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Home » Calculate 30% of 120: $ 0.30 \times 120 = 36 $. - Crosslake

Calculate 30% of 120: $ 0.30 \times 120 = 36 $. - Crosslake

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 But wait: is this the minimum? Since the expression inside is always greater than $ 0 $, the absolute value is minimized exactly when $ 2\sin x + 3\cos x $ is minimized.

📌 \min (2\sin x + 3\cos x + 4) = 4 + \min(2\sin x + 3\cos x) = 4 + (-\sqrt{13}) = 4 - \sqrt{13}

📌 And since this value is positive, the absolute value does not introduce a smaller value.

📌 Thus, the minimum value is $ \boxed{4 - \sqrt{13}} $.

📌 Question: An anthropologist studying ritualistic circular dance formations interprets rhythmic movements as vectors; find the vector $ \mathbf{v} = \langle x, y, z \rangle $ satisfying $ \mathbf{v} \times \langle 1, 2, 3 \rangle = \langle 1, -2, 1 \rangle $ and $ \mathbf{v} \cdot \langle 1, 2, 3 \rangle = 0 $.

📌 Solution: Let $ \mathbf{a} = \langle 1, 2, 3 \rangle $, $ \mathbf{b} = \langle 1, -2, 1 \rangle $. We are to find $ \mathbf{v} $ such that:

📌 \mathbf{v} \times \mathbf{a} = \mathbf{b}, \quad \mathbf{v} \cdot \mathbf{a} = 0

📌 We use the vector triple product identity. From $ \mathbf{v} \times \mathbf{a} = \mathbf{b} $, taking the cross product with $ \mathbf{a} $ on both sides:

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