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Question 8.6. The solid inside the sphere x? + y2 + 2? 3 4 and outside...
1. (20 points) Suppose B is the solid region inside the sphere 2+ y2 +2 4, above the plane = 1, a...
Please show all steps. Thank you, need to verify what I'm doing
wrong.
1. (20 points) Suppose B is the solid region inside the sphere 2+ y2 +2 4, above the plane = 1, and in the first octant (z, y, z 0)、z, y and z are measured in meters and the density over B is given by the function p(z, y, z)-(12 + y2 + ?)-1 kg/m3 (a) Set up and write the triple integral that gives the mass...
Consider the solid inside the hemispherez- 4-x2-y2, outside the cylinder x2+y2 -1 and y* , outside...
Consider the solid inside the hemispherez- 4-x2-y2, outside the cylinder x2+y2 -1 and y* , outside the cylinder x' +y 1 an above the plane z 1. Express the volume of this solid as a triple integral using the specified coordinate systerm Include a sketch of the solid. a. cylindrical coordinates. b. spherical coordinates.
Consider the solid inside the hemispherez- 4-x2-y2, outside the cylinder x2+y2 -1 and above the p...
Consider the solid inside the hemispherez- 4-x2-y2, outside the cylinder x2+y2 -1 and above the plane z 1.Express the volume of this solid as a triple integral using the specified coordinate system Include a sketch of the solid. ib. spherical coordinates
Consider the solid inside the hemispherez- 4-x2-y2, outside the cylinder x2+y2 -1 and above the plane z 1.Express the volume of this solid as a triple integral using the specified coordinate system Include a sketch of the solid. ib....
/ 3. (18 points) Consider the solid bounded above by x2 + y2 +ク= 15 and below by χ =-+ Set up th...
/ 3. (18 points) Consider the solid bounded above by x2 + y2 +ク= 15 and below by χ =-+ Set up the limits of integration for a triple integral of a function f(x, y, z) over this solid using (a) rectangular, (b) cylindrical, and (c) spherical coordinates.
/ 3. (18 points) Consider the solid bounded above by x2 + y2 +ク= 15 and below by χ =-+ Set up the limits of integration for a triple integral of a...
The solid E is bounded below z = sqrt(x^2 + y^2) and above the sphere x^2 + y^2 + z^2 = 9. a. Ske...
The solid E is bounded below z = sqrt(x^2 + y^2) and above the sphere x^2 + y^2 + z^2 = 9. a. Sketch the solid. b. Set up, but do not evaluate, a triple integral in spherical coordinates that gives the volume of the solid E. Show work to get limits. c. Set up, but do not evaluate, a triple integral in cylindrical coordinates that gives the volume of the solid E. Show work to get limits.
5. (2 points) Let S be the solid inside both x2+y2 = 16 and x2+y2 +...
5. (2 points) Let S be the solid inside both x2+y2 = 16 and x2+y2 + z2 = 32. Consider (a) Write an iterated integral for the triple integral in rectangular coordinates. (b) Write an iterated integral for the triple integral in cylindrical coordinates. (c) Write an iterated integral for the triple integral in spherical coordinates. (d) Evaluate one of the above iterated integrals.
5. (2 points) Let S be the solid inside both x2+y2 = 16 and x2+y2 +...
For the described solid S, write the triple integral f(x,y, z)dV as an iterated integral in (i) r...
For the described solid S, write the triple integral f(x,y, z)dV as an iterated integral in (i) rectangular coordinates (x,y, z); (ii) cylindrical coordinates (r, 0, 2); (iii) spherical coordinates (p, φ,0). a. Inside the sphere 2 +3+224 and above the conezV b. Inside the sphere x2 + y2 + 22-12 and above the paraboloid z 2 2 + y2. c. Inside the sphere 2,2 + y2 + z2-2 and above the surface z-(z2 + y2)1/4 d. Inside the sphere...
5a. The solid E lies above the cone z =V3V2 + y and below the sphere...
5a. The solid E lies above the cone z =V3V2 + y and below the sphere cº + y2 + 2 = 9. Completely set up, but DO NOT EVALUATE, the triple integral Ssse (y+z)dV in spherical coordinates. Show appropriate work for obtaining the limits of integration and include a sketch. Your answer should be completely ready to evaluate. (9 points) 5b. Completely set up, but DO NOT EVALUATE, the same triple integral ple (y + x)2V from part (a),...
Consider the triple integral SISE g(x,y,z)d), where E is the solid bounded above by the sphere...
