Chapter 13.4, Problem 7PSC

(a)

To determine

To plot: The graph the solution set of each system of inequalities.

Answer to Problem 7PSC

The graph is shown below.

Explanation of Solution

Given:

The given system of inequalities are:

  $\begin{array}{c}y<x^2+8\\ y>-x+12\end{array}$

Graph is described as:

  $\begin{array}{c}0<0^2+8\left[\text{true}\right]\\ 0>-0+12\left[\text{false}\right]\end{array}$

The table for the graph $y=x^2+8$ is given as:

$x$	$0$	$\pm 2$
$y$	$8$	$12$

The table for the line graph $y=-x+12$ is given as:

$x$	$0$	$12$
$y$	$12$	$0$

The graph is given as:

  

Therefore, the graph is shown above.

(b)

To determine

To plot: The graph the solution set of each system of inequalities.

Answer to Problem 7PSC

The graph is shown below.

Explanation of Solution

Given:

The given system of inequalities are:

  $\begin{array}{c}{x}^2+y^2\le 25\\ y\ge \left|x\right|\end{array}$

Graph is described as:

  $\begin{array}{c}{0}^2+0^2\le 25\left[\text{true}\right]\\ 0\ge 0\left[\text{true}\right]\end{array}$

The table for the graph $x^2+y^2=25$ is given as:

$x$	$0$	$\pm 5$
$y$	$\pm 5$	$0$

The table for the graph $y=\left|x\right|$ is given as:

$x$	$-1$	$1$
$y$	$1$	$1$

The graph is given as:

  

Therefore, the graph is shown above.

(c)

To determine

To plot: The graph the solution set of each system of inequalities.

Answer to Problem 7PSC

The graph is shown below.

Explanation of Solution

Given:

The given system of inequalities are:

  $\begin{array}{c}xy<12\\ x^2+y^2<16\end{array}$

Graph is described as:

  $\begin{array}{c}0\cdot 0<12\left[\text{false}\right]\\ 0^2+0^2<16\left[\text{true}\right]\end{array}$

The table for the graph $xy=12$ is given as:

$x$	$1$	$12$
$y$	$12$	$1$

The table for the graph $x^2+y^2=16$ is given as:

$x$	$0$	$\pm 4$
$y$	$\pm 4$	$0$

The graph is given as:

  

Therefore, the graph is shown above.