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📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 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 \(x(t) = y(t)\).

📌 To find when \(x(t) = y(t)\), set the expressions equal:

📌 5t^2 + 3t + 2 = 2t^2 + 7t + 1

📌 Subtract \(2t^2 + 7t + 1\) from both sides:

📌 5t^2 + 3t + 2 - 2t^2 - 7t - 1 = 0

📌 3t^2 - 4t + 1 = 0

📌 Solve this quadratic equation using the quadratic formula:

📌 where \(a = 3\), \(b = -4\), and \(c = 1\). Substituting:

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