple steps, but as long as you have a good conceptual understanding then you re good. |
Can someone explain to me how Sal simplifies square roots, like at 8:50? Thank you! | AA6RfgP-AHU | Prime factorization |
At 5:01, It says that a squared + b squared = c squared. Why square it at all? Wouldn't it be easier to just add them together and get the simpler version? | AA6RfgP-AHU | You would get a different answer. Let s say a = 3 and b = 4. Now let s solve for c... a + b = c 3 + 4 = 7 OR a^2 + b^2 = c^2 3^2 + 4^2 = c^2 9 + 16 = c^2 25 = c^2 5 = c The only way it works is if you square each term. |
At 7:21 I don't understand how they did the circles and squares can someone explain that? | f15zA0PhSek | Don t worry about the circles, Sal was just using them to highlight the 3 s in the equation on the left hand side of the screen. The squares are another way of trying to visualise what it means to divide 5 by 3 . If you use shapes (like squares) to represent the ones , then you can get some idea of what it means to divide 5 of these ones into 3 portions . He draws 2 lines through the 5 squares to divide the into 3 equal portions, and ends up with 1 and 2/3 for each portion. |
what were u talking about on 7:42 or 7:38 | f15zA0PhSek | he had reduced the equation to be 5 =3x so he represents that as 5 blocks = x x x to make the equation work 1 2/3 blocks would equal an x |
At 7:50, I didn't get how he broke the 5 squares into groups...... can you explain how he did it? | f15zA0PhSek | You may wish to look at the videos on fractions in the arithmetic playlist to help you understand. 5 doesn t divide evenly into 3 parts, so you need to use fractions to represent it. |
Around 6:59, does it really matter if if you write 5/3 or 1 2/3? | f15zA0PhSek | yes |
1:33 if x +x is 2x
then what is X multiplied by x ? | f15zA0PhSek | X + X means one something plus another of that something, making two of that something or 2X (X being just any something). X TIMES X means one of that something times one of that something, making X squared, since it is an unknown number times itself. |
Hello, at 6:13 it said that the answer to the question was 5/3 or 1 2/3, what if we put this in decimal form? Would it still be a correct answer? Thanks and have a great day. | f15zA0PhSek | Well it would if you wrote it correctly as a repeating decimal |
I don't understand why he didn't cross out the other x's at 3:14>. | f15zA0PhSek | im sorry i miss read you question he didnt because thos are the ones that needed to be there for him to visualize his work and to check the answer be sure to always do that good luck on finding out other ways people think why! |
OK so at 8:53 you can add 2x and 3??? i thought you could only add like 2x and 3x cuz 3 has an x, was i wrong pls explain:/ | f15zA0PhSek | I think you got the time wrong, because 8:53 is the end of the video. But In short, you can add terms that are the same kind so x can be added to other x, y can be added to other y, and numbers can be added to numbers. Once you know x s value, you can also treat it as a number. Hope this helps. |
At 2:41 Sal claims to minus 2x from both sides, why couldn't you just subtract 5x from each side. Since 5x is on the other side? Also why does he add 2 to -2 instead of 3 plus negative 3? At 4:40 | f15zA0PhSek | You can indeed minus 5x instead. Using the example given: 2x + 3 = 5x -2 -3x + 3 = -2 ----->5x was subtracted from both sides. -3x = -5 --------> 3 was subtracted from both sides. -x = -5/3 -------->Dividing both sides by 3. (Note we now have -x not x, so we can times both sides by -1, or if you prefer add x to both sides and add 5/3 to both sides) x = 5/3 So essentially if you minus 5x, you are simply adding in an extra step to solving the equation. You would still arrive at the same answer either way. |
At 0:49, what does isolate mean? Is it a math word? | f15zA0PhSek | Isolate ain t a math word but it means to seperate or set a part from others pretty much what jrt.levi said . |
