The function graphed is of the form y $$y = a \sin b x \text { or } y = a \cos b x , \text { where } b 0$$ Determine the equation of the graph.
-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, $\mathrm { A } = 7700$, and $B = 3000$. Determine the month with the greatest total sales and give the sales in that month.
A) December; $\$ 10,700$
B) June; $\$ 7700$
C) September; $\$ 4700$
D) March; $\$ 10,700$

Question

The function graphed is of the form y $$y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0$$ Determine the equation of the graph.
-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, $\mathrm { A } = 7700$, and $B = 3000$. Determine the month with the greatest total sales and give the sales in that month.
A) December; $\$ 10,700$
B) June; $\$ 7700$
C) September; $\$ 4700$
D) March; $\$ 10,700$

Quizplus · Accepted Answer

The greatest total sales occur when the sine function reaches its maximum value, which is 1. The equation given is $S = 7700 + 3000 \sin(\pi x / 6)$. The sine function reaches its maximum value of 1 when $x = 3$ (March), making the total sales $S = 7700 + 3000(1) = 10700$.

The Function Graphed Is of the Form Y y=asin⁡bx or y=acos⁡bx, where b>0y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0y=asinbx or y=acosbx, where b>0

The Function Graphed Is of the Form Y $y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0$