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(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?

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