Given an instance (s, k) of the subset-sum problem, where s is a set of integers and k is another integer, we transform it into an instance s’ = s ∪ { x, y } of the partition problem, where x = sum(s) + k, y = 2sum(s) – k, and sum(s) = σx∈s x. prove that s’ can be constructed from s in polynomial time and there exists a subset x ⊆ s’ such that sum(x) = k iff s’ can be partitioned into x and y such that sum(x) = sum(y), where s’ = x∪y and x∩y = ∅

The force on a cutting tool are 2600n vertically downward and 2100 horizontal. determine the resultant force acting on the tool and the angle at which it acts.

Adouble-strand no. 60 roller chain is used to transmit power between a 13-tooth driving sprocket rotating at 300 rev/min and a 52-tooth driven sprocket. a) what is the allowable horsepower of this drive? b) estimate the center-to-center distance if the chain length is 82 pitches. c) estimate the torque and bending force on the driving shaft by the chain if the actual horsepower transmitted is 30 percent less than the corrected (allowable) power.

Thermal stresses are developed in a metal when its a) initial temperature is changed b) final temperature is changed c) density is changed d) thermal deformation is prevented e) expansion is prevented f) contraction is prevented