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Home » So, \(x^2 - 5x - 8 = 0\). - Veritas Home Health

So, \(x^2 - 5x - 8 = 0\). - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 k \cdot \frac{\sqrt{3}}{2} = 4\pi r^2 \frac{dr}{dt}

📌 Solving for $ \frac{dr}{dt} $:

📌 \frac{dr}{dt} = \frac{k \sqrt{3}}{8\pi r^2}

📌 The rate of volume increase is given directly as $ \frac{dV}{dt} = k \cdot \frac{\sqrt{3}}{2} $, so the rate is:

📌 \frac{dV}{dt} = \frac{k\sqrt{3}}{2}

📌 Thus, the rate of volume increase at $ \theta = 60^\circ $ is $ \boxed{\frac{k\sqrt{3}}{2}} $.

📌 Question: A data analyst plots a triangle on a coordinate plane with side lengths corresponding to data intervals of 13 cm, 14 cm, and 15 cm. What is the length of the longest altitude of this triangle?

📌 Solution: The triangle has side lengths $ a = 13 $, $ b = 14 $, and $ c = 15 $. First, compute the semi-perimeter $ s $:

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