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7th: 11.390625 - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 For $ x < -3 $, test $ x = -4 $: $ \frac{-12}{-1} = 12 > 0 $.

📌 For $ -3 < x < 8 $, test $ x = 0 $: $ \frac{-8}{3} < 0 $.

📌 For $ x > 8 $, test $ x = 9 $: $ \frac{1}{12} > 0 $.

📌 Include $ x = 8 $, exclude $ x = -3 $. Solution: $ (-\infty, -3) \cup [8, \infty) $. \boxed{(-\infty, -3) \cup [8, \infty)}Question: A cone has a radius of \(3y\) units and a height of \(4y\) units. A sphere has a radius of \(2y\) units. What is the ratio of the volume of the cone to the volume of the sphere?

📌 The volume \(V\) of a cone with radius \(r\) and height \(h\) is given by the formula:

📌 V_{\text{cone}} = \frac{1}{3} \pi r^2 h

📌 Substituting \(r = 3y\) and \(h = 4y\), we get:

📌 V_{\text{cone}} = \frac{1}{3} \pi (3y)^2 (4y) = \frac{1}{3} \pi \cdot 9y^2 \cdot 4y = \frac{1}{3} \pi \cdot 36y^3 = 12\pi y^3

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