Find the maximum of f (x, y) = 4x + 2y + x2 − 2x4 + 2xy − 3y2 using the steepest ascent method with initial guess x = 0 and y = 0. (a) (5 points) find the gradient vector and hessian matrix for the function f (x, y). (b) (5 points) find the direction of steepest ascent at (0,0). the direction found in this step will be our search direction in the next iteration. (c) (10 points) find the point that maximizes the function f along the search direction. 2.

Amass of m 1.5 kg of steam is contained in a closed rigid container. initially the pressure and temperature of the steam are: p 1.5 mpa and t 240°c (superheated state), respectively. then the temperature drops to t2= 100°c as the result of heat transfer to the surroundings. determine: a) quality of the steam at the end of the process, b) heat transfer with the surroundings. for: p1.5 mpa and t 240°c: enthalpy of superheated vapour is 2900 kj/kg, specific volume of superheated vapour is 0. 1483 m/kg, while for t 100°c: enthalpy of saturated liquid water is 419kj/kg, specific volume of saturated liquid water is 0.001043m/kg, enthalpy of saturated vapour is 2676 kj/kg, specific volume of saturated vapour is 1.672 m/kg and pressure is 0.1 mpa.

The y form of iron is known as: a) ferrite b) cementite c) perlite d) austenite

A-mn has a cubic structure with a0 0.8931 nm and a density of 7.47 g/cm3. b-mn has a different cubic structure, with a0 0.6326 nm and a density of 7.26 g/cm3. the atomic weight of manganese is 54.938 g/mol and the atomic radius is 0.112 nm. determine the percent volume change that would occur if a-mn transforms to b-mn.