Question

the temperature of a 10m long metal bar is 15 degrees celcius at one end and 30 degrees celcius on the other end. Assuming that the temperature increases linearly from the cooler end to the hotter end, what is the average temperature of the bar? Also, explain why at least one place on the bar must hae this temperature.

Answer 1

The average temperature of the bar can be calculated by finding the mean of the two given temperatures.

(15°C + 30°C) / 2 = 45°C / 2 = 22.5°C

So, the average temperature of the bar is 22.5°C.

At least one place on the bar must have this temperature because of the Intermediate Value Theorem, which states that if a continuous function takes on two values a and b at two distinct points, then it must take on any value between a and b at least once. In this case, the temperature function increases linearly from 15°C to 30°C, so it must take on any intermediate value, including the average temperature of 22.5°C, at least once along the length of the bar.