Consider the vector field F = (y + x,x) and curve C: r(t) = (4 cost, 4 sint) for 0 Sts 2x. a. Based on the picture, make a conjecture about whether the circulation of F on C is positive, negative, or zero. b. Compute the circulation. a. Choose the best answer below. O A. The circulation is probably positive because the vector field resembles a clockwise rotation field O B. The circulation is probably positive because the vector field resembles a counterclockwise rotation field. C. The circulation is probably close to zero because the vector field is nearly symmetric across a line that passes through the center of the circle b. The circulation is. (Type an exact answer, using it as needed.)Consider the vector field F= (y,x) shown on the right. a. Compute the outward flux across the quarter circle C: r(t) = (7 cost,7 sint) for 0st= > b. Compute the outward flux across the quarter circle C: r(t) = (7 cost,7 sint) for , Ets x. c. Explain why the flux across the quarter circle in the third quadrant equals the flux computed in part (a). d. Explain why the flux across the quarter circle in the fourth quadrant equals the flux computed in part (b). e. What is the outward flux across the full circle? a. Compute the outward flux across the quarter circle C: r(t) = (7 cost,7 sint) for Ost= > The outward flux isGiven the force field F, find the work required to move an object on the given orientated curve. F = (y,x) on the parabola y = 9x" from (0,0) to (4,144) The amount of work required is (Simplify your answer.)