At 2:50, why would you subtract 2x instead of dividing by 2 to get the x alone? Sorry if this is a dumb question but I am in 7th grade trying to teach myself and going over each bit helps :/ | f15zA0PhSek | If you divide by 2, you would have to divide all the terms by 2 to keep both sides of the equation equal. Then you would have to divide the 5x by 2 which would give you 2.5x on the right side. You would have x by itself on the left side, but it wouldn t really help you because you d have to deal with the 2.5x on the other side. Your goal is to get all the x s together first. I hope that helps. |
At 2:11, why does he write the equation out as x+x+1+1+1=x+x+x+x+x-1-1? Would that just make the math simpler or would that do nothing but spread it out to see the equation easier? | f15zA0PhSek | It s just to see the equation easier. |
why do we at 3:50 add 2 to each side instead of dividing 3 by 3 and dividing 3x by 3 instead? | f15zA0PhSek | If you divide by three, in order to keep both sides equal, you have to divide EVERYTHING by 3, including the 2. You could do this, but it makes the work easier if you get rid of the two first. If you only divide parts of the two sides by three, then they are no longer equal. Think about it with numbers in place instead of variables 8 = 6 + 2..... is 8/3 = 6/3 + 2...that is 8/3 = 2+2? Now with dividing all parts 8 /3 = 6/3 + 2/3.... 2 2/3 = 2 + 2/3. Does that help? |
Hi, at 2:47 how do you now what do subtract or add to what side you have to do the operation on first. My second question is when you get your answer as a fraction can you turn it into a decimal? Thank you. | f15zA0PhSek | You have to first divide the numerator by the denominator to find the whole number then slide the decimal over the left two times. |
at 5:31 he said 5 = 3x. is that true | f15zA0PhSek | Yes. 2x +3 = 5x - 2 Subtracting 2x... 3 = 3x-2 Adding 2, 5 = 3x. ^ There. :) Hope this helps. |
At 2:16 why do you subtract two from both sides | f15zA0PhSek | It maintains the equality. You always have to keep it balanced to maintain it as true. |
At 2:53, why would he subtract 2x? Should't it be dividing instead because 2x and 5x means it's a multiplication problem. | f15zA0PhSek | The equation is 2x+3=5x-2. This can also be written as +2x+3=+5x-2. Yes it is 2*x and 5*x, but we are not trying to separate the x from the 2 or 5, so we don t want to divide. To move a term to the opposite side of the equality, we must do the opposite operation. Since 2x is currently positive, or added, we must do the negative, or subtract. |
At 2:15 in the video what x's is he talking about subtracting | f15zA0PhSek | He is talking about the 2x on the right side of the equation. |
How come at 6:34 minutes he didn't divide the 5 by 3 in 5/3, instead he turned it into a mixed number, why is that? How do you know when to stop reducing in an equation? | f15zA0PhSek | You stop reducing the fraction when the numerator and the denominator have no common factor to divide by. |
why did u do x+x and stuff at 1:07 | f15zA0PhSek | so people could know it s basics |
In 3:01 of the video, are you supposed to remove the 2x so that you can get x on one side of the equation? And if so, why? | f15zA0PhSek | Because you want one side with a variable. When we solve an equation, we want to end up with x = some number. If you have an equation like 3x + 5= 2x +7, your main goal is to get ride of an x on one side so you only have one answer, which would then look something like x = 2. I ll write the steps on how I got that answer: Step 1: Subtract 2x from both sides. 3x+5â2x=2x+7â2x x+5=7 Step 2: Subtract 5 from both sides. x+5â5=7â5 x=2 Let me know if this helps or if you have anymore questions! |
At 5:44 he says to Divide the left side by 3, but instead just leaves it as a fraction 5 over 3, i don't understand why this happens. i would have just divided 5 by 3 and got 1.66 repeating.. | f15zA0PhSek | Either way works. In a case like that when you would get a repeating decimal, it is better to leave it as a fraction because it very difficult to work with a repeating decimal and get an exact answer. |
At 1:29 Sal did the other set of 5x's in blue. When he did the 2x's in Pinkish-orange. Why did he do this? The x's did not change. Did he do this because he just wanted to change the color (to explain or something)?
