the number of hours of daylight, h, on day t of any given year (on january 1, t = 1) in a particular city…

the number of hours of daylight, h, on day t of any given year (on january 1, t = 1) in a particular city can be modeled by the function h(t)=13 + 8.7 sin \\frac{2\\pi}{365}(t - 85).\na. march 26, the 85th day of the year, is the spring equinox. find the number of hours of daylight in the city on this day.\nb. june 26, the 177th day of the year, is the summer solstice, the day with the maximum number of hours of daylight. find the number of hours of daylight in the city on this day.\nc. december 26, the 360th day of the year, is the winter solstice, the day with the minimum number of hours of daylight. find the number of hours of daylight in the city on this day.\na. the number of hours of daylight in the city on march 26 is about 13.\n(round to one decimal place as needed.)\nb. the number of hours of daylight in the city on june 26 is about \\square.\n(round to one decimal place as needed.)

the number of hours of daylight, h, on day t of any given year (on january 1, t = 1) in a particular city can be modeled by the function h(t)=13 + 8.7 sin \\frac{2\\pi}{365}(t - 85).\na. march 26, the 85th day of the year, is the spring equinox. find the number of hours of daylight in the city on this day.\nb. june 26, the 177th day of the year, is the summer solstice, the day with the maximum number of hours of daylight. find the number of hours of daylight in the city on this day.\nc. december 26, the 360th day of the year, is the winter solstice, the day with the minimum number of hours of daylight. find the number of hours of daylight in the city on this day.\na. the number of hours of daylight in the city on march 26 is about 13.\n(round to one decimal place as needed.)\nb. the number of hours of daylight in the city on june 26 is about \\square.\n(round to one decimal place as needed.)

Answer

Explanation:

Step1: Substitute (t = 177) into the function

Given (H(t)=13 + 8.7\sin\left[\frac{2\pi}{365}(t - 85)\right]), when (t = 177), we first calculate (\frac{2\pi}{365}(177 - 85)). (\frac{2\pi}{365}(177 - 85)=\frac{2\pi}{365}\times92=\frac{184\pi}{365}\approx1.59) (in radians)

Step2: Calculate the sine value and then (H(t))

We know that (\sin(1.59)\approx1) (since (\sin\left(\frac{\pi}{2}\right) = 1) and (1.59\approx\frac{\pi}{2}\approx1.57)). Then (H(177)=13 + 8.7\times\sin(1.59)) Substitute (\sin(1.59)\approx1) into the formula: (H(177)=13 + 8.7\times1)

Answer:

(21.7)