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Home » The inradius \( r = \fracAs = \frac5418 = 3 \). - DNSFLEX

The inradius \( r = \fracAs = \frac5418 = 3 \). - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 5Question: An ichthyologist models the growth of a fish population with the quadratic function $ f(x) = x^2 - 4x + m $. If the population at $ x = 3 $ is 7, find $ m $.

📌 Solution: Substitute $ x = 3 $ into $ f(x) $:

📌 f(3) = (3)^2 - 4(3) + m = 9 - 12 + m = -3 + m.

📌 Set this equal to 7:

📌 + m = 7 \implies m = 10.

📌 Question: A virologist studies the replication rate of a virus using the equation $ g(x) = x^2 - 4x + 3m $. If the replication rate at $ x = 2 $ equals the rate of a control sample modeled by $ f(x) = x^2 - 4x + m $, find $ m $.

📌 Solution: Compute $ g(2) $ and $ f(2) $:

📌 g(2) = (2)^2 - 4(2) + 3m = 4 - 8 + 3m = -4 + 3m,

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