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wyndham garden fort walton beach destin - Anadea

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 Question: What is the greatest common divisor of 108 and 144, reflecting the largest uniform interval for monitoring volcanic gas emissions?

📌 Solution: Prime factorization: $108 = 2^2 \cdot 3^3$, $144 = 2^4 \cdot 3^2$. GCD takes the lowest powers: $2^2 \cdot 3^2 = 4 \cdot 9 = 36$.

📌 \boxed{36}

📌 $$**Question:** A circle is inscribed in a right triangle with legs of lengths 9 cm and 12 cm. Determine the radius of the inscribed circle.

📌 To find the radius of the inscribed circle in a right triangle, we can use the formula:

📌 where \( a \) and \( b \) are the legs of the right triangle, and \( c \) is the hypotenuse. First, calculate the hypotenuse \( c \) using the Pythagorean theorem:

📌 Now, apply the formula for the radius:

📌 r = \frac{9 + 12 - 15}{2} = \frac{6}{2} = 3

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