URGENT HELP PLEASE the temperature of a room during an experiment can be modeled by the function f(x)=23.7 cos (Pi x /60) +18. Where f(x) is the temperature F degrees and x is the number is hours into the experiment. What is the lowest temperature the room reached during the expriement?
I got -5.7 F *
cos reaches -1
the range of cos or sin is from -1 to +1
so
-23.7 + 18 = -5.7 indeed
Thank you Damon!
You are welcome.
To find the lowest temperature that the room reached during the experiment, you need to determine the minimum value of the given function. In this case, the function is f(x) = 23.7 cos (πx/60) + 18, where f(x) represents the temperature in Fahrenheit and x represents the number of hours.
To find the minimum value of the function, you can look at the amplitude of the cosine function. The amplitude gives the maximum and minimum values of the function. In this case, the amplitude is 23.7. Since the cosine function swings between -1 to 1, the lowest temperature will be the amplitude subtracted from the horizontal shift of the function.
The horizontal shift is given by the term "πx/60" inside the cosine function. To find the value of x that gives the minimum temperature, you need to solve the equation πx/60 = π/2, corresponding to the cosine of the minimum value being -1.
πx/60 = π/2
x/60 = 1/2
x = 30
Substituting x = 30 back into the function, we get:
f(30) = 23.7 cos (π(30)/60) + 18
f(30) = 23.7 cos (π/2) + 18
f(30) = 23.7 * (-1) + 18
f(30) = 18 - 23.7
f(30) = -5.7
Therefore, the lowest temperature the room reached during the experiment is -5.7 degrees Fahrenheit.