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Home » For \(2\), the highest power is \(2^2\) - Leaselab

For \(2\), the highest power is \(2^2\) - Leaselab

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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📌 Question: An anthropologist is modeling cultural diffusion between three villages located at points $ A = (0, 0), B = (6, 0), C = (3, 6) $. If the influence of each village on the total cultural score is inversely proportional to the square of its distance from the center of mass, and the total influence is 1, what is the influence from village $ A $?

📌 Solution: First, compute the center of mass (centroid) of triangle $ ABC $:

📌 G = \left( \frac{0 + 6 + 3}{3}, \frac{0 + 0 + 6}{3} \right) = (3, 2)

📌 Now compute the squared distances from each vertex to $ G $:

📌 From $ A = (0, 0) $:

📌 d_A^2 = (3 - 0)^2 + (2 - 0)^2 = 9 + 4 = 13

📌 From $ B = (6, 0) $:

📌 d_B^2 = (3 - 6)^2 + (2 - 0)^2 = 9 + 4 = 13

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