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\boxed{\frac\pi cc + z} - Feedz API

📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 Solution: The shortest altitude corresponds to the longest side, since area is fixed and altitude is inversely proportional to base. The longest side is 21 km, so we compute the altitude to this side.

📌 First, compute the area using Herons formula. The semi-perimeter $s$ is:

📌 Let $h$ be the altitude to the side of length 21 km. Then:

📌 Thus, the shortest altitude is 8 km.

📌 $$Question: An anthropologist observes 8 distinct cultural rituals, each performed by a different tribe. If she wishes to compare pairs of rituals only if they originate from neighboring tribes, and there are 3 such neighboring pairs among the 8 tribes, how many valid comparisons can she make?

📌 Solution: The anthropologist can only compare ritual pairs that originate from neighboring tribes. There are exactly 3 such neighboring pairs. Since each comparison is between a unique pair of rituals, and no pair is repeated or overlap implied, the total number of valid comparisons is simply the number of given neighboring pairs:

📌 Question: A science journalist is designing an infographic showing all possible 3-color combinations from a palette of 10 scientifically significant colors, where each combination must include at least one of three emblematic colors. How many such color combinations are possible?

📌 Thus, the number of meaningful color combinations is:

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