nt) Compute the flux of the vector field F = 5xi + 5yj through the surface S, which is the part of the surface z = 9(²+ y2) above the disk of radius 3 centered at the origin, oriented upward. flux =

Q: Find the flux of the vector field F = (y, z, x) across the - part of the plane z = 4+3x+2y above the…

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Q: f is a potential function for the vector field F = (2x - 2yz, 3y2 - xz, -2xy) so what is the value…

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Q: Compute the flux of the vector field F = yi + 3j – xzk through the surface S, which is the surface y…

A: We compute the flux of the vector field through the surface.

Q: .) Compute the flux of the vector field F = 4x + 4yj through the surface S, which is the part of the…

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Q: State the theorem for Surface Independence for Curl Vector Fields.

A: Stokes' Theorem Stokes’ theorem says we can calculate the flux of curl F across surface S by knowing…

Q: Determine the flow of the vector field (image 1), through the surface S, outwards, with S being the…

A: Given :- The flow of the vector field through the surface S , outwards , with S  being the…

Q: point -2 has parameterization F(t) = (4(1-t), 3t) for 0 s 2

A: This is a problem of vector calculus.

Q: 3) Let S be a portion of the surface 3z = 12 – 6x – 3y in the first octant. Suppose that S is…

A: 3z=12-6x-3y divide by 3 z=4-2x-y ⇒2x+y+z=4 clearly it's plane The plane cuts the x-axis at (2,0,0),…

Q: a) Calculate the flux of the vector field F(x, y, z) = 275k through a sphere of radlus 4 centered at…

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Q: Find the flux of the vector field F = across the part of the plane z = 3 + 2x + 4y above the…

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Q: Compute the flux of the vector field F =2xi +3yj through the cylindrical surface shown below, if a=3…

A: Given that the vector field is F(x,y)=2xi+3yj Let us parametrize the cylinder as x=cosθ, y=sinθ, z=r…

Q: Let F and G be vector fields with differentiable components. Express curl (F × G) in term of div and…

A: Let F and G be vector fields with differentiable components.Let We will compute .The cross product…

Q: Q2) Find the flux of the vector field F(x,y,z) = (x,y, z) , where the surface S is the portion of…

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Q: Calculate the flux of the vector field F(x, y, z) = (4x+8) through a disk of radius 6 centered at…

A: Given,                    To find the flux of the given vector field through a disk of radius 6…

Q: a 3d vector field given by V=5xyi+5yj-4zk represents the flow of water out of a system. use gausses…

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Q: 10) Use Green's Theorem to find the work done by the force field F(r, y)% = -ry i+yj in moving a…

A: Given force field  Fx,y=-x2yi+yj The particle follows starts from 1,0 moves along the circle x2+y2=1…

Q: For the vector field (x2,0₁ - 2x² -z²), evaluate its line integral along the closed curve, made by…

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Q: -y Consider the vector field F = (y²¹, ²²), and the curve defined by 1% + 2 + 2 = 2 and z = c.…

A: Consider the vector field .The curve is given by  and z=c.Substituting, we getThe curve is an…

Q: = + 1³ 2³ +²²³ +22+ Calculate the flux of the given vector field F where S is the sphere centered at…

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Q: Compute the flux of the vector field F 3yi + 4j – 3xzk through the surface S, which is the surface y…

A: We apply formula for finding this

Q: Calculate Vø and V?o of the scalar field: 6 = eV=²+y?+z?

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Q: disk

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Q: Compute the flux of the vector field F = yi + 5j - xzk through the surface S, which is the surfac y…

A: A vector field F→=yi^+5j^-xz through a surface S, which is the y=x2+z2  , x2+z2≤1. To Find: The flux…

Q: a) Compute the flux of the vector field F = (-2, 3, z³) across the disk in the xy- plane of radius…

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Q: a-) Determine the whether the vector field F = y²₁ + x²Ĵ + xyl can be written as a gradient of a…

A: We are given the vector field  F(x,y,z)=yzi+xzj+xykwe have to find the if it is conservative and…