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where to watch knicks vs orlando magic - NBX Soluciones

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Question:** A philosopher of science contemplates the growth of scientific knowledge as a sequence defined by the recursive relation \(a_{n} = 2a_{n-1} + 3\), with \(a_1 = 1\). Compute \(a_4\).

📌 We will compute the terms of the sequence step-by-step using the recursive relation:

📌 \(a_1 = 1\)

📌 \(a_2 = 2a_1 + 3 = 2(1) + 3 = 2 + 3 = 5\)

📌 \(a_3 = 2a_2 + 3 = 2(5) + 3 = 10 + 3 = 13\)

📌 \(a_4 = 2a_3 + 3 = 2(13) + 3 = 26 + 3 = 29\)

📌 Therefore, the value of \(a_4\) is:

📌 Question:** In a futuristic navigation system, the position of a spacecraft is given by the expressions \(x(t) = 5t^2 + 3t + 2\) and \(y(t) = 2t^2 + 7t + 1\). Find the value of \(t\) when the spacecraft is at the point where \(x(t) = y(t)\).

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