Question

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) = 12 + 8.5 sin (t-76). a. March 17, the 76th day of the year, is the spring equinox. Find the number of hours of daylight in the city on this day. b. June 17, the 168th 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. c. December 17, the 351st 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. 1. a. The number of hours of daylight in the city on March 17 is about (Round to one decimal place as needed.) . b. The number of hours of daylight in the city on June 17 is about (Round to one decimal place as needed.) C. The number of hours of daylight in the city on December 17 is about (Round to one decimal place as needed.)

Answer 1

The detail solution is provided:
sin)211 365 (t-フ6: Hlt) = 8.S 12 + ta) t= 76 no 21 (76-76) 365 Hlt) =12 2n ご124 &-s Sin 365 * ニ12+55sinD 2 t 0 2 So) Hours わamben of 12 hrs t 168 HCJ 12 +8.5 Sin) 2 (t-76) ニ(2+8-5Sin2T(168-76) S124 85 sin x 42 = 2+8-5 sin0s04 T こ1248-5x1 intoseT)1 20 S 12+9 5

七= 351 HE 12+85sin2(2576)) 315 2 75 こ(248-5 Sin 365 こ12+ 55 sin 「1.507TT Sin (SDAT ニ-ロ-999 +85xCイ) こ12 Z12-85 こ3.5 hrs.