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Home » Basketball players at the 1980 Summer Olympics - Upplift

Basketball players at the 1980 Summer Olympics - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 Since the maximum amplitude is 3, the midline is likely centered at 0 (symmetric about \( y = 0 \)), so \( d = 0 \). Then:

📌 a \sin(c) = 0 \implies \sin(c) = 0 \implies c = 0 \quad \text{(since sine is zero at multiples of } \pi\text{, and we want minimal phase shift)}

📌 Thus, \( a = 3 \), \( b = 2 \), \( c = 0 \), \( d = 0 \).

📌 The function becomes \( f(x) = 3\sin(2x) \), which satisfies all conditions.

📌 Final values:

📌 a = 3, \quad b = 2, \quad c = 0, \quad d = 0

📌 \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.

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