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Numerade Educator

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Problem 82 Hard Difficulty

In Example 1.3.4 we arrived at a model for the length of daylight (in hours) in Philadelphia on the $ t $ th day of the year:
$ L(t) = 12 + 2.8 \sin [ \frac {2 \pi}{365}(t - 80] $
Use this model to compare how the number of hours of daylight is increasing in Philadelphia on March 21 and May 21.

Answer

$80 < t < 171.25$

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Video Transcript

So here we take it ho. The number of hours of daylight is increasing. So? So how much is increasing? We can take the derivative, and this one should be two point eight times to pie over his three sixty five co sign to pie over three sixty five T minus eighty. They just have to ah, clubbing those t value. So So for march twenty first, t should be generally has just thirty one days. February, assuming it's not a special years is twenty eight days and made twenty one. You have thirty one clause twenty, eh? Post large and April there are thirty days. So you just pulling these two t value kes into the original equation and you can use culturally threatened simplify that.