Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter5: Trigonometric Functions: Right Triangle Approach
Section5.1: Angle Measure
Problem 87E: Which A winch of radius 2 ft is used to lift heavy loads. If the winch makes 8 revolutions every 15...
Related questions
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81f3f949-7ae2-4353-a4cd-4ca1b5b0a4ce%2Fb890f739-5e0c-42e8-b9bb-691cde52a3ff%2F2l054d_processed.jpeg&w=3840&q=75)
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81f3f949-7ae2-4353-a4cd-4ca1b5b0a4ce%2Fb890f739-5e0c-42e8-b9bb-691cde52a3ff%2Fzhpobyc_processed.jpeg&w=3840&q=75)
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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