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Chapter 7: Problem 28
In Exercises \(21-38,\) let $$\mathbf{u}=2 \mathbf{i}-5 \mathbf{j}, \mathbf{v}=-3 \mathbf{i}+7 \mathbf{j}, \text { and } \mathbf{w}=-\mathbf{i}-6 \mathbf{j}$$ Find each specified vector or scalar. $$6 \mathbf{v}$$
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Test for symmetry and then graph each polar equation. $$r=\frac{3 \sin 2 \theta}{\sin ^{3} \theta+\cos ^{3} \theta}$$
Explaining the Concepts What is the graph of a polar equation?
You want to fly your small plane due north, but there is a 75-kilometer wind blowing from west to east. a. Find the direction angle for where you should head the plane if your speed relative to the ground is 310 kilometers per hour. b. If you increase your airspeed, should the direction angle in part (a) increase or decrease? Explain your answer.
Use a graphing utility to graph each butterfly curve. Experiment with the range setting, particularly \(\theta\) step, to produce a butterfly of the best possible quality. $$r=\sin ^{4} 4 \theta+\cos 3 \theta$$
In Exercises \(69-76,\) find all the complex roots. Write roots in rectangular form. If necessary, round to the nearest tenth. The complex cube roots of 1
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