math

In Philadelphia the number of hours of daylight on day t (where t is the number of days after Jan. 1) is modeled by the function
L(t)= 12+2.83sin(2pi/365(t-365))

A) Which days of the year have about 10 hours of daylight?
B) Which days of the year have more than 10 hours of daylight?

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  1. (A) Solve
    10 = 12 + 2.83 sin[(2*pi/365*(t-365)]

    -2 = 2.83 sin[(2*pi*/365)(t-365)]
    -0.7067 = sin[(2*pi*/365)(t-365)]
    sin[(2*pi*/365)(t-365)] = -0.7848
    Solve for t.

    [(2*pi*/365)(t-365)] = -0.90244
    Use the first value

    t-365 = -52
    t = 313 days
    Oct 1 is day 303. So Oct 11 is one answer. The other day will be 52 days after the winter solstice, or about Feb 11.

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