DHS 13.3 - Option 9. Decisions Ryabushko AP

1. Calculate the mass of the D heterogeneous plate, given the limited lines, if the areal density at each point μ = μ (x, y)

1.9. D: x = 0, y = 2x, x + y = 2, μ = 2 - x - y

2. Calculate the static moment of a homogeneous plate the D, limited data lines, with respect to said axis, using polar coordinates.

2.9. D: x2 + y2 - 2ax ≥ 0, x2 + y2 + 2ay ≤ 0, x ≥ 0, Ox

3. Calculate the coordinates of the center of mass of a homogeneous body, occupying the area of the V, bounded by said surfaces.

3.9. V: 9y = x2 + z2, x2 + z2 = 4, y = 0

4. Calculate the moment of inertia with respect to said homogeneous body axes, occupying the area of the V, the limited data surfaces. body density δ taken equal to 1.

4.9. V: y = 2√x2 + z2, y = 2, Oy