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Question #17. Find the centroid of the region bounded by the graphs of y=radicalx and y=x^2

Question #17. Find the centroid of the region bounded by the graphs of y=radicalx and y=x^2

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.2: Ellipses
Problem 63E
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Question #17. Find the centroid of the region bounded by the graphs of y=radicalx and y=x^2

3-6 Find the centroid of the region by inspection and con- firm your answer by integrating. 6.7 Moments, Centers of Grav 3. FOCUS ON CONCEPTS (1. 1) 21. Use symmetry consideratic of an isosceles triangle lies the triangle. 22. Use symmetry considerati of an ellipse lies at the minor axes of the ellipse. 23-26 Find the mass and cento 5. density 6. 23. A lamina bounded by the curve y = Vx; 8 = 2. (2, 1) 24. A lamina bounded by the x = 1; 6 = 15 25. A lamina bounded by th y = 1; 6 = 3. 26. A lamina bounded by the 7-20 Find the centroid of the region. tion y = 1 - x²; 6 = 3. 7. C 27-30 Use a CAS to find the lamina with density 6. 8. 27. A lamina bounded by y 8 = 4. y =x 28. A lamina bounded by y = x2 8 = 1/(e – 1). 29. A lamina bounded by th the line x = 2; 6 = 1. 30. A lamina bounded by x 0, and x= /4; 6 9. 10. A v = 2 - x2 y = VI - x2 31-34 True-False Detern false. Explain your answo (rotated) square lies in the 31. The centroid of a rec nals of the rectangle. 32. The centroid of a rho 11. The triangle with vertices (0, 0), (2, 0), and (0, 1). nals of the rhombus. 12. The triangle with vertices (0,0), (1, 1), and (2,0). 13. The region bounded by the graphs of y = x and x+y = 6. 33. The centroid of an e the medians of the t 14. The region bounded on the left by the y-axis, on the right by the line x = 2, below by the parabola y = x2, and above by the line y =x+6. 34. By rotating a square the volume of the s ing the square abou 15. The region bounded by the graphs of y = x and y = x+ 2. 16. The region bounded by the graphs of y = x2 and y = 1. 17. The region bounded by the graphs of y = 18. The region bounded by the graphs of x = 1/y, x 0, y = 1, and y = 2. 35. Find the centroid and (a, -b). Vĩ and y = x? 36. Prove that the cer section of the thre coordinates so tha 19. The region bounded by the graphs of y = x, x = 1/y2, and y = 2. 20. The region bounded by the graphs of xy = 4 and x + y = 5. (0,-а), (0, а), an 37. Find the centroic (-a, 0), (a, 0), (-
Transcribed Image Text:3-6 Find the centroid of the region by inspection and con- firm your answer by integrating. 6.7 Moments, Centers of Grav 3. FOCUS ON CONCEPTS (1. 1) 21. Use symmetry consideratic of an isosceles triangle lies the triangle. 22. Use symmetry considerati of an ellipse lies at the minor axes of the ellipse. 23-26 Find the mass and cento 5. density 6. 23. A lamina bounded by the curve y = Vx; 8 = 2. (2, 1) 24. A lamina bounded by the x = 1; 6 = 15 25. A lamina bounded by th y = 1; 6 = 3. 26. A lamina bounded by the 7-20 Find the centroid of the region. tion y = 1 - x²; 6 = 3. 7. C 27-30 Use a CAS to find the lamina with density 6. 8. 27. A lamina bounded by y 8 = 4. y =x 28. A lamina bounded by y = x2 8 = 1/(e – 1). 29. A lamina bounded by th the line x = 2; 6 = 1. 30. A lamina bounded by x 0, and x= /4; 6 9. 10. A v = 2 - x2 y = VI - x2 31-34 True-False Detern false. Explain your answo (rotated) square lies in the 31. The centroid of a rec nals of the rectangle. 32. The centroid of a rho 11. The triangle with vertices (0, 0), (2, 0), and (0, 1). nals of the rhombus. 12. The triangle with vertices (0,0), (1, 1), and (2,0). 13. The region bounded by the graphs of y = x and x+y = 6. 33. The centroid of an e the medians of the t 14. The region bounded on the left by the y-axis, on the right by the line x = 2, below by the parabola y = x2, and above by the line y =x+6. 34. By rotating a square the volume of the s ing the square abou 15. The region bounded by the graphs of y = x and y = x+ 2. 16. The region bounded by the graphs of y = x2 and y = 1. 17. The region bounded by the graphs of y = 18. The region bounded by the graphs of x = 1/y, x 0, y = 1, and y = 2. 35. Find the centroid and (a, -b). Vĩ and y = x? 36. Prove that the cer section of the thre coordinates so tha 19. The region bounded by the graphs of y = x, x = 1/y2, and y = 2. 20. The region bounded by the graphs of xy = 4 and x + y = 5. (0,-а), (0, а), an 37. Find the centroic (-a, 0), (a, 0), (-
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