anonymous
  • anonymous
HELP ME PLEASE???? If the volume of the cube is 64x^3-240x^2+300x-125, what is the length of one side?
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
Is that = 125 or - 125?
anonymous
  • anonymous
-125
anonymous
  • anonymous
@genius12 can you solve it?????

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anonymous
  • 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?
anonymous
  • anonymous
i guess it is the cube of something, so you have to figure out what it is the cube of
anonymous
  • anonymous
@genius12 oh yeaa it also says the the volume of a cube is s^3
anonymous
  • anonymous
i would make a guess at \((4x-5)^3\) otherwise, how knows
anonymous
  • anonymous
yeah, that works, it is the cube of \(4x-5\)
anonymous
  • anonymous
they really stretch for these word problems, don't they? the question was asking "what would you cube to get \(64x^3-240x^2+300x-125\)?"
anonymous
  • anonymous
ya lol
anonymous
  • 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:\[\sqrt[3]{V}=s \rightarrow \sqrt[3]{V}=4x-5 \rightarrow s=4x-5\]
anonymous
  • anonymous
anonymous
  • anonymous
@genius12 can you explain it easier??
anonymous
  • 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
anonymous
  • anonymous
@genius12 THANK YOU SO MUCH SORRY FOR BUGGING YOU but how did you get to (4x-5)
anonymous
  • anonymous
I would appreciate a medal. @saa15
anonymous
  • anonymous
@genius12 you are a life saver!
anonymous
  • 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?
anonymous
  • anonymous
anonymous
  • anonymous
THANK YOU!! @genius12

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