(only answer sub part D) During the time interval 0 ≤ t ≤ 4.5 hours, water flows into tank A at a rate of a(t) = (2t XXXXXXXXXX5e^(2sin t) liters per hour. During the same time interval, water flows...

(only answer sub part D)

During the time interval 0 ≤ t ≤ 4.5 hours, water flows into tank A at a rate of a(t) = (2t - 5) + 5e^(2sin t) liters per hour. During the same time interval, water flows into tank B at a rate of b(t) liters per hour. Bothtanks are empty at time t = 0. The graphs of y = a(t) and y = b(t), shown in the image, intersect at t = k and t = 2.416.

(a) How much water will be in tank A at time t = 4.5 ?

(b) During the time interval 0 ≤ t ≤ k hours, water flows into tank B at a constant rate of 20.5 liters per hour. What is the difference between the amount of water in tank A and the amount of water in tank B at time t = k ?


(c) The area of the region bounded by the graphs of y = a(t) and y = b(t) for k ≤ t ≤ 2.416 is 14.470. How much water is in tank B at time t = 2.416

(d) During the time interval 2.7 ≤ t ≤ 4.5 hours, the rate at which water flows into tank B is modeled byw(t) = 21 - ((30t)/(t - (8^2)) liters per hour. Is the difference w(t) - a(t) increasing or decreasing at time t = 3.5 ? Show the work that leads to your answer.