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for a ratio, the opposite of it, such as 2:3 & 3:2 is the same. but when you turn each of these equivalents into fractions, they are completely different! I don't get it! someone explain this to me. | UK-_qEDtvYo | No, 3:2 and 2:3. Is nearly (not completely same) the same because if 2:3 is comparing apple to number of oranges 3:2 is comparing oranges to apples Take it as a fraction 2:3 is 2/3 but not 3/2( same as 3:2) Hope you understood that they are different, the opposite in one way :) :) good question! |
Are fractions and ratios the same thing?Are they different?Is 2:5the same as 2/5? | UK-_qEDtvYo | Well... fractions and ratios are not the same thing, but 2:5 can mean the same thing as 2/5. |
I saw him box 2 apples and 3 oranges, but it was 2:5. Isn't it supposed to be 2 apples for every 5 oranges? | UK-_qEDtvYo | It is 2 apples for every 5 pieces of fruit, not for every 5 oranges. |
How do I solve this question.
The ratio of selling price to cost price is 4:3. How much is the profit if the selling price is K1, 200? | UK-_qEDtvYo | Start by finding the cost price. You can do this using a proportion: 4/3 = 200/x Cross multiply, then solve for X Once you have X (the cost), subtract: selling price (200) - cost (x) and you will know the profit. Hope this helps. |
I get how he got 2:5- 8:20 (sorry if it says part of the video, it should be the ratio 8 to 20), dividing by their LCM. But in the picture it shows 2 apples for every 3 ORANGES not five, like the ratio says. So would the picture be accurate or not? | UK-_qEDtvYo | It shows 2 apples for every 3 oranges, but Sal is not trying to find the ratio of apples to oranges, 2:5 is just the simplified version of apples to all of the fruit. Imagine if the picture showed 8 apples for every 20 pieces of total fruit; then, you could simplify it down to 2 apples for every 5 pieces of fruit (including the two apples) |
How did he get 8:20 | UK-_qEDtvYo | 8 apples. 8 apples + 12 oranges = 20 pieces of fruits. ratio apples to fruit is 8/20 |
I didn't quite understand from 2:33 on, can i have some help explaining. | UK-_qEDtvYo | Well it s just like a division promplem but sometimes on worksheets it would tell u write it in colon form and that s what u write |
Why is the ratio 8:20 and not 2:3 ? | UK-_qEDtvYo | You have to make sure to simplify your answer or it could be counted wrong in many cases. 8:20 simplified/divided by 4 is 2:5! :) Hope it helps :) |
how did you get 8:20 | UK-_qEDtvYo | The total number of fruits is 20. The total number of apples is 8. Boom! You get 8:20 ;) Hope it helps! |
At 2:07 (and a little before) what is he talking about?
Thanks in advance! | UK-_qEDtvYo | It s just a fraction. It is basically telling us how much more or less is the numerator than the denominator, as all fractions do. Basically like Sal says, 2/5, it means 0.4 of how many fruits there are. All ratios are fractions but not always the other way around. |
at 3:00 , the fraction for oranges and the total amount of fruits is 3/5 right | UK-_qEDtvYo | Yes... the ratio for oranges to total fruit would be 3/5 |
Well, at 2:39, what does it mean when it says "2/5 of the fruit are apples"? | UK-_qEDtvYo | This sentence 2/5 of the fruit are apples translates into: 2/5 x the number of fruit = the number of apples We know there are 20 pieces of fruit. So, if we do: 2/5 * 20, it will tells us the number of apples. |
Solve 5:x-3=25:10 | UK-_qEDtvYo | You have one fraction = another fraction. This is a proportion. Cross multiply to solve. 5 / (x-3) = 25 / 10 5(10) = 25(x-3) 50 = 25x - 75 I ll let you finish from here. If you get stuck, comment back. |
At 0:52, Sal said 8 to 20, or 8 : 20. Anyway, I've heard people express it as 8 is to 20. So is saying is to and to the same thing? | UK-_qEDtvYo | so ratios are |
at 2:47, how did he get 2/5 when it was 2/3? | UK-_qEDtvYo | i like to eat, i like to eat, apples and bananas ,apples and bananas i like to oat, i like to oat, oppols and banoonoos (so on and so on with different vowels) This is a song i grew up with. |
is 3:5 same as 3/5 | UK-_qEDtvYo | Yes, 3:5 same as 3/5. |
At 0:55, shouldn't the ratio be 8 : 12 because there are 8 apples and 12 oranges? | UK-_qEDtvYo | It will not be 8:12 because he is comparing apples to all the fruit as a whole. There s 20 fruits in total, (8+12). Therefore, there s 8 apples, but 20 fruit, which makes the ratio 8:20. |
I understand that it's # of apples to # of fruit, but the 2:5 or 8:20 makes no sense to me, could you help make some sense? | UK-_qEDtvYo | 2x4=8 5x4=20 So, 2:5 = 8:20 |
I still don't understand the difference between the regular fractions and fractions that are from ratio. Ex. 1/2 When I picture 1/2, I think of a circle divided into two parts where one piece is shaded. However with 1:2 or 1/2 as a ratio, I think of 3 units (comparing as a circle divided into 3 parts) where a part is shaded into one colour and two other parts is shaded into another coulour.
