Problem #9: Find the flux of the vector field F = xi + ex j + k through the surface S given by that portion of the plane 4x+y+ 7 = 9 in the first octant, oriented upward.
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- A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v=(x-y,z+y+7,z2) and the net is decribed by the equation y=1-x2-z2, y20, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.)A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by = (x - y, z + y + 9, z) and the net is decribed by the equation y = V1-x - z, y 2 0, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.) V. dS =A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v = (x-y, z + y + 3, z²) and the net is decribed by the equation y = √1-x²-2², y ≥ 0, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.)
- Let S be the cube with side length 7, faces parallel to the coordinate planes, and centered at the origin. Enter the exact answers. (a) Calculate the total flux of the constant vector field ? = - í +7j + k out of S by computing the flux through each face separately. Total flux = i (b) Calculate the flux out of S for any constant vector field v = a 7 +b} +ck. Total flux = i Save for Later Attempts: unlimited Submit AnswerA net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by (x - y, z + y + 7, z?) and the net is decribed by the equation y = V1 – x? – z?, y 2 0, and oriented in the positive y- V = direction. (Use symbolic notation and fractions where needed.) v • dS =Use the equation giving the flux of the vector field across the curve to calculate the flux of F(x, y) = (e", 4x – 1) across C, the parabola y = x for 0 < x < 9, oriented left to right. (Use symbolic notation and fractions where needed.) F. dr = Ttterf (9i) - 2025 Incorrect