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Math Help - velocity

  1. #1
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    velocity

    if:

    V= (6-(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.


    I think you have to find what r^2 is...and then plug it in or something? although that doesnt seem to be working for me, however it may be because im doing that wrong as well.....can anyone help?
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  2. #2
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    Quote Originally Posted by samtheman17 View Post
    if:

    V= (6-(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.


    I think you have to find what r^2 is...and then plug it in or something? although that doesnt seem to be working for me, however it may be because im doing that wrong as well.....can anyone help?
    \frac{h}{2 - r} = \frac{5}{2}

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

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

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

    r = \frac{10h - 2}{5h}.


    So

    V = \left(6 - \frac{r^2}{3}\right)h

     = \left[6 - \frac{\left(\frac{10h - 2}{5h}\right)^2}{3}\right]h

     = \left[6 - \frac{\frac{(10h - 2)^2}{25h^2}}{3}\right]h

     = \left[6 - \frac{(10h - 2)^2}{75h^2}\right]h

     = 6h - \frac{(10h - 2)^2}{75h}

     = \frac{450h^2 - (10h - 2)^2}{75h}

     = \frac{450h^2 - 100h^2 + 40h - 4}{75h}

     = \frac{350h^2 + 40h - 4}{75h}.
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