Chapter 1.5, Problem 79E

a.

To determine

To find:the function that represents the total stopping distance T.

Answer to Problem 79E

The function that represents the total stopping distance Tis $T=\frac{3}{80}{x}^2$.

Explanation of Solution

Given information :

The distance function when a car travels during the drive’s reaction time is $R\left(x\right)=\frac{3}{4}x$.

The distance travelled while the driver is braking is given by $B\left(x\right)=\frac{1}{15}{x}^2$.

Calculation : to find the total stopping distance, substitute the value of x of function $B\left(x\right)$ by the function $R\left(x\right)$ ,

  $\begin{array}{l}T=B\left(R\left(x\right)\right)\\ T=B\left(\frac{3}{4}x\right)\text{ [}R\left(x\right)=\frac{3}{4}x]\\ T=\frac{1}{15}\left(\frac{9}{16}\right)x^2\text{ [}B\left(x\right)=\frac{1}{15}{x}^2]\\ T=\frac{3}{80}{x}^2\text{ [simplify]}\end{array}$

Thus, the function is $T=\frac{3}{80}{x}^2$.

b.

To determine

To graph: the functions by using graphing utility.

Explanation of Solution

Given information :

The functions are $R\left(x\right)=\frac{3}{4}x$ , $B\left(x\right)=\frac{1}{15}{x}^2$ , $T=\frac{3}{80}{x}^2$

Graph : Sketch the graph using graphing utility.

Step 1: Press WINDOW button to access the Window editor.

Step 2: Press $\boxed{\text{Y=}}$ button.

Step 3: Enter the expression $\frac{3}{4}x,\frac{1}{15}{x}^2,\frac{3}{80}{x}^2$ which is required to graph.

Step 4: Press GRAPH button to graph the function.

The graph is obtained as:

  

Interpretation: from the above graph it can be observed that the function $B\left(x\right)$ contributes most to the magnitude of the sum at higher speeds.

c.

To determine

To state : that which function contributes most to the magnitude of the sum at higher speeds.

Answer to Problem 79E

The function $B\left(x\right)$ , contributes most to the magnitude of the sum at higher speeds.

Explanation of Solution

Given information : The functions are $R\left(x\right)=\frac{3}{4}x$ , $B\left(x\right)=\frac{1}{15}{x}^2$ , $T=\frac{3}{80}{x}^2$

the function $B\left(x\right)$ , contributes most to the magnitude of the sum at higher speeds. Because comparing to functions, the function $B\left(x\right)$ increases rapidly corresponding to x.