# To express: The given expression as equation. ### 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 1.11, Problem 33E

(a)

To determine

## To express: The given expression as equation.

Expert Solution

The equation of given expression is P=ks3 .

### Explanation of Solution

The given expression is,

Power (P) from a windmill is directly proportional to cube of the wind speed (s) .

Direct variation:

If the quantities a and b are related by the equation a=Cb then for C0 , a is directly proportional to b and C is called constant of proportionality.

So, P is directly proportional to cube of s .

Write the given expression as,

P=ks3 (1)

Here,

P is the power obtained from windmill.

s is the wind speed.

k is constant of proportionality.

Thus, the equation of given expression is P=ks3 .

(b)

To determine

### To find: The constant of proportionality (k) for the windmill.

Expert Solution

The constant of proportionality of given windmill is 0.012 .

### Explanation of Solution

Given:

Power produced by windmill (P) is 96watts .

Speed of the wind (s) is 20mi/h .

Calculation:

In equation (1) substitute 96 for P and 20 for s and solve for k .

P=k(s3)96=k(203)96=k(8000)0.012=k (2)

Thus, the value of proportionality constant k is 0.012 .

(c)

To determine

### To find: Power produced by windmill.

Expert Solution

The power produced is 324watts .

### Explanation of Solution

Given:

The wind speed (s) is increased to 30mi/h .

Calculation:

Wind speed is increased to 30mi/h , Now the value of s is 30.

Substitute 30 for s and 0.012 for k from equation (2) in equation (1).

P=k(s3)P=0.012(303)P=0.012(27000)P=324

Thus, the value of power (P) is 324watts .

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