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Magazine Problem 45
Graph the following equations. Use a graphing utility to check your work and produce a final graph. $$r^{2}=16 \cos \theta$$
Problem 46
Use a graphing utility to graph the following curves. Be sure to choose an interval for the parameter that generates all features of interest. $$x=2 \cot t, y=1-\cos 2 t$$
Problem 46
Find an equation of the following hyperbolas, assuming the center is at the origin. Sketch a graph labeling the vertices, foci, and asymptotes. Use a graphing utility to check your work. A hyperbola with vertices (卤1,0) that passes through \(\left(\frac{5}{3}, 8\right)\)
Problem 46
Graph the following equations. Use a graphing utility to check your work and produce a final graph. $$r^{2}=16 \sin 2 \theta$$
Problem 47
Use a graphing utility to graph the following curves. Be sure to choose an interval for the parameter that generates all features of interest. $$x=\frac{3 t}{1+t^{3}}, y=\frac{3 t^{2}}{1+t^{3}}$$
Problem 47
Graph the following equations. Use a graphing utility to check your work and produce a final graph. $$r=\sin 3 \theta$$
Problem 47
Find the areas of the following regions. The region common to the circles \(r=2 \sin \theta\) and \(r=1\)
Problem 47
Find an equation of the following hyperbolas, assuming the center is at the origin. Sketch a graph labeling the vertices, foci, and asymptotes. Use a graphing utility to check your work. A hyperbola with vertices (卤2,0) and asymptotes \(y=\pm 3 x / 2\)
Problem 48
Find the areas of the following regions. The region inside the inner loop of the lima莽on \(r=2+4 \cos \theta\)
Problem 48
Graph the following equations. Use a graphing utility to check your work and produce a final graph. $$r=2 \sin 5 \theta$$
