Posted by jessica on Saturday, August 13, 2011 at 7:52pm.
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?

math  drwls, Saturday, August 13, 2011 at 10:13pm
(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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