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Home » The perimeter is \( 2(x + 2x) = 36 \). - Aurero

The perimeter is \( 2(x + 2x) = 36 \). - Aurero

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 Verify: \( 11.85^{2.5} = 11.85^2 \cdot \sqrt{11.85} \approx 140.2 \cdot 3.44 \approx 483 \), close to 489.6.

📌 Adjust: try \( h = 12.1 \): \( h^{5/2} = 12.1^2 \cdot \sqrt{12.1} = 146.41 \cdot 3.477 \approx 508.4 \) → too high.

📌 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:

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