Define a vector field outward-facing flux through the cylinder Φ every page. The cylinder "cover" in this case is the disc xylevel, where = = 4. Φ kansi pohja Φ vaippa What is a field F total flux surface as through? F(x, y, z) $= xi + 3 - k S = {(x, y, z) | x² + y² ≤ 9, −4 ≤ = ≤ 4}

Q: poin) Determine whether the line integral of each oriented vector field (in blue) along the…

A: 1) line integral for vector field Is positive So answer is positive  2) line integral for vector…

Q: 1. For each curve, construct dr. • Let C1 be r? + y? = 16 • Let C2 be y = 5 – 2x • Let C3 be r = 2 –…

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Q: Compute the flux of the vector field F = yi + 3j – xzk through the surface S, which is the surface y…

A: We compute the flux of the vector field through the surface.

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: The figure shows the vector field F (x,y) = {2xy,x2 } and three curves that start at (1,2) and end…

A: Given, vector field F→x,y=2xy,x2 and three curves that start at 1,2 and end at 3,2.

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: point -2 has parameterization F(t) = (4(1-t), 3t) for 0 s 2

A: This is a problem of vector calculus.

Q: Describe the vector field by drawing some of its vectors. F(x, y) = 5xi - 5yj WebAssign Plot

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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: Let F and G be vector fields with differentiable components. Express curl (F × G) in term of div and…

A: Let F and G be vector fields with differentiable components.Let We will compute .The cross product…

Q: Match each vector field with its graph. ? 1. F(x, y) = x² + yj ? ? 2. H(x, y) = x² - yj 3. G(x, y) =…

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Q: Find the flux of the constant vector field =-7-j+ k through a square plate of area 25 in the…

A: A constant vector field  and a square plate of area 25 in the xy plane oriented in the positive z…

Q: Let C₁ be the line segment from the point (-4, 8) to the point (2, -4), C₂ be the arc on the…

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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: (x, y) = x(x + y)

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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: Let S be the closed surface consisting of the part of the cone x2 + y – z2 = 0 that lies between the…

A: The vector field is Fx,y,z=-x i-y j+z3 k and the surface is the part of the cone z2=x2+y2 between…

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

A: Given data net velocity (v) V=x-y, z+y+9, z2 net equation  y=1-x2-z2   , y≥0 find  ∫∫sv.ds= ? in…

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: A vector field representing wind speeds is given by v = æy³ i + 3x³y³j. %3D A walker can take one of…

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Q: Sketch the vector field of F = (-y,0) in the xy-plane. %3D

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