6) Given a hemisphere bounded by S,: z = /25 – x2 – y? and S2:z = 0.Find the outward flux of the vector field F(x,y,z) = x³1+ y³] +z³k across the surface S1, using Gauss theorem. Ans: 3750n

Q: What is the flux of the vector field F(x, y, z) = [9y, 2xy, 4yz + 234xy] through the unit cube [0,1]…

A: We find the flux of the vector field F(x, y, z) = [9y, 2xy, 4yz + 234xy] through the unit cube [0,1]…

Q: Suppose we have part of a hyperboloid of two sheets -4x? -4y? + z? = 9 where z 20 (so the upper…

A: Equation of hyperboloid of two sheets is: −4x2−4y2+z2=9 Where z≥0 and z≤15

Q: The following figure shows a half-cylindrical closed surface, defined by the cylinder x² + y² = 4…

A: As per the question we have to find the total flux of the vector field V through the flat top…

Q: - In Exercises 5-9 compute the flux of the vector field F through the parameterized surface S. 9. F…

A: GIVEN: F = x2 y2 zk

Q: Compute the flux, || Foñds, across the slanted face of the tetrahedron 2 = 4-1- y bounded in the…

A:

Q: b) Given the vector field SUTM F(r, y, 2) = 3z cos ri+rlnyj+e* tan rk. Determine UTM i. div F, ii.…

A:

Q: 3. Use Green's theorem to find the work done by the force field F(x,y) = xyi + (;x² + yy)j on a…

A:

Q: I. Use the Divergence Theorem: (² F. ds = Ifv. Fav SSS E = to calculate the flux of the field F…

A: Divergence theorem uses  Double integration converts into triple integration.

Q: 3. Consider the vector field F = (y, -x, x² + y?). Find the flux of F through S if: 9– x2 – y? above…

A:

Q: 4. Compute the outward flux of the vector field F(r) = (r, y', =') through the unit sphere r² + y² +…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: (b) Given a vector field F = 5(x² + y²)i+ 2xyj – 3zk, evaluate JI, V· FdV for which the solid D is…

A: Here we use polar form of circle .

Q: Consider the vector field F = = (x + y)i+ (x² + y² )j. What is the downward flux across the line…

A:

Q: Consider again the vector field F = (x +y)i + (x² + y²)j_what is the downward flux across the line…

A:

Q: 2) Given the vector field F = (- Vx²+y² 2z2) write the integral to calculate the outward x²+y² flux…

A: We have to find the outward flux across the cylinder x2+y2=100.

Q: 5) Find the work done by the force field F(r, y, z) = ri-zj+y k in moving an object along the…

A: Work = Force X Displacement

Q: Consider the following velocity vector field v = (2xz + y?) i + (2xy) j + (3z2 +x²) k, (a) Show that…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: Consider the semicircle r(t) = a cos(t)i + a sin(t)j with 0 0. For a given vector field F, the flux…

A: Given  rt = acosti+asintj, 0≤t≤π & a>0 for a given vector f the flux across r(t) = ∫CF.Nds…

Q: Calculate the flux of the vector field (x°, y), out of the annular region between the a + y? = 16…

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Q: Calculate the flux of the vector field (x, y³), out of the annular region between the x? + y? = 1…

A:

Q: (c) Determine the flux of the vector field F = x³i – 2yĵ + 7z²k across a cone z = x2 + y2 + 3 that…

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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: Q.3) Use the divergence theorem to find the outward flux of the vector field F(r, y, r) = ri %3!…

A: Here, Fx,y,x=xi

Q: find the work done by the given vector field F along the specified curve C.   F(x, y) = yi − x j,…

A: Given, F(x,y)=yi^-xj^ where curve, x2+y2=4 W=∫F.dr W=∫ydx-xdy from curve, dx=-dy W=∫xdx+ydy limit of…

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 =…

A:

Q: . Verify that Stokes' theorem is true for the vector field F(r, y, z) = (x, y, 2), where S is the…

A:

Q: (a) Compute the flux of the field F = r i+yj-zk across the cylindrical surface a + z = 1, 0 <y53…

A: If E be a  solid region bounded by surface of S with positive orientation then for a vector field…

Q: 4. Use the Divergence Theorem to find the outward flux of the vector field F(x,y, z) = v3;1 v3;173…

A:

Q: 12. Use a parameterization to find the flux across the surface cut from the cylinder x? + y? = 1 by…

A: Image is attached with detailed explanation.

Q: Consider the vector field f (x, y, z) = xz i + yz j+ x²y² k . Let S be the surface of the sphere of…

A: Using parametrization of the surface and curve

Q: Given that the vector field F(x, y) = (2x-3y, 2y-3x) is conservative in the xy-plane. If (x, y) is a…

A: We have to find the value

Q: For what values of a and d does the vector field F = ⟨ax, dy⟩ have zero flux across the unit circle…

A: A vector field, have zero flux. Across the unit-circle centered at the origin and oriented…

Q: Given the vector field F (x, y, z) = 2xyi + (x² + z?) j +2yzk a. Verify that the vector field…

A: Ans :A)

Q: 2.4) Use the divergence theorem to find the outward flux of the vector field F(x, y, x) = x³i+ y³j+…

A: The divergence of the given vector field is  ∇·F=∂∂xx3+∂∂yy3+∂∂zz3=3x2+3y2+3z2 Let, S be the surface…

Q: Compute the flux of the vector field F = zi + 8xk through the parameterized surface S oriented…

A:

Q: I have trouble getting to the answer. Just wondering if I can get it step by step.

A:

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

A:

Q: (10) Given that the vector field F= 2z i- 3 x j + 4 y k Evaluate f F. dr where S is the portion of…

A:

Q: 8. Use the Divergence Theorem to compute the flux across the sphere x² + y? + z? = 1 within the…

A:

Q: Consider the surface integral of the vector field F= [xy², 3x², x²z]over a surface S, where S…

A: From Gauss divergence theorem, we have ∬SF→⋅dS=∭VdivF→dV   The vector field is F→=xy2,3x2,x2z.…

Q: 2. Find the surface integral SS. ř · dS for the vector field F = xyî + yzĵ + zxk where S is part of…

A: To find Surface integral ∬SF→·dS→: The Surface S is of the form z=g(x,y) and is oriented upwards.…

Q: he temperature in a temperature-controlled chamber is given by a 3D scalar field Tlx, y, 2) = Ax®yz…

A: Note- Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Consider again the vector field F = (x + y)i + (x² + y² )j. What is the downward flux across the…

A:

Q: 2) Given that the total flux across the surface, S of the tetrahedron bounded by the planes x = 0, y…

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Q: o) Find the flux of the vector field F (x,y,z) = 3xi – yj + 2zk; across o where o is

A: The given question belonging to the vector calculus  in which we have to find the value flux of the…

Q: (b) A particle moves once around the circular path with radius of 1. Using Greens' Theorem, compute…

A: see below the answer

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: Consider the force field F(x, y, z) = xi + yj + zk. Compute the work done in moving a particle along…

A:

Q: Compute the flux of the vector field F = zi + 8xj through the parameterized surface S oriented…

A: We have find the flux of the given vector field through the parameterized surface S oriented upward.