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Home » Given \( d = 10\sqrt2 \), solve for \( s \): - ToelettAPP

Given \( d = 10\sqrt2 \), solve for \( s \): - ToelettAPP

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 = 1 + 2(1) + \sec^2 x + 2(1) + \csc^2 x = 1 + 2 + 2 + \sec^2 x + \csc^2 x = 5 + \sec^2 x + \csc^2 x

📌 Now write in terms of sine and cosine:

📌 \sec^2 x = \frac{1}{\cos^2 x}, \quad \csc^2 x = \frac{1}{\sin^2 x}

📌 \Rightarrow \text{Expression} = 5 + \frac{1}{\cos^2 x} + \frac{1}{\sin^2 x}

📌 Use identity:

📌 \frac{1}{\cos^2 x} + \frac{1}{\sin^2 x} = \frac{\sin^2 x + \cos^2 x}{\sin^2 x \cos^2 x} = \frac{1}{\sin^2 x \cos^2 x}

📌 And $ \sin(2x) = 2\sin x \cos

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Probability both green = (8/20) × (7/19) = 56/380 = 14/95
Combine logs: log₂[(x + 3)(x − 1)] = 3
x² + 2x − 3 = 8
x² + 2x − 11 = 0
Using quadratic formula: x = [-2 ± √(4 + 44)] / 2
x = [-2 ± √48] / 2
x = [-2 ± 4√3] / 2
x = -1 ± 2√3
Only x = -1 + 2√3 is valid (since x > 1)
x ≈ -1 + 3.464 = 2.464

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