A lune occupies the region inside the circle x² + y² 10y but outside the circle x² + y2 = 25. Assume that the density at any point is inversely proportional to its distance from the origin. Find the center of mass (T, y) of the lune. 21

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter8: Further Techniques And Applications Of Integration
Section8.3: Volume And Average Value
Problem 12E
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How do you find the center of mass of the lune?

2
A lune occupies the region inside the circle x² + y² = 10y but outside the circle x² + y² = 25. Assume that
the density at any point is inversely proportional to its distance from the origin. Find the center of mass
(T, y) of the lune.
18
Y
-
=
Transcribed Image Text:2 A lune occupies the region inside the circle x² + y² = 10y but outside the circle x² + y² = 25. Assume that the density at any point is inversely proportional to its distance from the origin. Find the center of mass (T, y) of the lune. 18 Y - =
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