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+ k = -3 + 9k - ClickBalance

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 After reducing each side by 4 m, the new side is $ s - 4 $, and the new area is:

📌 Question: A coastal monitoring buoy is positioned at the center of a circular storm zone with radius 10 km. A rectangular sensor array measuring 8 km by 15 km is placed such that all its corners lie on the storm boundary. What is the distance from the buoy to any corner of the array, expressed in simplest radical form?

📌 Solution: The rectangular array is inscribed in a circle of radius 10 km, so the diagonal of the rectangle equals the diameter of the circle:

📌 Let the sides be 8 km and 15 km. Then, the diagonal $ d $ satisfies:

📌 Unless the array is not required to have orthogonal sides? But rectangles do.

📌 Question: A spherical energy storage unit has radius $ r $ meters, while a hemispherical backup unit has radius $ 3r $ meters. What is the ratio of the volume of the spherical unit to the volume of the hemispherical unit?

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

📌 Volume of a hemisphere of radius $ 3r $ is half the volume of a full sphere of that radius:

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