The desert temperature, H, oscillates daily between 36°F at 4 am and 56°F at 4 pm. Write a possible formula for H in terms of t, measured in hours from 4 am.
I thought the answer is -10cos(1/6pi times t) +46
but it got marked wrong.
I thought that the amplitude is 10 because 56-36 divided by 2 is 10.
I got the 46 by doing 56+36 divided by 2.
I got the 1/6pi times t by doing 2pi/12.
Your period is not correct
If the temp is 36° at 4:00am and 56° at 4:00pm
you only have 1/2 a period. Doesn't the temperature have to come back down at 4:00am
so you should have 2π/24 or π/12
so try:
Temp = -10 cos (πt/24) + 46
thank you!!!!
I did mess up the period. I didn't think about it that way. Thank you so much!
Well, it seems like you were on the right track, but just took a little detour. Let's do a little clown math to figure it out:
First, let's find the period of the temperature oscillation. The temperature goes from 36°F to 56°F in 12 hours (from 4 am to 4 pm), so the period is 12 hours.
Now, the formula for the temperature oscillation should be of the form:
H = A*cos(B*t) + C
where A is the amplitude, B is the frequency (angular velocity), and C is the average temperature.
You correctly determined the amplitude, which is 10°F. Good job!
But, the angular velocity should be calculated as 2*pi divided by the period, which gives us:
B = 2*pi/12 = pi/6
So, the correct formula for H in terms of t should be:
H = -10*cos((pi/6)*t) + 46
Keep in mind that this formula assumes that t=0 at 4 am. Now, let's hope it doesn't make any more mistakes, or we might have to send the math police after it!
To write a possible formula for H in terms of t, let's break down the steps:
1. Determine the period: The temperature oscillates between 36°F and 56°F in a 12-hour period. So, the period is 12 hours.
2. Find the midline: The midline represents the average temperature between the maximum and minimum values. In this case, the midline is (36°F + 56°F) / 2 = 46°F.
3. Determine the amplitude: The amplitude is half the difference between the maximum and minimum values. In this case, it is (56°F - 36°F) / 2 = 10°F.
4. Convert the period to radians: Since the cosine function typically uses radians, we need to convert the period of 12 hours to radians. The conversion factor is 2π radians per one period, so the angle in radians is 2π / 12 = π / 6.
Putting it all together, a possible formula for H in terms of t measured in hours from 4 am is:
H = -10cos((π/6)t) + 46.
It seems like your answer is indeed correct. If it was marked wrong, there might be a mistake in the way the answer was entered or a misunderstanding of the question's requirements. Double-check the instructions and ensure that you correctly inputted the formula.