A 6-foot-high conical water tank is filled to the top. When a valve at the bottom of the tank is opened, the height h, in feet, of the water in the tank is given by h = (88.18 − 3.18t)2/5, where t is the time in seconds after the valve is opened. Round answers to the nearest tenth. Find the height of the water 10 s after the valve is opened. ftHow long will it take to empty the tank? s

Question
Asked Nov 16, 2019

A 6-foot-high conical water tank is filled to the top. When a valve at the bottom of the tank is opened, the height h, in feet, of the water in the tank is given by 

h = (88.18 − 3.18t)2/5,

 where t is the time in seconds after the valve is opened. Round answers to the nearest tenth.

 

Find the height of the water 10 s after the valve is opened.
 ft

How long will it take to empty the tank?
 s

 

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Expert Answer

Step 1

A 6-foot-high conical water tank is filled to the top, the height h, in feet, of the water in the tank is given by 

h(88.18-3.18)
3....(1)
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h(88.18-3.18) 3....(1)

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Step 2

The height of water at t=10s, plug t=10 in equation (1)

h(88.18-3.18x10)š
h=(88.18-31.8)3
h 5.017
h=5 foot (round to the nearest tenth)
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h(88.18-3.18x10)š h=(88.18-31.8)3 h 5.017 h=5 foot (round to the nearest tenth)

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Step 3

The water tank will be empty when h...

h (88.18-3.18t)
plug h-0
0 (88.18-3.181)
0 88.18-3.18t
88.18
t =
3.18
t 27.729
t 27.7 s (round to the nearest tenth)
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h (88.18-3.18t) plug h-0 0 (88.18-3.181) 0 88.18-3.18t 88.18 t = 3.18 t 27.729 t 27.7 s (round to the nearest tenth)

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