IS F. ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the Is Evaluate the surface integral positive (outward) orientation. F(x, y, z) = -xi - yj + z³k, S is the part of the cone z = x² + between the planes z = 1 and z = 3 with downward orientation

Q: What is the flux through the described surface?

A: The surface is described by The vector field is F=<1, 3x, 2y>To evaluate the Flux for the…

Q: Your friends correctly calculate the gradient vector for f(x, y)=x²+y at the point (2,-3) as…

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Q: Find a vector function r(t) that describes the curve of intersection be- tween the elliptical…

A: Given To find a vector function r(t) that describes the curve of intersection between the elliptical…

Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

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Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A: Given that v=<x-y, z+y+9, z2> and the given curve is y=1-x2-z2,y≥0 To find: The value of ∬S…

Q: :::.. V : 5+j wi +4j Find the specific Scalar .(.. )

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Q: Q3. Find out values of a, b, c for which curl of vector V is zero, where V = (2xy+ 3 yz) i +(x² +…

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Q: he vector v = , is tangent to the surface x2 + 2y3 - 3z2 = 3 at the point (2, 1, 1).  Find a.

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Q: 3. Find a vector function that represents the curve of intersection of the paraboloid z =. and the…

A: To find the vector function that represents the curve of intersection of the paraboloid z=x2+y2, and…

Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A: Adding the plane surface y=0 to close the surface and apply the gauss divergence theorem.

Q: 4. Consider the vector function r(z, y) = (x, y, x² + 2y*). (a) Re-write this vector function as…

A: For the given vector function, PART A The surface function is given by, f(x,y)=xi^+yj^+(x2+2y2)k^…

Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

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Q: 13. For the vector fields: A = x + 2y ŷ + 3z 2; B = 3y - 2x ŷ. Check both product rule given in…

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Q: For vector field F = (-2y, y), y > 0. Find all points P such that the amount of fluid flowing into P…

A: The vector field given is as follows: Fx, y=-2y, y We are asked to find points P=x, y such that the…

Q: Find the flux of the vector field V(x, y, z) = 2xy²i+ 5x²yj + 3z³k out of the unit sphere. Flux =

A: Denote the unit sphere by S If the sphere is closed,  then the flux of v(x, y, z) out of S is given…

Q: Let S be the surface obtained by revolving the plane curve 2x=sqrt(9−y2) about the y-axis.Obtain a…

A: Given- Let S be the surface obtained by revolving the plane curve 2x = 9 - y2 about the y-axis. To…

Q: calculate div(F) and curl(F). F = (xy, yz, y² – x³)

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Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

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Q: Consider the following function. T: R? - R, T(x, y) = (2x?, 3xy, y²) Find the following images for…

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

A: Given: F→=xi→+yj→ z=36-x2+y2 ds=1+∂z∂x2+∂z∂y2dxdy       =1+4x2+4y2dxdy   and…

Q: Vector F is mathematically defined as F = M x N, where M = p 2p² cos + 2p2 sind while N is a vector…

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: Trigonometric function can be used as parameterization of many curves, here we use the following…

Q: B-For the surface z² = x² + y² find the directional derivative at the point (√2, √2,-2) in the…

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Q: Consider the curve F(t) that represents the intersection of the surfaces x + y? -1=0 and y= 2x a.…

A: Given: The curve r(t) represents the intersection of the surfaces x2+y2-1=0 and y=z/2x.

Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi - 2xzj + yzk; (3,-9, 9) 15i…

A: To find the curl of the vector field at the given point.;

Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A: To Determine: A net is dipped in a river .determine the flow rate of water across the net if the…