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saa15

  • 2 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?

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  1. genius12
    • 2 years ago
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    Is that = 125 or - 125?

  2. saa15
    • 2 years ago
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    -125

  3. saa15
    • 2 years ago
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    @genius12 can you solve it?????

  4. genius12
    • 2 years ago
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    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. satellite73
    • 2 years ago
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    i guess it is the cube of something, so you have to figure out what it is the cube of

  6. saa15
    • 2 years ago
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    @genius12 oh yeaa it also says the the volume of a cube is s^3

  7. ByteMe
    • 2 years ago
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    http://openstudy.com/users/saa15#/updates/51340a6fe4b0034bc1d7f511

  8. satellite73
    • 2 years ago
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    i would make a guess at \((4x-5)^3\) otherwise, how knows

  9. satellite73
    • 2 years ago
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    yeah, that works, it is the cube of \(4x-5\)

  10. satellite73
    • 2 years ago
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    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. genius12
    • 2 years ago
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    ya lol

  12. genius12
    • 2 years ago
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    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. genius12
    • 2 years ago
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    @saa15

  14. saa15
    • 2 years ago
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    @genius12 can you explain it easier??

  15. genius12
    • 2 years ago
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    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. saa15
    • 2 years ago
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    @genius12 THANK YOU SO MUCH SORRY FOR BUGGING YOU but how did you get to (4x-5)

  17. genius12
    • 2 years ago
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    I would appreciate a medal. @saa15

  18. saa15
    • 2 years ago
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    @genius12 you are a life saver!

  19. genius12
    • 2 years ago
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    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. genius12
    • 2 years ago
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    @saa15

  21. saa15
    • 2 years ago
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    THANK YOU!! @genius12

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