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Home » So from the first condition: first + fifth = $2a = 14 \Rightarrow a = 7$ - Crosslake

So from the first condition: first + fifth = $2a = 14 \Rightarrow a = 7$ - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Interpolate: \( h \approx 12.0 - \frac{9.17}{2(12^{5/2} \cdot \frac{5}{2 \cdot 0.4})) \) — too messy.

📌 Use numerical solver: After careful integration and evaluation, the height after 10 min is approximately 9.9 cm.

📌 Actually, recalculate:

📌 \( h^{5/2} = 12^{5/2} - \frac{288}{25\pi} \cdot \frac{10}{2} \times \frac{1}{\text{const}} \) — correction:

📌 From \( \frac{2}{5} h^{5/2} = \frac{288}{25\pi} \) → \( h^{5/2} = \frac{5}{2} \cdot \frac{288}{25\pi} = \frac{720}{50\pi} = \frac{72}{5\pi} \approx \frac{72}{15.708} \approx 4.58 \)? No — mistake.

📌 Correction:

📌 \( \frac{dh}{dt} = -\frac{28.8}{25\pi} h^{-3/2} \) →

📌 \( \int h^{3/2} dh = -\frac{28.8}{25\pi} \int dt \) →

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