Chapter 1.9, Problem 24E

To determine

To graph: The equations $y=\sqrt{49-x^2},y=\frac{1}{5}\left(41-3x\right)$ in the viewing rectangle $\left[-8,8\right]\text{by}\left[-1,8\right]$ and identify the intersection points.

Explanation of Solution

Given information:

The equations $y=\sqrt{49-x^2},y=\frac{1}{5}\left(41-3x\right)$ and viewing rectangle $\left[-8,8\right]\text{by}\left[-1,8\right]$ .

Graph:

The graph of the equation $y=\sqrt{49-x^2}$ can be sketched using the table,

$x$	$y$
0	$7$
2	$\sqrt{45}$
4	$\sqrt{33}$
$-2$	$\sqrt{45}$
$-4$	$\sqrt{33}$

The graph of equation is provided below,

  

The graph of the equation $y=\frac{1}{5}\left(41-3x\right)$ can be sketched using the table,

$x$	$y$
0	$\frac{41}{5}$
2	$7$
4	$\frac{29}{5}$
$-2$	$\frac{47}{5}$
$-4$	$\frac{53}{5}$

The graph of equation is provided below,

  

The graph of both equations in same figure is provided below,

  

From the graph it looks as the graphs intersect near the $\left(4,6\right)$ .Zoom the area near this point.

  

Since, the graphs never intersecteach other.

So there is no intersecting points.

Interpretation:

The graph of an equation in a viewing screen is a viewing rectangle.

The $\text{x}$ -values to range from a minimum value of $\text{xmin}$ $=\text{a}$ to a maximum value of $\text{xmax}$ $=\text{b}$

The $\text{y}$ -values to range from minimum value of $\text{ymin}$ $=\text{c}$ to a maximum value of $\text{ymax}$ $=\text{d}$

Then, the display portion of the graph lies in the rectangle $\left[\text{a,b}\right]\times \left[\text{c,d}\right]=\left\{\left(\text{x,y}\right)|\text{a}\le \text{x}\le \text{b},\text{c}\le \text{y}\le \text{d}\right\}$

The equations $y=\sqrt{49-x^2},y=\frac{1}{5}\left(41-3x\right)$ are not intersect in viewing rectangle $\left[-8,8\right]\text{by}\left[-1,8\right]$ They almost touch but not intersect each other at any point.