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# thousand unit

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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:

$$(t-10)^2=0$$

$$t-10=0$$

$$t=10$$