during a certain time of year, the daily temperature in a certain city, in degrees fahrenheit follows a…
during a certain time of year, the daily temperature in a certain city, in degrees fahrenheit follows a periodic pattern. the graph below shows the temperature over two days, where time t is measured in hours after 12:00 a.m. (midnight) on the first day. what is the midline and what does it represent in this context?
Answer
Explanation:
Step1: Identify maximum and minimum
The maximum temperature is 69°F (at (t = 13.5) and (t=37.5)) and the minimum temperature is 48°F (at (t = 1.5) and (t = 25.5)).
Step2: Calculate the mid - line
The formula for the mid - line of a periodic function (y = A\sin(Bx - C)+D) (or for a temperature - time graph) is (D=\frac{y_{max}+y_{min}}{2}). So, (D=\frac{69 + 48}{2}=\frac{117}{2}=58.5).
Step3: Interpret the mid - line
In the context of temperature, the mid - line represents the average or baseline temperature around which the daily temperature fluctuates.
Answer:
The mid - line is 58.5°F. It represents the average or baseline temperature around which the daily temperature in the city fluctuates.