?[T] The solid \(Q=\left\{(x, y, z) \mid x^{2}+y^{2} \leq 9,0 \leq z \leq 1, x \geq 0, y
Chapter 5, Problem 337(choose chapter or problem)
[T] The solid \(Q=\left\{(x, y, z) \mid x^{2}+y^{2} \leq 9,0 \leq z \leq 1, x \geq 0, y \geq 0\right\}\) has density equal to the distance to the xy-plane. Use a CAS to answer the following questions.
a. Find the mass of Q.
b. Find the moments \(M_{x y}\), \(M_{x z}\), and \(M_{y z}\) about the xy-plane, xz-plane, and yz-plane, respectively.
c. Find the center of mass of Q.
d. Graph Q and locate its center of mass.
Text Transcription:
Q={(x, y, z) mid x^2 + y^2 leq 9,0 leq z leq 1, x geq 0, y geq 0}
M_xy
M_xz
M_yz
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