Chapter 9.8, Problem 22PPS

(a)

To determine

To calculate: To write and graph a function to represent area of the section inside the border,

Answer to Problem 22PPS

The function to represent area of the section inside the border is $A=x\left(16-x\right)$

Graph is plotted

Explanation of Solution

Given information: M has $30$ inches of ribbon to make a rectangular border for a scrapbook page

  

Calculation:

Scrapbook is given as

  

From figure, one side of scrapbook is $x$

Other side of scrapbook $=16-x$

Given that total length of ribbon $=30$

Function for area is given as

  $A=x\left(16-x\right)$

Now, in order to graph the equation, let’s find the points on the graph

When $x=1$

  $\begin{array}{l}A=1\left(16-1\right)\\ A=15\end{array}$

When $x=2$

  $\begin{array}{l}A=2\left(16-2\right)\\ A=2\left(14\right)\\ A=28\end{array}$

When $x=3$

  $\begin{array}{l}A=3\left(16-3\right)\\ A=3\left(13\right)\\ A=39\end{array}$

Plotting the points on graph:

  

Conclusion:

Hence, function to represent area of the section inside the border is $A=x\left(16-x\right)$

(b)

To determine

To calculate: To find the time it would take the car to travel $125$ feet

Answer to Problem 22PPS

Thecar would take $5.97$ seconds to travel $125$ feet.

Explanation of Solution

Given information: Function $d=\frac{1}{2}a{t}^2$ represents the distance $d$ that a race car will travel over an amount of time $t$ given the rate of acceleration $a$

Calculation:

Function is given as

  $d=\frac{1}{2}a{t}^2$

Also, given that car is accelerating at a rate of $7$ feet per second

Substituting value of $a=7$ in above equation:

  $\begin{array}{l}d=\frac{1}{2}\left(7\right)t^2\\ d=\frac{7}{2}{t}^2\end{array}$

Graph of the equation is as follows:

  

From graph, car would take $5.97$ seconds to travel $125$ feet.

Conclusion:

Hence, car would take $5.97$ seconds to travel $125$ feet.