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Home » Thus, the GCD of 48 and 256 is: - Baxtercollege

Thus, the GCD of 48 and 256 is: - Baxtercollege

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Substitute $ r = 12 $, $ \theta = 60^\circ $:

📌 A = \frac{60}{360} \cdot \pi \cdot 144 = \frac{1}{6} \cdot 144\pi = 24\pi

📌 The area of the visual sector is $ \boxed{24\pi} $ m².Question: A biologist studying amphibian breeding patterns observes that a certain species lays eggs in clutches that follow a number pattern: each clutch size is one more than a multiple of 7, and also one more than a multiple of 11. What is the smallest such clutch size greater than 50?

📌 We are given that the clutch size $ n $ satisfies:

📌 n \equiv 1 \pmod{7} \quad \text{and} \quad n \equiv 1 \pmod{11}

📌 This implies:

📌 n - 1 \equiv 0 \pmod{7} \quad \text{and} \quad n - 1 \equiv 0 \pmod{11}

📌 So $ n - 1 $ is a common multiple of 7 and 11. Since 7 and 11 are coprime, their least common multiple is:

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