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Home » Use the Pythagorean Theorem: \(c^2 = a^2 + b^2\). - ToelettAPP

Use the Pythagorean Theorem: \(c^2 = a^2 + b^2\). - ToelettAPP

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Try $ k=3 $: $ 1.125^3 = 1.125 \times 1.125 = 1.265625 \times 1.125 = 1.423828125 < 1.484375 $

📌 $ k=4 $: $ 1.423828125 \times 1.125 = 1.60040625 > 1.484375 $

📌 So $ n-1 = 4 $ → $ n = 5 $? No: $ k = n-1 $, so $ n-1 = 4 $ → $ n = 5 $? But wording: after how many weeks — if at end of week 4, and we want first time, it’s after 4 weeks.

📌 But after 4 weeks is ambiguous.

📌 Better: solve $ 64 \times (1.125)^t > 95 $ → $ t = \log_{1.125}(95/64) \approx \log(1.484375)/\log(1.125) \approx 0.17116 / 0.051161 \approx 3.348 $

📌 So $ t > 3.348 $ weeks → first full week when true is week 4. But after how many weeks means after $ t $ weeks — so the smallest integer $ t $ such that inequality holds is $ t = 4 $.

📌 But at $ t=

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