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📅 April 29, 2026 👤 scraface

Apr 29, 2026

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📌 An oceanographer is analyzing the movement of ocean currents and models a small spherical region of water with a radius of $y$ meters. Nearby, there is a hemisphere-shaped region with a radius of $3y$ meters. What is the ratio of the volume of the spherical region to the volume of the hemisphere?

📌 Thus, the ratio of the volume of the sphere to the hemisphere is:

📌 First, compute the length of the diagonal using the Pythagorean theorem:

📌 Therefore, the circumference of the circle is:

📌 Find the length of the shortest altitude in a triangle with side lengths 13 cm, 14 cm, and 15 cm.

📌 We use the formula for the area of a triangle using Herons formula and then compute altitudes.

📌 The shortest altitude corresponds to the longest side (15 cm), which is 11.2 cm.

📌 Question: A herpetologist studies 15 endangered amphibian species, 6 of which are frogs. What is the ratio of frogs to non-frogs, simplified?

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