Chapter 4, Problem 196RE

a.

To determine

To complete: The given table using a graphing utility.

Answer to Problem 196RE

Table is completed below.

Explanation of Solution

Given Information: Function is $\tan \theta =\frac{0.672s^2}{3000}$ .

Calculation:

  $\begin{array}{l}\tan \theta =\frac{0.672s^2}{3000}\\ \\ \theta ={\tan }^{-1}\frac{0.672s^2}{3000}\end{array}$

Putting the given values of $s$ in function to derive corresponding $\theta$ and arranging data in a table,

  $\begin{array}{lllllll}s\hfill & 10\hfill & 20\hfill & 30\hfill & 40\hfill & 50\hfill & 60\hfill \\ \theta \hfill & \text{0}\text{.0224}\hfill & \text{0}\text{.0894}\hfill & \text{0}\text{.1989}\hfill & \text{0}\text{.3441}\hfill & \text{0}\text{.5105}\hfill & \text{0}\text{.6786}\hfill \end{array}$

Thus, table is completed.

b.

To determine

To explain: The reason behind the given statement.

Answer to Problem 196RE

The reason is that given function is not a simplistic linear function.

Explanation of Solution

Given Information: Statement is regarding increase in $\theta$ with respect to $s$ .

  $\theta ={\tan }^{-1}\frac{0.672s^2}{3000}$

The given function is not a simplistic linear function, it has trigonometric component and $s$ is raised to power $2$ , that’s why $\theta$ doesn’t increase by equal increments as $s$ .

Thus, the reason is that given function is not a simplistic linear function.