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C
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Difficulty:
85%
(hard)
Question Stats:
50% (02:29) correct
50%
(02:04)
wrong
based on 88
sessions
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Not Attempted Yet
The revenue R, in dollars, that is generated by selling “x” units of a certain product is given by \(9x^2 + bx + c\), where x > 0 and b and c are constants. Find the value of b.
(1) The revenue generated by selling 200 units of the product is 54,0000.
(2) The roots of the equation \(ax^2 - bx + c\) are 20 and 9.
(1) The revenue generated by selling 200 units of the product is 54,0000.
(2) The roots of the equation \(ax^2 - bx + c\) are 20 and 9.
04 Jan 2022, 14:20
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Bunuel
Statement 1 Alone:
\(9*200^2 + 200b + c = 54000\). However, we have two variables so there is no unique solution for b or c. Then statement 1 alone is insufficient.
Statement 2 Alone:
Using quadratic equation knowledge, we can find \(\frac{b}{a} = 20 + 9 = 29\) and \(\frac{c}{a} = 20*9\), however that is not enough to find \(b\) or \(c\). Then statement 2 alone is insufficient.
(There may be a typo in this statement since \(a\) was not declared, so the intended equation might have been \(9x^2 - bx + c\), and this statement would be sufficient in that case).
Statement 2 Alone:
Combined we have three equations with three variables. Plug \(b = 29a\) and \(c = 180a\) into the first equation to find \(a\), then \(b\) and \(c\). Thus by combining statements, it is sufficient.
Answer: C
09 Jan 2022, 04:55
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Bunuel pease provide detailed solution for this one
