Let G be an arbitrary flow network, with a source s, a sink t, and a positive integer capacity ce on every edge e; and let (A, B) be a mimimum s-t cut with respect to these capacities {ce : e ∈ E}. Now suppose we add 1 to every capacity; then (A, B) is still a minimum s-t cut with respect to these new capacities {1+ce :e∈E}.

Ariver flows from north to south at 8 km/h. a boat is to cross this river from west to east at a speed of 20 km/h (speed of the boat with respect to the earth/ground). at what angle (in degrees) must the boat be pointed upstream such that it will proceed directly across the river (hint: find the speed of the boat with respect to water/river)? a 288 b. 21.8 c. 326 d. 30.2

Air is compressed isentropically from an initial state of 300 k and 101 kpa to a final temperature of 1000 k. determine the final pressure using the following approaches: (a) approximate analysis (using properties at the average temperature) (b) exact analysis

The characteristic roots of a dynamic system are: 1.7920 1.8160 i, -1.7920 1.8160 i, -0.4160 what is the order of this system? what are the settling time and damping ratio of the system?