Does someone have an explanation that will help me integrate the two ideas? Thank you | UK-_qEDtvYo | A ratio is a different way of displaying the fraction, because when you are reading an equation, this; 21/8 could be read as a division question instead of a fraction. So if it helps, you can instead picture this; 7:3, as this 7/3 if it helps, but it is so that you don t misinterpret the question |
how can i change to the simplify 6:9 ? | UK-_qEDtvYo | im guessing you are asking how to simplify 6:9. well first to simplify we need to find what number can I divide both numbers by(not including 1) SO THAT THERE IS NO REMAINDER? well 2 doesn t work. 3 does work! so if we divide 6 by 3 we get 2. if we divide 9 by 3 we get 3. so 6:9 is 2:3 simplified. we can also right our final ratio like this;::: 2:3 2 to 3 two to three 2/3 Hope This Helps!! =) |
Could this be a example. 9:36 could also be 3:12 or 1:4 please help meeeeee? | UK-_qEDtvYo | Yes, the ratio of 9 : 36 can be (and should be) reduced to 1 : 4. Ratios are fractions, and like fractions, they should be fully reduced. |
Can you have a fraction ratio, where you have a number like 2 1/2:5? Like you cut a apple in half? Just something I want to think about. | UK-_qEDtvYo | No you can not unless you are looking for the unit rate |
at 1:35 what are you dividing? | UK-_qEDtvYo | you are dividing the number of apples by the total number of fruit in each group. There are 2 apples and 3 oranges in each group. So the total number of fruit is 5. Therefore the number of apples divided by the total number of fruit is: 2/5 2:5 2 to 5 It can be written in any of these ways. |
So, 3:4 and 6:8 are equivalent ratios? | eb-GHXCqkhQ | Yes, because when you simplify 6:8 by dividing by 2 you get a ratio of 3:4. |
how do u get the ratio does 3:2 refer to the 2x and 3x in the problem | J1HAY8E3gms | Remember that if we have a ratio of 3 to 2, we can still write this ratio as 3x to 2x because multiplying the numerator and denominator by x is equivalent to multiplying the fraction by 1. This does not change the fraction s value. |
At 4:11, why is it 6x squared? Why do you make it squared. | J1HAY8E3gms | 3x * 2x = 3 * x * 2 * x = 3 * 2 * x * x = 6x^2 |
At 4:32,how is 21x+16x=37x?Why it is not 37x^2 | J1HAY8E3gms | Danilo, The reason that 37x is correct and 37x^2 is not is because at that point in the problem (video time 4:32) we are combining like terms. So the two terms of 21x + 16x add together, if we were multiplying then it would be x^2 but then 32 would be wrong. |
At 2:19 he said rectangle instead of square | xMz9WFvox9g | A square is a rectangle with 4 equal sides. |
At 0:31 What is the meaning of "unit length"? | xMz9WFvox9g | A unit length is just what we say to mean, any unit of [whatever we re measuring, length or volume or whatever]. It s just what we say instead of specifying that we re using meters or feet or inches or miles. The math works the same way as it would it anyone said [inches, meters, or whatever] |
at 4:22 is there a 4th dimention? | xMz9WFvox9g | in theory, yes there is, just dont count on finding a 4th dimension in this universe |