Consider the triple integral SISE g(x,y,z)d), where E is the solid bounded above by the sphere x2 + y2 + z2 = 18 and below by the cone z? = x2 + y2. a) Set up the triple integral in rectangular coordinates (x,y,z). b) Set up the triple integral in cylindrical coordinates (r, 0,z). c) Set up the triple integral in spherical coordinates (2,0,0).
5. The solid E lies above the cone z = 3V x2 + y2, inside the...
5. The solid E lies above the cone z = 3V x2 + y2, inside the cylinder x2 + y2 = 4 and below the plane z = 8; see Fig.2. (a) Write the equations of those three surfaces in cylindrical coordinates and say in which horizontal plane the cone intersects the cylinder. (b) Set up a triple iterated integral in cylindrical coordinates, for this triple integral SSI r’dV
Please show all steps. Thank you, need to verify what I'm doing
wrong.
1. (20 points) Suppose B is the solid region inside the sphere 2+ y2 +2 4, above the plane = 1, and in the first octant (z, y, z 0)、z, y and z are measured in meters and the density over B is given by the function p(z, y, z)-(12 + y2 + ?)-1 kg/m3 (a) Set up and write the triple integral that gives the mass...
Consider the solid inside the hemispherez- 4-x2-y2, outside the cylinder x2+y2 -1 and y* , outside the cylinder x' +y 1 an above the plane z 1. Express the volume of this solid as a triple integral using the specified coordinate systerm Include a sketch of the solid. a. cylindrical coordinates. b. spherical coordinates.
Consider the solid inside the hemispherez- 4-x2-y2, outside the cylinder x2+y2 -1 and above the plane z 1.Express the volume of this solid as a triple integral using the specified coordinate system Include a sketch of the solid. ib. spherical coordinates
Consider the solid inside the hemispherez- 4-x2-y2, outside the cylinder x2+y2 -1 and above the plane z 1.Express the volume of this solid as a triple integral using the specified coordinate system Include a sketch of the solid. ib....
/ 3. (18 points) Consider the solid bounded above by x2 + y2 +ク= 15 and below by χ =-+ Set up the limits of integration for a triple integral of a function f(x, y, z) over this solid using (a) rectangular, (b) cylindrical, and (c) spherical coordinates.
/ 3. (18 points) Consider the solid bounded above by x2 + y2 +ク= 15 and below by χ =-+ Set up the limits of integration for a triple integral of a...
5. (2 points) Let S be the solid inside both x2+y2 = 16 and x2+y2 + z2 = 32. Consider (a) Write an iterated integral for the triple integral in rectangular coordinates. (b) Write an iterated integral for the triple integral in cylindrical coordinates. (c) Write an iterated integral for the triple integral in spherical coordinates. (d) Evaluate one of the above iterated integrals.
5. (2 points) Let S be the solid inside both x2+y2 = 16 and x2+y2 +...
For the described solid S, write the triple integral f(x,y, z)dV as an iterated integral in (i) rectangular coordinates (x,y, z); (ii) cylindrical coordinates (r, 0, 2); (iii) spherical coordinates (p, φ,0). a. Inside the sphere 2 +3+224 and above the conezV b. Inside the sphere x2 + y2 + 22-12 and above the paraboloid z 2 2 + y2. c. Inside the sphere 2,2 + y2 + z2-2 and above the surface z-(z2 + y2)1/4 d. Inside the sphere...
5a. The solid E lies above the cone z =V3V2 + y and below the sphere cº + y2 + 2 = 9. Completely set up, but DO NOT EVALUATE, the triple integral Ssse (y+z)dV in spherical coordinates. Show appropriate work for obtaining the limits of integration and include a sketch. Your answer should be completely ready to evaluate. (9 points) 5b. Completely set up, but DO NOT EVALUATE, the same triple integral ple (y + x)2V from part (a),...
Consider the triple integral SISE g(x,y,z)d), where E is the solid bounded above by the sphere x2 + y2 + z2 = 18 and below by the cone z? = x2 + y2. a) Set up the triple integral in rectangular coordinates (x,y,z). b) Set up the triple integral in cylindrical coordinates (r, 0,z). c) Set up the triple integral in spherical coordinates (2,0,0).
5. The solid E lies above the cone z = 3V x2 + y2, inside the cylinder x2 + y2 = 4 and below the plane z = 8; see Fig.2. (a) Write the equations of those three surfaces in cylindrical coordinates and say in which horizontal plane the cone intersects the cylinder. (b) Set up a triple iterated integral in cylindrical coordinates, for this triple integral SSI r’dV
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