Find the center of mass of a thin piate covering the region between the x-axis and the curve The center of mass is (g, 37) = 20 y = 2, 6 S x 510, if the plate's density at a point (x,y) is an} = 2x2. x (Type an ordered pair. Type integers or simplied fractions.) Using the fact that the centroid of a triangle lies at the intersection of the triangle's medians, which is the point that lies one-third of the way from each side toward the opposite vertex, find the centroid of the triangle whose vertices are ( - 1,0), (1,0), and (0,5). . . . The centroid of the triangle is (x,y) , where x = ]and y =]. (Type integers or simplified fractions.)Find the centroid of the thin plate bounded by the graphs of g(x) = x and f(x) = x + 56. Use the equations shown below with 8 = 1 and M = area of the region covered by the plate. X = M 8x[f(x) - g(x)] dx . . . The centroid of the thin plate is (x,y) , where x = and y =]. (Type integers or simplified fractions.)