(1) Find the hydrostatic pressure on the side of the vertical shape submerged in water as in the picture below. Assume water density p = 103 kg/m3 and gravitational constant 9 = 9.8 m f .32, use similar triangles to nd the widths of cross-sections at different depths. 6m 4m (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: d6_tse06 6(x/h17)=0. E i 6652 l (4) Find orthogonal trajectories for the family of curves below, parameterized by k: _ 1 y a? + k. (5) Find a formula expressing the n-th term of the sequences below, assuming the patterns you see here continue: 4 8 16 2 (a){ 3! 3 3591 273 } (6) Determine if the sequences below converge, nd limits where applicable: (a) an : mm2 + 1) 1 ln(n2 + 1) (b) an : 3n7n. (b) {5, 8, 11, 14,17, ...}