Let us say that a graph G = (V, E) is a near-tree if it is connected and has at most n + 8 edges, where n = |V|. Give an algorithm with running time O(n) that takes a near-tree G with costs onits edges and returns a minimum spanning tree of G. You may assume that all of the edge costsare distinct.

Air enters a horizontal, constant-diameter heating duct operating at steady state at 290 k, 1 bar, with a volumetric flow rate of 0.25 m°/s, and exits at 325 k, 0.95 bar. the flow area is 0.04 m2. assuming the ideal gas model with k = 1.4 for the air, determine (a) the velocity at the inlet and exit, each in m/s, and (c) the rate of heat transfer, in kw flow rate, in kg/s, (b) the mass kg 0.3

An air-conditioning system consists of a heating section and an evaporative cooler. air enters the heating section at 10°c and 70 percent relative humidity at a rate of 30m^3/min, and it leaves the evaporative cooler at 20°c and 60 percent relatively humidity. if the air conditioning system operates at a total pressure of 98 kpa, determine (a) the temperature and relative humidity of the air when it leaves the heating section, (b) the rate of heat transfer in the heating section, and (c) the rate of water added to air in the evaporative cooler

Agas contained in a piston-oylinder assembly is initially at p1=100 ibf/ft^2? and occupies a volume of 3.75 ft. the gas is compressed to a pressure p2=500 ibf/ft^2 and a final volume of 0.5 ft. during the process, the relationship between pressure and volume is given as p= a +bv, where a and b are constants a)-determine the values and units for a and b b)-determine the volume, in ft, at an intermediate state where the pressure is 300 ibt/t2.