Chapter 8.9, Problem 33E

a.

To determine

To graph:

The given inequality.

Answer to Problem 33E

The graph of our given inequality would look like:

Explanation of Solution

Given:

A wide screen format for a movie or TV show is one in which the image’s height x and width y satisfy the inequality $y>\frac{4}{3}x$ .

Calculation:

First of all, we will replace the inequality sign with an equal to sign to graph the boundary line as: $y=\frac{4}{3}x$ . Since we have a greater than sign $(>)$ , so our boundary line will be a dashed line as shown below:

  

Now, we will test a point $(1,0)$ to shade in the correct region.

  $\begin{array}{l}y>\frac{4}{3}x(\text{Given inequality)}\\ 0>\frac{4}{3}(1)(\text{Substituting }x=1\text{ and }y=0)\\ 0>\frac{4}{3}\end{array}$

Since point $(1,0)$ doesn’t satisfy our given inequality, so we will shade in the region, which excludes point $(1,0)$ .

Upon shading in the region that excludes point $(1,0)$ , we will get our required graph as shown below:

  

b.

To determine

Suppose the height of wide screen image is 18 inches. Describe the possible widths of the image.

Answer to Problem 33E

The possible widths of the image are 25, 26, 27.

Explanation of Solution

Given:

A wide screen format for a movie or TV show is one in which the image’s height x and width y satisfy the inequality $y>\frac{4}{3}x$ .

Calculation:

To find the possible widths of the widescreen image, we will substitute $x=18$ in our given inequality as shown below:

  $\begin{array}{l}y>\frac{4}{3}x\left(\text{Given inequality}\right)\\ y>\frac{4}{3}(18)\left(\text{Substituting }x=18\right)\\ y>4(6)\\ y>24\end{array}$

Therefore, the width of image can be any integer greater than 24.