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Home » The shortest altitude is $ \boxed{\frac6013} $. - DNSFLEX

The shortest altitude is $ \boxed{\frac6013} $. - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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A cylindrical tank with a radius of 3 meters and a height of 5 meters...
The volume of the sphere is \(\frac{4}{3} \pi (1)^3 = \frac{4}{3} \pi\...
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#### \(\frac{4}{27}\)
The sum of the first \(n\) positive integers is 210. What is \(n\)?
The sum of the first \(n\) integers is \(\frac{n(n+1)}{2} = 210\).
Solving, \(n(n+1) = 420\).
Using the quadratic formula, \(n = \frac{-1 \pm \sqrt{1 + 1680}}{2}\).
\(n = \frac{-1 \pm \sqrt{1681}}{2}\).

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