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Home » \frac66 + x5 = 16. - Veritas Home Health

\frac66 + x5 = 16. - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Question: A spherical data storage unit has a radius of $ y $ units, and a hemispherical backup dome has a radius of $ 3y $ units. What is the ratio of the storage unit's volume to the backup dome's volume?

📌 Solution: The volume of a sphere is $ \frac{4}{3}\pi y^3 $, and the volume of a hemisphere is $ \frac{2}{3}\pi (3y)^3 = \frac{2}{3}\pi \times 27y^3 = 18\pi y^3 $. The ratio is $ \frac{\frac{4}{3}\pi y^3}{18\pi y^3} = \frac{4}{54} = \frac{2}{27} $. \boxed{\dfrac{2}{27}}

📌 Question: A triangular geological fault line has side lengths of 10 cm, 13 cm, and 15 cm. Compute the length of the shortest altitude.

📌 Solution: First, compute the area using Heron's formula. The semi-perimeter $ s = \frac{10 + 13 + 15}{2} = 19 \, \text{cm} $. The area is $ \sqrt{19(19-10)(19-13

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