29. Let K be the part of the cone z = Vx2 + y? between z = 1 and z 3, oriented upward. Let F(x, y, z) = (z, -x,1+ 2). Calculate the flux of the field through K.

Q: Compute the flux of the vector field F = 5xi + 2yj through the cylindrical surface shown below, if a…

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Q: Consider the solid E determined by the inequalities x² + y² + z≤ 4, and let S denote the surface…

A: Here we will use Stokes theorem  to calculate  flux of curl (F) on surface S bounded by curve C…

Q: 4. Find the positively oriented flux over the surface created by the paraboloid z = 16 – x² – y2…

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Q: Find the work done by the force field F on a particle moving along the given path. F(x, y, z) = yzi…

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Q: Let divF(x,y, z) = 4x³ + 4y³ + 42³ , where F represents the flow of a vector field. Estimate the…

A: Concept Used:- Divergence Theorem Flux=∫∫∫∇.F dVwhere ∇.F is the divergence of FVolume of the…

Q: Q3) Compute the work done by the force field F(x,y,z) = (3x, xz, y) on the curve C, where C is the…

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Q: Compute the flux SS F.nds through the piece of the cylinder of radius 2, centered on the z-axis,…

A: The given surface is the cylinder of radius 2 centered on z-axis, where 0≤x, 0≤y and 0≤z≤4. The…

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

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Q: ) Compute the flux of the vector field F = 5xi + 2yj through the cylindrical surface shown below, if…

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Q: Find the flux of the field F = xy i - z k outward (normal away from the z-axis) through the cone z =…

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Q: Find the work done by the force field F on a particle moving along the given path. F(x, y, z) = yzi…

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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: 5. Is the following vector field F(r, y) = (2x – y, -x + 3y?) conservative? If so, find a potential…

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Q: Q2: Find the work done S. F.dr in the force field F = yzî + xzĵ + xyk in moving from (1,1,1) to…

A: The equation of a line joining by the points and is given as the following.

Q: Find a potential function for the vector field F by inspection. F = (4x, 4y) P(x, y) =

A: Given:

Q: Compute the flux of the vector field F(x, y, z) = 2xj+ 4yk through the surface S, where S is the…

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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: 8. Show that the vector field, -y a² + y?' x² + yj²' ) is not conservative in R³, despite the fact…

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

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

Q: 1. Determine the velocity field v so that the surface F(r, y.t) = (y+t)+ (z+t)? - a² = 0 to be a…

A: The given surface is - F(x,y,t) = (y+t)2 + (x+t)2-a2.......(1) The velocity field (V→) components…

Q: Compute the line integral of the vector field F = (3zy1, 4z, -y) over the path c(t) = (e*, e', t)…

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Q: The work done by the force field F(x, y) = 5y'i + (x² – 2)j in moving a particle along the arc y =…

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost…

Q: Evaluate the outward flux of the vector field F = (2x² – 5e" + sin(z²), –4ry + In(x*), 5z – 3x²y®)…

A: We can see that the region given here is closed, so…

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

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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: 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: Find the upward flux of the vector field F(x,y,z)= (-y, x, 9) across the part of the hemisphere…

A: Consider the provided question,

Q: Suppose that v = (0, y, 0) is the velocity field of a fluid and let S be the surface defined by y =…

A: Given, the velocity field v→=0, y, 0and S be the surface defined by y=x2+z2, with y≤1.

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: Find the flux of the field F up through the part of the 1+ xy paraboloid z = 1 – x² – y? that…

A: FORMULA: Flux=∬F.n^ dS According to Stokes theorem, ∬F.n^ dS =∬∇×F . n^ dS According to the…

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: Compute the flux of the vector field F(x, y, z) = 3x + 3yk through the surface S, where S is the…

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Q: Compute the flux

A: Compute the flux

Q: Compute the line integral of the vector field F = (4y, –4r) over the circle z2 + y? = 16 oriented…

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

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

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Q: Find the outward flux of the field F = 3xz2 i + y j - z3 k across the surface of the solid in the…

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Q: 3. Find a potential for the conservative vector field: F(x, y, z) = (2xy + 2x, x² – 2yz³, -6z –…

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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: 10. Use the Divergence Theorem and the vector field F = to compute the outward flux from the region…

A: Here we will evaluate the outward flux.

Q: 6) Given the vector field F = (-x,-y,-z) '(x²+y2+z²)3/2! write the integral to calculate the outward…

A: First we parameterize field F then we calculate the Flux across the sphere using following formula:

Q: Compute the flux of the vector field F(x,y,z)=5xj+2yk→through the surface S, where S is the part of…

A: Flux problem...

Q: Find the flux of the field F = z k across the portion of the sphere x2 + y2 + z2 = a2 in the first…

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Q: 12. Find the flux of the field F(x, y, z) = 4xi + 4yj + 2k outward (away from z-axis) through the…

A: Flux of the given field is given by

Q: Compute the flux of the vector field F = 2xi + yj through the cylindrical 5 and b = 4 and it is…

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

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Q: 12. Find the flux of the field F(x, y, z) = 4xi + 4yj + 2k outward (away from z-axis) through the…

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Q: Compute the flux of the vector field F = 2xi + 3yj through the cylindrical surface shown below, if a…

A: We have to compute the flux of the  given vector field.