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Use Stokes' theorem to find the work done by the force field F(z, y, z)-<-r, z, y > along the positively oriented curve of intersection of the cylinder 2+y 1 and the plane 3x +z 4 9....
Use Stokes’ Theorem to calculate the work done by the force F⃗ = ⟨2y, xz, x...
Use Stokes’ Theorem to calculate the work done by the force F⃗ = ⟨2y, xz, x + y⟩ on a particle moving counterclockwise around the curve of intersection of the plane z − y = 2 and the cylinder x2 + y2 = 1
Use Stokes' Theorem to evaluate F. dr where Cis oriented counterclockwise as viewed from above. F(x,...
Use Stokes' Theorem to evaluate F. dr where Cis oriented counterclockwise as viewed from above. F(x, y, z) - xy + 27 + 6yk, C is the curve of intersection of the plane X + 2-1 and the cylinder + 9.
Help Entering Answers 1 point) Verify that Stokes' Theorem is true for the vector field F that li...
Help Entering Answers 1 point) Verify that Stokes' Theorem is true for the vector field F that lies above the plane z1, oriented upwards. 2yzi 3yj +xk and the surface S the part of the paraboloid z 5-x2-y To verify Stokes' Theorem we will compute the expression on each side. First computecurl F dS curl F0,3+2y,-2 Edy dx curl F dS- where x2 = curl F ds- Now compute F.dr The boundary curve C of the surface S can be...
please show all work Use Stokes' Theorem to evaluate Sc F. dr where C is oriented...
please show all work
Use Stokes' Theorem to evaluate Sc F. dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = xyl +22+ 4yk, C is the curve of intersection of the plane X + 2 = 10 and the cylinder x2 + y2 - 36.
1 Help Entering Answers 1 point) Use Stokes' Theorem to evaluateF.dr where F(x,y,z) 6yzi 3xzj +3e...
1 Help Entering Answers 1 point) Use Stokes' Theorem to evaluateF.dr where F(x,y,z) 6yzi 3xzj +3e k and C is the circy4,z 5 oriented counterclockwise as viewed from above Since the circle is oriented counterclockwise as viewed from above the surface we attach to the circle is oriented upwards The easiest surface to attach to this curve is the disk x2 + y2 < 4, z-5. Using this surface in Stokes' Theorem evaluate the following. F-dr = where sqrt(4-xA2) sqrt(4-x^2)...
Find the work done by the force field F= (y2/2, Z, x) in moving a particle...
Find the work done by the force field F= (y2/2, Z, x) in moving a particle along the curve C, where C is the intersection curve of the plane x +z = 1 and the ellipsoid x2 + 2y2 + x2 = 1 oriented counterclockwise when viewed from positive z— axis.
C is the curve of intersection of the paraboloid z (++y and the plane z 2x+2. 2. Evaluate [ F -dr using Stokes' Theorem. Choose the simplest surface with boundary curve C and orient it upward....
C is the curve of intersection of the paraboloid z (++y and the plane z 2x+2. 2. Evaluate [ F -dr using Stokes' Theorem. Choose the simplest surface with boundary curve C and orient it upward.
C is the curve of intersection of the paraboloid z (++y and the plane z 2x+2. 2. Evaluate [ F -dr using Stokes' Theorem. Choose the simplest surface with boundary curve C and orient it upward.
1 Use Stokes' theorem to evaluate the integrals: F(x, y, z) dr a) where F(r, y,z)(3yz,e, 22) and C is the boundary of the triangle i the plane y2 with vertices b) where F(x, y,z (-2,2,5xz) an...
1 Use Stokes' theorem to evaluate the integrals: F(x, y, z) dr a) where F(r, y,z)(3yz,e, 22) and C is the boundary of the triangle i the plane y2 with vertices b) where F(x, y,z (-2,2,5xz) and C is in the plane 12- y and is the boundary of the region that lies above the square with vertices (3,5, 0), (3,7,0),(4,5,0), (4,7,0) c) where F(x, y,z(7ry, -z, 3ryz) and C is in the plane y d) where intersected with z...
(1 point) Use Stokes' Theorem to evaluate / (2xyi + zj+ 3yk) dr where C is the intersection of th...
