DHS 13.3 - Option 6. 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)

1.6. D: x2 + y2 = 1, 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.

2.6. D: x2 + y2 - 2ay ≥ 0, x2 + y2 + 2ax ≤ 0, y ≥ 0, Oy

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

3.6. V: x = 6√y2 + z2, y2 + z2 = 9, x = 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.

4.6. V: y = x2 + z2, y = 2, Oy