Chapter 8.8, Problem 39PPS

(a)

To determine

The equation in slope intercept form to represent the data, describes the slope.

Answer to Problem 39PPS

The equation in slope intercept form to represent the data, the slope is

Slope $=30$ .

Explanation of Solution

Given:

Shell Radius	Height of Fireworks
$3$	$120$
$4$	$150$
$5$	$180$
$6$	$210$

Let, Radius $=x$ and Height $=y$

  $\begin{array}{l}\therefore \left(x_1,y_1\right)=\left(3,120\right)\\ \left(x_2,y_2\right)=\left(4,150\right)\end{array}$

Equation:

  $\begin{array}{l}y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)\\ y-120=\frac{150-120}{4-3}\left(x-3\right)\\ y-120=30x-90\\ y-120=30x-90\\ y=30x+30\end{array}$

Slope $=30$

It means for every radius increase in radios.

It means for every inch increase in radius the height increases by $30$ m.

Conclusion:

Thus the equation in slope intercept form to represent the data, the slope is

Slope $=30$ .

(b)

To determine

Predicts the total height of fireworks that have the shells with the radius 9 inches.

Answer to Problem 39PPS

The total height of fireworks that have the shells with the radius 9 inchesis $300m$.

Explanation of Solution

Given:

Shell Radius	Height of Fireworks
$3$	$120$
$4$	$150$
$5$	$180$
$6$	$210$

When radius, $x=9$

Height

  $\begin{array}{l}y=30\left(9\right)+30\\ =270+30\\ =300m\end{array}$

Conclusion:

The total height of fireworks that have the shells with the radius 9 inchesis $300m$