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Home » Let $ h $ be the altitude to the hypotenuse. Using the area formula: - Decision Point

Let $ h $ be the altitude to the hypotenuse. Using the area formula: - Decision Point

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 After reducing the radius by 2, the new radius is \( r - 2 \), and the new volume is:

📌 V_{\text{new}} = \frac{4}{3}\pi (r - 2)^3

📌 The volume decrease is:

📌 \frac{4}{3}\pi r^3 - \frac{4}{3}\pi (r - 2)^3 = 128\pi

📌 Divide through by \( \frac{4}{3}\pi \):

📌 r^3 - (r - 2)^3 = 96

📌 Expand \( (r - 2)^3 \):

📌 r^3 - (r^3 - 6r^2 + 12r - 8) = 96

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A soil scientist is evaluating nitrogen retention in three soil types:...
Nitrogen applied:
Sandy: \( 0.6 \times 80 = 48 \, \text{kg} \)
Loam: \( 0.4 \times 80 = 32 \, \text{kg} \)
Clay: \( 0.5 \times 80 = 40 \, \text{kg} \)
Retention:
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