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Math Help - Rates of Change

  1. #1
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    Rates of Change

    So, the question is this:
    Suppose oil spilled from a tanker spreads in a circle whose area increases at a constant rate of 6 square miles per hour. How fast is the radius of the spill increasing when the area is 9 square miles?

    Now, I think dA/dt= 6 square miles. I'm not as sure about the 9, because if you take the derivative there is no A it's just dA/dt= pi*2r*dr/dt. So, if I solve for dr/dt then won't I still have the 2r left?

    Help would be much appreciated with this, thanks.
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    Quote Originally Posted by instantchaos View Post
    So, the question is this:
    Suppose oil spilled from a tanker spreads in a circle whose area increases at a constant rate of 6 square miles per hour. How fast is the radius of the spill increasing when the area is 9 square miles?

    Now, I think dA/dt= 6 square miles. I'm not as sure about the 9, because if you take the derivative there is no A it's just dA/dt= pi*2r*dr/dt. So, if I solve for dr/dt then won't I still have the 2r left?

    Help would be much appreciated with this, thanks.
    You will but this is where the 9 comes into play via the equation

    A=\pi r^2 so Since you know A you can solve for r.
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