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\boxed3t^2 + 11t + 10 - Moon Smoking

📅 May 14, 2026 👤 scraface

May 14, 2026

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📌 \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 $:

📌 The altitude corresponding to a side is $ h = \frac{2A}{\text{side}} $. The longest altitude corresponds to the shortest side, which is 13 cm:

📌 h_{\text{longest}} = \frac{2 \cdot 84}{13} = \frac{168}{13} \approx 12.92

📌 Thus, the length of the longest altitude is $ \boxed{\frac{168}{13}} $ cm.

📌 Question: An equilateral triangle has a perimeter of $ 36 $ cm. If each side is increased by $ 2 $ cm, by how many square centimeters does the area increase?

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