(1 point) Use Stokes' Theorem to evaluate / (2xyi + zj+ 3yk) dr where C is the intersection of the plane x z 8 and the cylinder x2 y9oriented counterclockwise as viewed from above. Since the ellipse is oriented counterclockwise as viewed from above the surface we attach is oriented upwards curl(2xyi+zj +3yk)- 2,0,-2x The easiest surface to attach to this curve is the interior of the cylinder that lies on the plane x + z-8. Using this surface in...
the plane 7-1 with the cylinder Consider the vector field F(x, y, z) = (x²); +...
the plane 7-1 with the cylinder Consider the vector field F(x, y, z) = (x²); + (x+y); + (4y2Z) K and the curve C defined by the intersection Counter clockwise as viewed from above. Evaluate the Work- SF. dr done by F along in the following ways (a) Directly, using parametrization of C (b) Using stakes theorem
Use Stokes' Theorem to evaluate F. dr where Cis oriented counterclockwise as viewed from above. F(x, y, z) - xy + 27 + 6yk, C is the curve of intersection of the plane X + 2-1 and the cylinder + 9.
Help Entering Answers 1 point) Verify that Stokes' Theorem is true for the vector field F that lies above the plane z1, oriented upwards. 2yzi 3yj +xk and the surface S the part of the paraboloid z 5-x2-y To verify Stokes' Theorem we will compute the expression on each side. First computecurl F dS curl F0,3+2y,-2 Edy dx curl F dS- where x2 = curl F ds- Now compute F.dr The boundary curve C of the surface S can be...
please show all work
Use Stokes' Theorem to evaluate Sc F. dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = xyl +22+ 4yk, C is the curve of intersection of the plane X + 2 = 10 and the cylinder x2 + y2 - 36.
1 Help Entering Answers 1 point) Use Stokes' Theorem to evaluateF.dr where F(x,y,z) 6yzi 3xzj +3e k and C is the circy4,z 5 oriented counterclockwise as viewed from above Since the circle is oriented counterclockwise as viewed from above the surface we attach to the circle is oriented upwards The easiest surface to attach to this curve is the disk x2 + y2 < 4, z-5. Using this surface in Stokes' Theorem evaluate the following. F-dr = where sqrt(4-xA2) sqrt(4-x^2)...
Find the work done by the force field F= (y2/2, Z, x) in moving a particle along the curve C, where C is the intersection curve of the plane x +z = 1 and the ellipsoid x2 + 2y2 + x2 = 1 oriented counterclockwise when viewed from positive z— axis.
C is the curve of intersection of the paraboloid z (++y and the plane z 2x+2. 2. Evaluate [ F -dr using Stokes' Theorem. Choose the simplest surface with boundary curve C and orient it upward.
C is the curve of intersection of the paraboloid z (++y and the plane z 2x+2. 2. Evaluate [ F -dr using Stokes' Theorem. Choose the simplest surface with boundary curve C and orient it upward.
1 Use Stokes' theorem to evaluate the integrals: F(x, y, z) dr a) where F(r, y,z)(3yz,e, 22) and C is the boundary of the triangle i the plane y2 with vertices b) where F(x, y,z (-2,2,5xz) and C is in the plane 12- y and is the boundary of the region that lies above the square with vertices (3,5, 0), (3,7,0),(4,5,0), (4,7,0) c) where F(x, y,z(7ry, -z, 3ryz) and C is in the plane y d) where intersected with z...
(1 point) Use Stokes' Theorem to evaluate / (2xyi + zj+ 3yk) dr where C is the intersection of the plane x z 8 and the cylinder x2 y9oriented counterclockwise as viewed from above. Since the ellipse is oriented counterclockwise as viewed from above the surface we attach is oriented upwards curl(2xyi+zj +3yk)- 2,0,-2x The easiest surface to attach to this curve is the interior of the cylinder that lies on the plane x + z-8. Using this surface in...
the plane 7-1 with the cylinder Consider the vector field F(x, y, z) = (x²); + (x+y); + (4y2Z) K and the curve C defined by the intersection Counter clockwise as viewed from above. Evaluate the Work- SF. dr done by F along in the following ways (a) Directly, using parametrization of C (b) Using stakes theorem
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