Given the following phasors and the information related to the frequency of that phasor, provide the corresponding time-domain representation. (It is somewhat hard to tell the difference, but the terms on the left are the symbols for the phasor, e. g., V, while the terms in the interior provide the units, e. g., V is volts.) (a) V = 7e jπ/6 V, ω = 100 rad/s (b) V = √ 2e −j0.25 V, f = 100 Hz (c) V = 42 π/6 V, T = 10−6 s (d) I = 17 45◦ A, ω = 2π2 × 103 rad/s (e) I = 7 −π/2 A, f = 0.5 Hz

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 the air is well mixed within the room, and an equal mass flow of air at room temperature (changing with time) is withdrawn through a return duct.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.