(1) Find the hydrostatic pressure on the side of the vertical shape submerged in water as in the picture below. Assume water density p = 10" kg/m" and gravitational constant g = 9.8 m/s, use similar triangles to find the widths of cross-sections at different depths. 6 m 4 m (2) Find the position of the center of mass of the shape from the previous question, assuming it is a thin plate with constant density. (3) Find the solution of the differential equation satisfying the given initial condition: de t sec 0 at 0( V In 2) = 0. (4) Find orthogonal trajectories for the family of curves below, parameterized by k: 1 y = x + k (5) Find a formula expressing the n-th term of the sequences below, assuming the patterns you see here continue: 4 8 16 (a) -3, 2, - 3' 9' -27 ... (b) {5, 8, 11, 14, 17, .. . }. (6) Determine if the sequences below converge, find limits where applicable: (a) an = In(2n2 + 1) - In(n2 + 1) (b) an = 307-n