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16. Ris the circle sector bounded by x + y = 25 in the first quadrant; 6(x, y) = (vx² + y² + 1)kg/m² %3D %3D

16. Ris the circle sector bounded by x + y = 25 in the first quadrant; 6(x, y) = (vx² + y² + 1)kg/m² %3D %3D

Advanced Engineering Mathematics
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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16.
In Exercises 11 – 18, find the mass/weight of the lamina de- scribed by the region R in the plane and its density function 8(x, y). 11. R is the rectangle with corners (1, -3), (1, 2), (7, 2) and (7, –3); 8(x, y) = 5gm/cm? 12. R is the rectangle with corners (1, –3), (1,2), (7, 2) and (7, –3); 8(x, y) = (x+y²)gm/cm? |3D 13. R is the triangle with corners (-1,0), (1,0), and (0, 1); 8(x, y) = 2lb/in? 14. R is the triangle with corners (0,0), (1,0), and (0, 1); 6(x, y) = (x² + y² + 1)lb/in? 15. Ris the disk centered at the origin with radius 2; 8(x, y) = (x +y+ 4)kg/m² %3D 16. Ris the circle sector bounded by x +y = 25 in the first quadrant; 6(x, y) = (Vx² +y² + 1)kg/m² 17. Ris the annulus in the first and second quadrants bounded by x² +y² = 9 and x? +y} = 36; 8(x, y) = 4lb/ft? %3D
Transcribed Image Text:In Exercises 11 – 18, find the mass/weight of the lamina de- scribed by the region R in the plane and its density function 8(x, y). 11. R is the rectangle with corners (1, -3), (1, 2), (7, 2) and (7, –3); 8(x, y) = 5gm/cm? 12. R is the rectangle with corners (1, –3), (1,2), (7, 2) and (7, –3); 8(x, y) = (x+y²)gm/cm? |3D 13. R is the triangle with corners (-1,0), (1,0), and (0, 1); 8(x, y) = 2lb/in? 14. R is the triangle with corners (0,0), (1,0), and (0, 1); 6(x, y) = (x² + y² + 1)lb/in? 15. Ris the disk centered at the origin with radius 2; 8(x, y) = (x +y+ 4)kg/m² %3D 16. Ris the circle sector bounded by x +y = 25 in the first quadrant; 6(x, y) = (Vx² +y² + 1)kg/m² 17. Ris the annulus in the first and second quadrants bounded by x² +y² = 9 and x? +y} = 36; 8(x, y) = 4lb/ft? %3D
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