## anonymous 3 years ago HELP ME PLEASE???? If the volume of the cube is 64x^3-240x^2+300x-125, what is the length of one side?

1. anonymous

Is that = 125 or - 125?

2. anonymous

-125

3. anonymous

@genius12 can you solve it?????

4. anonymous

I can, but usually the equation would be like 64x^3-240x^2+300x-125 = ? It should be like equal to something for me to solve it. Did you forget to type something up?

5. anonymous

i guess it is the cube of something, so you have to figure out what it is the cube of

6. anonymous

@genius12 oh yeaa it also says the the volume of a cube is s^3

7. anonymous
8. anonymous

i would make a guess at $$(4x-5)^3$$ otherwise, how knows

9. anonymous

yeah, that works, it is the cube of $$4x-5$$

10. anonymous

they really stretch for these word problems, don't they? the question was asking "what would you cube to get $$64x^3-240x^2+300x-125$$?"

11. anonymous

ya lol

12. anonymous

So, that expression is that cube of 4x - 5. So the Volume is:$V=(4x-5)^3$We know that the formula for the volume of a cube is V = s^3, where is the is one of the sides. So if we take the third root of both sides, you get:$\sqrt[3]{V}=s \rightarrow \sqrt[3]{V}=4x-5 \rightarrow s=4x-5$

13. anonymous

@saa15

14. anonymous

@genius12 can you explain it easier??

15. anonymous

If we have a cube, we know that the cube has 6 sides of equal length. The volume of a cube is Volume = S x S x S = (S)^3, where S is one of the six side lengths. Here we know that the long expression is the Volume of the cube. If we take the third root of that expression, meaning find an expression that when taken to the power of 3 gives us that long expression, we find 4x - 5, because (4x - 5)^3 = 64x^3-240x^2+300x-125 = S^3 Since we are looking for the side length of the cube and we know that Volume = S^3 (S is the side length) and that the Volume of this cube is Volume = (4x - 5)^3 Then we can say that S^3 = (4x - 5)^3, which is the Volume. To get the value of just S, because that's what we are trying to find, we take the third root of both sides to get: S = 4x - 5 --> Therefore, the side length of the cube is 4x - 5. @saa15

16. anonymous

@genius12 THANK YOU SO MUCH SORRY FOR BUGGING YOU but how did you get to (4x-5)

17. anonymous

I would appreciate a medal. @saa15

18. anonymous

@genius12 you are a life saver!

19. anonymous

You take the third root of both sides. Since we know that:$S^3=(4x-5)^3\rightarrow \sqrt[3]{S^3}=\sqrt[3]{(4x-5)^3}\rightarrow S =4x-5$ You see, when I say take the third root of both sides, I'm saying that find a value that when raise to the power of 3, gives us our original value again. For example, third root of 64 is 4 x 4 x 4, same as saying 4^3. So when I say take the third root of both sides of the equation S^3=(4x-5)^3, I'm really saying to find the value that when multiplied by itself 3 times, gives us the original value again. So third root of S^3 would be just S, because S x S x S = S^3 and third root of (4x - 5)^3 is just 4x -5 because 4x -5 * 4x - 5 * 4x-5 = (4x-5)^3 So we get S = 4x - 5 Get it?

20. anonymous

@saa15

21. anonymous

THANK YOU!! @genius12

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