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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)

1.23. D: y = x2 + 1, x + y = 3, μ = 4x + 5y + 2

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

2.23. D: x2 + y2 + 2ax = 0, y - x ≥ 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.

3.23. V: y2 + z2 = 3x, x = 9

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.

4.23. V: y = 4 - x2 - z2, y = 0, Oy
Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)
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