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Home » 2&10: The Secret Code That Changed Everything—We Won’t Tell You Why! - Appcentric

2&10: The Secret Code That Changed Everything—We Won’t Tell You Why! - Appcentric

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 The derivative \(f'(x) = 6x - 2\).

📌 Evaluating at \(x = 2\): \(f'(2) = 6(2) - 2 = 12 - 2 = 10\).

📌 Question:** A ladder 10 feet long rests against a wall. If the bottom slides away at 1 ft/s, how fast is the top sliding down when the bottom is 6 feet from the wall?

📌 Let \(x\) be the base distance, \(y\) the height.

📌 \(x^2 + y^2 = 100\). Differentiate: \(2x \frac{dx}{dt} + 2y \frac{dy}{dt} = 0\).

📌 Given \(\frac{dx}{dt} = 1\), \(x = 6\), so \(y = \sqrt{100 - 36} = 8\).

📌 \(12(1) + 16 \frac{dy}{dt} = 0 \implies \frac{dy}{dt} = -\frac{12}{16} = -\frac{3}{4}\) ft/s.

📌 #### \(-\frac{3}{4}\)

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