# The expression for the piecewise defined expression.

### 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 2.1, Problem 79E

(a)

To determine

## To find: The expression for the piecewise defined expression.

Expert Solution

The complete expressions is F(x)={15(40x)if0<x<400if40x6515(x65)ifx>65 .

Given:

The maximum speed permitted on freeways is 65mi/h and the minimum is 40mi/h . And the fine F for violating these limits is $15 for every mile above the maximum or below the minimum. Calculation: Let x be the speed for driving. The speed below 40mi/h is, Speed=40x . The fine for the speed below 40mi/h is, F(x)=15(40x) . There is no fine for the speed between 40mi/h and 65mi/h . So the fine for speed between 40mi/h and 65mi/h is, F(x)=0 . The speed above 65mi/h is, Speed=x65 . The fine for speed above the 65mi/h is, F(x)=15(x65) . Hence, the complete expressions is, F(x)={15(40x)if0<x<400if40x6515(x65)ifx>65 . (b) To determine ### To find: The value of expression F(x) at given nights. Expert Solution ## Answer to Problem 79E Total fine at F(30) is$150 , at F(30) is 0 and at F(75) is $150 . ### Explanation of Solution Given: The given expression is, F(x)={15(40x)if0<x<400if40x6515(x65)ifx>65 Calculation: The given expression is, F(x)={15(40x)if0<x<400if40x6515(x65)ifx>65 Expression for speed 30mi/h , F(x)={15(40x)if0<x<40 Substitute 30 for x in the above expression to find the value of F(30) , F(30)=15(4030)=$150

So, total fine at F(30) is $150 . Expression for speed 50mi/h , F(x)={0if40x65 So, total fine at F(30) is 0 . Expression for speed 75mi/h , F(x)={15(x65)ifx>65 Substitute 75 for x in the above expression to find the value of F(75) , F(30)=15(7565)=$150

So, total fine at F(75) is $150 . Hence, total fine at F(30) is$150 , at F(30) is 0 and at F(75) is $150 . (c) To determine ### To explain: The resultant of given function at certain values mentioned in part (b). Expert Solution ## Answer to Problem 79E This represents the total cost of staying at the hotel. ### Explanation of Solution From part (b), Total fine at F(30) is$150 , at F(30) is 0 and at F(75) is \$150 .

This represents the total fine at the violating the speed limits.

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