91Ó°ÊÓ

Neglect air resistance. For the numerical calculations, take \(g\) as 32 feet per second \(\mathrm{p}\) er second or as 9.8 meters per second per second. Supplies are dropped from a stationary helicopter and seconds later hit the ground at 98 meters per second. How high was the helicopter?

An airplane is flying at constant speed and altitude on a line that will take it directly over a radar station on the ground. At the instant the plane is 12 miles from the station, it is noted that the plane's angle of elevation is \(30^{\circ}\) and is increasing at the rate of \(0.5^{\circ}\) per second. Give the speed of the plane in miles per hour.

A power line is needed to connect a power station on the shore of a river to an island 4 kilometres downstream and 1 kilometre offshore. Find the minimum cost for such a line given that it costs 50,000 dollar per kilometre to lay wire under water and 30,000 dollar per kilometre to lay wire under ground.

Neglect air resistance. For the numerical calculations, take \(g\) as 32 feet per second \(\mathrm{p}\) er second or as 9.8 meters per second per second. To estimate the height of a bridge, a man drops a stone into the water below. How high is the bridge (a) if the stone hits the water 3 seconds later? (b) if the man bears the splash 3 seconds later? (Use 1080 feet per second as the speed of sound.)

Sketch the graph of the function showing all vertical and oblique asymptotes. $$f(x)=\frac{2 x^{2}+3 x-2}{x+1}$$

The Hot wheels Rent-A-Car Company derives an average net profit of 12 dollar per customer if it services 50 customers or fewer. If it services more than 50 customers, then the average net profit is decreased by 6 cents for each customer over 50 . What number of customers produces the greatest total net profit for the company?