Chapter 0.13, Problem 1E

To determine

Define variable and write and inequality.

Find the minimum height the swing still has higher to swing.

Answer to Problem 1E

Variable is h; $h+45\le 137$ ; $h\le 92$

Explanation of Solution

Given:

A thrill ride swings passengers back and forth, a little higher each time up to 137 feet. Suppose the height of the swing after 30 seconds is 45 feet Concept Used:

Let the minimum height the swing still has higher to swing is $h\text{feet}$

Height of swing at time t is $\le 137\text{ft}$

After $t\text{=}\text{30}\text{sec}$ the height $h=45\text{feet}$

Inequality: $h+45\le 137$

Calculation:

Height of swing at time t is $\le 137\text{ft}$

After $t\text{=}\text{30}\text{sec}$ the height $h=45\text{feet}$

Since the highest height h = 137 ft

Inequality: $h+45\le 137$

Solve for h , the minimum height the swing can go.

  $\begin{array}{l}h+45\le 137\\ h+45-45\le 137-45\\ h\le 92\end{array}$

The swing still has 92 ft it can go to reach the maximum height of 137 ft.

Thus, the swing still has 92 ft it can go to reach the maximum height of 137 ft.