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Home » The formula for the area \( A \) of a regular hexagon with side length \( s \) is: - Simpleprint

The formula for the area \( A \) of a regular hexagon with side length \( s \) is: - Simpleprint

📅 March 15, 2026 👤 scraface

Mar 15, 2026

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📌 M(25) = 50 \cdot \left(\frac{1}{2}\right)^{25/10} = 50 \cdot \left(\frac{1}{2}\right)^{2.5} = 50 \cdot \frac{1}{5.6569} \approx 8.84 \, \text{g}

📌 The remaining mass after 25 years is approximately 8.84 grams.

📌 A pendulum swings with a period \( T \) given by \( T = 2\pi \sqrt{\frac{L}{g}} \), where \( g = 9.8 \, \text{m/s}^2 \) and \( T = 4 \, \text{s} \). Solve for the length \( L \).

📌 Rearranging the formula:

📌 T = 2\pi \sqrt{\frac{L}{g}} \implies \frac{T}{2\pi} = \sqrt{\frac{L}{g}} \implies \left(\frac{T}{2\pi}\right)^2 = \frac{L}{g} \implies L = g \left(\frac{T}{2\pi}\right)^2

📌 Substituting:

📌 L = 9.8 \left(\frac{4}{2\pi}\right)^2 = 9.8 \left(\frac{2}{\pi}\right)^2 \approx 9.8 \cdot 0.4053 \approx 3.97 \, \text{m}

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