Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 5.5 mi2/hr. How rapidly is radius of the s

Question

Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 5.5 mi2/hr. How rapidly is radius of the spill increasing when the area is 6 mi2?

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Thạch Thảo 1 year 2021-09-01T21:03:06+00:00 1 Answers 8 views 0

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    2021-09-01T21:04:14+00:00

    The radius will increase at the rate of 0.64 mi/hr

    Explanation:

    The area of a circle can be represented by  A = π r²            I

    Differentiating both sides w.r.t time

    [tex]\frac{dA}{dt}[/tex] = 2π r [tex]\frac{dr}{dt}[/tex]                                    II

    Dividing II by I , we have

    [tex]\frac{dA}{A}[/tex] = 2 x  [tex]\frac{dr}{r}[/tex]

    substituting the values

    [tex]\frac{dr}{r}[/tex] = [tex]\frac{5.5}{12}[/tex] = 0.46 mi per unit radius

    or dr = 1.4 x 0.46 = 0.64 mi/hr

    here 1.4 mi is the radius , when area of circle is 6 mi²

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