1. Calculate the mass of the D heterogeneous plate, given the limited lines, if the areal density at each point μ = μ (x, y)
1.25. D: x = 0, y = 0, y = 4, x = √25 - y2, μ = x
2. Calculate the static moment of a homogeneous plate the D, limited data lines, with respect to said axis, using polar coordinates.
2.25. D: x2 + y2 + 2ax = 0, x + y ≤ 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.
3.25. V: x = y2 + z2, y2 + z2 = 9, 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.
4.25. V: z = 9 - x2 - y2, z = 0, Oz
Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)
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