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Home » \(\sin(60°) = \sqrt3/2\). - Dachbleche24

\(\sin(60°) = \sqrt3/2\). - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 An epidemiologist models a virus spreading in a population of 2 million. The infection rate doubles every 3 days, starting with 10 cases. After how many days will at least half the population (1 million) be infected?

📌 Use exponential growth: cases = 10 × 2^(t/3)

📌 Set 10 × 2^(t/3) ≥ 1,000,000

📌 Divide both sides by 10: 2^(t/3) ≥ 100,000

📌 Take log base 2: t/3 ≥ log₂(100,000) ≈ log₂(10⁵) = 5 × log₂(10) ≈ 5 × 3.3219 = 16.6095

📌 So t ≥ 3 × 16.6095 ≈ 49.8285

📌 Thus, after 50 days, cases exceed 1 million.

📌 An industrial designer creates a circular sustainable packaging prototype with inner radius 8 cm and outer radius 10 cm. If the material thickness is uniform and the total volume of material used is 144π cm³, what is the thickness of the packaging?

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