Find the circulation and flux for the field F(x, y) = (y – 6x² , x+y²) around and across the triangle given by y = 0, y = x, and x = 1.

Q: Draw the slope field (direction field) for the following DE: y'=y-t

A: Given DE is Make table as follows:…

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: 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: 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: Determine the parametric equation for a line that is tangent (intersection) of the two fields below:…

A: We have to find out parametric equation for a line that is tangent (intersection)of the two fields…

Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F = (y -…

A: By using green theorem, we calculate the counterclockwise circulation and outward flux of the given…

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: Find the curl of the vector field F (6x sin(y), 2y cos(x)). curl F =

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Q: Find curl(zi + xj+ yk).

A: Using definition of curl of vector.

Q: Find the flux of the constant vector field i = -4 i – 5j- 2 k through a square plate of area 16 in…

A: The solution is given below

Q: Find the curl of the vector field F curl F= (5y cos(x), 2x sin(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…

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

Q: Q.3) Graph the vector field F(x, y) = –yi. Find V.(F × G) where F(x, y, z) = xi – 3j+ zk and G(r, y,…

A: given vector field Fx,y=-yi^  graph of the vector field

Q: Suppose F(x, y) = (x² + 3y, 7x − 7y²). Use Green's Theorem to calculate the circulation of F around…

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Q: Find the upward flux of F= (14e2,-7e²,-6) through the first-octant part of the triangle a+2y+3z-6.…

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