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calculus

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A snowball has a radius of 3 inches. Assume the rate with which the volume of the snowball melts is proportional to its surface area. If, after 1 hour, the radius of the snowball is 2.9 inches, predict what the radius will be after one day.

  • calculus -

    dv/dt = k (4 pi r^2) given

    v = (4/3) pi r^3 geometry
    dv/dr = 4 pi r^2
    dv/dt = dv/dr dr/dt = 4 pi r^2 dr/dt
    so
    k is dr/dt which is constant
    dr/dt = (2.9 - 3)/1 = -0.1 in/hr

    starts at 3 in
    r = 3 - .1(24) = 3-2.4 = 0.6 inches

  • calculus -

    can you solve it with separation of differential equation

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