Problem 25 Medium Difficulty

The city of New Orleans is located at latitude 30 $ ^{\circ} N $. Use Figure 9 to find a function that models the number of hours of daylight at New Orleans as a function of the time of year. To check the accuracy of your model, use the fact that on March 31 the sun rises at 5:51 am and sets at 6:18 pm in
New Orleans.

Answer

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Video Transcript

Okay. First, we're gonna sketch the graph for figures. Nyeon ssi. What can we read from the nine Bill? So, first, the day lasts for 13 hours. A mortuary first. That's but it's given me in the figure nine and the curve, The angle Alpha. It's 60 degree. That's all we're official data and how to how to sketch the curved bill. So it's gonna be a sine function that your magic function and that the period that the function is gonna be 3 65 days, that's the period. So the happened period is gonna be, um it's roughly 1 82 point that base. So that's how periods. So here these things, this link stands for 1 90 to 1 but base. So this half a year, and the empty tube is 614 hours, it's from over figure. And, uh, boys start from day 80 so it should be right here. So this is this is acts. This is why an AC system for days y stands for the hours they like ours. We start from 80. So here is actually was 80 days, and there's a whole length. So now we have the period we have the empty tubes, and we have a face shaped cause. It's shaped up a trip to the white by 80 days and hands. We can get this graph so y equals X equal 614 time sign at the to buy over CAS. The period is 3 65 right now, and, uh, we have the function that she equals to buy over omega. So to make Alberti to be 63 60 fire, we have to let your Omega to be too high over 3 65 That's over. Frequency there and the face shape this 80 days and plus trail right there because we start from cell overs. So this is our Wyatt exit. This is actually acts excess. And here this is actually on these perverts. Actually, um, wife was felt five hours, so that's over ordinance. And this is over Final function for this crap. Okay,