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Home » This eerie AI Called ‘Sentry The Void’ Is Changing the Mystery Genre Forever! - Carbonext

This eerie AI Called ‘Sentry The Void’ Is Changing the Mystery Genre Forever! - Carbonext

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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📌 Since \(\|\mathbf{u} - \mathbf{u} \cdot \mathbf{v} \mathbf{v}\| \geq 0\), the projection of \(\mathbf{u}\) onto the plane perpendicular to \(\mathbf{v}\) satisfies:

📌 \|\mathbf{u}_\perp\|^2 = \|\mathbf{u}\|^2 - (\mathbf{u} \cdot \mathbf{v})^2 = 4 - 1 = 3.

📌 Let \(\mathbf{u}_\perp = \mathbf{u} - \frac{1}{9} \mathbf{v}\) (since \(\mathbf{v}\) has norm 3), so:

📌 \|\mathbf{u}_\perp\|^2 = \|\mathbf{u}\|^2 - (\mathbf{u} \cdot \mathbf{v})^2 / \|\mathbf{v}\|^2 \cdot

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From the third equation, $-v_2 = -4 \implies v_2 = 4\), which contradi...
Thus, no such vector \(\mathbf{v}\) exists because the system is incon...
\boxed{\text{No solution}}
Question: Among all the roots of \(z^8 + z^4 + 1 = 0\), the maximum im...
Consider the equation:
z^8 + z^4 + 1 = 0
Let \(w = z^4\), then:
w = \frac{-1 \pm \sqrt{1 - 4}}{2} = \frac{-1 \pm \sqrt{-3}}{2} = \frac...
So \(z^4 = \frac{-1 \pm i\sqrt{3}}{2} = e^{\pm 2\pi i/3}\), since thes...
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