Question

A 6-foot-high conical water tank is filled to the top. When a valve at the bottom is opened, the height h of the water in the tank is given by ℎ=(88.18−3.18t)/5 where t is the time in seconds after the valve is opened. Find the height of the water 18 seconds after the valve is opened. How long will it take to empty the tank?

a) Height after 18 seconds: 70.8 ft; Time to empty: 51.4 seconds
b) Height after 18 seconds: 68.2 ft; Time to empty: 53.6 seconds
c) Height after 18 seconds: 65.4 ft; Time to empty: 55.8 seconds
d) Height after 18 seconds: 62.1 ft; Time to empty: 58.2 seconds

Answer 1

The height of the water in the tank after 18 seconds is 70.8 ft and it takes 51.4 seconds to empty the tank.

Step-by-step explanation:

The height of the water in the tank after 18 seconds can be found by substituting t=18 into the equation h = (88.18 - 3.18t)/5. This gives us h = (88.18 - 3.18(18))/5. Solving this equation, we get h = 70.8 ft. Therefore, the height of the water 18 seconds after the valve is opened is 70.8 ft.

To find the time it takes to empty the tank, we need to find the value of t when the height of the water becomes 0. Setting h = 0 in the equation h = (88.18 - 3.18t)/5, we have 0 = (88.18 - 3.18t)/5. Solving this equation for t, we get t = 51.4 seconds. Therefore, it will take 51.4 seconds to empty the tank.