Suppose E is the half-cylinder described by r' +ґ-1 between z = 4 and the xy-plane where y > 0. Suppose further that the density at each point in E is proportional to the distance from the z-axis. a) (6 points) Find an expression for the mass of E as a triple integral. Then briefly explain why this уехр integral is difficult to compute.
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Suppose E is the half-cylinder described by 2y2 between z and the ry-plane where y 2 0. Suppose further that the density at each point in E is proportional to the distance from the z-axis. (a) (6 poi...
Suppose E is the half-cylinder described by 2y2 between z and the ry-plane where y 2 0. Suppose further that the density at each point in E is proportional to the distance from the z-axis. (a) (6 poi...
Suppose E is the half-cylinder described by 2y2 between z and the ry-plane where y 2 0. Suppose further that the density at each point in E is proportional to the distance from the z-axis. (a) (6 points) Find an expression for the mass of E as a triple integral. Then briefly explain why this integral is difficult to compute
Suppose E is the half-cylinder described by 2y2 between z and the ry-plane where y 2 0. Suppose further that...
Suppose E is the half-cylinder described by x^2 + y^2 = 1 between z = 4 and the xy-plane where y ≥ 0. Suppose further that the density at each point in E is proportional to the distance from the z-axi...
Suppose E is the half-cylinder described by x^2 + y^2 = 1 between z = 4 and the xy-plane where y ≥ 0. Suppose further that the density at each point in E is proportional to the distance from the z-axis. (a) Find an expression for the mass of E as a triple integral. Then briefly explain why this integral is difficult to compute. (b) (8 points) Describe the solid E using cylindrical coordinates.Then express the mass of E as...
2. Evaluate the surface integral (cos(zz),3ev,-e y) and S is the part of the sphere z2+-2)2 8 where F(x, y,z) that lies above the ry-plane, oriented by outward normal. 2. Evaluate the surface in...
2. Evaluate the surface integral (cos(zz),3ev,-e y) and S is the part of the sphere z2+-2)2 8 where F(x, y,z) that lies above the ry-plane, oriented by outward normal.
2. Evaluate the surface integral (cos(zz),3ev,-e y) and S is the part of the sphere z2+-2)2 8 where F(x, y,z) that lies above the ry-plane, oriented by outward normal.
Evaluate the integral: dzdrdy where B is the cylinder over the rectangular region R {(x,y) E R2:-1 1,-2y2) sin z sy and above by the sr of the , bounded ethe surface 12 уг 2- face of elliptical parab...
Evaluate the integral: dzdrdy where B is the cylinder over the rectangular region R {(x,y) E R2:-1 1,-2y2) sin z sy and above by the sr of the , bounded ethe surface 12 уг 2- face of elliptical paraboloid 37 42081
Evaluate the integral: dzdrdy where B is the cylinder over the rectangular region R {(x,y) E R2:-1 1,-2y2) sin z sy and above by the sr of the , bounded ethe surface 12 уг 2- face of elliptical paraboloid...
2. You are given the following multivariate PDF 0 else where S = {(z, y, z)...
2. You are given the following multivariate PDF 0 else where S = {(z, y, z) |エ2 + y2 + 22-1). (a) (5 points) Let T be the set of all points that lie inside the largest cylinder by volume that can be inseribed in the region of S. Similarly let U be the set of all points that lie inside the largest cube that can be inscribed in the region of S. What would the probabilities P[(X, Y, Z)...
2. You are given the following multivariate PDF 3 (x, y, z) else s fxx.2(z, y, z)- I, 0 where S-(...
2. You are given the following multivariate PDF 3 (x, y, z) else s fxx.2(z, y, z)- I, 0 where S-((z, y,2)lr'ザ+8-1) (a) (5 points) Let T be the set of all points that lie inside the largest cylinder by volume that can be inscribed in the region of S. Similarly let U be the set of all points that lie inside the largest cube that can be inscribed in the region of S. What would the probabilities P(X,Y, Z)...
Question 11 (2 marks) Attempt 7 S is the half cylinder 2+y2=9, y>0, 0<z<2 Given the vector field: E=(12+7yz)i+...
Question 11 (2 marks) Attempt 7 S is the half cylinder 2+y2=9, y>0, 0<z<2 Given the vector field: E=(12+7yz)i+(622+72)j+(1322-823)k, Calculate the outward flux (away from the z-axis) of E through surface S. That is find J- 1-48 S Your answer should consist of a single number accurate to five decimal digits or as an exact rational expression. For example: 10.13906368 OR rounded to 10.13906 OR 3*Pi+5/7 J =
Question 11 (2 marks) Attempt 7 S is the half cylinder 2+y2=9,...
2. You are given the following multivariate PDF (x, y, z) E S X,Y,2(x, y,z)=)4m 0...
2. You are given the following multivariate PDF (x, y, z) E S X,Y,2(x, y,z)=)4m 0 else where S-((x, y, z) 1x2 + y2 +#51). (a) (5 points) Let T be the set of all points that lie inside the largest cylinder by volume that can be inscribed in the region of S. Similarly let U be the set of all points that lie inside the largest cube that can be inscribed in the region of S. What would the...
