Alculate the moment of inertia for the following cases. (a) A piece of thin uniform wire of mass 3m and length 3b is bent into an equilateral triangle. Find the moment of inertia of the wire triangle about an axis perpendicular to the plane of the triangle and passing through one of its vertices. (You do not need to simplify the expression.)

Consider a one meter long horizontal pipe with a constant 100 cm^2 cross sectional area. water flows rightward into the pipe at x = 0 with flow velocity 02m/sec at every point within the pipe intake area. at x=1, the rightward flow rate is 0.192 m/sec. assume the water is a conserved quantity in the pipe, so there must be a leak (a sink) somewhere in the pipe. 1. compute net volumetric flow of the source if the system to be in equilibrium. 2. now assume the pipe in the problem has no leaks. compute the net volumetric rate of change for the system.