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Home » \[ \fracx^2a^2 - \fracy^2b^2 = 1 \] - Deep Underground Poetry

\[ \fracx^2a^2 - \fracy^2b^2 = 1 \] - Deep Underground Poetry

📅 May 4, 2026 👤 scraface

May 04, 2026

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2^{n-1} > \frac{500}{3} \approx 166.67
Now compute powers of 2:
$ 2^7 = 128 $, $ 2^8 = 256 $
So $ 2^{n-1} > 166.67 $ implies $ n-1 \geq 8 $, thus $ n \geq 9 $.
On day 9, the count is $ 3 \cdot 2^8 = 3 \cdot 256 = 768 > 500 $.
On day 8: $ 3 \cdot 2^7 = 384 < 500 $, so day 9 is the first.
Question: A self-healing polymer film repairs itself over time, with t...
Solution: We are given $ r(t) = \sqrt{(t - 8)^2} $.
But $ \sqrt{(t - 8)^2} = |t - 8| $.
Set this equal to 4:

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