Use a parametrization to find the flux I F.n do across the surface in the given direction. F= - xi - yj+ 3z°k outward (normal away from the z-axis) through the portion of the cone z= +y between the planes z =1 and z = 3.

Q: Find an equation of the tangent plane to the given parametric surface at the specified point. r(u,v)…

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Q: Let F(x, y) = 3 i + j + 2k, and let S be a square whose side lengths are 3, parallel to the…

A: Flux is F.dA Where F is the Field and A is the area

Q: For vector A = , calculate the surface integral (f, A · ds)

A: In this question, we find the surface integral for the given vector function A=<x2yz, xy2z,…

Q: Let F Use Stokes' Theorem to evaluate F · dī, where C is the curve of intersection of the parabolic…

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Q: Q) S = the part of the paraboloid z = 10-x^2-y^2 above z = 1 F = [x^3, xy, z] Find the flux of F…

A: Step:-1 Given that S is part of paraboloid z=10-x2-y2 above z=1 Since, given that z=10-x2-y2 and…

Q: use a parametrization to find the flux f f s F . n dsacross the surface in the specified direction.…

A: Consider the function: Given   F=4xi+4yj+2kSurface cut from the bottom of the paraboloid z=x2+y2 by…

Q: use a parametrization to find the flux ∬S F . n dδacross the surface in the specified direction. F =…

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Q: Find the unit tangent, normal, and binormal of the following parametrization: c (t) = (4cos3t,…

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Q: find a parametrization of the surface Circular cylinder band The portion of the cylinder y2 +(z -…

A: Given:The portion of the cylinder y2+(z-5)2=25 between the planes x=0 and x=10.

Q: Find the area of the surface with the following parametrization: u COS V Τ (u, υ) - u sin v u? 0<u<…

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Q: Use the divergence theorem to find the outward flux of F across the boundary of the region D. F=x'i-…

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Q: Let F = Use Stokes' Theorem to evaluate F dī, where Cis the curve of intersection of the parabolic…

A: Given F¯=xy,4z,6y We have to evaluate ∫CF¯⋅dr¯ by using stokes theorem, where C is the curve of…

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

A: The field lines of a vector field F through surfaces with unit normal n, the angle from n to F is θ.…

Q: Find the parametrization r(t) = [x(t), y(t), z(t)] of the curve obtained by intersecting the…

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Q: Use a parameterization to find the flux | F.n do of F = 5xy i- 4z k outward (normal away from the…

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Q: Find an equation of the tangent plane to the given parametric surface at the specified point. r(u,v)…

A: Please see the explanation below

Q: Find the center of mass, the moment of inertia about the coordinate axes, and the polar moment of…

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Q: Let F < xy, 6z, 3y Use Stokes' Theorem to evaluate F · dī, where C is the curve of intersection of…

A: The given problem is to evaluate the line integral using stokes theorem, we have to find the limits…

Q: Calculate the moments of inertia (Ix and Iy) of the shaded area given in the figure with respect to…

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Q: use a parametrization to find the flux f f s F . n dsacross the surface in the specified direction.…

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Q: Compute the flux of F= xi+yj+ z*k across the cone z =Vx2 + y? , 0szs1, in the downward direction.…

A: We have to find the flux in the downward direction.   Let us assume that x=rcosθ, y=rsinθ, z=r Then…

Q: Use a parametrization to find the flux F•n do across the surface in the given direction. F= - xi -…

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Q: Suppose that C is the curve of interesection between the plane z = x and the cylinder x² + y? be the…

A: Consider the given function. z=x and x2+y2=1 As, the function S be the interior of this ellipse…

Q: Find the outward flux across the domain D xi + yj + zk x2 +y? + z? F(x,v,z) = across the sphere x2…

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Q: Let F = . Use Stokes' Theorem to evaluate curlF · dS , where S is the part of the paraboloid z = 14…

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Q: Use the divergence theorem to evaluate I = F.N dS, where F = (ry?, yz², zx² ), and N is the the unit…

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Q: Find the surface area of the surface given by the parametrization F(s, t) = (s – 2t, –2s + 3t, s –…

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Q: Let F = %3D So Use Stokes' Theorem to evaluate F · dī, where C is the curve of intersection of the…

A: Here, the given function is F=xy,5z,4y To use Stroke's theorem: ∫CF·dr=∫∫S∇×F·N^ dA And,…

Q: Q2. Use the Stokes' Theorem to find fF.dr where F(x,y,z) = and C z=9-x²-y² on the xy plane oriented…

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Q: Calculate the flux integral f(2i + 2j + 2k) · dA where S is a disk of radius 5 in the plane æ + y +…

A: Given F=2i+2j+2k,radius=5 and x+y+z=1 plane

Q: Use the divergence theorem to find the outward flux of F across the boundary of the region D. F=x°i-…

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Q: Use a parametrization to find the flux F•n do of F = 5zk across the portion of the sphere x +y +z =…

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Q: Use the Divergence Theorem to calculate the outward flux of F = (r3 + y, y + z3, z3 + 23) across S:…

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Q: Find the moment of inertia of the plane area generated by the equations y = 8x³, y = 0, and x = 1…

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

Q: Use cylindrical coordinates to evaluate y dV where D is the solid that lies be- tween the cylinders…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Use a parameterization to find the flux F•n do of F = z'i+ xj - 2zk in the outward direction (normal…

A: Firstly we find intersection of parabolic cylinder and plane .

Q: Use Stoke’s Theorem to evaluate the line integral ∮C(x+z)dx +(x−y)dy +xdz. The curve C is the…

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Q: Find a parametrization, using cos(t) and sin(t), of the following curve: The intersection of the…

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Q: Use Stokes' theorem to evaluate V ×F· î dS where = (9y²z, 4xz, 2x²y²) and S is the paraboloid z = x²…

A: Step:-1 Stoke's Theorem:- ∬s∇×F→.n dS=∫F.dr Now, given that F→=9y2z, 4xz, 2x2y2 and paraboloid…

Q: Let F = Use Stokes' Theorem to evaluate F. dī, where C is the curve of intersection of the…

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Q: Find the work done by the force field F(x,y)=5x2i−2xyj on a particle that moves once around the…

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Q: use a parametrization to find the flux ∬S F . n dδacross the surface in the specified direction. F =…

A: Given surface, F=2xyi+2yzj2xzk           ...(1) Given plane, x+y+z=2a                ...(2) Where…

Q: Find D at P(0,0,8) due to a disk of surface charge 15nC/m2, p< 5 m lies on the z=0 plane

A: To find the electric field due to a charged disk. The surface charge of the disk is, σ=15…

Q: Find the flux of F = (y +xz)i + (y + yz)j – (2x + z²)k upward through the first octant part of the…

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Q: 2. Use Stokes' Theorem to evaluate curlF.dS whereF = 2y i + 3z j+(z – z) k and S is the portion of y…

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Q: C is the intersection curve between the paraboloid z = x² + y? and the plane 6x + 8y – z = 21,…

A: Strokes theorem:

Q: find the outward flux of F across the boundary of D. F = xz i + yz j + k D: The entire surface of…

A: Consider the given vector field. F = xz i + yz j + k

Q: Let F = . Use Stokes' Theorem to evaluate curlF · dS , where S S is the part of the paraboloid z = 9…

A: Find your answer below

Q: Find an equation for the plane through the origin such that the circulation of the flow field F = zi…

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Q: Use a parametrization to find the flux •n do across the surface in the given direction. S 2 F= - 2xi…

A: We have to find the flux using parametrization.