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Math Help - Rate of Change problem

  1. #1
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    Rate of Change problem

    A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60 cm/s. Find the rate at which the area within the circle is increasing after 3 seconds.

    What do I do? I think I am supposed to use the formula of the area of a circle, but I am not sure how to use it.
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  2. #2
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    Quote Originally Posted by Maziana View Post
    A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60 cm/s. Find the rate at which the area within the circle is increasing after 3 seconds.

    What do I do? I think I am supposed to use the formula of the area of a circle, but I am not sure how to use it.
    take the time derivative of the area equation ...

    \frac{d}{dt}[A = \pi r^2]<br />

    ... then use the given info to determine \frac{dA}{dt}
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    I don't understand what I do to get rid of the r and plug in s...
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    Quote Originally Posted by Maziana View Post
    I don't understand what I do to get rid of the r and plug in s...
    what do you mean by "s" ?
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    Seconds, which is 3 in this problem.
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  6. #6
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    Quote Originally Posted by Maziana View Post
    Seconds, which is 3 in this problem.
    you only need the 3 sec to determine the size of the radius which is increasing at 60 cm per second.

    \frac{dA}{dt} = 2\pi r \cdot \frac{dr}{dt}

    \frac{dA}{dt} = 2\pi (180 \, cm) \cdot (60 \, cm/s)
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