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Home » Solución: Primero, calcula el área usando la fórmula de Herón. - Londonproperty

Solución: Primero, calcula el área usando la fórmula de Herón. - Londonproperty

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 \boxed{\text{No solution exists}}

📌 Question:** A quantum AI model uses complex numbers to represent states. Compute $(\cos 36^\circ + i \sin 36^\circ)^5$.

📌 Solution:** Using De Moivre’s Theorem:

📌 Question:** In a 3D vector space modeling neural network parameters, suppose $\mathbf{x}, \mathbf{y}, \mathbf{z}$ are unit vectors such that $\mathbf{x} + \mathbf{y} + \mathbf{z} = \mathbf{0}$. Find the maximum possible value of $\mathbf{x} \cdot \mathbf{y}$.

📌 Solution:** Since $\mathbf{x} + \mathbf{y} + \mathbf{z} = \mathbf{0}$, then $\mathbf{z} = -(\mathbf{x} + \mathbf{y})$.

📌 Since $\mathbf{z}$ is a unit vector:

📌 \|\mathbf{z}\|^2 = \|\mathbf{x} + \mathbf{y}\|^2 = 1

📌 \Rightarrow \|\mathbf{x}\|^2 + \|\mathbf{y}\|^2 + 2\mathbf{x} \cdot \mathbf{y} = 1

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$ (19a + 5b + c) - (7a + 3b + c) = 6 - (-4) $
$ \Rightarrow 12a + 2b = 10 \Rightarrow 6a + b = 5 \quad \text{(8)} $
$ (37a + 7b + c) - (19a + 5b + c) = -12 - 6 $
$ \Rightarrow 18a + 2b = -18 \Rightarrow 9a + b = -9 \quad \text{(9)}...
Subtract (8) from (9):
$ (9a + b) - (6a + b) = -9 - 5 \Rightarrow 3a = -14 \Rightarrow a = -\...
$ 6(-\frac{14}{3}) + b = 5 \Rightarrow -28 + b = 5 \Rightarrow b = 33...
Substitute $ a = -\frac{14}{3}, b = 33 $ into (5):
$ 7(-\frac{14}{3}) + 3(33) + c = -4 \Rightarrow -\frac{98}{3} + 99 + c...
$ \Rightarrow \frac{-98 + 297}{3} + c = -4 \Rightarrow \frac{199}{3} +...

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