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), (10,0), and (0,5) O A. 0 В. 250 ОС. 100 D. 50

Q: SSF. = SSST. F Angr the boundary of the cylinder x² + y2 = 4, and includes Find the outward flux of…

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Q: Find the work done by the force field F on a particle that moves along the curve C. F(x, y) = (x2 +…

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Q: use Green's Thearum. to fina the counterclockwise Circulation. and outward Flux for the flela F and…

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Q: Work In Exercises 39 and 40, find the work done by the force field F on a particle moving along the…

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Q: Use lhe Diveryeru Tlaure lo evaluale N ds and find the outward flux of F through the surface of the…

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Q: Verify Stoke’s theorem for the given vector field F and surface S. (b) F(x, y, z) = (x + y)i + (y +…

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Q: Calculate the flux of the field F across the closed plane curve C. F=xi+yj; the curve C is the…

A: by using green theorem if curve is the closed and counter clockwise  ∫F.dr→=∫Mdx+Ndy =…

Q: Use Stokes theorem to find the work performed by the force field F= (x. xy',xy') on a particle that…

A: Given that: F→=x3, xy3, xy2F→=x3i^+ xy3j^+ xy2k^ And: φ=z-y∇φ=i∂∂x+j∂∂y+k∂∂zz-y∇φ=-j+k The unit…

Q: (b) Compute the flux of the vector field F(x, y, z) = y i– 2.xyk over the triangle T with vertices…

A: Given vector field is: F→=yi^-2xyk^ Given vertices of the triangle are: 1,0,0, 0,1,0 and 0,0,2 Then…

Q: 9 The outward flux of the vector field F(x, y, z) = (+0 the boundary of the region E = {(x, y, z) =…

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Q: F(x, y, z) = (ze" – ye²) i + (2cos y – xe²) j+ (e² – xye²) k

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Q: Let F (x, y, z) = (e*y - 2x, ex + 2yz, e*xy + y?). a) Using the Curl-test decide whether F is…

A: Let F→x,y,z=ezy-2x,ezx+2yz,ezxy+y2

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

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Q: A buffalo stampede (see the left figure) is described by a velocity vector field F = (xy -y',x + y)…

A: The value of F: F=xy-y2i^+x2+yj^ According to Green Theorem, ∫y=ab∫x=ab∂M∂x-∂L∂y=∮ Ldx+M dy Putting…

Q: x= J y= K z=L Look for flux of G (J,K,L) = across surfase Z: K(a, b) = where (a, b) = [0, 1] × [0,…

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Q: the gradient vector field of f. f(x, y, z) = 7

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Q: Find the flux of the vector field F = (y, – 2, 1) across the part of the plane z 2 + 3x +y above 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: Use a parameterization to find the flux The flux is SS F•n do of F = 5xy i+ 5yzj +5xz k upward…

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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…

A: Using greens theorem to evaluate

Q: Find the flux S S;F · dS of the constant vector field F(x, y, z) = (0,0, 1) across the surface S…

A: Let F be a constant vector field over a surface S given as  F(x,y,z)=0,0,1  The surface S is…

Q: Find the gradient vector field of f. Vf(x, y, z): Need Help? f(x, y, z) = 10√x² + y² + z² Read It…

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

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Q: Exercise: 1. Find a unit normal vector to the surface at the given point. [Hint: Normalize the…

A: Given surface equation is  3x+ 4y + 12z ,   At points(0,0,0)We need to find the normal vector to the…

Q: Find the gradient fields of the functions ƒ(x, y, z) = ln√(x2 + y2 + z2)

A: The given function is fx,y,z=lnx2+y2+z2   The gradient field of a function is represented by,…

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: Calculus 16.6.25 Use a parameterization to find the flux F•n do of F = 6xy i- 2z k outward (normal…

A: Given field F=⟨6xy, 0, -2z⟩ where S:z=9x2+y2 , 0≤z≤9 Let x=rcosθ , y=rsinθ ⇒z=9r& 0≤z≤9…

Q: h) Given vector field F (x, y, z) = (2x + 2y + 4z) i + (2y + 2x – 32) j + (2z – 3y + 4x) k. (a)…

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Q: Use a parameterization to find the flux The flux is 61a 3 SS₁ F-n do of F = 3xy i+ 3yzj + 3xz k…

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Q: 6. (a) Determine whether the given velocity vector of a fluid is rotational or irrotational. I) F(x,…

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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: 5. Find the flux of F = 2xi + (x- y)j across the circle r(t) = acos[t] i + asin[t]j,t e [0,2n]

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Q: F(x,y,z) = (x, – y, z) on the surface s={(x.y,z): z=x² +y², 0<x<2,0< y<2} Determine the flux of F…

A: Find the vector F and consider the formula for the flux.

Q: we look at the function f : R? → R mit f(x, y) = y sin(2x)determain the tangential plane at point…

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Q: Find the work done by the force field F(x,y,z) = (x – y²,y – z², z – x²) on a particle that moves…

A: Here we will use line integral to calculate Work done by vector field

Q: Let S be the boundary of the unit cube {(x,y,z):0sxs1,0sys1,0szs1}. Find the outward flux through S…

A: Let S be the boundary of the unit cube x,y,z:0≤x≤1,0≤y≤1,0≤z≤1. Then we have to find the outward…

Q: Rain on a roof Consider the vertical vector field F = ⟨0, 0, -1⟩, correspondingto a constant…

A: Given, vector field = F = &lt;0, 0, -1&gt; and the plane is z = 4 – 2x – y. we have to calculate the…

Q: a) Sketch and label the contours z = 0, z =±1, and +4 for the function z = f(x, y) = -x² + y?. Plot…

A: (a) The given function is: z=f(x,y)=-x2+y2 Find the cantor z=0: z=0=-x2+y2-x2+y2=0y2=x2y=±x The…

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: Evaluate F-dS, that is, find the flux of F across S. Flx, y, z)=-zi+ 2yj-4xk: S is the hemisphere…

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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: Q3: A- Use Greens theorem to evaluate the circulation or flux for the velocity field : 1 f(x, y)=-…

A: GIVEN: f(x, y) = 1x + yi - 1x + yj

Q: 5. Find a potential function corresponding to the vector field F(x, y, z) = (2x, 3Y, 4z).

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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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Q: onsider the vector of electric field E(x,y,z) (sinh x)i – (cosh y)j – xyz k %3D a. Compute the…

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