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Home » This Trick Will Let You Calculate Cubic Feet in Seconds—Say Goodbye to Guesswork! - Appcentric

This Trick Will Let You Calculate Cubic Feet in Seconds—Say Goodbye to Guesswork! - Appcentric

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 A radioactive substance decays exponentially with a half-life of 10 years. If the initial mass is 50 grams, calculate the remaining mass after 25 years.

📌 The decay formula is \( M(t) = M_0 \left(\frac{1}{2}\right)^{t/T_{1/2}} \), where \( M_0 = 50 \), \( T_{1/2} = 10 \), and \( t = 25 \).

📌 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

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