On a particular day, the linear function

$$f(x)=-3.52 x+58.6$$

approximates the temperature in degrees Fahrenheit above the surface of Earth, where $x$ is in thousands of feet and $f(x)$ gives the temperature.

(a) When the height is $5000$ feet, what is the temperature? Solve analytically.

(b) When the temperature is $-15^{\circ} \mathrm{F}$, what is the height? Solve analytically.

(c ) Explain how the answers in parts (a) and (b) can be supported graphically.

Determine the domain $D$ and range $R$ of this relation, and tell whether the relation is a function. Assume that a calculator graph extends indefinitely and a table includes only the points shown.

$$\overset{\normalsize f}{ {{\begin{array}{|c|} \hline 2 \\ \\ 5 \\ \\ 11 \\ \\ 17 \\ \\ 3\\ \hline \end{array}}} {{\begin{array}{c} \longrightarrow \\ \nearrow \\\\\\ \longrightarrow \\\\\\ \searrow \\ \longrightarrow\\ \end{array}}} {{\begin{array}{|c|} \hline 1 \\ \\\\\\ 7 \\ \\\\\\ 20 \\ \hline \end{array}}}}$$

Find the equation of the line described, giving it in slope-intercept form if possible.

Through $(1,6)$, perpendicular to $3 x+5 y=1$

Use the intersection-of-graphs method to approximate the solution to the nearest hundredth.

$$2 \pi x+\sqrt[3]{4}=0.5 \pi x-\sqrt{28}$$

Find the slope (if defined) of the line that passes through the given points.

$\left(\frac{2}{3}, 9\right)$ and $\left(\frac{1}{2}, 9\right)$

Solve the problem.

A water tank in the shape of an inverted cone has height 11 feet and radius 5.0 feet, as illustrated in the accompanying figure. Find the volume of the water in the tank when the water is 6 feet deep.

Find the slope (if defined) of the line that passes through the given points.

$(-8,2)$ and $(-8,1)$

Find the equation of the line described, giving it in slope-intercept form if possible.

Through $(3,-2)$, parallel to $2 x-y=5$

Use the intersection-of-graphs method to approximate the solution to the nearest hundredth.

$$9(-0.84 x+\sqrt{17})=\sqrt{6} x-4$$

Solve the formula for approximate annual interest rate for the variable indicated.

$A=\frac{24 f}{B(p+1)}$ for $B$

Solve the problem.

The maximum load that a horizontal beam can carry is directly proportional to its width. If a beam 1.5 inches wide can support a load of 250 pounds, find the load that a beam of the same type can support if its width is 3.5 inches. What is the constant of variation?

Find the slope (if defined) of the line that passes through the given points.

$(-11,3)$ and $(-11,5)$

Find the equation of the line described, giving it in slope-intercept form if possible.

Through $(-1,4)$, parallel to $x+3 y=5$

Solve the problem.

The cost of tuition is directly proportional to the number of credits taken. If 11 credits cost $720.50, find the cost of taking 16 credits. What is the constant of variation?