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Math Help - stone problem

  1. #1
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    stone problem

    a stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 3 ft/s. how rapidly is the area enclosed by the ripple increasing at the end of 10s? ok im not sure how to set this up? would it be A = pi(r)^2 so i take the derivative with respect to r? right? i got 1960 pi as an answer..
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  2. #2
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    Quote Originally Posted by slapmaxwell1 View Post
    a stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 3 ft/s. how rapidly is the area enclosed by the ripple increasing at the end of 10s? ok im not sure how to set this up? would it be A = pi(r)^2 so i take the derivative with respect to r? right? i got 1960 pi as an answer..
    your solution is incorrect.

    this is a related rates problem. you were given \frac{dr}{dt} = 3 ft/s

    take the derivative of A w/r to time, t , and calculate the value of \frac{dA}{dt} when r = 30 ft
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