# V − 1 and define what V − 1 mean. ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2.7, Problem 82E

a.

To determine

## To find: V−1 and define what V−1 mean.

Expert Solution

V1(x)=40(1x100)

V1(x) represents the time duration from the starting of draining out of water to reach the water volume x .

### Explanation of Solution

Given information:

A tank holds 100 gallons of water, which drains from a leak at the bottom, causing the tank to empty in 40 minutes. Toricelli’s Law gives the volume of water remaining in the tank after t minutes as

V(t)=100(1t40)2

Concept used: If f be a one-to-one function with domain A and range B. Then its inverse function f1 has domain B and range A and is defined by

f1(y)=x      f(x)=y

Calculation:

V(t)=100(1t40)2y=100(1t40)2y100=(1t40)2y100=(1t40)t40=1y100t=40(1y100)V1(y)=40(1y100)V1(x)=40(1x100)

V1(x) represents the time duration from the starting of draining out of water to reach the water volume x .

b.

To determine

### To find: V−1(15) and state what it means.

Expert Solution

V1(15)=24.5080

V1(15)means that after 15 minutes from the start of draining out water, the tank holds 24.5080 gallon of water.

### Explanation of Solution

Given information:

A tank holds 100 gallons of water, which drains from a leak at the bottom, causing the tank to empty in 40 minutes. Toricelli’s Law gives the volume of water remaining in the tank after t minutes as

V(t)=100(1t40)2

V1(x)=40(1x100)

Concept Used:

If f be a one-to-one function with domain A and range B. Then its inverse function f1 has domain B and range A and is defined by

f1(y)=x      f(x)=y

Calculation:

V1(x)=40(1x100)V1(15)=40(115100)V1(15)=24.5080

V1(15)means that after 15 minutes from the start of draining out water, the tank holds 24.5080 gallon of water.

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