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Hi everyone,
I need help with these two calculus problems and was wondering if anyone had any ideas. Thanks!
A thin, constant density plate covers the region in the xy-plane bounded
by the ellipse (x/a)2 + (y/b)2 = 1 (where a, b > 0). Find the polar moment of
inertia of the plate about the origin.
an incompressible fluid onto the
xy-plane at the origin. At all times he pours at a constant rate and tries to keep
the fluid level constant. Moreover, the fluid flows radially outward from the ori-
gin. (i) Write down a two-dimensional vector field that would model the rate and
direction at which fluid passes any point. (ii) Compute the divergence of this vec-
tor field. (iii) Use Greens theorem to explain why the flux leaving any region
that does not contain the origin must vanish. (iv) Is the same true for regions
containing the origin? Explain.
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