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how do you figure out your gpa from your grades - Imagemakers

📅 May 1, 2026 👤 scraface

May 01, 2026

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📌 $ 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 $.

📌 Solution: Given $ s(t) = t - \frac{t^5}{5} $, $ c_1 = \frac{1}{2} $. Compute recursively:

📌 $ c_2 = s\left(\frac{1}{2}\right) = \frac{1}{2} - \frac{1}{5} \left(\frac{1}{2}\right)^5 = \frac{1}{2} - \frac{1}{5} \cdot \frac{1}{32} = \frac{1}{2} - \frac{1}{160} = \frac{80 - 1}{160} = \frac{79}{160} $

📌 $ c_3 = s\left(\frac{79}{160}\right) = \frac{79}{160} - \frac{1}{5} \left(\frac{79}{160}\right)^5 $

📌 First compute $ \left(\frac{79}{160}\right)^5 $. Since this is tedious by hand, we compute step-by-step:

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