91Ó°ÊÓ

A straight road rises with an inclination of 0.10 radian from the horizontal (see figure). Find the slope of the road and the change in elevation over a two-mile stretch of the road.

A moving conveyor is built so that it rises 1 meter for each 3 meters of horizontal travel. (a) Draw a diagram that gives a visual representation of the problem. (b) Find the inclination of the conveyor. (c) The conveyor runs between two floors in a factory. The distance between the floors is 5 meters. Find the length of the conveyor.

The center field fence in Yankee Stadium is 7 feet high and 408 feet from home plate. A baseball is hit at a point 3 feet above the ground. It leaves the bat at an angle of \(\theta\) degrees with the horizontal at a speed of 100 miles per hour (see figure). (a) Write a set of parametric equations that model the path of the baseball. (See Exercises 93 and \(94 .\) ) (b) Use a graphing utility to graph the path of the baseball when \(\theta=15^{\circ} .\) Is the hit a home run? (c) Use the graphing utility to graph the path of the baseball when \(\theta=23^{\circ} .\) Is the hit a home run? (d) Find the minimum angle required for the hit to be a home run.

Repeat Exercise 99 for a projectile with a path given by the rectangular equation $$y=6+x-0.08 x^{2}$$

Convert the polar equation to rectangular form. $$r=\frac{2}{1+\sin \theta}$$

Convert the polar equation to rectangular form. Then sketch its graph. $$r=6$$

Convert the polar equation to rectangular form. Then sketch its graph. $$\theta=3 \pi / 4$$

Convert the polar equation to rectangular form. Then sketch its graph. $$r=-3 \sin \theta$$