Consider the region in the plane bounded by the graph of
Chapter 14, Problem 33(choose chapter or problem)
Consider the region R in the xy-plane bounded by the graph of the equation
\(\left(x^{2}+y^{2}\right)^{2}=9\left(x^{2}-y^{2}\right)\)
(a) Convert the equation to polar coordinates. Use a graphing utility to graph the equation.
(b) Use a double integral to find the area of the region R.
(c) Use a computer algebra system to determine the volume of the solid over the region R and beneath the hemisphere \(z=\sqrt{9-x^{2}-y^{2}}\).
Text Transcription:
(x^2 + y^2)^2 = 9(x^2 - y^2)
z = sqrt{9 - x^2 - y^2}
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