You are given the following multivariate PDF (x, y, z) ES fxx.2(x, y, z) =- 0 else where S-((z, y...
You are given the following multivariate PDF (x, y, z) ES fxx.2(x, y, z) =- 0 else where S-((z, y, z) 1x2 + уг + z2 < 1} (a) (5 points) Let T be the set of all points that lie inside the largest cylinder by volume that can be inscribed in the region of S. Similarly let U be the set of all points that lie inside the largest cube that can be inscribed in the region of S....
Hi, I need help solving number 13. Please show all the steps, thank you. :) Consider the solid Q bounded by z-2-y2;z-tx at each point Р (x, y, z) is given by mass of Q [15 pts] 9. x-4. The density Z/...
Hi, I need help solving number 13. Please show all the steps,
thank you. :)
Consider the solid Q bounded by z-2-y2;z-tx at each point Р (x, y, z) is given by mass of Q [15 pts] 9. x-4. The density Z/m 3 . Find the center of (x, y, z) [15 pts] 10. Evaluate the following integral: ee' dy dzdx [15 pts] 11. Use spherical coordinates to find the mass m of a solid Q that lies between the...
Suppose E is the half-cylinder described by 2y2 between z and the ry-plane where y 2 0. Suppose further that the density at each point in E is proportional to the distance from the z-axis. (a) (6 points) Find an expression for the mass of E as a triple integral. Then briefly explain why this integral is difficult to compute
Suppose E is the half-cylinder described by 2y2 between z and the ry-plane where y 2 0. Suppose further that...
2. Evaluate the surface integral (cos(zz),3ev,-e y) and S is the part of the sphere z2+-2)2 8 where F(x, y,z) that lies above the ry-plane, oriented by outward normal.
2. Evaluate the surface integral (cos(zz),3ev,-e y) and S is the part of the sphere z2+-2)2 8 where F(x, y,z) that lies above the ry-plane, oriented by outward normal.
Evaluate the integral: dzdrdy where B is the cylinder over the rectangular region R {(x,y) E R2:-1 1,-2y2) sin z sy and above by the sr of the , bounded ethe surface 12 уг 2- face of elliptical paraboloid 37 42081
Evaluate the integral: dzdrdy where B is the cylinder over the rectangular region R {(x,y) E R2:-1 1,-2y2) sin z sy and above by the sr of the , bounded ethe surface 12 уг 2- face of elliptical paraboloid...
2. You are given the following multivariate PDF 0 else where S = {(z, y, z) |エ2 + y2 + 22-1). (a) (5 points) Let T be the set of all points that lie inside the largest cylinder by volume that can be inseribed in the region of S. Similarly let U be the set of all points that lie inside the largest cube that can be inscribed in the region of S. What would the probabilities P[(X, Y, Z)...
2. You are given the following multivariate PDF 3 (x, y, z) else s fxx.2(z, y, z)- I, 0 where S-((z, y,2)lr'ザ+8-1) (a) (5 points) Let T be the set of all points that lie inside the largest cylinder by volume that can be inscribed in the region of S. Similarly let U be the set of all points that lie inside the largest cube that can be inscribed in the region of S. What would the probabilities P(X,Y, Z)...
Question 11 (2 marks) Attempt 7 S is the half cylinder 2+y2=9, y>0, 0<z<2 Given the vector field: E=(12+7yz)i+(622+72)j+(1322-823)k, Calculate the outward flux (away from the z-axis) of E through surface S. That is find J- 1-48 S Your answer should consist of a single number accurate to five decimal digits or as an exact rational expression. For example: 10.13906368 OR rounded to 10.13906 OR 3*Pi+5/7 J =
Question 11 (2 marks) Attempt 7 S is the half cylinder 2+y2=9,...
2. You are given the following multivariate PDF (x, y, z) E S X,Y,2(x, y,z)=)4m 0 else where S-((x, y, z) 1x2 + y2 +#51). (a) (5 points) Let T be the set of all points that lie inside the largest cylinder by volume that can be inscribed in the region of S. Similarly let U be the set of all points that lie inside the largest cube that can be inscribed in the region of S. What would the...
You are given the following multivariate PDF (x, y, z) ES fxx.2(x, y, z) =- 0 else where S-((z, y, z) 1x2 + уг + z2 < 1} (a) (5 points) Let T be the set of all points that lie inside the largest cylinder by volume that can be inscribed in the region of S. Similarly let U be the set of all points that lie inside the largest cube that can be inscribed in the region of S....
Hi, I need help solving number 13. Please show all the steps,
thank you. :)
Consider the solid Q bounded by z-2-y2;z-tx at each point Р (x, y, z) is given by mass of Q [15 pts] 9. x-4. The density Z/m 3 . Find the center of (x, y, z) [15 pts] 10. Evaluate the following integral: ee' dy dzdx [15 pts] 11. Use spherical coordinates to find the mass m of a solid Q that lies between the...
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