Please help me with the following questions. Please show each steps.

1.

Find the center of the mass of a thin plate of constant density 5 covering the region bounded by The center of the mass is located at ()1, it) = n 1': (Type an ordered pair. Round to the nearest hundredth.) the xiaxis and the curve y=2 cos x, sxs g. _ _ 20 - ' ' Find the center of mass of a thin plate covering the region between the XaXiS and the curve y = 7: The center 0f mass I? (X' y). 7 ' x2 (Type an ordered pair. Type integers 0r simpiified fractions ) 6 s x510 ifthe plate's denSIty at a point (in!) IS 6(x) 22x2. Find the centroid of the thin plate bounded by the graphs of g(x) = x" and f(x) = - x + 2. Use the equations shown below with 8 = 1 and M = area of the region covered by the plate. b X = 8x[f(x) - g(x)] dx a The centroid of the thin plate is (x,y) , where x = _]and y = . (Type integers or simplified fractions.)