Calculus

The rate of change in the volume of a tank is known to be dV/dt=0.6t*cos(0.08t^2 -1), where V(t) is in gallons per minute and 0<=t<=10 (0 is less than or equal to t which is less than or equal to 10). If the tank has a volume of 14 gallons initially, what is its volume at 10 minutes?

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asked by Jamie
  1. dv/dt = 0.6t cos(0.08t^2-1)
    v = 3/8 sin(0.08t^2-1) + c
    Since v(0) = 14, c = 14+3/8 sin(1) = 14.3

    v(t) = .375 sin(.08t^2-1)+14.3
    Now just evaluate v(10)

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    posted by Steve

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