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E) $ \frac2425 $ - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 egin{pmatrix} 1 \ -2 \end{pmatrix} + 1.8 egin{pmatrix} 3 \ 1 \end{pmatrix} = egin{pmatrix} 1 + 5.4 \ -2 + 1.8 \end{pmatrix} = egin{pmatrix} 6.4 \ -0.2 \end{pmatrix}

📌 Thus, the closest point on the bridge to the water source is \(oxed{egin{pmatrix} 6.4 \ -0.2 \end{pmatrix}}\).

📌 An online STEM student is exploring complex numbers and discovers the expression \((\cos rac{\pi}{6} + i \sin rac{\pi}{6})^6\). Compute this value and express it in the form \(a + bi\).

📌 Using De Moivreâs Theorem:

📌 Here, \( heta = rac{\pi}{6}\), \(n = 6\):

📌 \left( \cos rac{\pi}{6} + i \sin rac{\pi}{6}

📌 ight)^6 = \cos\left(6 \cdot rac{\pi}{6}

📌 ight) + i \sin\left(6 \cdot rac{\pi}{6}

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