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is menards open on thanksgiving day - Deep Underground Poetry

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 Question: A pharmacologist models the diffusion of a spherical drug particle in a gel medium. The particle has radius $ x $, and it interacts with a hemispherical receptor of radius $ 3x $. What is the ratio of the volume of the particle to the volume of the receptor?

📌 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:

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