a metallic rod was heated to 300¡ãc and left for cooling. after every 2 menute it becomes colder by 15¡ãc. what will be the temperature of the rod after half an hour?
after t minutes, the temperature T will be
T(t) = 300 - 15(t/2)
Confused
To find the temperature of the rod after half an hour, we need to calculate the number of 2-minute intervals in 30 minutes.
Since there are 60 minutes in an hour, half an hour would be 30 minutes.
So, the number of 2-minute intervals in 30 minutes can be calculated as follows:
Number of 2-minute intervals = 30 minutes / 2 minutes per interval = 15 intervals
Now, we know that after every 2-minute interval, the temperature decreases by 15°C. Therefore, we can multiply the number of intervals by the decrease in temperature to find the total decrease in temperature:
Total decrease in temperature = 15 intervals * 15°C per interval = 225°C
Finally, to find the temperature of the rod after half an hour, we subtract the total decrease in temperature from the initial temperature of 300°C:
Temperature after half an hour = 300°C - 225°C = 75°C
Therefore, the temperature of the rod after half an hour would be 75°C.
To find the temperature of the rod after half an hour, we need to determine how many 2-minute intervals there are in half an hour and calculate the reduction in temperature during that time.
First, we need to convert half an hour into minutes:
30 minutes × 1 minute/1 minute = 30 minutes
Next, we need to find the number of 2-minute intervals in 30 minutes:
30 minutes ÷ 2 minutes = 15 intervals
Now, we can calculate the reduction in temperature during 15 intervals:
15 intervals × 15°C reduction per interval = 225°C reduction
Since the rod was initially heated to 300°C, we need to subtract the reduction from the initial temperature:
300°C - 225°C = 75°C
Therefore, the temperature of the rod after half an hour of cooling will be 75°C.