(a) Using the parametrization F(r, 0) = (r cos 0, r sin 0, 5r²), set up a double integral for calculating the flux of the vector field F(x, y, z) = (x, y, z), through the part of the upward oriented surface z = 5(x² + y²) that lies above the disk x² + y² ≤ 25. Flux = 110 Disk Flux = dr de (b) Evaluate the integral. ff. d. S F.dA=

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Q: Is g = {(x, y) ∈ [−5, 5] × R : x^2 + y^2 = 25} a function from [−5, 5] to R.

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Q: Find the flux of the vector field F(x, y, z) = [xy, yz, zx] through the cylinder x2+y2 <= 1, 0 <= z…

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Q: nt) Compute the flux of the vector field F = 5xi + 5yj through the surface S, which is the part of…

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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: 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: calculate the flow of the vector field a(M) = (x-y)i + (x+y)j +(z2)k through the surface of a…

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Q: 10 12 14 10 12 14 (b) Calculate dB at t = 2. dt 64 dollars per month (c) Explain what the number you…

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Q: Find the flux through through the boundary of the rectangle 0 < x < 6,0 < y < 5 for fluid flowing…

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Q: (a) Calculate the flux of the vector field F(x, y, z) = 3i – 9k through a sphere of radius 2…

A: We will use divergence theorem to find flux through the sphere of radius 2 centered at origin .

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Q: A vector field is given as F=3x²i – yj + z'k a) Find the streamline of the vector field and also the…

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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…

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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 flow rate of F = across the portion of the surface z = over the unit square [0, 1] × [0, 1]…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Find the flux of the vector field F(x, y, z) =(x)i+(y)j+(z)k through the surface S of the…

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Q: Compute the flux of the vector fields F(x,y, z) = (, y, z) across the 1 and z = 4 whose vertical…

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Q: (b) Compute the flux of the vector field F(x, y, z) = yi + zk upwards through portion of the cone z…

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Q: b) F(x,y) represents a velocity field of a fluid over a surface S defined by z= 6-3x-2y. If the…

A: The flux over the surface S in the first octant is given by the following integral: Flux=∫SF⋅ndS…

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: Determine the flux of the vector field F(x, y, z) = (x, y, z) across the portion of the paraboloid z…

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Q: Use Green's theorem to calculate the work done by the force F(x, y) = xy'i + 3xyj on a particle that…

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