At 4:28 he drew the three dimension cube. Why didn't he draw the back line? | xMz9WFvox9g | It can appear more confusing than it has to |
I've been learning this topic. How do you find the specific measurement if it doesn't tell you how much the base is and only tells you the base of the bigger figure on a composite figure? I've tried dividing the base of the larger piece into however much of the piece the smaller one takes up. It doesn't seem to work. Can someone help me? 0:00 | xMz9WFvox9g | You can try using the Pythagorean theorem or trigonometric ratios. They tend to be extremely helpful and is very basic and easy when coming to triangles. These methods are simple and will work for any grade. In other words this method is as easy as adding 1+1 |
at 14:08, why it become r, rather than r^T? | QOTjdgmNqlg | No, w is linear combination of C(A^t), so you transpose A and every row is transposed again = r^t becomes (r^t)^t = r (transposition of transposition of r is just r). |
at 16:00 is every member of N(A) also orthogonal to every member of the column space? | QOTjdgmNqlg | every member of N(A) also orthogonal to every member of the column space of A transpose. |
@ 22:00, why is "N(B^t)" the "left nullspace", when "B^t" is the same matrix as "A", and so therefore if N(A) = {x | Ax=0}, then N(B^t) must be {x | (B^t)x=0}? | QOTjdgmNqlg | N(A^t) is represented by span of vectors, which satisfy the equation: (A^t)x=0 , lets take transpose from both sides of this equation to obtain A instead of A^t : ((A^t)x)^t=0^t -> (x^t )*A=0. So, as you can see, vector x is on the left side for now, therefore we call N(A^t) the left Null Space. |
At 1:01 why does Sal halve (1/2) to find the area of the triangle?why does he multiply 1/2 by dimensions 8 and 12?why does just not multiply 12 by 8 to know the area?
WAITING FOR THE ANSWER. Thanks | mtMNvnm71Z0 | Because when you do 8*12 you are getting a square and half of a square is a triangle. Also answer this question, How much swiss cheese does it take to fill my bathtub that is 6 ft. long 3 ft. wide and 2 ft. deep? |
At 5:06, Sal's equation is S(t) = -0.25t +2. Is S(t) the dependent variable or just S? | W7H-VcaSSu8 | S(t) is a function not a dependent variable. A function is kind of a box which takes a number and throws a different number back. The name of the box is S and the number you put in is t ( which could be any number ). Let us say that t is 4 and we throw 4 in the S box, inside the box, we multiply 4 * -0.25 which equals -1 , then we add 2 to it. If we see it in the equation form it will look like this: S(4) = -0.25 * (4) + 2 |
At 0:19 what exactly does denote mean in math terms? | W7H-VcaSSu8 | It comes from L. nota (letter) and means among other things to be the outward or visible mark or sign of, to indicate as letters indicate a word. |
why is it negative 0.75 @ 2:10. Why couldn't it just be 0.75? | W7H-VcaSSu8 | you could if you subtracted 1.25 from 2 instead of 2 from 1.25 then you would subtract 3 from 0 and you would still get the same slope of -0.25 |
At 2:13 and 2:19, he says that the 5 and 3 can be either negative or positive, why is this so? Wouldn't it be just positive 5 and positive 3 since those are the square roots of 25 and 9?
