Solve the problem.
-The total sales in dollars of some small businesses fluctuates according to the equation $\mathrm { S } = \mathrm { A } + \mathrm { B } \sin \pi \mathrm { x } / 6$, where $\mathrm { x }$ is the time in months, with $\mathrm { x } = 1$ corresponding to January, $\mathrm { A } = 5900$, and $B = 2700$. Determine the month with the greatest total sales and give the sales in that month.
A) June; $\$ 5900$
B) December; $\$ 8600$
C) March; $\$ 8600$
D) September; $\$ 3200$

Question

Quizplus · Accepted Answer

The total sales are maximized when the sine function is at its maximum, which is 1. The sine function reaches its maximum value when $\pi x / 6 = \pi / 2$, which corresponds to $x = 3$ or March. Plugging these values into the equation gives $S = 5900 + 2700 \times 1 = 8600$.

Solve the Problem S=A+Bsin⁡πx/6\mathrm { S } = \mathrm { A } + \mathrm { B } \sin \pi \mathrm { x } / 6S=A+Bsinπx/6

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