4. The volume (in gallons) of water in a tank after t hours is given by f(t) = 600 sin2(Pi*t/12) for 0
£ t £ 6. What is the rate of flow of water into the tank, in gallons per hour?|
A.100(Pi)sin(Pi*t/12) |
B.100(Pi)cos(Pi*t/12)sin(Pi*t/12) |
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C.1200cos(Pi*t/12)sin(Pi*t/12) |
D.50(Pi)cos2(Pi*t/12) |
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E.600cos2(Pi*t/12) |
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Solution: The answer is B
The rate of change of the flow of water into the tank after t hours is the rate of change of the volume with respect to time. Since the volume is f(t) then the rate of change of the volume is given by (d/dt)f(t). By using the properties of differentiation we can find (d/dt)f(t) as follows,
multiplying both sides by d/dt,
by properties of differentiation,