Thanks in advance. | f15zA0PhSek | There wasn t any particular reason for it. He could have used the same color for both. I guess he just felt like changing colors. |
At 2:27, Sal says that as long as you use legitimate operations, the solution will be the same no matter how you do it. So what would an illegitimate operation be? | f15zA0PhSek | That is a great question. There are two ways of doing this one which is the normal way 4(3+5) = 4(8) =32 or you can use the distributive property...... 4x3=12+4x5=20 so 20+12=32. But later on when you use Algebraic expressions you have no choice but to use the distributive property. Sorry this answer is late but hope this helps. |
Why did he put stuff in boxes at 1:30 | f15zA0PhSek | When he breaks down the equation on the right, the information he shows is in the same color as the box it corresponds to. 1+1+1 was done in purple because it relates.\ to the 3 in the purple box. |
At 4:34 he talks about adding plus 2 on both sides ,my ? is how and why. | f15zA0PhSek | When solving equations, you do the same thing to both sides. In order to get 3x by itself, Sal needed to get rid of the -2, so he added 2 to both sides. That left 3x by itself. |
Shouldn't the W vector in the directional derivative equation around 4:00 be a unit vector? | m2mW2FQJgEE | yes w vector should be normalized. the problem is i think grant has never applied this or created a simulation of directional derivative and that is why he forgets to normalize the w |
at 3:29 we found two roots. r= -2+i and r=-2-i why we choose u=1 instead of u=-1? | rGaM6pwqhB0 | It doesn t make a difference, since both constants are arbitrary. C1 cos -x = C1 cos x, and C2 sin -x = -C2 sin x. You can just use C2 instead of -C2, since it s arbitrary. |
at "3:55", how come mu is equal to 1 instead of +-1? | rGaM6pwqhB0 | Because we have that cos(x)=cos(-x) and -sin(x)=sin(-x). In the case of cos(x), the minus sign gets cancelled out automatically. But in the case of a negative x for sin(x), namely, sin(-x), this becomes -sin(x), and the negative sign gets absorbed by whatever constant C right in front of it. |
At 0:38, how did Sal tell that the graph of the function would be a downward sloping line just by looking at the function definition? | PQiXRrT_14o | For example, we have a linear function, y = mx + b. IF the value of m is positive, it is an upward slope. IF it is negative, it will be a downward slope. Now, @0:38, the given is -0.125x + 4.75 where in the value of m is negative that s why Sal said that is a downward slope. |
At 1:02 in the video why did he write the equation out like that? PLEASE HELP ASAP! | PQiXRrT_14o | At 1:02, in the video, he wrote out the equation like that in order to find the y coordinate at x= -10. He knew that at x=-10 he has to use the equation [-0.125x+4.75]. So in order to find the f(x) coordinate at that point, he replaced x in that equation with -10. If he had wanted to find the f(x) value at x= -5, he could have used the same equation, except replace the x with -5. |
At around 3:07 Sal mentioned perfect squares, what even is a perfect square? | 4STGvuoBi5U | A perfect square an anything raised to a power of 2. You should learn to recognize them in their exponent form and the form they take if you complete the exponent. In this video, Sal is teaching you what a perfect square looks like when you square a binomial. Here are examples: with exponent (and after exponent where possible) 5^2 = 25 x^2 (x^3)^2 = x^6 (x+2)^2 = x^2 + 4x + 4 (2x-3)^2 = 4x^2 - 12x + 9 Hope this helps. |
I don't really get the whole thing about the repeating 3s at 8:48. Can anybody here explain it please? | _SpE4hQ8D_o | You have to know how to change decimals into fractions. For example: 0.52 = 52/100 (divide top and bottom by 4) = 13/25. Another example: 0.5 = 5/10 (divide top and bottom by 5) = 1/2. This next one is a little tricky, but what you have to know is that every time that you see recurring 3 s, 6 s, and 9 s you have to divide by [9], not 10, not a 100, not 1000 etc. For example: 0.333333... = 3/9 (divide to and bottom by 3) = 1/3. |
At 1:27, would you do the same with 60% of ___ is 15? | _SpE4hQ8D_o | Your question is: 60% of ? = 15 The problem Sal was working was: 0.2% of 7 = ? So the unknown is not in the same place in the two problems. Here s one way to 60% of ? = 15: 60% of x = 15 is the same as 60/100 * x = 15 so we can multiply both sides by 100: 60 * x = 15 * 100 => 60 * x = 1500 then divide both sides by 60: x = 1500 / 60 so x = 25 60% of 25 = 15 |
At 9:51, how do I figure out what % of 200=2? | _SpE4hQ8D_o | It s 1% because in 100 the percentage of the number is the number with a % added to it, but in 200 you divide it by 2 and add a % so 2 divided by 2 is 1 add a percent 1%. I hope you find that helpful. Please vote up! |
