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For the walkway with radius \(5r\): - Professionaloutdoormedia

📅 May 14, 2026 👤 scraface

May 14, 2026

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📌 u(u^2 - 5u + 6) = 0 \Rightarrow u(u - 2)(u - 3) = 0

📌 So $ u = 0, 2, $ or $ 3 $. Since $ x = u^2 $, the corresponding $ x $-values are:

📌 $ u = 0 \Rightarrow x = 0 $

📌 $ u = 2 \Rightarrow x = 4 $

📌 $ u = 3 \Rightarrow x = 9 $

📌 All are non-negative. The sum of roots is $ 0 + 4 + 9 = 13 $.

📌 Thus, the sum of all real solutions is $ \boxed{13} $.

📌 Question: A museum curator uses a digital model where the position $ s(t) $ of a rotating exhibit arm is given by $ s(t) = t - \frac{t^5}{5} $. Define $ c_n $ by $ c_1 = \frac{1}{2} $ and $ c_{n+1} = s(c_n) $. Compute $ c_3 $.

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