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1401 west paces - Deep Underground Poetry

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 Assume: the volume is growing due to dwid/dt and dhi/dt, and length is constant. Let le latent.

📌 VDot = (dw/dt)(h)(l) + w(dh/dt)(l) + w×h(dl/dt)? But dl/dt not defined.

📌 Assume length is constant, so only dw/dt and dh/dt contribute to dV/dt.

📌 Then dV/dt = (dw/dt)(h)(l) + w(dh/dt)(l) = l [ (dw/dt)h + w(dh/dt) ]

📌 But l unknown.

📌 But V = w×h×l = 1,440 m³

📌 And dV/dt = 1,440 × (dw/dt × (1/h) + w × (dh/dt)/h)? No.

📌 Correct: dV/dt = (dw/dt)(h×l) + (dh/dt)(w×l) + (dw/dt)(dh/dt)×l? No — chain rule gives:

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