91Ó°ÊÓ

For each equation, find an equivalent equation in rectangular coordinates. Then graph the result. $$r=\frac{3}{4 \cos \theta-\sin \theta}$$

Solve each problem. Distance between an Airplane and a Mountain A person in a plane flying straight north observes a mountain at a bearing of \(24.1^{\circ} .\) At the time, the plane is 7.92 kilometers from the mountain. A short time later, the bearing to the mountain becomes \(32.7^{\circ} .\) How far is the airplane from the mountain when the second bearing is taken?

Find the dot product of each pair of vectors. $$\langle 1,2\rangle,\langle 3,-1\rangle$$

Find each product in rectangular form, using exact values. $$\left[\sqrt{2} \operatorname{cis} \frac{5 \pi}{6}\right]\left[\sqrt{2} \operatorname{cis} \frac{3 \pi}{2}\right]$$f

For each equation, find an equivalent equation in rectangular coordinates. Then graph the result. $$r=2 \sec \theta$$

Find each quotient in rectangular form, using exact values. $$\frac{4\left(\cos 120^{\circ}+i \sin 120^{\circ}\right)}{2\left(\cos 150^{\circ}+i \sin 150^{\circ}\right)}$$

The bearing of a lighthouse from a ship was found to be \(N 37^{\circ} \mathrm{E}\) After the ship sailed 2.5 miles due south, the new bearing was N \(25^{\circ} \mathrm{E}\). Find the distance between the ship and the lighthouse at each location.

Solve each problem. Distance between a Satellite and a Tracking Station \(\mathrm{A}\) satellite traveling in a circular orbit 1600 kilometers above Earth is due to pass directly over a tracking station at noon. Assume that the satellite takes 2 hours to make an orbit and that the radius of Earth is 6400 kilometers. Find the distance between the satellite and the tracking station at 12: 03 P.M. (Source: NASA.) (figure cannot copy)

Find the dot product of each pair of vectors. $$4 \mathbf{i}, 5 \mathbf{i}-9 \mathbf{j}$$

Find the dot product of each pair of vectors. $$2 \mathbf{i}+4 \mathbf{j},-\mathbf{j}$$