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Home » \(\sqrt289 = 17\), and \(17 \times 17 = 289\). - AIKO, infinite ways to autonomy.

\(\sqrt289 = 17\), and \(17 \times 17 = 289\). - AIKO, infinite ways to autonomy.

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 A mechanical engineer in California develops energy-efficient heating systems and models heat loss with \( H(t) = 4t^2 - 12t + 9 \). Find the minimum heat loss and the time at which it occurs.

📌 The function \( H(t) = 4t^2 - 12t + 9 \) is a quadratic in standard form \( at^2 + bt + c \), with \( a = 4 > 0 \), so it opens upwards and has a minimum at its vertex.

📌 t = -rac{b}{2a} = -rac{-12}{2 \cdot 4} = rac{12}{8} = rac{3}{2}

📌 Substitute \( t = rac{3}{2} \) into \( H(t) \):

📌 H\left(rac{3}{2}

📌 ight) = 4\left(rac{3}{2}

📌 ight)^2 - 12\left(rac{3}{2}

📌 ight) + 9 = 4 \cdot rac{9}{4} - 18 + 9 = 9 - 18 + 9 = 0

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