The first sunrise in the United States each day is observed from Cadillac Mountain on Mount Desert Island in Maine. The time of the sunrise can be modeled by t(m) = 1.665 sin pi/6 (m + 3) + 5.485, where t is hours after midnight and m is the number of months after January 1. When does the sunrise at 6:00 A.M.?

a.
November 9 and February 13
c.
December 9 and January 13
b.
October 9 and March 13
d.
December 9 and February 13

Question

The first sunrise in the United States each day is observed from Cadillac Mountain on Mount Desert Island in Maine.  The time of the sunrise can be modeled by t(m) = 1.665 sin pi/6 (m + 3) + 5.485, where t is hours after midnight and m is the number of months after January 1.  When does the sunrise at 6:00 A.M.?

a.
November 9 and February 13
c.
December 9 and January 13
b.
October 9 and March 13
d.
December 9 and February 13

Vocaloid · Answer

the function gives you the sunrise time in terms of months m

so for a 6:00 AM sunrise, this is 6 hours after midnight, so t(m) = 6. plug in and evaluate the two m-values. from there, you can determine what day it would be based on the decimal part of each month. (for example, if you get something like 1.5 that's the first month (January) + 0.5 of a month (so it would be about the 15th or 16th).