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Math Help - derivative problem

  1. #1
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    derivative problem

    assuming that the volume of the trunk is directly proportional to the cube of its diameter,and that the latter increases uniformly from year to year,show that the rate of increase in the volume when the diameter is equal to 90 cm is 25 times the rate when its 18cm.
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  2. #2
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    Quote Originally Posted by inolas_cul View Post
    assuming that the volume of the trunk is directly proportional to the cube of its diameter,and that the latter increases uniformly from year to year,show that the rate of increase in the volume when the diameter is equal to 90 cm is 25 times the rate when its 18cm.
    V = k d^3

    so:

    \frac{dV}{dt} = 3k d^2 \frac{d}{dt}d

    but  ({d}/{dt}) d is constant, so

    <br />
\frac{ dV/dt |_{d=90}}{ dV/dt |_{d=18}} = 90^2/18^2= 25<br />

    RonL
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