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(t365))
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 answer

(A) Solve
10 = 12 + 2.83 sin[(2*pi/365*(t365)]
2 = 2.83 sin[(2*pi*/365)(t365)]
0.7067 = sin[(2*pi*/365)(t365)]
sin[(2*pi*/365)(t365)] = 0.7848
Solve for t.
[(2*pi*/365)(t365)] = 0.90244
Use the first value
t365 = 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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answered by drwls
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