Please answer fast! I need it for a math class (2nd grader) in 3 days! | liRNTieIU_k | What is 5 ⨠5? It s 25. What is 3 ⨠3? It s 9. What is -5 ⨠-5? It s 25 as well! What is -3 ⨠-3? It s 9 as well! When he means what you mean, where â25 or â9 are only +5 and +3, respectively, he will say principal square root . Hope this helps! âCT-2/002-24 |
You made a mistake at 2:25. B=+- not b+_ | liRNTieIU_k | The plus with the minus under it is the plus or minus sign which indicates a positive and negative solution. |
at 0:54 how did he get the formula (ax+b) squared? How do you know when or when nt to use that formula? | liRNTieIU_k | I THINK he used it because the a and the b values both appear to be perfect squares (25 and 9) so when you factor they will be in that form. (5x-3)^2 |
at 1:57 what did he do to get the numbers | liRNTieIU_k | The numbers are in the original problem stated in upper left. Sal just copied it over to the right side of the screen. |
At 1:04, is this what the FOIL method is? | liRNTieIU_k | Yes, First Outer Inner Last. First terms of the two groups, then the ones farthest apart, then the closest ones, then the last ones. (x+b)(x+c) First: x*x Outer: x*c Inner: b*x Last: b*c So then it s (x*x)+(x*c)+(b*x)+(b*c)= (x^2)+cx+bx+bc. cx and bx will usually combine into one term though. |
at around [3:25] Sal says both of them work out. my question is when will one not work out and the other work? | liRNTieIU_k | in a perfect square trinomial it will always work i think hope that helped |
A 3:09,how did he get a2x2+2abx+b2? That just made me get confused.... | liRNTieIU_k | Hi Brittany, he got that by simply multiplying the two terms (ax+b) * (ax+b). FOIL is a useful acronym to remember here. First * First: ax * ax = a^2x^2 Outside * Outside: ax * b = abx Inside * Inside: b * ax = abx Last * Last: b * b = b^2 This yields: a^2x^2 + abx + abx + b^2 You then add the two middle terms as if they were both simple x s and you get: a^2x^2 + 2abx + b^2. Hope this helps. |
Do you have to do the transformations with one point in common, like in 0:40? Or can you do them on any point? | Tn9U8hLu9aI | I m not quite sure what you mean, but I ll try to answer your question. -You can do the transformations anywhere, but it s much easier if you do have one point of each pentagon match up. -Transformations shouldn t change the angles or the length of the sides, so as long as the two pentagons were congruent in the first place they will have all five points the same. -Sorry that I was the first to answer this and was a year late... -.-; |
At 2:30 Isn't being a square also redundant?
I mean, if it is in R^n, shouldn't it has always n basis vectors? If not, could you show me a case where this doesn't happen?
Because, if it's a n-dimensional space, then there are n diferent basis vectors (and n coeficients) to describe it, aren't there? | meibWcbGqt4 | No, for example a plane in R^3 has 2 basis vectors. a*(1,1,0)+b*(0,0,1) |
At 5:30, just do 56 divided by 8, then add three zeros. Then you should get 7000. | ccS5Fy5yLjk | yep! true :) :) :) :) :) :) :) :) :) :) :) :) :) :) :) :) :) :) |
At around 0:50 why does Sal say a sub 2⦠shouldn't the sequence start at a sub 1?
He also states at around 2:35 that the index is one less than the exponent, what is the first index then, if there isn't one then shouldn't the index start with one making the exponents two points higher than the index? | yvddTWa9ptU | Note the notation at the beginning of the video: loosely translated into lay English, it would read the sum of a sub n from n equals two to infinity is equal to negative eight fifths etc. Specifically, the starting index is n=2, which would logically lead to starting the sequence at a sub 2. |
How come at 0:46 sal starts with a2(a sub 2) instead of a1(a sub 1) | yvddTWa9ptU | This is simply a matter of what we re given as part of the problem. The notation underneath the sigma symbol tells us the starting point, and in this case it says n=2, so we begin counting at 2. |
Once we establish that the slope of the secant line over [a, 0] is greater than a line with a slope of 1, how do we extrapolate that to mean that f(-a) is less than that (around 4:00, part I)? Is it implied that f(-a) atually means "the slope of the line tangent to f(-a)?" Or am I forgetting something that says if the slope is greater, then the value of the function is always greater? | H6ZNLD1AeM8 | The actual numeric value of f(-a) is less than 1 (as Sal points out between 0:45 - 1:00). He later shows that the value of the slope (average rate of change) between points (-a,f(-a)) and (0,1)) is greater than 1. (That s the 1-f(-a)/-a, part). So he is ultimately comparing the two values, not two slopes. It was confusing to me too, at first. :) |
At 1:35, why do you divide the original equation by 2? | OZtqz_xw0SQ | In order to simplify the equation and to also have a non-negative leading coefficient. |
