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costa rica marriott hotel hacienda belen - NBX Soluciones

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 So the only way to resolve this is to define theQuestion: A chemical engineer models the concentration of a reactant in a reactor over time with the function $ C(t) = rac{3t + 2}{t^2 + 4} $. For what values of $ t $ is the concentration increasing?

📌 Solution: To determine when the concentration is increasing, we analyze the derivative of $ C(t) $. Using the quotient rule:

📌 C'(t) = rac{(3)(t^2 + 4) - (3t + 2)(2t)}{(t^2 + 4)^2}

📌 3(t^2 + 4) - 2t(3t + 2) = 3t^2 + 12 - (6t^2 + 4t) = -3t^2 - 4t + 12

📌 C'(t) = rac{-3t^2 - 4t + 12}{(t^2 + 4)^2}

📌 To find where $ C(t) $ is increasing, we solve:

📌 -3t^2 - 4t + 12 > 0

📌 This is a quadratic inequality. First, find the roots:

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