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

1.12. D: y = x2, x = y2, μ = 3x + 2y + 6

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

2.12. 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.

3.12. V: 8x = √y2 + z2, x = 1/2

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.

4.12. V: x = y2 + z2, y2 + z2 = 1, x = 0, Ox
Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)
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