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 = ∅

What difference(s) did you notice using a pneumatic circuit over hydraulic circuit.explain why the pneumatic piston stumbles when it hits an obstacle.

Agas mixture consists of 8 kmol of h2 and 2 kmol of n2. determine the mass of each gas and the apparent gas constant of the mixture.

Refrigerant-134a enters the compressor of a refrigerator as superheated vapor at 0.14 mpa and -10°c at a rate of 0.05 ka/s and leaves at 0.8 mpa and 50°c. the refrigerant is cooied in the condenser to 0.72 mpa and 26'c. it is then throttled to 0.15 mpa. sketch the t-s diagram for the system and evaluate: 6) the rate of heat removai from the refrigerated space (kw), it) the power input to the compressor (kw), ii) the isentropic efficiency of the compressor (%), and iv) the cop of the refrigerator.