Chapter 7.5, Problem 77E

(A)

To determine

To find:

The system of inequality using the provided information

Answer to Problem 77E

Circle of radius $y\text{units}$ and $x\text{units}$ is at least $10sq$

Explanation of Solution

Given:

The equation

  $\begin{array}{l}\pi y^2-\pi x^2\ge 10\\ y>x\\ x>0\end{array}$

Concept used:

Since the formula related to area of a circle is $=\pi r^2$

Calculation:

The two concentric circles with radii $y$ and $x$

Where $y$ is the larger radaii and $x$ is smaller radaii

Also, the area between the two concentric circles is at least $10\text{square}$ units

Since the formula related to area of a circle is $=\pi r^2$

Where $r$ is the radius of circle

Area of circle related to the radius $y$ is $=\pi y^2$

Area of circle related to the radius $x$ is $=\pi x^2$

The radius $yunits$ is greater than $x\text{units}$

Also the area between these two concentric circles

That is circle of radius $y\text{units}$ and $x\text{units}$ is at least $10sq$

(B)

To determine

To find:

The system of inequality using the provided information

Explanation of Solution

Given:

The equation

  $\begin{array}{l}\pi y^2-\pi x^2\ge 10\\ y>x\\ x>0\end{array}$

Concept used:

Replace the inequality sign and sketch the graph of the resulting equation (use a dashed line for < or > and a solid line for $\le or\ge$

Test one point in each of the region formed by the graph

If the point satisfies the inequality then shade the entire region to denote that every point in the region satisfies the inequality

Calculation:

  $\begin{array}{l}\pi y^2-\pi x^2\ge 10\\ y>x\\ x>0\end{array}$

Test one point in each of the region formed by the graph

If the point satisfies the inequality then shade the entire region to denote that every point in the region satisfies the inequality

  $\begin{array}{l}\pi y^2-\pi x^2\ge 10\\ y>x\\ x>0\end{array}$

$x-axis$	$0$	$6.4$	$-0.98$	$0$
$y-axis$	$1.78$	$6.4$	$-2$	$-1.78$