The weekly sale S (in thousands of units) for the t^th week after the introduction of the product in the market is given by S=(120t)/(t2+100)S=(120t)/(t2+100). In which week would the sale (S) have been 6?
+178 (There seems to be some grammatical errors and duplicating values, but doesn't matter whatsoever)
\(S=\frac{120t}{t^2+100}\)
Given that \(S=6\)
\(\frac{120t}{t^2+100}=6\)
Multiply by \(t^2+100\) on both sides.
\(120t=6t^2+600\)
Move the \(120t\) to the right side.
\(6t^2-120t+600=0\)
Divide the polynomial by 6
\(t^2-20t+100=0\)
Factor it:
\((t-10)^2=0\)
\(t-10=0\)
\(t=10\)
Answer: The 10th week.
Q.E.D.
(I don't see how this question is "off-topic" in anyway to be honest.)
