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Home » inom73 = rac7!3!(7-3)! = rac7 imes 6 imes 53 imes 2 imes 1 = 35 - Silent Sales Machine

inom73 = rac7!3!(7-3)! = rac7 imes 6 imes 53 imes 2 imes 1 = 35 - Silent Sales Machine

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 \frac{z_A + z_B + z_C}{3} = 12

📌 Let $ z_A = a, z_B = b, z_C = c $. Then:

📌 \frac{a + b + c}{3} = 12 \Rightarrow a + b + c = 36

📌 Now, the elevation at the centroid is a weighted average of the heights at $ A, B, C $, with weights equal to the areas of sub-triangles from centroid to each edge. Since centroid divides the triangle into three equal-area sub-triangles, the elevation at the centroid is the average of the $ z $-coordinates:

📌 \frac{a + b + c}{3} = 12

📌 Thus, the $ z $-coordinate of the centroid is consistent with the average elevation:

📌 \boxed{\frac{11}{3}}

📌 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 $?

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