Chapter MPS, Problem 9.4MPS

a.

To determine

To find: The expression for the perimeter P in terms of $x$ .

Answer to Problem 9.4MPS

The expression for the perimeter P in terms of $x$ is $P=2\left(x+\frac{100}{x}\right)$ .

Explanation of Solution

Given information: The area of rectangle is $100{\text{cm}}^2$

Calculation:

Consider the equation.

  $\begin{array}{l}xy=A\\ xy=100\\ y=\frac{100}{x}\end{array}$

Consider the equation for perimeter.

  $\begin{array}{l}P=2\left(x+y\right)\\ P=2\left(x+\frac{100}{x}\right)\end{array}$

b.

To determine

To find: The graph for the perimeter function.

Answer to Problem 9.4MPS

The graph for the perimeter function is shown in Figure-1.

Explanation of Solution

Given information: The area of rectangle is $100{\text{cm}}^2$

Calculation:

The graph is shown below.

  

Figure-1

c.

To determine

To find: The range of the function.

Answer to Problem 9.4MPS

The range of the function is $y\ge 40,y\le -40$ .

Explanation of Solution

Given information: The area of rectangle is $100{\text{cm}}^2$

Calculation:

From the graph it is clear that range of the function is $y\ge 40,y\le -40$ .