Say that a variable A in CFG G is necessary if it appears in every derivation of some string w ∈ G. Let NECESSARY CFG = {hG, Ai| A is a necessary variable in G}.
a. Show that NECESSARY CFG is Turing-recognizable.
b. Show that NECESSARY CFG is undecidable.

Liquid flows at steady state at a rate of 2 lb/'s through a pump, which operates to raise the elevation of the liquid 100 ft from control volume inlet to exit. the liquid specific enthalpy at the inlet is 40.09 btu/lb and at the exit is 40.94 btub. the pump requires 3 btu/s of power to operate. if kinetic energy effects are negligible and gravitational acceleration is 32.174 tt/s, the heat transfer rate associated with this steady state process is most closely 1)-2,02 btu/s from the liquid to the surroundings 2)-3.98 btu/s from the surroundings to the liquid. 3)-4.96 btu/s from the surroundings to the liquid. 4)-1.04 btu/s from the liquid to the surroundings.

Aspherical thermocouple measurement errors a spherical thermocouple made of constantin transfer coefficient between the gas and the thermocouple is h used to measure the temperature of a gas. the heat 400 w/m2 k. calculate the maximum diameter d of the thermocouple if the thermocouple's measurement error should be w 23 within 5% of the initial temperature difference in 5 seconds. for constantin, k 8920 kg/m3, and c 410 j/kg. k.

Steam enters a converging nozzle at 3.0 mpa and 500°c with a negligible velocity, and it exits at 1.8 mpa. for a nozzle exit area of 32 cm2, determine the exit velocity, mass flow rate, and exit mach number if the nozzle: is isentropic (a) (b) has an efficiency of 94 percent