Chapter 1.4, Problem 25E

a.

To determine

To graph:

Given two distanceson a number line.

Explanation of Solution

Given information:

Minimum distance from earth to sun is $91.4millionmiles$

Maximum distance is $94.5millionmiles$

Graph:

  

Interpretation:

The given two distances are:

  $d_{\min }=91.4millionmiles$ and $d_{\max }=94.5millionmiles$

So for above given two distances graph is shown on umber line is as above.

b.

To determine

To calculate:

Absolute value equation that represents minimum and maximum distances.

Answer to Problem 25E

Absolute value equation that represents minimum and maximum distances is $\left|x-92.95\right|=1.55$

Explanation of Solution

Given information:

Minimum distance from earth to sun is $91.4millionmiles$

Maximum distance is $94.5millionmiles$

Calculation:

Here consider, $d_{\min }$ and $d_{\max }$ as solutions to an absolute value equation.

So we find halfway point between the solutions.

  $\begin{array}{l}d=\frac{d_{\min }+d_{\max }}{2}\\ d=\frac{91.4+94.5}{2}\\ d=\frac{185.9}{2}\\ d=92.95\end{array}$

Solution to each solution,

  $\begin{array}{l}d=\frac{d_{\max }+d_{\min }}{2}\\ d=\frac{94.5-91.4}{2}\\ d=\frac{31.2}{2}\\ d=1.55\end{array}$

Here make use of half way point and the distance to each solution to write an absolute value equation.

  $\begin{array}{l}\left|x-d\right|=d_{sol}\\ \left|x-92.95\right|=1.55\end{array}$

Results on Number line:

  

For checking results:

  $\begin{array}{l}\left|91.4-92.95\right|=\left|-1.55\right|=1.55\\ \left|94.5-92.95\right|=\left|1.55\right|=1.55\end{array}$