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Home » \[ r^2 \approx 25 \] - Nurtured Nest

\[ r^2 \approx 25 \] - Nurtured Nest

📅 May 9, 2026 👤 scraface

May 09, 2026

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📌 A: $\sqrt{2 + 0 + e^{-2}} = \sqrt{2 + e^{-2}}$

📌 B: $\sqrt{2^2 + 1 + e^{-1}} = \sqrt{4 + 1 + \frac{1}{e}}$

📌 C: $\sqrt{4 + 0 + 1} = \sqrt{5}$

📌 D: $\sqrt{1 + 1 + 1} = \sqrt{3}$

📌 Question: A civil engineer models the oscillation of a suspension bridge under wind load with the complex equation $(z - 3i)^8 = -16i$. Find the maximum imaginary part among all roots $z$, and express it in the form $\sin \theta$ for some $\theta \in (0, \pi)$.

📌 A: $\sin\left(\frac{3\pi}{8}\right)$

📌 B: $\sin\left(\frac{\pi}{4}\right)$

📌 C: $\sin\left(\frac{\pi}{2}\right) = 1$

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