7:02 I don't understand how that proof works. | _SpE4hQ8D_o | All Sal did was substitute his answer into 20% of x = 4 . His answer was 20. So he plugged 20 into his equation, and solved it. 20%->.2 .2*20=4 It checks out. |
At 4:08 Sal says "So always do a reality check to see if you have the right answer." What is a reality check, and how do i do one? | _SpE4hQ8D_o | A reality check is a way to make sure your final answer makes sense in the real world. For instance, if you are doing a calculation of how many people prefer basketball over baseball and your answer is over 100% you know something is wrong because it would be impossible for over 100% of people to prefer one thing over another. |
When Sal puts the decimal place 2 to the left instead of saying it was .2 in 2:22 through 2:27, do you do that with all percentages? | _SpE4hQ8D_o | Yes! To convert percents to decimals, divide by 100 or move decimal place 2 spaces to the left. To convert decimals to percents, multiply by 100 or move decimal place 2 spaces to the right. |
Wait, at 2:10-2:47, I always thought that .2% also equals .20 as a percentage. Please Help! | _SpE4hQ8D_o | 100% in decimal form is unity, so .2% is .2/100=.002 |
At 10:09, how do I figure what % of 75=7.5? | _SpE4hQ8D_o | You divide 7.5 by 75, and 7.5/75 is 0.1, which equals 10%. |
At 7:58 he says that 9% in decimal form would be 0.09, but wouldn't it be 0.9? | _SpE4hQ8D_o | No he is correct 9% would be 0.09 in decimal form because 0.9 would be 90% here are som examples 1% = 0.01 25% =0.25 30% = 0.3 45% =0.45 99% =0.99 100% = 1 |
4:59 my first thoughts were 8,but i was thinking to quick so i was wrong
)|
it was actualy 20 | _SpE4hQ8D_o | math is good for learning to make your mind go steadily, accurately, checking your own self, and getting to trust your own method. also read your own handwriting. stillness? nah... |
Can someone thoroughly explain what he was doing with the decimal points in the division problem at 6:14? I understand what you do with decimal points when calculating an answer, but what he did with the divisor and dividend does not make sense to me. Please explain it to me! | _SpE4hQ8D_o | Hello Brynne, I believe that what Sal is communicating in this lesson is that the ratio of the divisor to dividend is kept the same as long as both the divisor and dividend are multiplied by the same number. For example, when dividing 7.5 / 2.5, one could just as easily multiply 7.5 by 10 to get 75, and 2.5 by 10 to get 25 - making the new problem 75/25. Note: In both cases the quotient is 3. Moving the decimal place like this sometimes makes the dividing process more convenient or apparent. |
When Sal puts the decimal place 2 to the left instead of saying it was .2 in 2:22 through 2:27, do you do that with all percentages? | _SpE4hQ8D_o | yes, all percentages cent is latin-ish for a hundred, so saying per cent means ratio. We find this number for every hundred we count. 5% says 5 per 100. Percent gives you a proportion. |
Why did he put .2 at 5:30 instead of of .20.?? If you use .20 to do the problem you would get a totally different answer, How is .20 and 2 the same? | _SpE4hQ8D_o | Oh................................. I get it so like .3 is the same like 3 tenths which is 3 10s which equals 30. Thanks so much you explained it so simple. |
At 3:10 he explains how the absolute value of -8 is equal to 8 because they are the same distance from zero, but when doing the practice concept the question -1___1 came up I chose equal and it said -1< 1 can someone explain this please? | hKkBlcnU9pw | In that particular problem, the answer would be -1 < 1 Now, if the problem was | -1 | ___ 1 , then the answer would be | -1 | = 1 The symbol used for absolute value is | | |
At 0:09, when Sal draws the lines on either sides of the numbers, what do they mean? Are they just to separate the numbers from each other so it doesn't become confusing? | hKkBlcnU9pw | When you see: | -2 | The bars are the symbol to indicate that you need to find the absolute value of the number. The absolute value of a number is its distance from zero. Thus: | -2 | = 2 because -2 is 2 units from zero. In the video, Sal is asking you to compare absolute values. Hope this helps. |
in 3:17 how did the -9 turn into a positive 9 | hKkBlcnU9pw | Because the absolute value symbol makes the negative a positive UNLESS the negative is outside of the absolute value symbol |
At 0:04 sal says carrying absolute value. Why? | hKkBlcnU9pw | because at 0:04 he is introducing the topic... :D |
At 3:00 Absolute value of a negative number is just the number but positive? | hKkBlcnU9pw | Yes. The absolute value of a number is the same number with a positive sign. |
At 3:59, did Sal forget to add the " | " on both sides of the 2, or is that just how you do it? Or is it redundant? | hKkBlcnU9pw | The | symbols are not numbers (there is no addition). They are the symbols to indicate absolute value. | 2 | is read as the absolute value of 2 , it = 2. | -3 | is read as the absolute value of -3 , it = 3 Hope this |
