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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?

Guest Aug 8, 2017
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(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.)

Jeffes02  Aug 8, 2017
edited by Jeffes02  Aug 8, 2017

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