The average daily high temperature in Madrid peaks at 92 times degree F in the summer and drops as low as 33 times degree F in the winter. The temperature can be modeled by cap t times d is equal to 29 point 5 cosine open paren 2 pi over 365 times open paren d minus 204 close paren close paren plus 62 point 5 , where d represents the day number of the year (January 1 is 1, January 2 is 2, and so on). During which day is the high temperature expected to be closest to 75 times degree F ?
Set the model equal to 75°F: 29.5 cos((2π/365)(d − 204)) + 62.5 = 75, so the cosine must be about 12.5/29.5 = 0.424. This occurs about 66 days before or after day 204, giving days near 138 and 270. Of the choices, day 270 is closest to 75°F; it is choice B.
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