Solve the problem.
-The temperature in Fairbanks is approximated by
$$T ( x ) = 37 \sin \left[ \frac { 2 \pi } { 365 } ( x - 101 ) \right] + 25$$
where $T ( x )$ is the temperature on day $x$, with $x = 1$ corresponding to Jan. 1 and $x = 365$ corresponding to Dec. 31 . Estimate the temperature on day 300 .
A) $15 ^ { \circ }$
B) $- 25 ^ { \circ }$
C) $315 ^ { \circ }$
D) $- 10 ^ { \circ }$

Question

Quizplus · Accepted Answer

To estimate the temperature on day 300, substitute $x = 300$ into the given equation: $T(300) = 37 \sin \left[ \frac{2\pi}{365}(300 - 101)\right] + 25$. Simplifying inside the sine function and calculating the sine value, then multiplying by 37 and adding 25, gives a result close to 15 degrees.

Solve the Problem T(x)=37sin⁡[2π365(x−101)]+25T ( x ) = 37 \sin \left[ \frac { 2 \pi } { 365 } ( x - 101 ) \right] + 25T(x)=37sin[3652π​(x−101)]+25

Solve the Problem $T ( x ) = 37 \sin \left[ \frac { 2 \pi } { 365 } ( x - 101 ) \right] + 25$