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Home » Solution: The circle has radius $ 5 $ micrometers, so its area is: - Moon Smoking

Solution: The circle has radius $ 5 $ micrometers, so its area is: - Moon Smoking

📅 May 15, 2026 👤 scraface

May 15, 2026

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📌 Density halves every 20 cm, so the decay has a half-life of 20 cm.

📌 From 10–30 cm: depth interval = 20 cm → density halved → expected count = 450 / 2 = 225

📌 From 30–50 cm: another halving → 225 / 2 = 112.5

📌 But we want 20–40 cm: this is 20 to 40, so 10–20 cm and 20–30 cm overlap? Wait:

📌 Better: define depth = d (cm from surface)

📌 At d = 10, density = d₀ · (1/2)^(d/20)

📌 Let N(d) = k × (1/2)^(d/20)

📌 At d = 10, N(10) = 450 = k × (1/2)^(10/20) = k × (1/2)^(0.5) = k / √2

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