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Home » $ u = 5 $: $ 5^3 = 125 $ - Treasure Valley Movers

$ u = 5 $: $ 5^3 = 125 $ - Treasure Valley Movers

📅 April 15, 2026 👤 scraface

Apr 15, 2026

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📌 \( h^{5/2} = 12^{5/2} - \frac{288}{25\pi} \cdot \frac{5}{2} = 12^{5/2} - \frac{288}{10\pi} \)

📌 \( 12^{5/2} = (12^2)\sqrt{12} = 144 \cdot 2\sqrt{3} \approx 144 \cdot 3.464 = 498.816 \)

📌 Subtract \( \frac{28.8}{\pi} \approx 9.17 \), so \( h^{5/2} \approx 489.65 \) → \( h \approx (489.65)^{2/5} \approx (489.65)^{0.4} \approx 14.3 \) — but check: 12 to lower? Wait: negative sign means decreasing.

📌 Actually: \( h^{5/2} = 498.816 - 9.17 = 489.65 \) → \( h = (489.65)^{2/5} \).

📌 \( 489.65^{0.4} \): \( \ln(489.65) \approx 6.19 \), \( 0.4 \times 6.19 = 2.476 \), \( e^{2.476} \approx 11.94 \).

📌 But more accurately: let \( u = h^{5/2} \), \( u = 498.816 - 9.17 = 489.646 \), \( h = u^{2/5} \approx 489.646^{0.4} \).

📌 \( 489.646^{0.4} = (e^{\ln 489.646})^{0.4} = e^{0.4 \times 6.189} = e^{2.4756} \approx 11.85 \).

📌 Verify: \( 11.85^{2.5} = 11.85^2 \cdot \sqrt{11.85} \approx 140.2 \cdot 3.44 \approx 483 \), close to 489.6.

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