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Home » A: $\sqrt3^2 + 4^2 = 5$ - IX Labs

A: $\sqrt3^2 + 4^2 = 5$ - IX Labs

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 \(S_9 = 3(9)^2 + 5(9) = 243 + 45 = 288\).

📌 Thus, \(a_{10} = 350 - 288 = 62\).

📌 A train travels 120 km at a speed of \(v\) km/h and then 180 km at \(v + 20\) km/h. If the total time for the journey is 5 hours, find \(v\).

📌 The time for the first part is \(\frac{120}{v}\) hours.

📌 The time for the second part is \(\frac{180}{v+20}\) hours.

📌 The total time is \(\frac{120}{v} + \frac{180}{v+20} = 5\).

📌 Multiply through by \(v(v+20)\):

📌 \(120(v+20) + 180v = 5v(v+20)\).

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