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pacers blow 3-0 lead - RTA

📅 May 10, 2026 👤 scraface

May 10, 2026

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📌 Now use Herons formula to find the area $K$:

📌 Solution: Let the side length of the original equilateral triangle be $s$. The area $A$ of an equilateral triangle is:

📌 After reducing each side by 4 mm, the new side length is $s = 12$ mm. The new area is:

📌 Question: An oceanographer analyzing spherical underwater sensor buoy designs compares a full buoy of radius $2r$ to a hemispherical float of radius $r$. What is the ratio of the volume of the buoy to the volume of the float?

📌 Solution: Volume of a sphere with radius $2r$ is:

📌 Volume of a hemisphere with radius $r$ is half the volume of a sphere:

📌 Question: A cartographer analyzing satellite triangulation data determines that a signal path forms a triangle with side lengths 10 km, 17 km, and 21 km. Find the length of the shortest altitude in kilometers.

📌 Solution: The shortest altitude corresponds to the longest side, since area is fixed and altitude is inversely proportional to base. The longest side is 21 km, so we compute the altitude to this side.

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