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Home » Strong Emoji Alignments: The Secret Behind Viral Social Media Posts! - Sterling Industries

Strong Emoji Alignments: The Secret Behind Viral Social Media Posts! - Sterling Industries

📅 April 18, 2026 👤 scraface

Apr 18, 2026

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📌 How many distinct arrangements of the letters in the word MATHEMATICS are there such that the two Ms are not adjacent?

📌 Letters: M, A, T, H, E, M, A, T, I, C, S

📌 Now subtract arrangements where the two Ms are adjacent.

📌 Treat the two Ms as a single entity MM. Then we arrange 10 entities: MM, A, A, T, T, H, E, I, C, S

📌 We begin by computing the semi-perimeter $ s $ of the triangle:

📌 Using Herons formula, the area $ A $ of the triangle is:

📌 Question: A triangle has foot altitudes of lengths $ 6 $, $ 8 $, and $ 12 $. Determine the area of the triangle.

📌 Let the side lengths of the triangle be $ a $, $ b $, and $ c $, and the corresponding altitudes be $ h_a = 6 $, $ h_b = 8 $, $ h_c = 12 $.

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