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Home » x_n - \fracx_n^39 = \frac1n. - Blask

x_n - \fracx_n^39 = \frac1n. - Blask

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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Solution:** Start: 1 atm at surface.
Each 100 m multiplies pressure by 1.1.
We solve: \( 1 \times (1.1)^n = 1000 \) → \( (1.1)^n = 1000 \)
Take log: \( n = \log_{1.1}(1000) = \frac{\log 1000}{\log 1.1} = \frac...
So depth: \( 72.45 \times 100 \approx 7245 \) meters (round to nearest...
At 7200 m: \( (1.1)^{72} \approx 999.9 \) → just below
At 7300 m: \( (1.1)^{73} \approx 1099.9 \) → exceeds
So it reaches 1000 atm during ascent at ~7300 meters. But question ask...
Since 72.45 × 100 = 7245, check:
\( (1.1)^{72.45} = 1000 \) → depth = 7245 m exceeds, so first depth wh...

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