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📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 Question: A primatologist models a fruit-bearing canopy as a sphere of radius $2x$ and compares it to a smaller resting dome of radius $x$. What is the ratio of the volume of the sphere to the volume of the smaller dome?

📌 Volume of the smaller dome (assumed spherical): radius $x$

📌 Thus, the ratio of the volume of the sphere to the smaller dome is:

📌 Question: A retired engineer analyzes a triangular support beam with side lengths 10 cm, 17 cm, and 21 cm. He determines the most efficient seismic brace corresponds to the shortest altitude. What is its length?

📌 Solution: Use Herons formula to compute the area. Side lengths: $a = 10$, $b = 17$, $c = 21$. Semi-perimeter:

📌 The shortest altitude is to the longest side, 21 cm:

📌 Solution: To find the center, complete the square for both $ x $ and $ y $. Start by grouping terms:

📌 Complete the square inside each parenthesis:

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