Hello, this is for my calc3 exam review, i don't know how to do this. can someone me out plz?

a lamina occupies the region inside the cardioid r = 1 + cos θ and outside the circle x 2 + y 2 = 9/4. the density at each point is inversely proportional to the distance to the y-axis. find the center of mass of the lamina. you may use symmetry where appropriate.