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Find the smallest and largest such \( n \) in range: - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Together, they fill \(\frac{1}{6} + \frac{1}{4} = \frac{2}{12} + \frac{3}{12} = \frac{5}{12}\) of the tank per hour.

📌 Time to fill the tank is \(\frac{1}{\frac{5}{12}} = \frac{12}{5} = 2.4\) hours.

📌 #### 2.4 hours

📌 A rectangular field is 50 meters longer than it is wide. If the area is 6000 m², what are the dimensions?

📌 Let the width be \(x\) meters. Then the length is \(x + 50\) meters.

📌 The area is \(x(x + 50) = 6000\).

📌 Solving \(x^2 + 50x - 6000 = 0\) using the quadratic formula: \(x = \frac{-50 \pm \sqrt{50^2 + 4 \times 6000}}{2}\).

📌 \(x = \frac{-50 \pm \sqrt{2500 + 24000}}{2} = \frac{-50 \pm \sqrt{26500}}{2}\).

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