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Chapter 7: Problem 54
Find the work done when a crane lifts a 6000 -pound boulder through a vertical distance of 12 feet. Round to the nearest foot-pound.
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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. $$\begin{aligned}&r=1.5^{\sin \theta}-2.5 \cos 4 \theta+\sin ^{7} \frac{\theta}{15} \quad \text { (Use } \quad \theta \min =0 \quad \text { and }\\\&\theta \max =20 \pi .)\end{aligned}$$
Graph the spiral \(r=\frac{1}{\theta} .\) Use a \([-1.6,1.6,1]\) by \([-1,1,1]\) viewing rectangle. Let \(\theta \min =0\) and \(\theta \max =2 \pi,\) then \(\theta \min =0\) and \(\theta \max =4 \pi,\) and finally \(\theta \min =0\) and \(\theta \max =8 \pi\)
Determine whether each statement makes sense or does not make sense, and explain your reasoning. I'm working with a polar equation that failed the symmetry test with respect to \(\theta=\frac{\pi}{2},\) so my graph will not have this kind of symmetry.
Use a graphing utility to graph the polar equation. $$r=\cos \frac{3}{2} \theta$$
Exercises \(119-121\) will help you prepare for the material covered in the next section. Find the obtuse angle \(\theta,\) rounded to the nearest tenth of a degree, satisfying. $$ \cos \theta=\frac{3(-1)+(-2)(4)}{| \mathbf{v}\|\mathbf{w}\|} $$ where \(\mathbf{v}=3 \mathbf{i}-2 \mathbf{j}\) and \(\mathbf{w}=-\mathbf{i}+4 \mathbf{j}\)
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