We say an edge e is "necessary" for the Minimum Spanning Tree T(G, E) if when we delete it, the weight of the MST increases. So we have that W(T(V, E \ {e})) > W(T(V, E))). Show that an edge e is necessary iff for every cycle C in G that contains it, e is not the maximum weight edge in this cycle (so there exists e 0 ∈ C such that we 0 > we)

Acertain flow of air (at stp) has a velocity distribution given by v i (in ft/s). if this flow is going through a 4 ft square area in the yz-plane (centered at the origin), what is the mass flow rate (in lbm/s)?

Air flows over a heated plate àt a velocity of 50m/s. the local skin factor coefficient at a point on a plate is 0.004. estimate the local heat transfer coefficient at this point.the following property data for air are given: density = 0.88kg/m3 , viscosity 2.286 x 10 ^-5 kgm/s , k = 0.035w/mk ,cp = 1.001kj/kgk. use colburn reynolds analogy.

Ahelical coil spring has a mean diameter of 50 mm, a wire diameter of 5.5 mm and is wound with a pitch of 10 mm. the spring steel has an ultimate strength of 1250 mpa. find the force needed to compress the spring solid and the wire stress in this condition. state whether the spring will return to its initial length.