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(VII) The unit upward normal to z = f(x,y) is: Find the outward unit normal to the solid unit hemisphere: 0 3S1-- spherical (upper) boundary What is the outward unit normal down on the xy-plane (...
6. (12pts) Use the divergence theorem to find the flux F.ndS with outward pointing normal n with F(x, y, z) =< x2,-y, z >, where s is the surface of the hemisphere z = V 1-x2-y2 and its base in...
6. (12pts) Use the divergence theorem to find the flux F.ndS with outward pointing normal n with F(x, y, z) =< x2,-y, z >, where s is the surface of the hemisphere z = V 1-x2-y2 and its base in the xy plane.
6. (12pts) Use the divergence theorem to find the flux F.ndS with outward pointing normal n with F(x, y, z) =, where s is the surface of the hemisphere z = V 1-x2-y2 and its base in...
Let F(x, y, 2)-3xi -4yi+2zk and let S be hemisphere- V9-y2 together with diskx29 in the xy- plane. Use the divergence theorem to calculate the outward flux 90π Let F(x, y, 2)-3xi -4yi+2zk an...
Let F(x, y, 2)-3xi -4yi+2zk and let S be hemisphere- V9-y2 together with diskx29 in the xy- plane. Use the divergence theorem to calculate the outward flux 90π
Let F(x, y, 2)-3xi -4yi+2zk and let S be hemisphere- V9-y2 together with diskx29 in the xy- plane. Use the divergence theorem to calculate the outward flux 90π
Let E-xi vi + 2zk be an electrostatic field. Use Gauss's Law to find the total charge enclosed by the closed surface consisting of the hemisphere- V1-x2 - y2 and its circular base in the xy-plane...
Let E-xi vi + 2zk be an electrostatic field. Use Gauss's Law to find the total charge enclosed by the closed surface consisting of the hemisphere- V1-x2 - y2 and its circular base in the xy-plane. Use the Divergence Theorem to evaluate F.N dS and find the outward flux of F through the surface of the solid bounded by the graphs of the equations. Use a computer algebra system to verify your results F(x, y, z) =xyì + 7yj +xzk...
Question 3. Let Q be the solid hemisphere bounded by x + y² + 2 =...
Question 3. Let Q be the solid hemisphere bounded by x + y² + 2 = 1 for 2 > 0 and by the plane z = 0, and let F = xi+yi + zk be a vector field. Verify the divergence theorem for Q and F by answering parts (a) and (b) below. Part (a) (5 points). Find the value of the triple integral of the divergence of F over the solid hemisphere Q. Part (b) (10 points). Evaluate...
1. Find the integral of the function f(x, y, z)xy+2 z over the region enclosed by the planex +y+z...
please answer question 3.
1. Find the integral of the function f(x, y, z)xy+2 z over the region enclosed by the planex +y+z 2 2. Find the volume and center of gravity for the solid in the first octant (x 20, y 20, z20) bounded by 3. Find the center of mass for the solid hemisphere centered at the origin with radius a if the density and the coordinate planes z0,y 0, and x0 the parabolic ellipsoid Z-4-r-y. function is...
Consider the vector field F(x, y, z) -(z,2x, 3y) and the surface z- /9 - x2 -y2 (an upper hemisph...
Consider the vector field F(x, y, z) -(z,2x, 3y) and the surface z- /9 - x2 -y2 (an upper hemisphere of radius 3). (a) Compute the flux of the curl of F across the surface (with upward pointing unit normal vector N). That is, compute actually do the surface integral here. V x F dS. Note: I want you to b) Use Stokes' theorem to compute the integral from part (a) as a circulation integral (c) Use Green's theorem (ie...
(23 pts) Let F(x, y, z) = ?x + y, x + y, x2 + y2?,...
(23 pts) Let F(x, y, z) = ?x + y, x + y, x2 + y2?, S be the top
hemisphere of the unit sphere oriented upward, and C the unit
circle in the xy-plane with positive orientation.
(a) Compute div(F) and curl(F).
(b) Is F conservative? Briefly explain.
(c) Use Stokes’ Theorem to compute ? F · dr by converting it to
a surface integral. (The integral is easy if C
you set it up correctly)
4. (23 pts)...
Suppose F(z, y, z) = (z, y, 5z). Let W be the solid bounded by the paraboloid z = x2 + y2 and the plane z = 16.
