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Home » \(D' = 10x + 14\). Set to zero: - High Altitude Science

\(D' = 10x + 14\). Set to zero: - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 4x - y &= 5

📌 Substitute into the first equation: \(2x + 3(4x - 5) = 6\).

📌 Simplify: \(2x + 12x - 15 = 6\), so \(14x = 21\).

📌 Solve: \(x = 1.5\).

📌 Substitute back to find \(y\): \(y = 4(1.5) - 5 = 1\).

📌 #### \(x = 1.5\), \(y = 1\)

📌 If the sum of the first \(n\) natural numbers is given by \(\frac{n(n+1)}{2}\), find \(n\) when the sum is 210.

📌 Set up the equation: \(\frac{n(n+1)}{2} = 210\).

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