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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)

1.13. D: y = x2, y = 4, μ = 2x + 5y + 10

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

2.13. D: x2 + y2 + 2ay = 0, x2 + y2 + ay = 0, x ≤ 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.

3.13. V: 2x = 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.

4.13. V: z2 = x2 + y2, z = 3, Oz
Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)
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