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Home » Divide: (1.25)^n > 95 / 64 = 1.484375 - Abu Waleed Tea

Divide: (1.25)^n > 95 / 64 = 1.484375 - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Bimodal (Tribe 1): two peaks at 18 and 22 — interpreted as concentrated around these values, width ~4 years (e.g., 16–20 and 20–24).

📌 Uniform (Tribe 2): from 18 to 22 → closed interval.

📌 Assume Bimodal: [16, 20] ∪ [20, 24] → simplified as [16, 24], but realistic peak between 18–22 range. More precisely, as two discrete modes at 18 and 22 with symmetric spread of 2 years: width of 4 years each.

📌 Uniform: [18, 22], length 4.

📌 Overlap between [16,24] and [18,22] is [18,22], which is fully contained. But if we model Bimodal as two pulses: from 16–18 and 20–22 (each 2 years), and uniform 18–22, overlap is 18–22 → 4 years.

📌 But simpler: treat Bimodal as union of [16,20] and [20,24] — but assume peak interest at 18 and 22. For simplicity and alignment with discrete interpretation, the overlap of support is [18,22], so the length of intersection is 22 − 18 = <<22-18=4>>4 years.

📌 Thus, expected overlap is 4 years.

📌 A robotics engineer builds a hierarchical robot system with one command unit, 4 sensor clusters (all same, but placed differently), and 3 task modules (distinct functions: navigation, analysis, repair). Each sensor cluster can be assigned to any of 4 mounting positions, but due to space constraints, only 2 clusters can be placed per unit. How many distinct robot setups can be created?

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g(6) = (6)^2 - 5(6) + 7m = 36 - 30 + 7m = 6 + 7m
Given $ f(6) = g(6) - 12 $:
+ 3m = (6 + 7m) - 12 = -6 + 7m
Now solve:
+ 3m = -6 + 7m
Subtract $ 3m $ from both sides:
= -6 + 4m
Add 6:
= 4m
Divide by 4:

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