Use the Divergence Theorem to compute the net outward flux of the vector field F = (x, - y,z) across the boundary of the region D, where D is the region in the first octant between the planes z = 8-x- y and z =7-x-y. The net outward flux is (Type an exact answer, using x as needed.)

Q: Find an equation of the plane through the origin such that the circulation of the field F = zi + xj…

A: Given the circulation of the field F = zi + xj + yk along the intersection of the planeand the…

Q: Use the divergence theorem to find the outward flux of the vector field F(x, y, z) = 4x²i + 5y²j +…

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Q: Evaluate the surface integral ∬SF⋅dS for the given vector field F and the oriented surface S. In…

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Q: Decide which integral of the Divergence Theorem to use and compute the outward flux of the vector…

A: From the Divergence theorem, for a positively oriented boundary surface (outward Normal) of region E…

Q: Use the divergence theorem to calculate the flux of the vector field F(x,y, z) = 2xyi + z8 j + 6yk…

A: Divergence Theorem:      ∬F→·dA→    = ∬∫∇·F→dv       s                       v

Q: Verify that the Divergence Theorem is true for the vector field F on the region E. Give the flux.…

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Q: Compute the total work done by the vector field F~ = i + j + k along the curve given by the…

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Q: Use the Divergence Theorem to compute the net outward flux of the vector field F across the boundary…

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Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, z)=-3ry-ly:j-Szak…

A: To find- Use the divergence theorem to calculate the flux of the vector field F→x, y, z = -3xyi^ -…

Q: Use the divergence theorem to find the outward flux of the vector field F(x,y,z)=3x2i+1y2j+2z2k…

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Q: Use the extended divergence theorem to compute the total flux of the vector field F(x, y, z) = −3x^2…

A: The function given to us is F→=-3x2+2xz-y, 7y3-6y, 9x2+4z2-3x. We are asked to find the total flux…

Q: Compute the flux of the vector field F = 3xzi + 5yk through the surface S, which is the hemisphere…

A: The flux is given byflux =∫S  F→·n^  dShere,n^=x, y, zx2+y2+z2 in spherical coordinatesF→·n^ =x, y,…

Q: Use the Divergence Theorem to find the outward flux of the vector field F(x,y, z) = xy2i + yz2j +…

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Q: Use the Divergence Theorem to compute the net outward flux of the field F=<x,2y,-z> across the…

A: From the Divergence theorem, for a positively oriented boundary surface (outward Normal) of region E…

Q: Use the divergence theorem to compute the flux integral P F·î dS where în is the outward pointing…

A: Given vector field: F→=4x,4y,4z The surface is a unit ball x2+y2+z2≤1 The divergence theorem is…

Q: Use the Divergence Theorem to compute the net outward flux of the vector field F=<x2 , -y2,…

A: The vector field is given as

Q: Use the Divergence Theorem to compute the net outward flux of the vector field F=rr= (x, y, z) x +y2…

A: Given: F=rr=x,y,zx2+y2+z2 D is region between the spheres of radius 2 and 2 centered at origin. To…

Q: Find the counterclockwise circulation and outward flux of the field F = xyi + y2j around and over…

A: Theorem used:

Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, z) = x³i + yj+ z°k out…

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Q: For the vector field: F = (x + y)i + (y + z)j + (z + x)k 1) Compute the flux out of the cube bounded…

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Q: Use the divergence theorem to find the outward flux || (F-n)dS, where the vector field is given by…

A: Given that the vector field,

Q: 2. Find the flux of the vector field F(x,y,z) = xi + yj + 2zk across o, where o is the portion of…

A: The given problem is to find the flux of the given vector field over the given portion of cone…

Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, z) = x³i + y³j+ z³k put…

A: According to the given conditions

Q: Use the Divergence Theorem to compute the net outward flux of the field F = (4x, y, - 2z) across the…

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Q: Verify that the Divergence Theorem is true for the vector field F on the region E. F(x, y, z) =3x i…

A: Given that to   Verify that the Divergence Theorem is true for the vector field F on the region E.…

Q: 4. Use the Divergence Theorem to find the outward flux of the vector field F(x,y, z) = v3;1 v3;173…

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Q: Evaluate the surface integral Js F · dS for the given vector field F(x,y, z) = 7xi+ 4yj+7zk and the…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Use the Divergence Theorem to compute the net outward flux of the vector field F = (x, - y,z") the…

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Q: Evaluate the surface integral ∬SF⋅dS for the given vector field F and the oriented surface S. In…

A: Given,

Q: Verify Stokes’ Theorem for the vector field F = 2xyi + xj + ( y + z)k and surface z = 4 - x2 - y2,…

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Q: Verify the Divergence Theorem for the vector field and region: F = (6z, 2z, 7y) and the region r? +…

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Q: Use the Divergence Theorem to compute the net outward flux of the field F = (x,yz) across the…

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Q: Use the Divergence Theorem to compute the net outward flux of the vector field F = (x, - y²,z²)…

A: To apply the divergence theorem, calculate ∇·F, where F=x2,-y2,z2.…

Q: Find the flux of the vector field F(x,y,z) = xi + yj + 2zk across ơ, where o is the portion of the…

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Q: Use the Divergence Theorem to compute the net outward flux of the field F = (x,y,z) across the…

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Q: (a) Set up a double integral for calculating the flux of the vector field F(x,y,z) = yi +5j − xzk…

A: Let r(x,z)=x,x2+z2,z Then the flux is given by, Flux=∬F.dS=∬F.(rx×rz)dxdz Here, rx=1,2x,0  ;…

Q: 3. Find the flux of the vector field F(x,y,z) = xi+ yj + 2zk across o, where o is the portion of the…

A: Find your answer below

Q: Use the Divergence Theorem to find the outward flux of the vector field F(x,y, z) = x³i + y³j+z³k…

A:

Q: Evaluate the surface integral F F. ds for the given vector field F and the oriented surface S. In…

A: To find- Evaluate the surface integral ∬SF·dS for the given vector field F and the oriented surface…

Q: Verify Stoke's theorem for the vector field F = (2x - y) I– yz"J - y z K over the upper half surface…

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Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, z) = x³i+y³j+z³k out of…

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Q: Use the Divergence Theorem to compute the net outward flux of the vector field F = (x, -y²¸z²)…

A: Given that F=x2,-y2,z2 The objective is to compute the net outward flux of the vector field across…

Q: Verify that the Divergence Theorem is true for the vector field F on the region E. Give the flux.…

A: According to the divergence theorem:

Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

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Q: Compute the flux of the vector field F = 2xzi + 5yk through the surface S, which is the hemisphere…

A: In this question, we find the flux for the given vector field across the surface of the hemisphere.

Q: Jse a CAS and the divergence theorem to compute the net outward flux for the vector field across the…

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Q: Verify Stokes' Theorem holds for the vector field F = yz i + x k where S is the portion of the plane…

A: The given vector field is F=yzi^+xk^ where S is the portion of the plane 3x+2y+6z=6 in the first…

Q: Verify that the Divergence Theorem is true for the vector field F on the region E. Give the flux.…

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Q: Use the Divergence Theorem to find the outward flux of the vector field F(x, y, z) = x³i + y³j+ z³k…

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Q: diverge

A: answer is in next step