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Math Help - circle word problem

  1. #1
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    circle word problem

    A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60 cm/s.

    a) Express the radius r of this circle as a function of the time t (in seconds).

    b) If A is the area of this circle as a function of the radius, A(r(x)) and interpret it.

    Please help! I don't even know how to start this problem.
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  2. #2
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    Quote Originally Posted by yoman360 View Post
    A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60 cm/s.

    a) Express the radius r of this circle as a function of the time t (in seconds).
    \frac{dr}{dt}= 60 \Rightarrow r = \int \left(\frac{dr}{dt}\right)dt= r = \int 60 dt= 60t+c

    as r = 0 at t = 0 \Rightarrow c=0

    therefore r = 60t
    Last edited by pickslides; June 29th 2009 at 09:12 PM. Reason: typo
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  3. #3
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    Quote Originally Posted by yoman360 View Post
    b) If A is the area of this circle as a function of the radius, A(r(x)) and interpret it.
    A= \pi r^2 and r = 60t therefore A= \pi (60t)^2 = 3600\pi t^2

    A = 3600\pi t^2 is the Area of the circle at time t
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  4. #4
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    Quote Originally Posted by pickslides View Post
    \frac{dr}{dt}= 60 \Rightarrow r = \int \left(\frac{dr}{dt}\right)dt= r = \int 60 dt= 60t+c

    as r = 0 at t = 0 \Rightarrow c=0

    therefore r = 60t
    If the speed is constant (and I assume it is because the question has been posted in the PRE-calculus subforum) then r = 60t can immediately be written (where unit of r is cm).
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  5. #5
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    Quote Originally Posted by pickslides View Post
    \frac{dr}{dt}= 60 \Rightarrow r = \int \left(\frac{dr}{dt}\right)dt= r = \int 60 dt= 60t+c

    as r = 0 at t = 0 \Rightarrow c=0

    therefore r = 60t
    We don't learn integrals in pre-cal. So I can't use integrals if we never learned about them.
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  6. #6
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    Can anyone else do this without using integrals?
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  7. #7
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    Quote Originally Posted by yoman360 View Post
    Can anyone else do this without using integrals?
    Mr F did in post 4
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  8. #8
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    Quote Originally Posted by e^(i*pi) View Post
    Mr F did in post 4
    well how did he get r=60t?
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  9. #9
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    Quote Originally Posted by yoman360 View Post
    well how did he get r=60t?
    The radius is extending at the rate of 60cm per second.

    After 1 second, the radius is 60cm
    After 2 seconds, the radius is 2 x 60cm
    After 3 seconds, the radius is 3 x 60cm, etc.

    So if t represents the time in seconds, the radius is t x 60cm.

    This is where the formula r = 60t comes from.
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  10. #10
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    Quote Originally Posted by Prove It View Post
    The radius is extending at the rate of 60cm per second.

    After 1 second, the radius is 60cm
    After 2 seconds, the radius is 2 x 60cm
    After 3 seconds, the radius is 3 x 60cm, etc.

    So if t represents the time in seconds, the radius is t x 60cm.

    This is where the formula r = 60t comes from.
    Thanks!
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