1. Water is flowing into a tank over a 12-hour period. The rate at which water is flowing into the tank at various times is measured, and the results are given in the below, where R(t) is measured in gallons per hour and t is measured in hours. The tank contains 150 gallons of water when t = 0. T(hours) 0, 5, 8, 12 Rt(gal/hour) 8, 8.8, 9.3, 9.2 a. Estimate the number of gallons of water in the tank at the end of 12 hours by using a left Riemann sum with three subintervals and values from the table. Draw the rectangles that you use, and show the computations that lead to your answer. b. Estimate the number of gallons of water in the tank at the end of 12 hours by using a right Riemann sum with three subintervals and values from the table. Draw the rectangles that you use, and show the computations that lead to your answer
1. Water is flowing into a tank over a 12-hour period. The rate at which water is flowing into the tank at various times is measured, and the results are given in the below, where R(t) is measured in gallons per hour and t is measured in hours. The tank contains 150 gallons of water when t = 0.
T(hours) 0, 5, 8, 12
Rt(gal/hour) 8, 8.8, 9.3, 9.2
a. Estimate the number of gallons of water in the tank at the end of 12 hours by using a left Riemann sum with three subintervals and values from the table. Draw the rectangles that you use, and show the computations that lead to your answer.
b. Estimate the number of gallons of water in the tank at the end of 12 hours by using a right Riemann sum with three subintervals and values from the table. Draw the rectangles that you use, and show the computations that lead to your answer.
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