Suppose F(z, y, z) = (z, y, 5z). Let W be the solid bounded by the paraboloid z = x2 + y2 and the plane z = 16. Let S be the closed boundary of W oriented outward. (a) Use the divergence theorem to find the mux of F through S. (b) Find the flux of F out the bottom of S (the truncated paraboloid) and the top of S (the disk).
(1 point) Suppose F(x, y, z) = (x, y, 4z). Let W be the solid bounded...
(1 point) Suppose F(x, y, z) = (x, y, 4z). Let W be the solid bounded by the paraboloid z = x2 + y2 and the plane z = 4. Let S be the closed boundary of W oriented outward. (a) Use the divergence theorem to find the flux of F through S. ſ FdA = 48pi S (b) Find the flux of F out the bottom of S (the truncated paraboloid) and the top of S (the disk). Flux...
(1 point) Find the mass of the solid bounded by the xy-plane, yz-plane, z-plane, and the...
(1 point) Find the mass of the solid bounded by the xy-plane, yz-plane, z-plane, and the plane (z/8) 1, if the density of the solid is given by o(r, y, z) = x + 3y (r/2)(y/4) mass
6. (12pts) Use the divergence theorem to find the flux F.ndS with outward pointing normal n with F(x, y, z) =< x2,-y, z >, where s is the surface of the hemisphere z = V 1-x2-y2 and its base in the xy plane.
6. (12pts) Use the divergence theorem to find the flux F.ndS with outward pointing normal n with F(x, y, z) =, where s is the surface of the hemisphere z = V 1-x2-y2 and its base in...
Let F(x, y, 2)-3xi -4yi+2zk and let S be hemisphere- V9-y2 together with diskx29 in the xy- plane. Use the divergence theorem to calculate the outward flux 90π
Let F(x, y, 2)-3xi -4yi+2zk and let S be hemisphere- V9-y2 together with diskx29 in the xy- plane. Use the divergence theorem to calculate the outward flux 90π
Let E-xi vi + 2zk be an electrostatic field. Use Gauss's Law to find the total charge enclosed by the closed surface consisting of the hemisphere- V1-x2 - y2 and its circular base in the xy-plane. Use the Divergence Theorem to evaluate F.N dS and find the outward flux of F through the surface of the solid bounded by the graphs of the equations. Use a computer algebra system to verify your results F(x, y, z) =xyì + 7yj +xzk...
Question 3. Let Q be the solid hemisphere bounded by x + y² + 2 = 1 for 2 > 0 and by the plane z = 0, and let F = xi+yi + zk be a vector field. Verify the divergence theorem for Q and F by answering parts (a) and (b) below. Part (a) (5 points). Find the value of the triple integral of the divergence of F over the solid hemisphere Q. Part (b) (10 points). Evaluate...
please answer question 3.
1. Find the integral of the function f(x, y, z)xy+2 z over the region enclosed by the planex +y+z 2 2. Find the volume and center of gravity for the solid in the first octant (x 20, y 20, z20) bounded by 3. Find the center of mass for the solid hemisphere centered at the origin with radius a if the density and the coordinate planes z0,y 0, and x0 the parabolic ellipsoid Z-4-r-y. function is...
Consider the vector field F(x, y, z) -(z,2x, 3y) and the surface z- /9 - x2 -y2 (an upper hemisphere of radius 3). (a) Compute the flux of the curl of F across the surface (with upward pointing unit normal vector N). That is, compute actually do the surface integral here. V x F dS. Note: I want you to b) Use Stokes' theorem to compute the integral from part (a) as a circulation integral (c) Use Green's theorem (ie...
(23 pts) Let F(x, y, z) = ?x + y, x + y, x2 + y2?, S be the top
hemisphere of the unit sphere oriented upward, and C the unit
circle in the xy-plane with positive orientation.
(a) Compute div(F) and curl(F).
(b) Is F conservative? Briefly explain.
(c) Use Stokes’ Theorem to compute ? F · dr by converting it to
a surface integral. (The integral is easy if C
you set it up correctly)
4. (23 pts)...
(1 point) Suppose F(x, y, z) = (x, y, 4z). Let W be the solid bounded by the paraboloid z = x2 + y2 and the plane z = 4. Let S be the closed boundary of W oriented outward. (a) Use the divergence theorem to find the flux of F through S. ſ FdA = 48pi S (b) Find the flux of F out the bottom of S (the truncated paraboloid) and the top of S (the disk). Flux...
(1 point) Find the mass of the solid bounded by the xy-plane, yz-plane, z-plane, and the plane (z/8) 1, if the density of the solid is given by o(r, y, z) = x + 3y (r/2)(y/4) mass
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