Find the flux of the vector field F across the surface S in the indicated direction. F = 4x i + 4y j + z k; S is portion of the plane x + y + z = 4 for which 0 ≤ x ≤ 4 and 0< or equal to y< or equal to 3  direction is outward (away from origin)   a) 174   b) - 78   c) 348   d) 150

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: ). The flux of the vector field F through the surface r(u,v) = (x(u, v), y(u, v), z(u, v) , where…

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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: Compute the flux of the vector field F(x, Y, z) = 6i + 5j + 3k through the rectangular region with…

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Q: Compute the flux of the vector field F(x, y, z) = (2y, 3, –2xz) through the surface S, which is the…

A: Given vector field is, Fx,y,z=2y,3,-2xz. The given surface is, y=x2+z2  and  x2+z2≤1. Now for the…

Q: Find a flux of the vector field ä(M)= (2z– y)i +6xj + yk through a part of the surface S: x - 4y+2z…

A: Given, a→M=2z-yi^ +6x j^ +y k^ Also given surface is, S: x-4y+2z-4=0 So the normal vector to the…

Q: Calculate the flux of the vector field of (xv.z = r-)i +0= 4xz) i +xzk across the box bounded by *=y…

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Q: Use the Divergence Theorem to calculate the flux of the vector fields F1 = -8zi + 8ak and F2 = -8zi…

A: Given vector fields are F1→=−8zi^+8xk^ and F2→=−8zi^+y+2j^+8xk^ We have to calculate the flux of the…

Q: Compute the flux of vector field V = .2 x +y2 x +y2 across the surface of the ellipsoid x2 y?, z2 +…

A: Divergence theorem establishes the relationship between line integral of vector field and the volume…

Q: (a) Calculate the work done in moving a particle in the vector field: F = xz i+ xy?j + 3xzk along…

A: Given that : F = xz i + xy² j + 3xz k along the intersection of the plane x + z = M and the cylinder…

Q: ompute the flux of the vector field F = ri + yj+ zk through the surface S, which is a closed…

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Q: ind the flux of the vector field F = yzi + 7yj + yk over the sphere x2 + y2 + z2 = 4.

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Q: a) Find the outward flux of the vector field F(x, y, z) = x³i+y³j + (z³ + xz)k across the surface of…

A: Concept: Divergence theorem: According to the Divergence theorem, the Surface Integral of the Normal…

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

A: Flux of  a vector field F on the surface S   =∫∫SF ds We will use divergence theorem  If surface S…

Q: Find the flux of the vector field V(x, y, z) = 6xy²i + 7x<yj + z°k out of the unit sphere.

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Q: Compute the net outward flux of the vector field F = (x i + y j + z k)/ (x2 + y2 + z2)^(3/2) across…

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Q: 2. Use Gauss' Theorem to compute the outward flux of the vector field F(r) = (x, y, z²) through the…

A: Outward flux by using gauss divergence theorem

Q: Find the flux of the vector field F = 2r2i+ 2y²j+ 4k across o in the direction of positive…

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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: Compute the flux of the vector field F(x, y, z) = 6ỉ +3j + 2k through the rectangular region with…

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Q: Find the flow of the vector field F(x, y, z) = zi + yj + xk through the unit sphere x² + y² + z² = 1…

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Q: Find the flux of the vector field F(x, y, z) 4y = "i+ 9 19 + Vr2 + y²k across S, where S is the…

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Q: Find the flux of the vector field F(x, y, 2) = yj + k where o is the portion of the cone =' = 4(x² +…

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Q: Compute the flux of the vector field F == through the surface S where S is the surface bounded by r…

A: Given thatF→=fr,fθ,fz=r2+sin2θ,rsincosθ,3z∂∂rrfr=∂∂rr22+sin2θ=2r2+sin2θ&amp; ∂∂θfθ=∂∂θr…

Q: Calculate the flux of the vector field through the given surface.  F = 2i −3j + 6x2yk through the…

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Q: Find the flux of the vector field F across the surface S in the indicated direction. F =x3y 2i+yj…

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Q: Compute the flux of the vector field F = across sphere a? + y² + z² = 9.

A: Let F be a vector field and S be the boundary of the surface D. To find the flux of the vector…

Q: 2. Use Gauss' Theorem to compute the outward flux of the vector field F(r) = (x, y, z²) through the…

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Q: Find the total flux of the vector field F= (x^2 z)i + (y^2 z)j+(z^3)k through the closed surface of…

A: Given vector field is  F=x2zi+y2zj+z3k              (i) Given surface is  x2+y2=16z=2z=-2 Let us…

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: Let S be the part of the plane 4x + 3y + z = 4 which lies in the first octant, oriented upward. Use…

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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: Compute the flux of the vector field 1 F(x, y, z) = -k x² + y2 + 1 out of the conical container K =…

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

A: Given: F→=xi→+yj→ z=36-x2+y2 ds=1+∂z∂x2+∂z∂y2dxdy       =1+4x2+4y2dxdy   and…

Q: Find the flux in the upward z direction of the vector field F(x, y, z) = (xz³, yz³, (x² + y²)²)…

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Q: Show that the work done by a constant force field F = a i + b j + c k in moving a particle along any…

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Q: Calculate the flux of the vector field F = x²i+ zk across the portion of the plane described as z =…

A: According to our company policy, we are supposed to answer only first question. For the rest please…

Q: Find the flux of the constant vector field i = -4 i – 5j- 2 k through a square plate of area 16 in…

A: The solution is given below

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: Compute the flux of the vector field F = xi + yj through the surface S, which is the part of the…

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Q: 2u?u? Σ: y = u with 0<u < 2,0 < v< 1. Z = V

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Q: Compute the flux of the vector field F(x, y, z) = 41 + 45 + Sk through the rectangular region with…

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Q: A vector field A is given by A = V×Fwhere F = (î+ĵ+k)eVæ²+y²+z². Consider an unknown surface that is…

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Q: Find the flux of the vector field F(x, y, z) = 3i– 7 j+ zk where o is the portion of the cylinder x…

A: We need to find the flux of the given vector field F(x, y, z) = 3i - 7j + zk where σ is the portion…

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: Find the flux of the vector field F = [x,y,z] through the oriented surface S: z= x^2 + y^2, z <= 1…

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Q: Show that on the saddle surface z= xy the two vector fields (Vī+x² ± i+ y°, yvī+x² ±xvI+y°) are…

A: Let f(x,y,z)=xy−zf(x,y,z)=xy−z , (a,b,c)∈the saddle surface, and calculate the total derivative…

Q: Let S be the part of the plane 2x + 2y + z = 4 which lies in the first octant, oriented upward. Use…

A: Given  plane  2x+2y+z=4

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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