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Home » Why These Cartoon Clouds Are Taking the Internet by Storm—Watch Now! - Upplift

Why These Cartoon Clouds Are Taking the Internet by Storm—Watch Now! - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 Question: A self-healing polymer film repairs itself over time, with the repair rate modeled by $ r(t) = \sqrt{(t - 8)^2} $ millimeters per hour. For how many integer values of $ t $ is the repair rate exactly 4 mm/hour?

📌 Solution: We are given $ r(t) = \sqrt{(t - 8)^2} $.

📌 But $ \sqrt{(t - 8)^2} = |t - 8| $.

📌 Set this equal to 4:

📌 |t - 8| = 4

📌 This gives two equations:

📌 $ t - 8 = 4 $ → $ t = 12 $

📌 $ t - 8 = -4 $ → $ t = 4 $

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