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Home » 4000(1.64872 - 1) = 4000(0.64872) = 2594.88 - DNSFLEX

4000(1.64872 - 1) = 4000(0.64872) = 2594.88 - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 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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n^3 \equiv 13 \pmod{125}
We search for a solution to \(n^3 \equiv 13 \pmod{125}\). Try lifting...
Try small values modulo 5 first:
Mod 5: \(n^3 \equiv 13 \equiv 3 \pmod{5}\)
Check cubes mod 5:
\(0^3 = 0\)
\(1^3 = 1\)
\(2^3 = 8 \equiv 3\)
\(3^3 = 27 \equiv 2\)
\(4^3 = 64 \equiv 4\)

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