Solve the problem.
-The total sales in dollars of some small businesses fluctuates according to the equation $S = A + B \sin \frac { \pi } { 6 } x$, where $x$ is the time in months, with $x = 1$ corresponding to January, $A = 8400$, and $B = 4300$. Determine the month with the greatest total sales and give the sales in that month.
A) March; \$12,700
B) June; $\$ 8400$
C) September; $\$ 4100$
D) December; $\$ 12,700$

Question

Quizplus · Accepted Answer

The greatest total sales occur when the sine function reaches its maximum value, which is 1. The sine function reaches its maximum value at $x = 6$, corresponding to June, because $\sin \frac{\pi}{6} \times 6 = \sin \pi = 0$. However, the question seems to have a mistake in interpreting the sine function's behavior. Correctly, the sine function reaches its maximum at $x = 3$ and $x = 15$, corresponding to March and September, given the period of the sine function in the equation. But since September is not an option with the highest sales, and considering the typical interpretation of the sine function's peak in a yearly cycle, March would be the correct answer if we're looking for the first peak within a year. The sales in that month would be $S = 8400 + 4300 \sin \frac{\pi}{6} \times 3 = 8400 + 4300 \times 1 = 12700$. However, the interpretation provided in the options seems to misalign with the standard behavior of the sine function, suggesting a possible error in the question or options provided.

Solve the Problem S=A+Bsin⁡π6xS = A + B \sin \frac { \pi } { 6 } xS=A+Bsin6π​x

Solve the Problem $S = A + B \sin \frac { \pi } { 6 } x$