91Ó°ÊÓ

Draw the following intervals on the number line. $$ [-1,4] $$

Let \(f(x)=x^{2}+1, g(x)=9 x\), and \(h(x)=5-2 x^{2}\). Calculate the following functions. $$ f(x)+g(x) $$

Draw the following intervals on the number line. $$ (4,3 \pi) $$

In Exercises \(1-28\), compute the numbers. $$ -4^{2} $$

$$ \text { Factor the polynomials in Exercises } \text { . } $$ $$ 30-4 x-2 x^{2} $$

Right to Drill A gas company will pay a property owner \(\$ 5000\) for the right to drill on his land for natural gas and \(\$ .10\) for each thousand cubic feet of gas extracted from the land. Express the amount of money the landowner will receive as a function of the amount of gas extracted from the land.

Velocity of a Baseball When a baseball thrown at 85 miles per hour is hit by a bat swung at \(x\) miles per hour, the ball travels \(6 x-40\) feet. (Source: The Physics of Baseball.) (This formula assumes that \(50 \leq x \leq 90\) and that the bat is 35 inches long, weighs 32 ounces, and strikes a waist-high pitch so that the plane of the swing lies at \(35^{\circ}\) from the horizontal.) How fast must the bat be swung for the ball to travel 350 feet?

A frozen yogurt stand makes a profit of \(P(x)=\) \(.40 x-80\) dollars when selling \(x\) scoops of yogurt per day. (a) Find the break-even sales level, that is, the level at which \(P(x)=0\). (b) What sales level generates a daily profit of $$\$ 30$$ ? (c) How many more scoops of yogurt will have to be sold to raise the daily profit from $$\$ 30$$ to $$\$ 40$$ ?

Cost of Cleaning a Pollutant Suppose that the cost (in millions of dollars) to remove \(x\) percent of a certain pollutant is given by the cost benefit function $$ f(x)=\frac{20 x}{102-x} \quad \text { for } 0 \leq x \leq 100 $$ (a) Find the cost to remove \(85 \%\) of the pollutant. (b) Find the cost to remove the final \(5 \%\) of the pollutant.

A cellular telephone company estimates that, if it has \(x\) thousand subscribers, its monthly profit is \(P(x)\) thousand dollars, where \(P(x)=12 x-200\). (a) How many subscribers are needed for a monthly profit of 160 thousand dollars? (b) How many new subscribers would be needed to raise the monthly profit from 160 to 166 thousand dollars?