A continuous time system has an output, y, which is given by LaTeX: y(t) = 0.5t3 - 5y(t)=0.5t3−5 It is sampled at a frequency of LaTeX: 1 Hz1Hz . Determine the expression that correctly represents the discrete signal obtained after sampling and its value for n = 2. a. y(n) = 0.5n3 - 5, value at n = 2 is -1b. y(n)=0.5n3−5,valueatn=2is−1 LaTeX: y(n) = 1.7n2 – 0.35, value at n = 2 is -0.7568c. y(n)=1.7n2–0.35,valueatn=2is−0.7568 LaTeX: y(n) =5.6 n2 – 1.3, value at n = 2 is 0d. y(n)=5.6n2–1.3,valueatn=2is0 LaTeX: y(n) =0.5n2 - 7, value at n = 2 is -1

To save energy, the air supply to a 2000 ft office has been shut off overnight and the room temperature has dropped to 40°f. in the morning, the thermostat is reset to 70°f and warm air at 120 f begins to flov in at 200ft'/min. the air is well mixed within the room, and an equal mass flow of air at room temperature (changing with time) is withdrawn through a return duct. the air pressure is nearly 1 atm everywhere. ignoring heat transfer with the surroundings and kinetic and potential energy effects, estimate how long it takes for the room temperature to reach 70°f. plot the room temperature as a function of time.