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Home » \[ \text弧长 = r \theta \] - Red Crowns

\[ \text弧长 = r \theta \] - Red Crowns

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Repeat the process:

📌 Divide \( 2x^2 \) by \( x^2 \) to get \( 2 \).

📌 Multiply \( 2 \) by \( x^2 + 1 \) to get \( 2x^2 + 2 \).

📌 The remainder is \(-1\). Therefore, the remainder when \( x^4 + 3x^2 + 1 \) is divided by \( x^2 + 1 \) is \(\boxed{-1}\).

📌 A science administrator is reviewing a grant application involving the hyperbola given by the equation \( 9x^2 - 16y^2 - 54x + 64y - 71 = 0 \). Find the center of this hyperbola.

📌 To find the center of the hyperbola, we rewrite the equation in standard form by completing the square.

📌 9x^2 - 54x - 16y^2 + 64y = 71

📌 Complete the square for \( x \):

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