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vodka [1.7K]
2 years ago
6

Please help as soon as possible this is for my FINAL EXAM! , this is easy but I forgot how to do it. Thanks

Mathematics
1 answer:
marysya [2.9K]2 years ago
7 0

I'm going to refer to the length of the pool as L.

2x + 2L = perimeter.

The width of pool multiplied by two added to the length of the pool multiplied by two equals to the perimeter.

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Answer:

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the moment of inertia of the lamina about one corner I_{corner} is:

I_{corner} = \int\limits \int\limits_R (x^2+y^2)  \rho d A \\ \\ I_{corner} = \int\limits^a_0\int\limits^b_0 \rho(x^2+y^2) dy dx

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I_{corner} =  \rho \int\limits^a_0 {x^2y}+ \frac{y^3}{3} |^ {^ b}_{_0} \, dx

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Thus; the moment of inertia of the lamina about one corner is I_{corner} =\frac{\rho _{ab}}{3}(a^2+b^2)

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