What is the distance of the resulting plate's center of mass from the origin?

A thin rectangular plate of uniform density σ₁ = 5.94 kg/m² has a length a = 0.740 m and a width of b = 0.330 m. The lower left hand corner is placed at the origin, (x, y) = (0, 0). A circular hole is cut in the plate of radius r = 0.064 m with center at (x, y) = (0.084 m, 0.084 m) and replaced with a circular disk with the same radius composed of another material of the same thickness with uniform density σ₂ = 1.67 kg/m². What is the distance of the resulting plate's center of mass from the origin? (in m)

xₘ=(σ₁ab a/2+πr²(σ₂-σ₁) x) / (σ₁ab a/2+πr²(σ₂-σ₁) x)
yₘ=(σ₁ab a/2+πr²(σ₂-σ₁) y) / (σ₁ab a/2+πr²(σ₂-σ₁) y)
d²=xₘ²+yₘ²
xₘ=(5.94*0.74*0.33*0.74/2 + (pi)*0.064^2*(1.67-5.94)*0.084)/(5.94*0.74*0.33+ (pi)*0.064^2*(1.67-5.94))=0.381260099
yₘ=(5.94*0.74*0.33*0.33/2 + (pi)*0.064^2*(1.67-5.94)*0.084)/(5.94*0.74*0.33+ (pi)*0.064^2*(1.67-5.94))=0.381260099=0.16818904902
d=sqrt(0.381260099^2+0.16818904902^2)=0.41670951429≈0.417 (m)

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