At 1:40 why did Sal divided the equation by -2? Could he also have simplified the original equation? | OZtqz_xw0SQ | he just took out a common factor, simplifying and also taking away the negative from the leading coefficient. He could do the division because 0 divided by anything is still 0. |
at 0:29 can someone provide me a link to the problems that Sal is talking about please? thanks! | OZtqz_xw0SQ | I don t know specifically, but he mentioned the physics content. You can get to Physics by selecting it off the subjects menu. Or, use the search bar. |
At 5:11, what did Sal do to evaluate 20(5/2) so quickly? | OZtqz_xw0SQ | You times 20 by the numerator (5) and divide by the denominator (2), which is: 20*5/2 = 100/2 = 50 |
At 2:39, who are Larry, Curly, and Moe? Are they the Three Stooges? | Xqfcy1rqMbI | Yes, that is correct. The original three stooges were Larry, Shemp, and Moe, but Shemp quit, and was replaced by Curly. Later on, I think Shemp got switched back in. |
At 1:38 why is it 2^8 instead of 3*8?? | Xqfcy1rqMbI | because sal is going to flip a coin 8 times and every flip will have 2 outcomes, either heads or tails...that s why 2(no of outcomes)^ 8(no. of flips) to calculate total outcomes |
From about 0:39 to 0:42 Sal mentions "...equally probable events..." I don't ever remember Sal defining what an event is exactly. Although I have a general idea what he means in the context of say this problem, could someone give a quick answer to that in the perspective of all basic probability? Thanks. | Xqfcy1rqMbI | An event is an outcome. When Sal talks about all equally probable events he s talking about all the possible outcomes something can have while meeting the requirements or conditions stated. That s why the numerator is different than the denominator at 1:17. The numerator is all possible outcomes that can have 3 heads and the denominator is all possible outcomes that can have any combination of Heads of Tails . Hope it helps. |
At 1:50, why do you multiply 2 by the number of flips? | Xqfcy1rqMbI | To calculate the total number of possible outcomes. For every flip there are 2 possibilities - heads or tails. So to find out the total number of possible outcomes for two flips we need to calculate 2*2 or 2². For eight flips this means 2^8. |
6:37 Doesn't he mean there's 56 ways of putting 8 flips into 3 heads? Is the number of ways the same for vice versa or am I missing something? | Xqfcy1rqMbI | If you flip a coin 8 times, there are 56 different ways to have those 8 flips result an outcome of 3 heads. Here are some of them: H=Heads, T=Tails HHHTTTTT TTTTTHHH HTHTHTTT TTHHHTTT . . . . . etc. There are 56 ways to arrange (combine) 3Hs and 5Ts. |
Starting at 2:55, Sal was comparing the combinations of 3 heads in eight flips to sitting 3 people in a car from a group of 8. I have a problem making this mental leap. In my head, each flip has two possible outcomes. But a person does not have this 50/50 of being H or T. Thus, it is not really C(8,3). Can someone help to explain? | Xqfcy1rqMbI | The idea is that he can pick a person to sit in the car, or not. This is binary: either the person goes in the car, or they do not. There is no third option. That s why he said pick 3 people : either a person is chosen, or they are not. Again, there is no third option. Just like there is no third option between heads or tails (disregarding the very unlikely physical possibility of the coin landing on its side). |
At 0:06 how is shouldn't Sal say 3 is worth 300? | jxA8MffVmPs | Watch the video... He does. |
I love when you explain how to do things, like in the way you did at 1:28 :) | jxA8MffVmPs | I do not know how to watch the video because I am on a iPad that is very pretected so if you can tell me how I would thank you |
at 2:16 sal doesnt mension 4 thousands but he mensions all the other place values... can someone please tell me why?! | jxA8MffVmPs | He did not say the thousands place because he was looking for the place of the 3, and the 3 happens to be in the hundreds place, so he stopped there. |
At 6:30 Sal talks about looking up the equation on khan academy of the sum of n^2 but where would we look it up at? Is it in the form of a video or a FAQ? | LwhJVURumAA | You can find the explanation for that formula used at 6:30 in the videos Finding the sum of n squares part1 and part2 |
Waait... where does Sal get the 7/6 at @4:10? | LwhJVURumAA | He gets it from the equation at 3:50. You can derive it yourself or find derivations for it. |
@ 3:45, Sal gives an example as a sum of fractions. Why? Shouldn't it be 1^2 +2^2+....+7^2? | LwhJVURumAA | He is using a formula to find the sum, rather than finding each value and adding them one by one. |
At 1:44 it is said that you should multiply both sides by the reciprocal. Reciprocals only exist for rational numbers that are nonzero. What would happen if the rational number happens to be zero?
