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📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Thus, the final answer is $ \boxed{49} $.

📌 Question: A seismologist models the time between two seismic events as a function $ T(x) = x^2 - 6x + 13 $, where $ x $ is the number of days since monitoring began. What is the minimum time between events predicted by this model?

📌 The function $ T(x) = x^2 - 6x + 13 $ is a quadratic. The minimum value of a quadratic $ ax^2 + bx + c $ occurs at $ x = -\frac{b}{2a} $.

📌 Here, $ a = 1 $, $ b = -6 $, so:

📌 x = -\frac{-6}{2(1)} = \frac{6}{2} = 3

📌 Now evaluate $ T(3) $:

📌 T(3) = (3)^2 - 6(3) + 13 = 9 - 18 + 13 = 4

📌 Thus, the minimum time predicted by the model is $ \boxed{4} $.

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