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Home » Sofa Sepsis: The Hidden Hazard Lurking in Your Living Room—You Cant Ignore It! - inBeat

Sofa Sepsis: The Hidden Hazard Lurking in Your Living Room—You Cant Ignore It! - inBeat

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 A = A_{ ext{sector}} - A_{ ext{triangle}} = rac{16\pi}{3} - 6\sqrt{3}

📌 But since the line \(y = x + 2\) cuts the circle from top-right to bottom-left, the region enclosed is actually the smaller segment. Hence, the area is:

📌 oxed{rac{16\pi}{3} - 6\sqrt{3}}

📌 Question: Find the remainder when \(x^4 + 3x^3 - 2x^2 + x + 5\) is divided by \(x^2 - x + 1\).

📌 Solution: We perform polynomial division or use the fact that the remainder when dividing by a quadratic is linear: let

📌 x^4 + 3x^3 - 2x^2 + x + 5 = (x^2 - x + 1)Q(x) + ax + b

📌 Let \(\omega\) be a root of \(x^2 - x + 1 = 0\). Then \(\omega^2 = \omega - 1\), and \(\omega^3 = \omega(\omega - 1) = \omega^2 - \omega = (\omega - 1) - \omega = -1\). So \(\omega^3 = -1\), and \(\omega^6 = 1\).

📌 Now evaluate at \(x = \omega\):

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