The temperature in degree celcius in a factory during the course of a working day from 6am to 10pm can be modelled by the function
H(t)=18+6sin(pit/8-5pi/4)for 6<t <22
_ _
where t is the time in hours in 24Hr clock.
what are the highest and lowest temperatures during the working day.
highest is when sin=1, lowest when sin=-1
Thigh= 18+6
Tlow= 18-6
To find the highest and lowest temperatures during the working day, we need to analyze the function H(t) and determine the maximum and minimum values it can reach.
The function H(t) = 18 + 6sin(pi*t/8 - 5pi/4) represents the temperature in degrees Celsius at a given time t during the working day. This function is defined for t between 6 and 22.
To find the highest temperature, we need to find the maximum value of the function H(t) within the given time interval.
To find the lowest temperature, we need to find the minimum value of the function H(t) within the given time interval.
To find the maximum and minimum values of the function over the interval, we can analyze the behavior of the sin function and its arguments.
The sin function has a maximum value of 1 and a minimum value of -1. The argument of the sin function, pi*t/8 - 5pi/4, can take any value between -5pi/4 and 3pi/4.
The coefficient 6 in front of the sin function determines the amplitude of the oscillations. In this case, it means that the temperature oscillates between 6 degrees Celsius below and above the average temperature of 18 degrees Celsius.
To find the highest and lowest temperatures during the working day, we need to add or subtract the amplitude from the average temperature:
Highest temperature = 18 + 6 = 24 degrees Celsius
Lowest temperature = 18 - 6 = 12 degrees Celsius
Therefore, the highest temperature during the working day is 24 degrees Celsius, and the lowest temperature is 12 degrees Celsius.