Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Question
30. A hemispherical tank has a radius of 10ft. Find the amount of work required to pump all the water out at the top of the tank given that the water weighs 62.4 lb/ft³. 15600 pi 0.57 31. Find the average ordinate of the curve y = arcsin x, from x = 0 to x = 1, with respect to x. 32. A cable 100 feet long and weighing 3 pounds per foot hangs from a windlass. Find the work done in winding up. 15000 33.22 x³y dx dy 42 34. Find the volume of the space above R abd below the surface of x + 2y + 4z = 8 10.67 35. Find the volume of the solid in the first octant lying within the cylindersx² + z² = 4 and y² + z² = 4 42.67
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Transcribed Image Text:30. A hemispherical tank has a radius of 10ft. Find the amount of work required to pump all the water out at the top of the tank given that the water weighs 62.4 lb/ft³. 15600 pi 0.57 31. Find the average ordinate of the curve y = arcsin x, from x = 0 to x = 1, with respect to x. 32. A cable 100 feet long and weighing 3 pounds per foot hangs from a windlass. Find the work done in winding up. 15000 33.22 x³y dx dy 42 34. Find the volume of the space above R abd below the surface of x + 2y + 4z = 8 10.67 35. Find the volume of the solid in the first octant lying within the cylindersx² + z² = 4 and y² + z² = 4 42.67
1. Find the area of the region bounded by: 1. y² = 2x and y=x-4 2. y² = 4ax and x² = 4ay 3, x² + 3y = 4 and x - 2y = 4 4. y³ = x² and 2x + y + 1 = 0 and x - y = 4 5. One leaf of r = 10cos50 6. r² = 20cose 7. y = 3sinx and y = 3cosx 8. r=4sin²0cos0 9. r= 6 + 6sine 10. inside r = 3cos8 nd outside the cardioid r = 1 + cose II. Find the volume of the solid formed by revolving the region bounded by: 11. y² = 2x and y = x - 4 about x-axis; y-axis and y=x-4 12. y = 4x - x², y = x about x=3. 13. ellipse 3x² + 4y2 - 6x + 16y-4 = 0 about its major axis; and minor axis. III. Find the centroid: 14. region bounded by x² + 3y = 4 and x - 2y = 4 15. solid formed by revolving the region bounded by y = 4x -x², y = x about x=3. 16. arc length of y= 4x - x² from x=0 to x=2. IV. Find the surface area formed by revolving the arc of the curve 17. x = 5cos³t and y = 5sin³t about x-0. 18. 4y = 2x² - Inx from x = 1 to x = 4 about the y axis. 19. (x-3)² + (y + 2)2 = 25 about the line x + 4 = 0. V. Find the moment of inertia and radius of gyration: 20. region bounded by x² + 3y = 0 and y + x=0 with respect to x axis. 18 sq. units 16/3 a² sq. units 15.26 sq. units 18.3 sq. units 5 pi sq. units 40 sq. units 28.27 sq. units pi/2 sq. units 54 pi sq. units pi sq. units 113.097 36 pi ću. units, 361.91 cu. units, 143.95 cu. units 42.41 cu. units 66.69 cu. units 77.01 cu. unite -0.75 units X-3 0.76 units 2.18 / 188.50 units 136.66 units 1381.74 units Ix=2.89 units k=1.39 21. Moment of inertia of a cone of radius 4m and altitude 10m relative to its axis and base. Axis=256 pi Base=167.55 KAxis 2.19 kBase=1 22. arc of the curve 4x = 2y² - Iny from y=2 to y-4 with respect to x-axis 23. volume of the solid formed by revolving the region bounded by y² + 2x = 0 and x = 2y about x axis with respect to y axis. 1286.80; 4.28 24. system of masses 4,6,10 @ (2,3,4), (-1,6,-8) and (-6,8,4), respectively Ix=1500 Axis 61.5 k Base-3.16 k ly=990 ly=1274 kx=8.66 -0.97 ky=7.04 kz=7.98 25. A spring has a natural length of 10 in and a 30 lb force stretches it to a length of 12 in. Find the work done in stretching the spring from 12 in to 14 in. 90 26. Given a force, F(x) = x^2+ 2x + sin 2x where x is in meter and F(x) is in Newton. What is the work required to move the object from x = 2 to x = 6? 