In Exercises 19- 26, find the center of mass of the lamina de- scribed by the region R in the plane and its density function 8(x, y). Note: these are the same lamina as in Exercises 11- 18. 19. R is the rectangle with corners (1, -3), (1, 2), (7,2) and (7,-3); 8(x, y) = 5gm/cm? %3D 20. R is the rectangle with corners (1,-3), (1, 2), (7,2) and (7,-3); 8(x, y) = (x+y²)gm/cm? 21. R is the triangle with corners (-1,0), (1,0), and (0, 1); 8(x, y) = 2lb/in? %3D 22. R is the triangle with corners (0,0), (1,0), and (0, 1); 6(x, y) = (x +y² +1)lb/in? %3D 23. R is the disk centered at the origin with radius 2; 8(x, y) = (x+y+4)kg/m? 24. R is the circle sector bounded by x + y = 25 in the first quadrant; 8(x, y) = (Vx? + y? + 1)kg/m? 25. Ris the annulus in the first and second quadrants bounded by x +y = 9 and x? + y = 36; 8(x, y) = 4lb/ft? olar %3| %3D 26. Ris the annulus in the first and second quadrants bounded by x +y = 9 and x +y = 36; 8(x, y) = vx² +y?lb/ft? %3D %3D
In Exercises 19- 26, find the center of mass of the lamina de- scribed by the region R in the plane and its density function 8(x, y). Note: these are the same lamina as in Exercises 11- 18. 19. R is the rectangle with corners (1, -3), (1, 2), (7,2) and (7,-3); 8(x, y) = 5gm/cm? %3D 20. R is the rectangle with corners (1,-3), (1, 2), (7,2) and (7,-3); 8(x, y) = (x+y²)gm/cm? 21. R is the triangle with corners (-1,0), (1,0), and (0, 1); 8(x, y) = 2lb/in? %3D 22. R is the triangle with corners (0,0), (1,0), and (0, 1); 6(x, y) = (x +y² +1)lb/in? %3D 23. R is the disk centered at the origin with radius 2; 8(x, y) = (x+y+4)kg/m? 24. R is the circle sector bounded by x + y = 25 in the first quadrant; 8(x, y) = (Vx? + y? + 1)kg/m? 25. Ris the annulus in the first and second quadrants bounded by x +y = 9 and x? + y = 36; 8(x, y) = 4lb/ft? olar %3| %3D 26. Ris the annulus in the first and second quadrants bounded by x +y = 9 and x +y = 36; 8(x, y) = vx² +y?lb/ft? %3D %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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22.
Transcribed Image Text:In Exercises 19- 26, find the center of mass of the lamina de-
scribed by the region R in the plane and its density function
8(x, y).
Note: these are the same lamina as in Exercises 11– 18.
19. R is the rectangle with corners (1, –3), (1, 2), (7,2) and
(7,-3); 8(x, y) = 5gm/cm?
20. R is the rectangle with corners (1, -3), (1, 2), (7,2) and
(7,-3); 8(x, y) = (x+ y²)gm/cm?
21. R is the triangle with corners (-1,0), (1,0), and (0, 1);
8(x, y) = 2lb/in?
%3D
22. R is the triangle with corners (0, 0), (1,0), and (0, 1);
5(x, y) = (x + y + 1)lb/in?
23. R is the disk centered at the origin with radius 2; 8(x, y) =
(x+y+ 4)kg/m?
24. R is the circle sector bounded by x +y = 25 in the first
quadrant; 6(x, y) = (vx? + y² + 1)kg/m?
25. Ris the annulus in the first and second quadrants bounded
by x +y = 9 and x? + y 36; 8(x, y) = 4lb/ft?
26. Ris the annulus in the first and second quadrants bounded
by x +y = 9 and x² +y = 36; 8(x, y) = Vx² + y²lb/ft?
ollows:
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