DHS 13.3 - Option 18. 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)

1.18. D: x = 1, y = 0, y = x, μ = x2 + 2y2 + 10

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

2.18. D: x2 + y2 + 2ax = 0, x2 + y2 + ax = 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.

3.18. V: x = 2√y2 + z2, y2 + z2 = 4, 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.

4.18. V: 2z = x2 + y2, z = 2, Oz