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when did the byzantine empire fall - ECD Germany

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Substitute \( a = 1 \) into Equation 4:

📌 Substitute \( a = 1 \) and \( b = 2 \) into the first equation:

📌 Thus, the values are \( a = 1 \), \( b = 2 \), \( c = 3 \).

📌 \boxed{a = 1, \, b = 2, \, c = 3}

📌 Question:** A zoologist observes that the population \( P(t) \) of a certain species in the Amazon rainforest follows the quadratic model \( P(t) = kt^2 + mt + n \). Given \( P(1) = 120 \), \( P(2) = 150 \), and \( P(3) = 210 \), find the coefficients \( k \), \( m \), and \( n \).

📌 \( P(1) = k(1)^2 + m(1) + n = 120 \implies k + m + n = 120 \)

📌 \( P(2) = k(2)^2 + m(2) + n = 150 \implies 4k + 2m + n = 150 \)

📌 \( P(3) = k(3)^2 + m(3) + n = 210 \implies 9k + 3m + n = 210 \)

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