Question

The number of hours of daylight, H, on day t of any given year (on January 1, t = 1) in Fairbanks, Alaska, can be modeled by the function
H(t)=12+8.3sin[2π365(t−80)]
June 21, the 172nd day of the year, is the summer solstice, the day with the maximum number of hours of daylight. To the nearest tenth of an hour, find the number of hours of daylight in Fairbanks on this day.

Answer 1

Answer:

The number of hours of daylight in Fairbanks on this day is 20.3

Step-by-step explanation:

The number of hours of sun in the day t is given by the following function:

$H(t) = 12 + 8.3\sin{\frac{2\pi}{365}*(t - 80)}$

Obs: (t-80) is part of the sin

June 21, the 172nd day of the year, is the summer solstice, the day with the maximum number of hours of daylight. To the nearest tenth of an hour, find the number of hours of daylight in Fairbanks on this day.

The number of hours is:

$H(172)$

$H(t) = 12 + 8.3\sin{2\pi*365(t - 80)}$

$H(172) = 12 + 8.3\sin{\frac{2\pi}{365}*(172 - 80)} = 20.3$

The number of hours of daylight in Fairbanks on this day is 20.3