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Home » Common difference $ d = 2 $ - Londonproperty

Common difference $ d = 2 $ - Londonproperty

📅 March 15, 2026 👤 scraface

Mar 15, 2026

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📌 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.

📌 #### \(-\frac{3}{4}\)

📌 Question:** A bag contains 3 red, 4 blue, and 5 green marbles. Two are drawn without replacement. What is the probability both are green?

📌 Total marbles = 12.

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1.08⁶ = 1.3605 × 1.1664 ≈ 1.5869
Rounded to nearest tenth: 23.8 cm
A = 300 × e^(-0.04×6) = 300 × e^(-0.24)
A ≈ 300 × 0.7866 = 235.98
At t =
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