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who were the sons of liberty - Parker Core Knowledge

📅 May 5, 2026 👤 scraface

May 05, 2026

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Here, \(a = -2\), \(b = 80\).
\(x = -\frac{80}{2 \times -2} = 20\).
Maximum profit: \(P(20) = -2(20)^2 + 80(20) - 150\).
\(= -800 + 1600 - 150 = 650\).
The sum of the first \(n\) positive integers is 5050. Find \(n\).
Formula: \(\frac{n(n+1)}{2} = 5050\).
\(n(n+1) = 10100\).
\(n^2 + n - 10100 = 0\).
Using quadratic formula: \(n = \frac{-1 \pm \sqrt{1 + 40400}}{2}\).
\(n = \frac{-1 \pm 201}{2}\).

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