In class we did different cases of Quicksort algorithm for various splits of the input data based on a choice of the pivot. For this problem we are going to assume that a pivot is selected such that data is partitioned in the ratio of 2 to 1 every time. The partition routine would remain the same as used in class and so would the number of comparisons in it. Answer the following questions:

(a) Write the recurrence equation, and the base case.
(b) What is the height of the recursion tree?
(c) Solve the recurrence equation using an appropriate method. Justify your method
(d) Verify the base case.

True or false (explain) (110)[111] is a slip system in bcc metals . the {111} family in fcc contains 8 planes. resolved shear stress (rss) in single crystals is just related to the applied stress. critical resolved shear stress (crss) in single crystal metals is direct proportional to the number of defects in the structure

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.

Acommercial grade cubical freezer, 4 m on a side, has a composite wall consisting of an exterior sheet of 5.0-mm thick plain carbon steel (kst= 60.5 w/m k), an intermediate layer of 100-mm thick polyurethane insulation (kins 0.02 w/m k), and an inner sheet of 5.0- mm thick aluminium alloy (kal polyurethane insulation and both metallic sheets are each characterized by a thermal contact resistance of r 2.5 x 104 m2 k/w. (a) what is the steady-state cooling load that must be maintained by the refrigerator under conditions for which the outer and inner surface temperatures are 25°c and -5°c, respectively? (b) for power saving purpose, which wall material should be increased/reduced in. thickness in order to reduce 50% of the cooling load found in part (a)? redesign the thickness of the proposed material. 177 w/m-k). adhesive interfaces between the q=575.93 w