Find the centroid (center of mass) of the following thin plate, assuming constant density. Use symmetry when possible to simplify the calculations. The region in the first quadrant bounded by x~ + yz = 144 Make a sketch of the region. Choose the correct answer below. O A. O B. O C. OD. Ay 14- 14 14 14- 14 Set up the double integral that gives My, the plate's first moment about the y-axis. Use increasing limits of integration. Assume a density of 1. 00 My = J J (0) dy dx (Type exact answers.) 00 If necessary, set up the double integral that gives Me, the plate's first moment about the x-axis. Use increasing limits of integration. Assume a density of 1. Select the correct choice below and, if necessary, fill in the answer boxes within your choice. O A. This integral is not necessary because the given function is symmetric about the x-axis. O B. This integral is not necessary because the given function is symmetric about the y-axis O C. This integral is not necessary because the given function is symmetric about the line y = x. O D. This integral is necessary; Mx = ] ] ( D) dy ax (Type exact answers.) The coordinates of the centroid are (x.y) =- (Type an ordered pair. Type an exact answer, using x as needed.) Plot the centroid on the sketch of the region. Choose the correct answer below. O A. O B. O C. OD. Ay 14- 147 Ay 14- 14- 14