91Ó°ÊÓ

The work \(W\) done when lifting an object varies jointly with the object's mass \(m\) and the height \(h\) that the object is lifted. The work done when a 120 -kilogram object is lifted 1.8 meters is 2116.8 joules. How much work is done when lifting a 100 -kilogram object 1.5 meters?

Transportation For groups of 80 or more people, a charter bus company determines the rate per person according to the formula Rate \(=8-0.05(n-80), \quad n \geq 80\) where the rate is given in dollars and \(n\) is the number of people. (a) Write the revenue \(R\) for the bus company as a function of \(n\) (b) Use the function in part (a) to complete the table. What can you conclude? $$\begin{array}{|l|l|l|l|l|l|l|l|} \hline n & 90 & 100 & 110 & 120 & 130 & 140 & 150 \\ \hline R(n) & & & & & & & \\ \hline \end{array}$$

Even, Odd, or Neither? Sketch a graph of the function and determine whether it is even, odd, or neither. Verify your answer algebraically. $$f(x)=5-3 x$$

Find the difference quotient and simplify your answer. $$f(t)=\frac{1}{t-2}, \frac{f(t)-f(1)}{t-1}, t \neq 1$$

A hospital purchases a new magnetic resonance imaging (MRI) machine for 500,000 dollar. The depreciated value \(y\) (reduced value) after \(t\) years is given by \(y=500,000-40,000 t, 0 \leq t \leq 8 .\) Sketch the graph of the equation.

A regulation NFL playing field (including the end zones) of length \(x\) and width \(y\) has a perimeter of \(346 \frac{2}{3}\) or \(\frac{1040}{3}\) yards. (a) Draw a rectangle that gives a visual representation of the problem. Use the specified variables to label the sides of the rectangle. (b) Show that the width of the rectangle is \(y=\frac{520}{3}-x\) and its area is \(A=x\left(\frac{520}{3}-x\right)\). (c) Use a graphing utility to graph the area equation. Be sure to adjust your window settings. (d) From the graph in part (c), estimate the dimensions of the rectangle that yield a maximum area. (e) Use your school's library, the Internet, or some other reference source to find the actual dimensions and area of a regulation NFL playing field and compare your findings with the results of part (d).

You are driving on a road that has a \(6 \%\) uphill grade. This means that the slope of the road is \(\frac{6}{100} .\) Approximate the amount of vertical change in your position when you drive 200 feet.

From the top of a mountain road, a surveyor takes several horizontal measurements \(x\) and several vertical measurements \(y\) as shown in the table \((x \text { and } y\) are measured in feet).$$\begin{array}{|c|c|c|c|c|}\hline x & 300 & 600 & 900 & 1200 \\\\\hline y & -25 & -50 & -75 & -100 \\\\\hline\end{array}$$. $$\begin{array}{|c|c|c|c|}\hline x & 1500 & 1800 & 2100 \\ \hline y & -125 & -150 & -175 \\\\\hline\end{array}$$.(a) Sketch a scatter plot of the data. (b) Use a straightedge to sketch the line that you think best fits the data. (c) Find an equation for the line you sketched in part (b). (d) Interpret the meaning of the slope of the line in part \((c)\) in the context of the problem. (e) The surveyor needs to put up a road sign that indicates the steepness of the road. For instance, a surveyor would put up a sign that states "8\% grade" on a road with a downhill grade that has a slope of \(-\frac{8}{100} .\) What should the sign state for the road in this problem?

The function $$y=0.03 x^{2}+245.50, \quad 0< x <100$$,approximates the exhaust temperature \(y\) in degrees Fahrenheit, where \(x\) is the percent load for a diesel engine. (a) Find the inverse function. What does each variable represent in the inverse function? (b) Use a graphing utility to graph the inverse function. (c) The exhaust temperature of the engine must not exceed 500 degrees Fahrenheit. What is the percent load interval?

Determine whether the statement is true or false. Justify your answer.If the inverse function of \(f\) exists and the graph of \(f\) has a \(y\) -intercept, then the \(y\) -intercept of \(f\) is an \(x\) -intercept of \(f^{-1}\).