3. Suppose that the density at each point in a lamina D = {(x, y) € R²|- a ≤x≤a,-√a²-x² ≤ y ≤ √a²-x²} in the xy-plane is directly proportional to thrice the point's distance from the origin. Find the center of mass of the lamina.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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3. Suppose that the density at each point in a lamina
D = {(x, y) € R²|- a ≤x≤ a,-√a²-x² ≤ y ≤ √a² − x²}
in the xy-plane is directly proportional to thrice the point's distance from the origin. Find the
center of mass of the lamina.
Transcribed Image Text:3. Suppose that the density at each point in a lamina D = {(x, y) € R²|- a ≤x≤ a,-√a²-x² ≤ y ≤ √a² − x²} in the xy-plane is directly proportional to thrice the point's distance from the origin. Find the center of mass of the lamina.
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