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categoryرياضيات
schoolبكالوريوس
event_available2026-07-13
السؤال
Transcribed Image Text:
9
Find the mass and center of mass of the thin constant-density plate shown in the figure to the right. Assume a density
of 1.
Le
(-5,7)
(5.7)
fol
The mass is m=119. (Type an exact answer in simplified form.)
Set up the double integral that gives My, the plate's first moment about the y-axis. Use increasing limits of integration.
=
☑
M, dy dx (Type exact answers.)
Set up the double integral that gives M, the plate's first moment about the x-axis. Use increasing limits of integration.
7 12-y
S
S
y
dx dy (Type exact answers.).
0y-12
The center of mass is located at
(Type an ordered pair. Type an exact answer in simplified form.)
(-12,0)
(12.0)
T: x
Ex
g
Let S = {0 sus 1,0 sv≤ 1} be a unit square in the uv-plane. Find the image of S in the xy-plane under the following transformation.
T:x=-3u cos (лv), y = -3u sin (TV)
Select the correct choice below and fill in the answer boxes within your choice.
(Simplify your answers.)
A. The lower half of the circle of radius
centered at the origin.
B. The upper half of the circle of radius
centered at the origin.
13
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