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Home » We use the **Remainder Theorem**: - Network4

We use the Remainder Theorem: - Network4

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 \(x = -\frac{80}{2 \times -2} = 20\).

📌 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: \(n = \frac{-1 \pm \sqrt{1 + 40400}}{2}\).

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