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Mathematics, 13.04.2020 08:43 mckinleyp4819
For time 0≤t≤10 , water is flowing into a small tub at a rate given by the function F defined by F(t)=arctan(π/2−t/10) . For time 5≤t≤10 , water is leaking from the tub at a rate given by the function L defined by L(t)=0.03(20t−t^2−75). Both F(t) and L(t) are measured in cubic feet per minute, and t is measured in minutes. The volume of water in the tub, in cubic feet, at time t minutes is given by W(t) .
(a) At time t=3 , there are 2.5 cubic feet of water in the tub. Write an equation for the locally linear approximation of W at t=3 , and use it to approximate the volume of water in the tub at time t=3.5 .
(b) Find W′′(8) . Using correct units, interpret the meaning of W′′(8) in the context of the problem.
(c) Is there a time t , for 5
(d) The tub is in the shape of a rectangular box that is 0.5 foot wide, 4 feet long, and 3 feet deep. What is the rate of change of the depth of the water in the tub at time t=6 ?
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For time 0≤t≤10 , water is flowing into a small tub at a rate given by the function F defined by F(t...
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