Calculate the flux of the vector field F(x, y, z) = (4x+8) through a disk of radius 6 centered at the origin in the yz-plane, oriented in the negative x-direction.
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- Find the work done by the vector field (5x + yx, x² + 3 ) or the boundary of the rectangle 0 < x< 3,0 < y < 6|in the counterclockwise direction. a particle moving along (The force is measured in newtons, length in meters, work in joules=(newton-meters).) W = joulesHow do I find the flux of this vector field in the image attached?Where the vector field is (-y^2, x, z^2)
- Find the flux of the constant vector field i = - 4i - 5j-2k through a square plate of area 16 in the zy-plane oriented in the positive r-direction. flux =find (a) div(f) (b) curl(f) if f=x^2(vector i)+y^2(vector j+2yz(vector k)Find a vector tangent to the curve of intersection of the two cyclinders x2+y2=32x2+y2=32 and y2+z2=32y2+z2=32 at the point (−4,−4,4)(−4,−4,4).
- Calculate the flux of the vector field F = 6i + 2x²j – 2k, through the square of side 4 in the plane y = 7, centered on the y-axis, with sides parallel to the x and z axes, and oriented in the positive y-direction. flux =Determine the domain of the vector function r(t)=(t^2−4)/(t−2)i+sqrt(t+5)j+(e^t)* k Select one: a. [−5,2)∪(2,∞) b. [−5,∞) c. (−∞,∞) d. (−5,2)∪(2,∞) e. (−∞,2)∪(2,∞)Let F(x, y) = ⟨xy^2+2x+1, x^2y − 3y⟩ be a vector field. Let C be the curve thatconsists of two line segments C1 and C2, where C1 has vertices (−1, 0) and (0, 1)and C2 has vertices (0, 1) and (1, 0). C is oriented clockwise.(a) Sketch C accurately.(b) Find the work done by F by moving a particle along the path C in the givendirection.