(10 points) Finale: This last problem of the semester isn't really a review problem, but it gives you a chance to put several things together and solve a cool word problem. Suppose you live near a bay where the water level fluctuates due to the tides. For the purpose of designing a small power plant you want to know how much water flows in or out of the bay per minute at any time. You do have data on the depth of the water in the bay, as a function of time. To simplify the mathematics we will consider an unrealistic but easily analyzed, bay, and very regular tides. So suppose your bay is an inverted cone with a radius of 1 mile, and a depth in the center of 100 feet. (There are 5280 feet in a mile.) Water flows through a channel in and out of the bay with the tides. You want to compute the water flow in that channel, measured in cubic feet per minute. Suppose the depth of the bay is given by d() = 90+10 sin( 360 where the time t is measured in minutes. (Thus we have 2 tides every day.) Accordingly, at time t water is flowing through the channel at the rate of cubic feet per minute. Your answer will be an expression in t.