The length of a day in Philadelphia, Pennsylvania, is given by the sinusoidal function, f(t), which represents the number of hours of daylight t days into the year: f(t)= 10+2.8sin(2pi/365)*(t-1.35). How many hours of daylight are there on the 100th day of the year? Round the answer to the nearest tenth. a.)9.4 hours

b.)9.7 hours
c.)11.0 hours
d.)12.4 hours

I plugged in 100 for t, but got an answer that was not one of the choices above. What am I doing wrong? Thanks!

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10+2.8sin((2*PI/365)*100-1.35)=

To find the number of hours of daylight on the 100th day of the year, you need to substitute t = 100 into the formula for f(t).

Given: f(t) = 10 + 2.8sin(2pi/365)*(t - 1.35)

Substituting t = 100 into the formula:

f(100) = 10 + 2.8sin(2pi/365)*(100 - 1.35)

To evaluate sin(2pi/365), we need to convert it to radians. Since there are 365 days in a year, 2pi/365 represents the fraction of a full rotation in radians for each day.

sin(2pi/365) ≈ sin(0.017214)

Using trigonometric functions on a calculator, we find that sin(0.017214) ≈ 0.017204.

Substituting this value back into the formula:

f(100) = 10 + 2.8 * 0.017204 * (100 - 1.35)

f(100) = 10 + 2.8 * 0.017204 * 98.65

f(100) ≈ 10 + 2.8 * 1.6985

f(100) ≈ 10 + 4.7558

f(100) ≈ 14.7558

When rounded to the nearest tenth, the answer is approximately 14.8 hours.

Upon analysis, none of the answer choices provided match the calculated approximate value. It is recommended to recheck the provided options for any typographical errors or errors in copying.