Solve the problem.
-The temperature in Verlander is modeled by $\mathrm { T } ( \mathrm { x } ) = 41 \sin \left[ \frac { 2 \pi } { 365 } ( \mathrm { x } - 102 ) \right] + 44$ where $\mathrm { T } ( \mathrm { x } )$ is the temperature in degrees Fahrenheit on day $x$, with $x = 1$ representing January 1 and $x = 365$ representing December 31 . Find the temperature on July 7 .
A) $105 ^ { \circ } \mathrm { F }$
B) $85 ^ { \circ } \mathrm { F }$
C) $78 ^ { \circ } \mathrm { F }$
D) $3 ^ { \circ } \mathrm { F }$

Question

Quizplus · Accepted Answer

To find the temperature on July 7, we first determine the day number $x$ for July 7. Since each month before July (January through June) has 31, 28, 31, 30, 31, and 30 days respectively, the total number of days before July is $31 + 28 + 31 + 30 + 31 + 30 = 181$. Thus, July 7 is the 187th day of the year ($181 + 6$). Plugging $x = 187$ into the given equation: $T(187) = 41 \sin\left[\frac{2\pi}{365}(187 - 102)\right] + 44$, we calculate the temperature. This calculation results in a temperature close to $85^\circ F$, making option B correct.

Solve the Problem T(x)=41sin⁡[2π365(x−102)]+44\mathrm { T } ( \mathrm { x } ) = 41 \sin \left[ \frac { 2 \pi } { 365 } ( \mathrm { x } - 102 ) \right] + 44T(x)=41sin[3652π​(x−102)]+44

Solve the Problem $\mathrm { T } ( \mathrm { x } ) = 41 \sin \left[ \frac { 2 \pi } { 365 } ( \mathrm { x } - 102 ) \right] + 44$