Using Green's Theorem, find the outward flux of F across the closed curve C. F = (x - y) i + (x + y) j; C is the triangle with vertices at (0, 0), (6, 0), and (0, 6) a) 216 b) 72 c) 0 d) 36

Q: Use Stokes' Theorem to evaluate   F · dr  where C is oriented counterclockwise as viewed from above.…

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Q: Work In Exercises 59 and 60, use Green's Theorem to calculate the work done by the force F on a…

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Q: Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. I F…

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Q: Let F(x,y,z) = ztan(y2) i + z³In(x² + 4)j+z k. Find the flux of F across the part of the paraboloid…

A: Given that, F(x,y,z)=ztan-1(y2)i+z3ln(x2+4)+zk To find flux of F: Divergence theorem:…

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Q: Using Green's Theorem, find the outward flux of F across the closed curve C. F = (-5x+ 2y) i + (8x -…

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Q: Exercise: 5 a) Find the outward flux of the vector field F(x, y, z) = x³i + y³j + (z³ + xz)k across…

A: Given the vector field  Fx,y,z=x3i+y3j+z3+xzk and z=a2-x2-y2

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A: The flux form of Green’s theorem relates a double integral over region D to the flux across boundary…

Q: Find the flux of the vector fleldF = (x – y*)i+ 4yj + x'k out of the rectangular solid [0, 1] x [1,…

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Q: The outward flux of F(x, y, z) = xi + yj + zk across any unit cube is.

A: Given flux is F=xi+yj+zk. Compute div F. divF=∂∂xx+∂∂yy+∂∂zz=1+1+1=3

Q: 6 The flux of the curl of the vector field F(x, y, z) = (y², r, 2) through the surface Σ = {(x, y,…

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Q: Exercise: 5 a) Find the outward flux of the vector field F(x, y, z) = x³i+y³j + (z³ + xz)k across…

A: a) find the outward flux of the vector field Fx,y,z=x3i+y3j+z3+xzk across the surface of the region…

Q: Use the Divergence Theorem to find the flux of F(x, y, z)=z³ i-x³j+y³ k across the sphere x² + y² +…

A: This is a problem of vector calculus.

Q: (a) Use the Divergence theorem to find the flux of F(x, y,z) = (x² + y)i + z²j+ (e° – z)k across the…

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Q: Compute the flux of F (x, y, z) = (y, z, x) across the surface S : R(u, v) = (u+2v, v – u, u), where…

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Q: Using Green's Theorem, find the outward flux of F across the closed curve C. F = (- 5x + 2y)i + (3x-…

A: Flux by using green's theorem

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

A: The vector field given is as follows: Fx, y, z=x3i^+y3j^+z3+xzk^ We are asked to find the outward…

Q: Using Green's Theorem, find the outward flux of F across the closed curve C. F= (x-y) i+ (x +y) j; C…

A: Using greens theorem to evaluate

Q: Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. F =…

A: Please see the explanation below....

Q: 6 The flux of the curl of the vector field F(x, y, z) = (y², x, z) through the surface = {{x, y, z)…

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Q: Find the flux of G(x, y, z) = (xz)i+ (yz)j+(z²)k outward across the part of the sphere x² + y² +z² =…

A: Here, surface, S={(x,y,z): x2+y2+z2=9, and 1≤z≤2}. For z=1, we get x2+y2=8 and for z=2, we get…

Q: Let C be a triangle with verticies (0, 0), (2,0), and (0, 3) oriented in the counterclockwise…

A: We have to find the outward flux.

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: Let F(x, y, z)=(y)i +(x)j+(z³)k. Find the flux of F the positively oriented across closed surface S…

A: Here  ∇·F→ = 2x + 2y + 2z = 2(x+y+z) R.H.S = ∫∫∫V ∇·F→.dv R.H.S =…

Q: Calculate the flux of the vector field F = (0, z, y) through the surface E: 2u?v? E:{y= u with…

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Q: Compute the flux ∮∂D F • n ds of F(x, y) = {x3, yx2) across the unit square D using the Flux Form of…

A: Given the equation F(x, y) = (x3, yx2)  The closed surface is the unit square the limits of x and  y…

Q: Using Green's Theorem, find the outward flux of F across the closed curve C. F =(x 2 + y 2) i + (x -…

A: The given question can be solved as shown in step 2.

Q: Compute the net outward flux across the sphere r²+y²+z (r*, y², 2ª).

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Q: Find the outward flux of F = across the boundary of D: the upper region cut from the solid sphere…

A: To find the outward flux use divergence theorem

Q: Find the flux of the vector field F = 2 i +3 j – 2 k through the rectangle with corners at (1,0,0),…

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Q: Using Green's Theorem, find the outward flux of F across the closed curve C. F= (x- y)i + (x+y)j; C…

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Q: Using Green's Theorem, find the outward flux of F across the dlosed curve C. F= (x² +y²}i+(x-y)]; C…

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Q: Using Green's Theorem, find the outward flux of F across the closed curve C. F = xy i + x j; C is…

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Q: Using Green's Theorem, find the outward flux of F across the closed curve C. F = (x2 +y2)i+ (x- y)j;…

A: here (x2+y2) is on x axis and x-y is on y axis

Q: ASK YOUR TEACHER DETAILS Let F(x, y, z) = z tan-(y2)i + z3 In(x2 + 6)j + zk. Find the flux of F…

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Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

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Q: Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C.  F…

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Q: oriented

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Q: The flux of the curl of the vector field F(x, y, z) = (y², x, z) through the surface E = {(x, y, z)…

A: Here first we find the curl of the given vector field using formula Curl…

Q: Using Green's Theorem, find the outward flux of F across the closed curve C.

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Q: Evaluate the flux, in the specified direction, of the vector field across the surface. F(x, y, z) =…

A: To calculate the flux, we shall use the standard formula of flux in terms of the vector form of the…

Q: 1. Use Green's Theorem to find the counterclockwise circulation and outward flux for the given filed…

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Q: Find the flux of the force field F(x, y, 2) = (2, x + r², 1 – a² + y) across the portion of the…

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Q: Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. F =…

A: Use Green's theorem

Q: QA-evaluate the flux of the filed F-xi+yj+zk through the upper part of the cylinder x² + z² = 1 that…

A: Given

Q: See attached photo.  Please provide the flux.

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Q: F

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Q: Find the flux of the vector field (y, x, z) in the negative z direction through the part of the…

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Q: Calculate the flux of F across G. F(x, y, z) = - yi + xj; G is the part of the plane z= 20x - 10y –…

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Q: Using Green's Theorem, find the outward flux of F across the closed curve C. F= (x-y)i+ (x+y)j; C is…

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