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Math Help - Quick diffrential equation question.

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    Quick diffrential equation question.

    When a mint is spherical mint is sucked, a simple model gives the rate of decrease of its radius as inversely proportional to the square of the radius. Initially, the radius of a mint is 5mm and after 5 mins the radius is 4mm
    Okey, my question is, does the differential equation for this start:
    \frac{dr}{dt} = \frac{r^2}{-k}
    I wasn't at school when this was taught(=( ) and there's no examples in my book on inverse proportion.
    Thank-you
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    Quote Originally Posted by AshleyT View Post
    Okey, my question is, does the differential equation for this start:
    \frac{dr}{dt} = \frac{r^2}{-k}
    I wasn't at school when this was taught(=( ) and there's no examples in my book on inverse proportion.
    Thank-you
    Try \frac{dr}{dt} = \frac{k}{r^2}
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    Quote Originally Posted by danny arrigo View Post
    Try \frac{dr}{dt} = \frac{k}{r^2}
    But its decreasing, won't it be negative?
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    k will be a negative value ...

    \frac{dr}{dt} = \frac{k}{r^2}

    r^2 \, dr = k \, dt

    \frac{r^3}{3} = kt + C

    when t = 0, r = 5

    \frac{125}{3} = k(0) + C

    \frac{r^3}{3} = kt + \frac{125}{3}

    when t = 5 , r = 4

    \frac{64}{3} = 5k + \frac{125}{3}

    -\frac{61}{15} = k
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