A very subtle counterexample.
Can anyone see how to reword the statement to make it true? | KT32CsdEZEY | You are right, this rule only works if multiplier is not equal to zero. Because everything multiplied by zero equals zero so you always get rational number as a result. |
At 0:38, how did you determine that the y intercept for y=g(x) was 3. I understand how you found it for the first equation because the y intercept was 4, but how did you find it for g(x)? | UdLYAqN0gNY | You look for the point on the y-axis that is (0, #). for that one it happened to be 3 |
Why did Sal refer to the x-solutions as "roots" @2:31 ? | UdLYAqN0gNY | A root is the solution to an equation. When a quadratic function is set equal to zero, it is simply a quadratic equation that can be solved. A zero is the value of a variable that makes a function equal to zero. For polynomials like quadratics, and many other types of functions (especially in two dimensional space), the root and zero are basically synonymous - they are both the x-values where the graph would intercept the x-axis (where the y is zero). |
at 5:30, when Grant compute the mixed partial derivative, he doesn't multiply sqrt(3) by 6: (Df/Dyx)=6x = 6*sqrt(3) = sqrt(108), so FxFy-Fxy^2 = -108
I understand that in this case, the magnitude of the mixed partial Derivative didn't matter since the other term =0, but is there another reason he didn't compute or might've he forgotten? | TqslX-bUTD8 | No. Chiarandini s right. All results are -108 except for one that s 36>0. I think Grant s very stressed doing these videos! That s too bad because he s doing an awesome job otherwise. |
At 1:12 on the video. You simplify the expression for the Total price from P+0.25P to 1.25P. I do not follow what you do - divide by P? What is th emath theory to explain that? Thank you! | ao9cx8JlJIU | P = 1 times p p = 1 p p + 0.25p does equal 1 p + 0.25 p Any thing equals one of itself. Hope that helps! ;-) |
In the previous video when Sal states the domain he just writes "Domain= and then the number" but in this video when he states the domain @0:45 he says the "Domain is equal to the "set" of and then the number. What's the reason behind the change? | ey_b3aPsRl8 | Its the same thing, maybe because the previous vid had 2 values that make the expression undefined. |
at 2:13 why do we multiply by -1 and then multiply by -1 AGAIN? why not just once? and home we don't do this to the denominator? please and thank yoU! | ey_b3aPsRl8 | You cannot change the expression, meaning you can modify it, but it must be equivalent, this is why you have to multiply 2 times by -1, because (-1)(-1) = 1, so you are not changing the expression. If you multiplied only once by -1 then you would be changing the expression, you would be making it negative, and that is not valid. Sal decided to to this on the numerator, but he could have done so in the denominator if he wanted to, the result would have been the same either way. |
3:00 how come you can just multiply by -1? | ey_b3aPsRl8 | Not just multiplying by -1. Using this equivalence to put the factors in a form to allow dividing them out. x - 6 = (-1)(-x + 6) = (-1)(6 - x) |
At 2:16, why do you have to multiply by -1 twice? What do you do with the negative one that is left out (2:47)? | ey_b3aPsRl8 | @ 2:16, he did that so that there s no net change (If he just multiplied by -1 that would be changing the expression). @ 2:47 both -1 s remain in effect - they both have an effect on the answer. (x^2-36)/(6-x) = ((x+6)(x-6))/(6-x) = ((x+6)(x-6)(-1)(-1))/(6-x) = ((x+6)(-x+6)(-1))/(6-x) = ((x+6)(6-x)(-1))/(6-x) = ((6-x)/(6-x))((x+6)(-1)) = (x+6)(-1) = -(x+6). |
At 0:58, how did he just immediately go, bam, it's 75? I could really use skills like that, so could somebody explain please? | TV5kDqiJ1Os | 75 goes into 150 twice, and 150 goes into 300 twice. |
