The monthly sales S (in hundreds of units) of baseball equipment for an Internet sporting goods site are approximated by S = 60.1 − 43.9 cos πt/ 6 where t is the time (in months), with t = 1 corresponding to January. Determine the months when sales exceed 7700 units at any time during the month.
a. march through september b. april through august c. march through august d. may through september e. april through august
+67 60.1 − 43.9 cos πt/ 6 ≥ 77
− 43.9 cos πt/ 6 ≥ 16.9
cos πt/6 ≤ - .38496...
consider cos πt/6 = - .38496...
I know cos 1.1756.. = +.38496
so πt/6 = π - 1.1756 = appr 1.966
t = 3.755
or
πt/6 = π + 1.1756.. = 4.3172..
t = 8.245
+118659 Thanks Michael,
Your first bit is good but then I am not sure what you did ://
Anyway, I want to take a quick look myself. :)
\( 60.1 − 43.9 cos\frac{ πt}{ 6}\ge 77\\ − 43.9 cos\frac{ πt}{ 6}\ge 16.9\\ cos\frac{ πt}{ 6}\le -16.9/43.9\\ cos\frac{ πt}{ 6}\le -0.385\\ \frac{ πt}{ 6}\le cos^{-1}(-0.385)\\ \frac{ πt}{ 6}\ge 1.966\\ πt\ge 11.796\\ t\ge3.75 \)
I will assume that 1 is the END of January SO 4 is the end of April.
So sales will be exceeded in April
Here is a graph that might help you to understand. Although the equation itself actually makes little sense.
