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Home » The longest side is \( 5x = 25 \) cm. - Midis

The longest side is \( 5x = 25 \) cm. - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 -3t^2 - 4t + 12 > 0

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

📌 -3t^2 - 4t + 12 = 0 \Rightarrow 3t^2 + 4t - 12 = 0

📌 t = rac{-4 \pm \sqrt{16 + 144}}{6} = rac{-4 \pm \sqrt{160}}{6} = rac{-4 \pm 4\sqrt{10}}{6} = rac{-2 \pm 2\sqrt{10}}{3}

📌 So the critical points are:

📌 t_1 = rac{-2 - 2\sqrt{10}}{3}, \quad t_2 = rac{-2 + 2\sqrt{10}}{3}

📌 Since the denominator of $ C'(t) $ is always positive, the sign of $ C'(t) $ depends on the numerator. The expression $ -3t^2 - 4t + 12 $ is positive between the roots. Therefore, $ C(t) $ is increasing for:

📌 oxed{ rac{-2 - 2\sqrt{10}}{3} < t < rac{-2 + 2\sqrt{10}}{3} }

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