At 2:30 Sal explains that the absolute value of both 9 and -9 was 9. Why is this? | hKkBlcnU9pw | -9_________0_________9 Both 9 and -9 are 9 units away from zero. Absolute value is distance, or how far away the value is from zero. It s always positive, so the absolute value of 9 and -9 is 9. |
At 2:10 how do you mark the slope in the co-ordinate plane in that slanting way? I mean, how could we infer the nature of that slope line, whether it is horizontal, vertical or slant in clockwise or slant in anti-clockwise?? | LoaagZPWvpM | In the column labeled dx/dy he has the slope value. He uses that value to plot the slope. A value of 0 is a horizontal slope, 1 is a slope increasing 1 , -1 is a slope decreasing. You could review slopes if necessary. |
Why was there a chart at 0:05? | i9j_VUMq5yg | The reason why there is a chart of table in 0:05 is because you need to use it in the algebraic problem. |
At 1:23, How do I know the difference between independent and dependent variables? Whats a easier way I can understand this concept? | i9j_VUMq5yg | the dependent variable depends upon the independent variable, while the independent does not depend on the dependent variable. |
At 10:00, wouldn't flipping the graph over the x-axis work as well? | 0zCcFSO8ouE | Well, in this select case, yes. But if you take some other function that isn t odd, f(-x) won t be the same as -f(x). In one case, we are flipping over the y-axis, and in the other, over the origin (respectively). You can draw a random line on a coordinate plane (not going through the origin, mind you) and try flipping it over the axes. The difference will be obvious :) |
In 2:12, why is sine of pi, one? | 0zCcFSO8ouE | Because in the unit circle, the sin of any angle is the y-coordinate at that point, and when you have an angle of pi on the unit circle, the y-coordinate is 1! |
At 8:24 in the video, sal said that the difference between the graphs sin(x) and sin(-x) was that they were reflections of each other. When I put cos(x) and cos(-x) into my calculator, both graphs were identical. So why is there a reflection with sin but not with cosine? | 0zCcFSO8ouE | sin(-x)=-sin(x) and that s why u need to reflect sine once over Oy and once over Ox to obtain the other half of the function. cos(x)=cos(-x) and hence u need to reflect it once over Ox Cos(x) is an even function like x^2 for example. If u plot x^2 u see is symmetrical of Ox like cos(x). Sin(x) is not symmetric of Ox. |
At roughly 12:20 the period is discussed. I'm a little unclear on the equation I can apply to any and all problems to solve for the "new period" when there are transformations and whether amplitude, vertical shifts, and phase shifts should be included in this. | 0zCcFSO8ouE | Suppose you have a function y = a sin (bx+c), then the period of the function will depend on b . since the period of y=sin x is 2pi , the period of the new function will be 2pi/b. This is because the graph will move b times faster , to put it simply. In general , if you have a function y = f(x) with a period =T then the period of the function y = a f(bx+c) will be = T/|b| the period will not be affected by a (the amplitude) or c (phase shift). Hope this helps |
At 8:25, couldn't it also have been reflected about the x-axis? | 0zCcFSO8ouE | Yes. That is conceptually what you are doing. |
At 4:40 why did you include (x+5<0 and x-2<0) | OP91XWBRI1w | becuase thats the factorization of the quadratic, and then up in the top right corner is where he proves the inverse is the same thing |
At 4:15, I am still confused why he did a second inequality. Why do you have to do the "or (x+5<0 and x-2<0)" along with the one before it? | OP91XWBRI1w | A * B > 0 A and B can both be positive. 2 * 2 > 0 or A and B can both be negative. -2 * -2 > 0 An x value has to be within one of the constrains set by the inequalities. A or B doesn t work because you could have one negative and one positive value for A as well as B. You say or not and because A and B don t have to meet both constraints, just one. |
at time 3:34 in the video sal says that the lowest X coordinate value is 3 but isn't it 1? | VgqsM-XdBD0 | Very good observation! I think you are right, and I think it would have helped if the Khan team had corrected this. Which vector has this x-value? (Thanks for the time-stamp: they really help with a question like this :-) |
@3:38 Why is the lowest x value 3 and not 1? | VgqsM-XdBD0 | I wondered about that too, but now realise that although Sal didn t say it, he was only looking at the original vectors and the first problem ( a + b ). He wasn t including the answer to the second problem ( a - b ). |
At 0:42, Sal did not write 2 to the power of 2, or 4. Is this a mistake? | bvcXEJbEzSs | Yes, it was a mistake. |