A cylindrical barrel with a diameter of 6 meters contains collected rainwater. The water drains out through a valve at the bottom of the barrel. The rate of change of the height h of the water in the barrel with respect to time t is modeled by dh/dt = -(1/5)(square root h), where h is measured in meters and t is measured in seconds. (The volume V of a cylinder with radius r and height h is V = (pi)(r^2)(h) .) (a) Find the rate of change of the volume of water in the barrel with respect to time when the height of the water is 10 meters. Indicate units of measure. (b) When the height of the water is 8 meters, is the rate of change of the height of the water with respect to time increasing or decreasing? Explain your reasoning. (c) At time t = 0 seconds, the height of the water is 16 meters. Use separation of variables to find an expression for h in terms of t.
A cylindrical barrel with a diameter of 6 meters contains collected rainwater. The water drains out through a valve at the bottom of the barrel. The rate of change of the height h of the water in the barrel with respect to time t is modeled by dh/dt = -(1/5)(square root h), where h is measured in meters and t is measured in seconds. (The volume V of a cylinder with radius r and height h is V = (pi)(r^2)(h) .)
(a) Find the rate of change of the volume of water in the barrel with respect to time when the height of the water is 10 meters. Indicate units of measure.
(b) When the height of the water is 8 meters, is the rate of change of the height of the water with respect to time increasing or decreasing? Explain your reasoning.
(c) At time t = 0 seconds, the height of the water is 16 meters. Use separation of variables to find an expression for h in terms of t.
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