91Ó°ÊÓ

Find the distance between the parallel lines. (Graph can't copy) $$\begin{aligned} &3 x-4 y=1\\\ &3 x-4 y=10 \end{aligned}$$

In Exercises \(71-90,\) convert the rectangular equation to polar form. Assume \(a > 0\). $$x^{2}+y^{2}=a^{2}$$

Use a graphing utility to graph the curve represented by the parametric equations. Hypocycloid: \(x=3 \cos ^{3} \theta, y=3 \sin ^{3} \theta\)

A straight road rises with an inclination of 0.20 radian from the horizontal. Find the slope of the road and the change in elevation over a one-mile stretch of the road.

In Exercises \(71-90,\) convert the rectangular equation to polar form. Assume \(a > 0\). $$x^{2}+y^{2}=9 a^{2}$$

Use a graphing utility to graph the curve represented by the parametric equations. Curtate cycloid: \(x=8 \theta-4 \sin \theta, y=8-4 \cos \theta\)

Use a graphing utility to graph the curve represented by the parametric equations. Witch of Agnesi: \(x=2 \cot \theta, y=2 \sin ^{2} \theta\)

In Exercises \(71-90,\) convert the rectangular equation to polar form. Assume \(a > 0\). $$x^{2}+y^{2}-2 a x=0$$

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.

Use a graphing utility to graph the curve represented by the parametric equations. Folium of Descartes: \(x=\frac{3 t}{1+t^{3}}, y=\frac{3 t^{2}}{1+t^{3}}\)