BuyFind

Precalculus: Mathematics for Calcu...

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

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

Answer to Problem 79E

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

Explanation of Solution

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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