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Home » Disaster? Miracle? The 232 Angel Number Is Rewriting Your Destiny—Here’s How! - Carbonext

Disaster? Miracle? The 232 Angel Number Is Rewriting Your Destiny—Here’s How! - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 A spherical balloon is being inflated such that its radius increases at a constant rate of 0.5 cm/s. At what rate is the volume increasing when the radius is 10 cm?

📌 Volume of a sphere:

📌 Differentiate with respect to time \( t \):

📌 \frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}

📌 Plug in \( r = 10 \) cm and \( \frac{dr}{dt} = 0.5 \) cm/s:

📌 \frac{dV}{dt} = 4\pi (10)^2 (0.5) = 4\pi \times 100 \times 0.5 = 200\pi \text{ cm}^3/\text{s}

📌 The position of a particle moving along a line is given by \( s(t) = t^3 - 6t^2 + 9t + 2 \), where \( s \) is in meters and \( t \) in seconds. Find the time(s) when the particle is at rest.

📌 The particle is at rest when velocity \( v(t) = s'(t) = 0 \).

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