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Home » The central angle in radians is \( \frac117 \). - go-checkin.com

The central angle in radians is \( \frac117 \). - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \boxed{a = 3,\ b = 2,\ c = 0,\ d = 0}

📌 Question:** During a workshop on AI ethics, a facilitator uses a geometric model where two vectors represent conflicting values: \( \vec{v} = \begin{pmatrix} 2 \\ -1 \end{pmatrix} \) and \( \vec{w} = \begin{pmatrix} x \\ 4 \end{pmatrix} \). Find \( x \) such that \( \vec{v} \) and \( \vec{w} \) are perpendicular, illustrating balanced ethical trade-offs.

📌 Two vectors are perpendicular if their dot product is zero.

📌 Compute the dot product:

📌 \vec{v} \cdot \vec{w} = (2)(x) + (-1)(4) = 2x - 4

📌 Set equal to zero:

📌 2x - 4 = 0 \implies 2x = 4 \implies x = 2

📌 Thus, when \( x = 2 \), the vectors are perpendicular, modeling balanced ethical alignment in decision-making.

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