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Home » The Hidden Secret Behind the Most Obsessed Emerald Ring! - Appcentric

The Hidden Secret Behind the Most Obsessed Emerald Ring! - Appcentric

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 A hydrologist is analyzing groundwater flow and models a particular aquifer's recharge rate as a function of time using integers. If the recharge rate at time \( t \) is given by \( R(t) = 3t^2 + 2t + 1 \), for \( t = 1, 2, 3, \ldots, 10 \), what is the greatest common divisor of all values \( R(1), R(2), \ldots, R(10) \)?

📌 First, compute \( R(t) = 3t^2 + 2t + 1 \) for \( t = 1 \) to \( 10 \):

📌 R(1) &= 3(1)^2 + 2(1) + 1 = 3 + 2 + 1 = 6, \\

📌 R(2) &= 3(4) + 4 + 1 = 12 + 4 + 1 = 17, \\

📌 R(3) &= 3(9) + 6 + 1 = 27 + 6 + 1 = 34, \\

📌 R(4) &= 3(16) + 8 + 1 = 48 + 8 + 1 = 57, \\

📌 R(5) &= 3(25) + 10 + 1 = 75 + 10 + 1 = 86, \\

📌 R(6) &= 3(36) + 12 + 1 = 108 + 12 + 1 = 121, \\

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