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Thread: V as a function of H

  1. #1
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    V as a function of H

    V = (3-(r^2/3))h and h/(2-r) = 5/2

    Write V as a function of H.

    Simplify the function so that you can express it as a polynomial in H.
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  2. #2
    Super Member Showcase_22's Avatar
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    Quote Originally Posted by gearshifter View Post
    V = (3-(r^2/3))h and h/(2-r) = 5/2

    Write V as a function of H.

    Simplify the function so that you can express it as a polynomial in H.
    $\displaystyle V=(3-r^{\frac{2}{3}})h$

    $\displaystyle \frac{h}{2-r}=\frac{5}{2}$

    Rearranging gives:

    $\displaystyle h=\frac{5(2-r)}{2}$

    $\displaystyle 2h=10-5r$

    $\displaystyle 2h-10=-5r$

    $\displaystyle r=\frac{10-2h}{5}$

    $\displaystyle r=2-\frac{2h}{5}$

    Now substitute the second one into the first one and you're home dry!
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  3. #3
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    I got:



    (-4h^3+125h)/75

    as my final answer.

    Would anybody know if it is correct?
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  4. #4
    Super Member Showcase_22's Avatar
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    We know that:

    $\displaystyle
    V=(3-r^{\frac{2}{3}})h
    $

    and

    $\displaystyle
    r=2-\frac{2h}{5}
    $

    Therefore:

    $\displaystyle V=(3-(2-\frac{2h}{5})^{\frac{2}{3}})h$

    hmm, I can't actually see a way of cancelling it down from here, can you post your working?
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