Chapter 8.1, Problem 19E

a.

To determine

To describe the domain and range of the function.

Answer to Problem 19E

  $d\ge 0$ , $z\ge 0$

Explanation of Solution

Given:

The breaking strength $z$ (in pounds) is modeled by the function $z=8900d^2$ where $d$ is the diameter in inches.

Calculation:

The domain is the set of all real numbers greater than zero since the negative numbers do not make any sense in the context of the problem.

So the domain is $d\ge 0$

And the range is $z\ge 0$

b.

To determine

To graph the function.

Explanation of Solution

Given:

The breaking strength $z$ (in pounds) is modeled by the function $z=8900d^2$ where $d$ is the diameter in inches.

Calculation:

The following is the graph of the function-

  

c.

To determine

To find whether the stronger rope will have the diameter $4$ times.

Answer to Problem 19E

No.

Explanation of Solution

Given:

The strength of the stronger rope is $4$ times another rope.

Calculation:

No, because the strength and diameter does not have linear relationship. A rope with diameter $4$ times will have $4^2=16$ times the breaking strength.