DHS 13.3 - Option 1. 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)

1.1. D: y2 = x, x = 3, μ = x

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

2.1. D: x2 + y2 - 2ay = 0, x - y ≤ 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.

3.1. V: x = 6 (y2 + z2), y2 + z2 = 3, 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.

4.1. V: y2 = x2 + z2, y = 4, Oy