At 0:24, why did he divide everything by 4 instead of dividing only 4x^2 and 0 by 4? | TV5kDqiJ1Os | If he divided only 4x^2 that would of changed the quadratic. To make it say the same you need to dived every term by 4. Someone tell me if I m wrong. |
How did you get 25 at 3:09 | TV5kDqiJ1Os | We have the identity of (x+a)^2 i.e x^2+2ax+a^2. Sal have just factorize 10x .i.e 2*5*x. So we get the value of a i.e. 5 . And Sal has just put the value of a in a^2 . By this we get the value 25. |
At 1:21, Sal just divided everything by four. However, when do we put the four on the outside of parenthesis? | TV5kDqiJ1Os | If you divide everything on both sides of the equation by 4, it can just go away. If he only factored it out on the left side, he would have to leave it there outside of parenthesis. |
@ 3:12 How come you don't subtract 25 too. Isn't that what you usually do? | TV5kDqiJ1Os | If you subtracted 25 then you would be doing different things to each side of the equation. You have to add 25 to each side in order to get the perfect square. |
Hi Sal,
These video's are very helpful. however id just like to know:
when you get to the pint in your working similar to what we see at 3:50 but you don't have equal brackets... how would you workout the answer? What happens to the constant on the other side of your equation?
Thanks
CBR | TV5kDqiJ1Os | I don t really know what you re talking about, but here s what he does from 3:50 onwards. (x+5)^2=100. He square roots everything => (x+5)=Positive or negative 10. Solving => x= -15 or 5. |
At 5:15, he mentions that "taking the cross section that is parallel to the xy-plane will give a smaller radius" what's the point of taking the cross section? what's the point of getting a smaller radius? If it's a sphere, shouldn't the radius always be the same? | E_Hwhp74Rhc | We have t being used to determine x and y, so we need something else to determine z, so that is why we take different cross sections at different values of z. The cross section is getting a smaller radius because some of the radius is being used for the z-component, so not as much can be used for the x and y components. |
At 1:00, why is the Celsius scale called the Celsius scale and why is the Fahrenheit scale called the Fahrenheit scale? | aASUZqJCHHA | Fahrenheit (symbol °F) is a temperature scale based on one proposed in 1724 by the physicist Daniel Gabriel Fahrenheit. Eighteen years later In 1742, Swedish astronomer Anders Celsius (1701â1744) created a temperature scale which was the reverse of the scale now known by the name Celsius : 0 represented the boiling point of water, while 100 represented the freezing point of water. |
3:22 i dont understand | hr_mTd-oJ-M | don t understand what? |
At 1:20 it is a very good pictorial representation on multiplying fractions | hr_mTd-oJ-M | When you multiply two fractions you do numerator times numerator and denominator times denominator and then you get a new fraction. If the numerator is bigger than the you need to divide it. If they are both even divide both by two Example: 3/4 x 2/5=6/20. The numerator is not bigger but you still divide both by two to get 3/10. |
at 0:22, does that work? I don't understand how it would work. can anyone help? | tvXRaZbIjO8 | Yes, if there is a parenthesis after a subtraction you MUST distribute the negative. This is because you are subtracting everything in the parenthesis. Remember subtracting a negative is the same as adding a positive. Essentially on the last term you have â(â18i) which is why it simplifies to + 18i |
1:01,how do we know that the numbers with the 'i' are imaginary? | tvXRaZbIjO8 | That s how we define it. How do we know that the numbers with the - are negative? |
At 4:14 he puts 11< square root 123 < 144
It should be 11< square root 123 < 12 | Lh7NMBPFVZw | If you watch the next few seconds he actually corrects that and 144 is greater than the square root of 123 anyway. |
At 0:45 how did Sal get the 5? | Lh7NMBPFVZw | 5 x 5 = 25 and 6 x 6 = 36. So the square root of 32 will be between 5 and 6. |