Question 3 A wire C is the intersection of z + x2 + y = 4 and x2 + 2 = 4 with x 2 0. If its density is p(x, y, z) = x, find the Tries mass and the center of mass of the wire. remaining: 3 Marked out of Solution: 10.00 Flag First, we parametrizati question Using the Cylindrical Coordinates (r, 0, z), along z- axis, we take 0 as the parameter to obtain parametric representation of C: r(0) = (2 cos 0, 2 sin 0, 0), where . sos The mass of the wire is given by m = pds = A / cos Ode, where A = 4 ,a= and b = + Hence, m = The center of mass (x, y, z) x = + ,y = + , z= + Check Question 4 The work done by the vector field F(x, y) = (-y2, x2) along the arc of the parabola y = 2x2 - 4x + 2 from the Tries point (1, 0) to the point (0, 2) followed by the line segment from the point (0, 2) to the point (-1, 2) equals: remaining: 2 Marked out of O a. 77/15 cross out 10.00 O b. 6/55 cross out Flag question O c. 55/13 cross out O d. 55/17 cross out O e. None of these. cross out Check