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Home » The formula for the \(n\)th term is \(a_n = a \cdot r^n-1\). - ClickBalance

The formula for the \(n\)th term is \(a_n = a \cdot r^n-1\). - ClickBalance

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 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 \( v(t) = s'(t) = 0 \).

📌 v(t) = \frac{ds}{dt} = 3t^2 - 12t + 9

📌 Set \( v(t) = 0 \):

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