Chapter 1.4, Problem 25E

a.

To determine

To represent: the minimum distance 91.4 million miles and the maximum distance 94.5 million miles on a number line.

Answer to Problem 25E

  

Explanation of Solution

The distances 91.4 million miles and 94.5 million miles on a number line are given below:

  

b.

To determine

To write: an absolute equation that represents the minimum distance 91.4 million miles and the maximum distance 94.5 million miles.

Answer to Problem 25E

  $\left|d-92.95\right|=1.55$

Explanation of Solution

Let d (in million miles) is the distance from Earth to the Sun.

Now the minimum distance is 91.4 million miles and the maximum distance is 94.5 million miles, then the mid-point between 91.4 and 94.5 is given by:

  $\begin{array}{c}91.4+\frac{94.5-91.4}{2}=91.4+\frac{3.1}{2}\\ =91.4+1.55\\ =92.95\end{array}$

  

Then, the required absolute

  $\left|d-92.95\right|=1.55$

Check:

  $\begin{array}{c}\left|91.4-92.95\right|=1.55\\ \left|-1.55\right|=1.55\\ 1.55=1.55\end{array}$

And

  $\begin{array}{c}\left|94.5-92.95\right|=1.55\\ \left|1.55\right|=1.55\\ 1.55=1.55\end{array}$

Both the statements are true.