100.58 27. A right circular cylindrical tank with a depth of 14 ft and a radius of 6 ft is half full of oil weighing 50 lb/ft^3. Find the work done in pumping the oil to a height 4 ft above the tank. 573968.98 28. As a flour sack is being raised a distance of 4m. Flour leaks out at such a rate that the number of pounds lost is directly proportional to the square root of the distance travelled. If the sack originally contained 400 N of flour and it loses a total of 80 kg while being raised to 4m, determine the work done in raising the sack. 1886.67 29. A tank in the form of an inverted right-circular cone is 4m across the top and 5m deep. The tank is filled to a height of 3m with water. Find the work necessary to pump half of the water to the top of the tank. 100.55 50.72
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Transcribed Image Text:1. Find the area of the region bounded by: 1. y² = 2x and y=x-4 2. y² = 4ax and x² = 4ay 3, x² + 3y = 4 and x - 2y = 4 4. y³ = x² and 2x + y + 1 = 0 and x - y = 4 5. One leaf of r = 10cos50 6. r² = 20cose 7. y = 3sinx and y = 3cosx 8. r=4sin²0cos0 9. r= 6 + 6sine 10. inside r = 3cos8 nd outside the cardioid r = 1 + cose II. Find the volume of the solid formed by revolving the region bounded by: 11. y² = 2x and y = x - 4 about x-axis; y-axis and y=x-4 12. y = 4x - x², y = x about x=3. 13. ellipse 3x² + 4y2 - 6x + 16y-4 = 0 about its major axis; and minor axis. III. Find the centroid: 14. region bounded by x² + 3y = 4 and x - 2y = 4 15. solid formed by revolving the region bounded by y = 4x -x², y = x about x=3. 16. arc length of y= 4x - x² from x=0 to x=2. IV. Find the surface area formed by revolving the arc of the curve 17. x = 5cos³t and y = 5sin³t about x-0. 18. 4y = 2x² - Inx from x = 1 to x = 4 about the y axis. 19. (x-3)² + (y + 2)2 = 25 about the line x + 4 = 0. V. Find the moment of inertia and radius of gyration: 20. region bounded by x² + 3y = 0 and y + x=0 with respect to x axis. 18 sq. units 16/3 a² sq. units 15.26 sq. units 18.3 sq. units 5 pi sq. units 40 sq. units 28.27 sq. units pi/2 sq. units 54 pi sq. units pi sq. units 113.097 36 pi ću. units, 361.91 cu. units, 143.95 cu. units 42.41 cu. units 66.69 cu. units 77.01 cu. unite -0.75 units X-3 0.76 units 2.18 / 188.50 units 136.66 units 1381.74 units Ix=2.89 units k=1.39 21. Moment of inertia of a cone of radius 4m and altitude 10m relative to its axis and base. Axis=256 pi Base=167.55 KAxis 2.19 kBase=1 22. arc of the curve 4x = 2y² - Iny from y=2 to y-4 with respect to x-axis 23. volume of the solid formed by revolving the region bounded by y² + 2x = 0 and x = 2y about x axis with respect to y axis. 1286.80; 4.28 24. system of masses 4,6,10 @ (2,3,4), (-1,6,-8) and (-6,8,4), respectively Ix=1500 Axis 61.5 k Base-3.16 k ly=990 ly=1274 kx=8.66 -0.97 ky=7.04 kz=7.98 25. A spring has a natural length of 10 in and a 30 lb force stretches it to a length of 12 in. Find the work done in stretching the spring from 12 in to 14 in. 90 26. Given a force, F(x) = x^2+ 2x + sin 2x where x is in meter and F(x) is in Newton. What is the work required to move the object from x = 2 to x = 6? 100.58 27. A right circular cylindrical tank with a depth of 14 ft and a radius of 6 ft is half full of oil weighing 50 lb/ft^3. Find the work done in pumping the oil to a height 4 ft above the tank. 573968.98 28. As a flour sack is being raised a distance of 4m. Flour leaks out at such a rate that the number of pounds lost is directly proportional to the square root of the distance travelled. If the sack originally contained 400 N of flour and it loses a total of 80 kg while being raised to 4m, determine the work done in raising the sack. 1886.67 29. A tank in the form of an inverted right-circular cone is 4m across the top and 5m deep. The tank is filled to a height of 3m with water. Find the work necessary to pump half of the water to the top of the tank. 100.55 50.72
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