For a function f, we know that the derivatives f^n(0) are non-zero only when n-1 is a multiple of 4. using richardson's extrapolation, find a formula for f'(0) adapted for this function with an error of at most o(h^10)

Refrigerant 134a enters an insulated compressor operating at steady state as saturated vapor at -26°c with a volumetric flow rate of 0.18 m3/s. refrigerant exits at 9 bar, 70°c. changes in kinetic and potential energy from inlet to exit can be ignored. determine the volumetric flow rate at the exit, in m3/s, and the compressor power, in kw.

For a gate width of 2 m into the paper, determine the force required to hold the gate abc at its location.

Atank with constant volume contains 2.27 kg of a mixture of water phases (liquid-vapor). in the initial state the temperature and the quality are 127 °c and 0.6, respectively. the mixture is heated until the temperature of 160 oc is reached. illustrate the process in a t-v diagram. then, determine (1) the mass of the vapor in kg at the initial state, (2) the final pressure in kpa.