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Home » embassy suites by hilton boston at logan airport - Deep Underground Poetry

embassy suites by hilton boston at logan airport - Deep Underground Poetry

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 Two trains start toward each other from cities 600 km apart, one at 90 km/h and the other at 110 km/h. How far from the first train’s start point do they meet?

📌 Combined speed: 90 + 110 = 200 km/h

📌 Time to meet: 600 ÷ 200 = 3 hours

📌 Distance from first train: 90 km/h × 3 h = 270 km

📌 #### 270 km

📌 A rare battery decays exponentially, with half-life of 8 years. If initially holding 64 Ah (amp-hours), how much charge remains after 24 years?

📌 Number of half-lives: 24 ÷ 8 = 3

📌 Remaining charge: \( 64 \times \left(\frac{1}{2}\right)^3 = 64 \times \frac{1}{8} = 8 \) Ah

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Using \( V(0) = \frac{V_0}{2} \):
\[ V(0) = V_0 \cos^2(\phi) = \frac{V_0}{2} \]
Divide by \( V_0 \):
\[ \cos^2(\phi) = \frac{1}{2} \quad \Rightarrow \quad \cos(\phi) = \pm...
So \( \phi = \pm \frac{\pi}{4} + k\pi \), for integer \( k \).
Using \( V\left(\frac{\pi}{2\omega}\right) = 0 \):
\[ V\left(\frac{\pi}{2\omega}\right) = V_0 \cos^2\left(\omega \cdot \f...
\[ \Rightarrow \quad \cos^2\left(\frac{\pi}{2} + \phi\right) = 0 \]
\[ \Rightarrow \quad \cos\left(\frac{\pi}{2} + \phi\right) = 0 \]
\[ \frac{\pi}{2} + \phi = \frac{\pi}{2} + n\pi \quad \Rightarrow \quad...

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