Solved: ?In the following exercises, consider a lamina occupying the region R and having
Chapter 5, Problem 318(choose chapter or problem)
In the following exercises, consider a lamina occupying the region R and having the density function \(\rho\) given in the preceding group of exercises. Use a computer algebra system (CAS) to answer the following questions.
a. Find the moments \(M_{x}\) and \(M_{y}\) about the x-axis and y-axis, respectively.
b. Calculate and plot the center of mass of the lamina.
c. [T] Use a CAS to locate the center of mass on the graph of R.
[T] \(R=\left\{(x, y) \mid 9 x^{2}+y^{2} \leq 1, x \geq 0, y \geq 0\right\}\); \(\rho(x, y)=\sqrt{9 x^{2}+y^{2}}\).
Text Transcription:
rho
M_x
M_y
R={(x, y) \mid 9 x^{2}+y^{2} leq 1, x geq 0, y geq 0}
rho(x, y)=sqrt{9 x^{2}+y^{2}}
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