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, $\mathrm { A } = 7900$, and $B = 2500$. Determine the month with the greatest total sales and give the sales in that month.
A) June; $\$ 7900$
B) December; $\$ 10,400$
C) March; $\$ 10,400$
D) September; $\$ 5400$

Question

Quizplus · Accepted Answer

The total sales are maximized when the sine function is at its maximum value, which is 1. The sine function reaches its maximum value when its argument is $\pi/2$, which corresponds to $x = 3$ or March. Plugging these values into the equation gives $S = 7900 + 2500 \cdot 1 = 10400$.

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