Quiz: Quiz 12 (5.1-5.3 This Question 1 pt 6 of 8 (0 complete) Suppose a gauge at

Question

Quiz: Quiz 12 (5.1-5.3 This Question 1 pt 6 of 8 (0 complete) Suppose a gauge at the outflow of a reservoir measures the flow rate of water in units of ft Ihr. The total amount of water that flows out of the reservoir is the area under the flow rate curve. Consider the flow rate function shown in the figure to the right. Complete parts (a through (d) below. a. Find the amount of water that flows out of the reservoir over the interval 10.4 The amount of water that flows out of the reservoir over the interval [0,4] is (Simplify your answer. Type an integer or a decimal.) b. Find the amount of water that flows out of the reservoir over the interval [7,1C fr The amount of water that flows out of the reservoir over the interval [7,10] is f Simplify your answer. Type an integer or a decimal c. Does more water flow out of the reservoir over the interval [0,4) o (4,6)? h2 v more water flows out of the reservoir over the interval (Simplify your answers. Type integers or decimals.) d. The units for the amount of water are the units of the water flow rate the time in Time Remaining: 00:55:07 Submit Quiz This Quiz: 8 pts possible 8000- 6000- 2000- Time (hr

Explanation / Answer

The amount of water flows out of the reservoir = AREA under the flow rate curve.

a.) Amount of water flows out over interval [0,4] = Area under curve form t= 0 to 4

= 1/2 x 4 x 8000 = 16,000 ft3

b.) Amount of water flows out over interval [7,10] = Area under graph from t = 7 to 10

= 3 x 10,000 = 30,000 ft3

c.) Water flows out over [4,6] = (1/2) x (8000+10000) x 1 + 1 x 10000 = 19,000 ft3

Water flows out over [0,4] = 16,000 ft3

More water flows out of the curve over [4,6] = 19,000 ft3

So, 3000 ft3 water more flows out over interval [4,6].

d.) The units of amount of water are the units of water flow rate multiplied by the time in hours.

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