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tom leonard's farmers market - Parker Core Knowledge

📅 May 4, 2026 👤 scraface

May 04, 2026

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Rate of change: \( \frac{dV}{dt} = -0.2\sqrt{h} \); but \( \frac{dV}{d...
Thus, \( \frac{25\pi}{144} h^2 \frac{dh}{dt} = -0.2 \sqrt{h} \) → \( \...
Separate variables and integrate from \( h = 12 \) at \( t = 0 \) to \...
\( \int_{12}^{h} h^{3/2} dh = -\frac{28.8}{25\pi} \int_0^{10} dt \)
\( \left[ \frac{2}{5} h^{5/2} \right]_{12}^{h} = -\frac{28.8}{25\pi} \...
\( \frac{2}{5}(h^{5/2} - 12^{5/2}) = -\frac{288}{25\pi} \)
\( h^{5/2} = 12^{5/2} - \frac{288}{25\pi} \cdot \frac{5}{2} = 12^{5/2}...
\( 12^{5/2} = (12^2)\sqrt{12} = 144 \cdot 2\sqrt{3} \approx 144 \cdot...
Subtract \( \frac{28.8}{\pi} \approx 9.17 \), so \( h^{5/2} \approx 48...
Actually: \( h^{5/2} = 498.816 - 9.17 = 489.65 \) → \( h = (489.65)^{2...

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