Please help me with the following questions.

1.

Find the area of the surface generated when the given curve is revolved about the x-axis. y= 1x+7 on [0,1] The area of the generated surface is square units. (Type an exact answer, using it as needed.)Find the center of mass of a thin plate of constant density o covering the region bounded by the parabola y = x and the line y = 10. 5 - . . The center of mass is located at (x, y) =] (Simplify your answer. Type an ordered pair.)Find the center of mass of a thin plate of constant density & covering the given region. The region bounded by the parabola y = x - x and the line y = - x The center of mass is . (Type an ordered pair.)Find the center of mass of a thin plate of constant density & covering the given region. The region bounded by the parabola y = x - x and the line y = - x The center of mass is . (Type an ordered pair.)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 (i! 9) : II: F. ' the x-axis and the curve y :2 cos x, 7 g sxs E- (Type an ordered pair. Round to the nearest hundredth.) 20 )1 ' : Find the center of mass eta thin plate covering the region between the xaxis and the curve y: . The center 0f mass '5 ( ' y) x2 (Type an ordered pair. Type integers or simpiitied fractions.) 6 5x510 if the plate's denSity at a point (xly) is 50:] = 2x2 Find the centroid of the thin plate bounded by the graphs of g(x) = x and f(x) = x + 90. Use the equations shown below with 8 = 1 and M= area of the region covered by the plate. *= |6x[f(x) - g(x)] dx a The centroid of the thin plate is (x,y) , where x = ]and y = . (Type integers or simplified fractions.)It takes 1400 J of work to stretch a spring from its natural length of 1 m to a length of 5 m. Find the force constant of the spring. The spring's force constant is | N/m. (Type an integer or a simplified fraction.)