posted by Lady .
A thin rectangular plate of uniform area density σ1 = 1.01 kg/m2 has a length a = 0.580 m and a width b = 0.240 m. The lower left corner is placed at the origin, (x, y) = (0, 0). A circular hole of radius r = 0.046 m with center at (x, y) = (0.066 m, 0.066 m) is cut in the plate. The hole is plugged with a disk of the same radius that is composed of another material of uniform area density σ2 = 5.46 kg/m2. What is the distance from the origin of the resulting plate's center of mass?