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Home » Therefore, the number of valid configurations is \(\boxed18150\). - Carbonext

Therefore, the number of valid configurations is \(\boxed18150\). - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 \(z = 180^\circ\): \(\sin 180 + \cos 180 = 0 - 1 = -1\) ✗

📌 \(z = 270^\circ\): \(\sin 270 + \cos 270 = -1 + 0 = -1\) ✗

📌 \(z = 360^\circ\): same as \(0^\circ\), so ✓

📌 Valid solutions: \(0^\circ, 90^\circ, 360^\circ\). Sum:

📌 + 90 + 360 = \boxed{450^\circ}

📌 Find the point on the line \(y = 2x + 1\) that is closest to the point \((3, 4)\).

📌 The shortest distance from a point to a line is along the perpendicular. The line is \(y = 2x + 1\), so its slope is \(2\), and the perpendicular slope is \(-\frac{1}{2}\).

📌 The perpendicular line through \((3, 4)\) is:

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