Li asked in Science & MathematicsMathematics · 1 year ago

Related rates: A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 2.6 ft/s.?

A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 2.6 ft/s.

(a) How rapidly is the area enclosed by the ripple increasing when the radius is 5 feet?

The area is increasing at _____ ft^2 /s.

(b) How rapidly is the area enclosed by the ripple increasing at the end of 8.2 seconds?

The area is increasing at _____ ft^2 /s.

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  • Mike G
    Lv 7
    1 year ago
    Favourite answer

    a) A = π(2.6t)^2 where t = time

    A(t) = 6.76πt^2

    A'(t) = 13.52πt

    t = 5/2.6 = 1.923

    A'(1.923) = 81.68 ft^2/s

    b) A'(8.2) = 348.29 ft^2/s

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  • Anonymous
    1 year ago

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  • 1 year ago

    A = pi*r^2 =>

    dA/dt = 2*pi*r dr/dt.

    When r = 5,

    dA/dt = 10*pi*(2.6) = 82 ft^2/s;

    when t = 8.2 s, the r = (8.2 s)(2.6 ft/s) =>

    dA/dt = 2*pi*8.2*2.6*2.6 = 348 ft^2/s.

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