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what does dare stand for - DevRocket

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 An astronomer calculates that a protoplanetary disk has a total mass of 5 × 10³⁰ kg, with 60% forming into planets and the rest dissipating. If the largest planet collects 2.4 × 10³⁰ kg, what fraction of the planetary mass did it receive?

📌 Mass forming planets = 60% of 5 × 10³⁰ = 0.6 × 5 × 10³⁰ = <<0.6*5e30=3e30>>3 × 10³⁰ kg.

📌 Fraction received = 2.4 × 10³⁰ / 3 × 10³⁰ = <<2.4/3=0.8>>0.8.

📌 A geographer uses GIS to analyze urban sprawl and finds that a city’s area grew from 400 km² to 750 km² over 25 years. If the growth was exponential, what is the annual growth rate (as a percent)?

📌 Model: A = A₀ × e^(rt) → 750 = 400 × e^(25r) → e^(25r) = 750/400 = 1.875.

📌 25r = ln(1.875) ≈ 0.6292 → r ≈ 0.6292 / 25 = 0.025168.

📌 Annual growth rate = 0.025168 × 100 ≈ <<0.025168*100=2.5168>>2.52%.

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