Question

HELP ME PLEASE????












If the volume of the cube is 64x^3-240x^2+300x-125, what is the length of one side?

Answer 1

Is that = 125 or - 125?

Answer 2

-125

Answer 3

@genius12 can you solve it?????

Answer 4

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?

Answer 5

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

Answer 6

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

Answer 7

http://openstudy.com/users/saa15#/updates/51340a6fe4b0034bc1d7f511

Answer 8

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

Answer 9

yeah, that works, it is the cube of \(4x-5\)

Answer 10

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

Answer 11

ya lol

Answer 12

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:\[\sqrt[3]{V}=s \rightarrow \sqrt[3]{V}=4x-5 \rightarrow s=4x-5\]

Answer 13

@saa15

Answer 14

@genius12 can you explain it easier??

Answer 15

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

Answer 16

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

Answer 17

I would appreciate a medal. @saa15

Answer 18

@genius12 you are a life saver!

Answer 19

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?

Answer 20

@saa15

Answer 21

THANK YOU!! @genius12