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how to get rust stains out of clothes - Redraw

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 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?

📌 Solution: The original side length of the equilateral triangle is $ \frac{36}{3} = 12 $ cm. The area of an equilateral triangle is given by:

📌 Original area:

📌 A_1 = \frac{\sqrt{3}}{4} \cdot 12^2 = \frac{\sqrt{3}}{4} \cdot 144 = 36\sqrt{3}

📌 New side length: $ 12 + 2 = 14 $ cm. New area:

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\binom{8}{4} = 70,\quad \binom{12}{2} = 66,\quad \binom{20}{6} = 38760
\frac{70 \cdot 66}{38760} = \frac{4620}{38760} = \frac{77}{646}
\boxed{\frac{77}{646}}
Question: A philosopher of science is analyzing 12 key scientific theo...
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\binom{5}{2} \cdot \binom{7}{2} = 10 \cdot 21 = 210
\frac{210}{495} = \frac{14}{33}

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