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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 3.8, Problem 18E

(a)

To determine

**To find:** At which rate the water is draining from the tank after 5 min.

Expert Solution

The rate at which the water is draining from the tank after 5 min is,

The volume of the remaining water after t minutes is,

The rate of change of the volume with respect to time is,

Substitute *t* = 5 in

Thus, the rate at which the water is draining from the tank after 5 min is,

(b)

To determine

**To find:** The rate at which the water is draining from the tank after 10 min.

Expert Solution

The rate at which the water is draining from the tank after 10 min is,

From part (a), the rate of change of the volume with respect to time is,

Substitute *t* = 10 in

Thus, the rate at which the water is draining from the tank after 10 min is,

(c)

To determine

**To find:** The rate at which the water is draining from the tank after 20 min.

Expert Solution

The rate at which the water is draining from the tank after 20 minutes is,

From part (a), the rate of change of the volume with respect to time is,

Substitute *t* = 20 in

Thus, the rate at which the water is draining from the tank after 20 min is,

(d)

To determine

**To find:** The rate at which the water is draining from the tank after 40 min; at what time is the water is draining out fastest and the slowest; summarize the results obtained from the parts (a), (b), (c) and (d).

Expert Solution

The rate at which the water is draining from the tank after 40 min is,

The water is flowing out the fastest at *t *= 5 min. and the slowest at *t* = 40 min.

From part (a), the rate of change of the volume with respect to time is,

Substitute *t* = 40 in

Thus, the rate at which the water is draining from the tank after 40 min is,

From the above sub parts, it is identified that the water flow is very fast at *t* = 5 min. and is too slow at *t* = 40 min.

Also, notice that at *t* = 40 min. the velocity is 0 and hence the water flow is very slow.