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Home » Question: Find the center of the hyperbola $9x^2 - 18x - 16y^2 + 64y = 144$. - AMAZONAWS

Question: Find the center of the hyperbola $9x^2 - 18x - 16y^2 + 64y = 144$. - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

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📌 A volcanologist is studying two volcanic sites. Site A has an eruption frequency of every 4 years, and Site B erupts every 6 years. If both sites erupted this year, in how many years will both sites erupt simultaneously again?

📌 Find the least common multiple (LCM) of 4 and 6.

📌 Prime factors of 4: \(2^2\)

📌 Prime factors of 6: \(2^1 \times 3^1\)

📌 LCM = \(2^2 \times 3^1 = 4 \times 3 = 12\)

📌 Both sites will erupt simultaneously in 12 years.

📌 A geophysicist monitors seismic activity and records an earthquake every 18 days at location X and every 24 days at location Y. If both locations experienced an earthquake today, after how many days will both locations experience an earthquake on the same day again?

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