X, y , and z are three independent and uniformly distributed random variables be- tween zero and one. find the pdf of w = x + y + z. (hint: first find the pdf of v = x + y . the pdf of v should look like an isosceles triangle. then, find the pdf of w = v + z.)

If a particle moves along a path such that r : (3 sin t) m and ? : 2t rad, where t is in seconds. what is the particle's acceleration in m/s in 4 seconds? a)- 16.43 b)- 16.29 c)- 15.21 d)- 13.79

Air is to be cooled in the evaporator section of a refrigerator by passing it over a bank of 0.8-cm-outer-diameter and 0.4-m-long tubes inside which the refrigerant is evaporating at -20°c. air approaches the tube bank in the normal direction at 0°c and 1 atm with a mean velocity of 4 m/s. the tubes are arranged in-line with longitudinal and transverse pitches of sl- st 1.5 cm. there are 30 rows in the flow direction with 15 tubes in each row. determine (a) the refrigeration capacity of this system and (b) pressure drop across the tube bank. evaluate the air properties at an assumed mean temperature of -5°c and 1 atm. is this a good assumption?

10 kg of co2 is initially contained at 400 kpa and 300 k. the gas constant for carbon dioxide is 189 j/lkg k) and has a specific heat ratio, k, of 1.289. isentropic expansion then occurs until the pressure is 200 kpa. a) determine the initial volume of co2 in m. b) determine the final temperature in k. c) determine the work done by the system during the expansion kl.