8. A room is initially at the outdoor temperature of 25°C. Now a large fan that consumes 200 W of electricity when running is turned on. The heat transfer rate between the room and the outdoor air is given as QUA(T-To) where U= 6 W/m2 °C is the overall heat transfer coefficient, A= 30 m² is the exposed surface area of the room, and T, and To are the indoor and outdoor air temperatures, respectively. Determine the indoor air temperature when steady operating conditions are established.

Iron is mixed with an acid in an insulated container. The temperature, T°C, above room temperature, at time t minutes after the metal is added to the acid is given by: a) b) T = 64tet Calculate the rate of change of the temperature 5 minutes after the metal is added. When t = 5 minutes then °C/min. Give your answer to two decimal places, if needed. Calculate the maximum temperature of the mixture. The maximum temperature of the mixture is Give your answer to two decimal places, if needed. °C above room temperature.

2) The rate of change of an electrical current, i, in a microprocessor circuit is given by di 0.4t 0.06t2 HA/s. Find the expression for i in terms of t if i=2µA when t=0s. %3D dt

Suppose a tank…

At 7 pm on a Wednesday evening. Mr Huxley's water tank was full. The capacity of the tank was 3 000 litres. Unfortunately, the tap on the tank was leaking in such a way that the change in volume at any time (r) hours was proportional to the volume (V) of the tank. This means that AP =-kV . dt Show that V= Ve is a solution of this equation. Given that the volume of the tank after 3 hours is 1900 litres, show that k = 0.1523 correct to 4 decimal places. (iii) By the time Mr Huxley discovered that the tank was leaking, there were only 250 litres of water remaining. At what time and on which day did Mr Huxley discover the leak (Answer correct to the nearest minute)?

Let C(t) be the daily cost in dollars per day to cool a house when the average outside temperature is t degrees Fahrenheit. What are the units of C'(95)?