Mathematics: I need help for this question 3 so can anyone help me please

I need help for this question 3 so can anyone

MichaelG07

03.03.2020

(a)11 hours

(b)19.5 hours

Step-by-step explanation:

The number of hours of daylight, H, on day t of any given year in a particular city can be modeled by the function :

$H(t)=11+8.5\sin\left(\dfrac{2\pi}{365}(t-83)\right)$

(a)When t=83

$H(83)=11+8.5\sin\left(\dfrac{2\pi}{365}(83-83)\right)\\=11+8.5\sin 0\\=11$ hours$

(b)When t=175

$H(175)=11+8.5\sin\left(\dfrac{2\pi}{365}(175-83)\right)\\=11+8.5\sin\left(\dfrac{2\pi}{365}\times 92 \right)\\=11+8.5\\=19.5$ hours$

(b)When t=358

$H(175)=11+8.5\sin\left(\dfrac{2\pi}{365}(358-83)\right)\\=11+8.5\sin\left(\dfrac{2\pi}{365}\times 275 \right)\\=11-8.5\\=2.5$ hours$

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