Chapter 4.6, Problem 29PPE

(a)

To determine

To find out the dependent variable and independent variable.

Answer to Problem 29PPE

  $c$ is independent variable and $p$ is the dependent variable.

Explanation of Solution

Given:

The $c$ is the total number of cars washed and $p$ is the profit.

Calculation:

Since the profit depends on the number of cars washed so $c$ is independent variable and $p$ is the dependent variable.

(b)

To determine

To find whether the relationship between $c$ and $p$ a function.

Answer to Problem 29PPE

Yes.

Explanation of Solution

Given:

The $c$ is the total number of cars washed and $p$ is the profit and each car is charged $\$5$

Calculation:

Yes, the relationship between $c$ and $p$ is a function because they will from a function using the given information which is “ $c$ is the total number of cars washed and $p$ is the profit and each car is charged $\$5$ ”.

(c)

To determine

To write an equation that shows the relationship.

Answer to Problem 29PPE

  $p=5c-34$

Explanation of Solution

Given:

The $c$ is the total number of cars washed and $p$ is the profit and each car is charged $\$5$ . The group can only spend $\$34$ which is enough for $40$ cars.

Calculation:

The following is the equation that shows the relationship-

  $p=5c-34$

(d)

To determine

To range and domain of the relationship.

Answer to Problem 29PPE

Domain $0\le c\le 40$ , Range $0\le p\le 166$

Explanation of Solution

Given:

The $c$ is the total number of cars washed and $p$ is the profit and each car is charged $\$5$ . The group can only spend $\$34$ which is enough for $40$ cars.

Calculation:

The domain of the relationship is-

  $0\le c\le 40$

And the range of the relationship is-

  $\begin{array}{l}p=5c-34\\ p=5\times 40-34\\ p=166\end{array}$

Therefore the range of the relationship is $0\le p\le 166$