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Home » The Widows Peak Hair That Defies Time: How This Look Still Stuns Millennials! - Redraw

The Widows Peak Hair That Defies Time: How This Look Still Stuns Millennials! - Redraw

📅 May 6, 2026 👤 scraface

May 06, 2026

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📌 From equation 3: \(a = 4 - 2b\). Substitute into equation 2: \(2c - 3(4 - 2b) = 7 \implies 2c - 12 + 6b = 7 \implies 2c + 6b = 19\). From equation 1: \(c = 5 - 3b\). Substitute into \(2c + 6b = 19\): \(2(5 - 3b) + 6b = 10 - 6b + 6b = 10 = 19\), which is a contradiction. Thus, no solution exists.

📌 \boxed{\text{No such vector } \mathbf{v} \text{ exists.}}

📌 Question: Determine the number of real solutions to the equation \(\sin(2x) = \frac{1}{2}$ for \(x \in [0, 2\pi]\).

📌 Solution: The equation \(\sin(2x) = \frac{1}{2}\) has solutions when \(2x = \frac{\pi}{6} + 2\pi n\) or \(2x = \frac{5\pi}{6} + 2\pi n\) for integer \(n\). Solving for \(x\) in \([0, 2\pi]\):

📌 \(x = \frac{\pi}{12} + \pi n\): Solutions are \(\frac{\pi}{12}, \frac{13\pi}{12}\).

📌 \(x = \frac{5\pi}{12} + \pi n\): Solutions are \(\frac{5\pi}{12}, \frac{17\pi}{12}\).

📌 Total of 4 solutions.

📌 Question: If \(\mathbf{u}\), \(\mathbf{v}\), and \(\mathbf{w}\) are unit vectors, find the maximum value of \(\mathbf{u} \cdot (\mathbf{v} + \mathbf{w})\).

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We want the number of 4-bird selections that include **at least one re...
This means the possible color distributions that satisfy this are:
We calculate the number of ways for each:
#### Case 1: 2 red, 1 green, 1 blue
\binom{5}{2} \cdot \binom{7}{1} \cdot \binom{3}{1} = 10 \cdot 7 \cdot...
#### Case 2: 1 red, 2 green, 1 blue
\binom{5}{1} \cdot \binom{7}{2} \cdot \binom{3}{1} = 5 \cdot 21 \cdot...
#### Case 3: 1 red, 1 green, 2 blue
\binom{5}{1} \cdot \binom{7}{1} \cdot \binom{3}{2} = 5 \cdot 7 \cdot 3...
### Step 3: Total favorable outcomes

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