DHS 13.3 - Option 5. 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)

1.5. D: x = 0, y = 1, y = x, μ = x2 + 2y2

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

2.5. 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.

3.5. V: z = 5 (x2 + y2), x2 + y2 = 2, z = 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.

4.5. V: x2 = y2 + z2, x = 2, Ox