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Related Rates

  1. Apr 6, 2017 #1
    1. The problem statement, all variables and given/known data
    A stone is dropped into some water and a circle of radius r is formed and slowly expands. The perimeter of the circle is increasing at 3 m/s. At the moment the radius is exactly 2m, what rate is the radius of the circle increasing?
    Answer ## \frac {dr} {dt} = 0.48 m/s##
    2. Relevant equations
    ## C = 2πr##
    ## A = πr^2##
    3. The attempt at a solution
    ## \frac {dC} {dt} = 3 m/s##
    ## \frac {dr} {dt} = ?##
    ## C = 2πr##
    Taking the derivative of circumference formula
    ## \frac {dC} {dt} = 2π \frac {dr} {dt}##
    Subbing in my ## \frac {dC} {dt} = 3 m/s##
    ## 3 = 2π \frac {dr} {dt}##
    Dividiving both sides by 2π gives me 4.71 m/s. I have also tried doing this with the Area of a circle formula but I still got 2.36 m/s which is no where near the 0.48 it is supposed to be. Any help would be greatly appreciated.
     
  2. jcsd
  3. Apr 6, 2017 #2

    LCKurtz

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    Check your arithmetic calculating ##\frac 3 {2\pi}##.
     
  4. Apr 6, 2017 #3
    That's weird. When I do 3/2pi it gives me 4.71 but if I do 3/6.28 I get my answer. Thanks for the help, I wish I had thought of trying that earlier!
     
  5. Apr 6, 2017 #4

    Rio Larsen

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    That's because the calculator interprets it as ## \frac{3}{2}\pi##, ## \frac{3\pi}{2}##, or ##\frac{3}{2}(\frac{\pi}{1}) ## as opposed to ## \frac{3}{2\pi}##.

    Next time, enter it into the calculator as 3/(2## \pi##)
     
    Last edited: Apr 6, 2017
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