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Home » \Rightarrow \gcd( - Blask

\Rightarrow \gcd( - Blask

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Dividing both sides by 1000:

📌 + 0.05t = (1.04)^t

📌 Solving numerically (logarithms or trial):

📌 Try \( t = 8 \):

📌 + 0.05(8) = 1.4, \quad (1.04)^8 \approx 1.3686

📌 Try \( t = 9 \):

📌 + 0.05(9) = 1.45, \quad (1.04)^9 \approx 1.4233

📌 Try \( t = 10 \):

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The vertex form is used for maximum: \(x = -\frac{b}{2a}\).
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: \(n = \frac{-1 \pm \sqrt{1 + 40400}}{2}\).

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