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Home » 15% reduction: \( 15 \times 0.85 = 12.75 \) seconds per field - Dachbleche24

15% reduction: \( 15 \times 0.85 = 12.75 \) seconds per field - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Solution: The volume of a sphere of radius $ x $ is $ V_{ ext{particle}} = rac{4}{3}\pi x^3 $. The volume of a hemisphere of radius $ 3x $ is half the volume of a full sphere:

📌 V_{ ext{receptor}} = rac{1}{2} \cdot rac{4}{3}\pi (3x)^3 = rac{2}{3}\pi \cdot 27x^3 = 18\pi x^3

📌 Now compute the ratio:

📌 rac{V_{ ext{particle}}}{V_{ ext{receptor}}} = rac{rac{4}{3}\pi x^3}{18\pi x^3} = rac{4}{3} \cdot rac{1}{18} = rac{4}{54} = rac{2}{27}

📌 Final answer: $ oxed{rac{2}{27}} $

📌 Question: Compute $ an 120^\circ $ using the unit circle and trigonometric identities.

📌 Solution: The angle $ 120^\circ $ lies in the second quadrant. Using the identity $ an(180^\circ - heta) = - an heta $, we write:

📌 an 120^\circ = an(180^\circ - 60^\circ) = - an 60^\circ

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