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saa15 Group Title

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

  • one year ago
  • one year ago

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  1. genius12 Group Title
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    Is that = 125 or - 125?

    • one year ago
  2. saa15 Group Title
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    -125

    • one year ago
  3. saa15 Group Title
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    @genius12 can you solve it?????

    • one year ago
  4. genius12 Group Title
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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?

    • one year ago
  5. satellite73 Group Title
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    i guess it is the cube of something, so you have to figure out what it is the cube of

    • one year ago
  6. saa15 Group Title
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    @genius12 oh yeaa it also says the the volume of a cube is s^3

    • one year ago
  7. ByteMe Group Title
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    http://openstudy.com/users/saa15#/updates/51340a6fe4b0034bc1d7f511

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

    • one year ago
  9. satellite73 Group Title
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    yeah, that works, it is the cube of \(4x-5\)

    • one year ago
  10. satellite73 Group Title
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    they really stretch for these word problems, don't they? the question was asking "what would you cube to get \(64x^3-240x^2+300x-125\)?"

    • one year ago
  11. genius12 Group Title
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    ya lol

    • one year ago
  12. genius12 Group Title
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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:\[\sqrt[3]{V}=s \rightarrow \sqrt[3]{V}=4x-5 \rightarrow s=4x-5\]

    • one year ago
  13. genius12 Group Title
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    @saa15

    • one year ago
  14. saa15 Group Title
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    @genius12 can you explain it easier??

    • one year ago
  15. genius12 Group Title
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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

    • one year ago
  16. saa15 Group Title
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    @genius12 THANK YOU SO MUCH SORRY FOR BUGGING YOU but how did you get to (4x-5)

    • one year ago
  17. genius12 Group Title
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    I would appreciate a medal. @saa15

    • one year ago
  18. saa15 Group Title
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    @genius12 you are a life saver!

    • one year ago
  19. genius12 Group Title
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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?

    • one year ago
  20. genius12 Group Title
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    @saa15

    • one year ago
  21. saa15 Group Title
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    THANK YOU!! @genius12

    • one year ago
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