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Home » $x^4 = -\omega$ - AssociationVoting

$x^4 = -\omega$ - AssociationVoting

📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 4(x - 4)^2 - 9(y - 3)^2 + 17 = -115 \implies 4(x - 4)^2 - 9(y - 3)^2 = -132.

📌 Divide by $ -132 $ to standardize:

📌 \frac{(y - 3)^2}{\frac{132}{9}} - \frac{(x - 4)^2}{\frac{132}{4}} = 1.

📌 The center is at $ (h, k) = (4, 3) $.

📌 Final answer: $\boxed{(4, 3)}$

📌 Question: Microfossil density $ d(t) $ in a sediment layer follows $ \sum_{k=1}^{n} \frac{1}{k(k+1)(k+2)} $. Compute this sum for $ n = 50 $.

📌 Solution: Use partial fractions to decompose $ \frac{1}{k(k+1)(k+2)} $. Let:

📌 \frac{1}{k(k+1)(k+2)} = \frac{A}{k} + \frac{B}{k+1} + \frac{C}{k+2}.

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