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where to watch houston astros vs mets - ECD Germany

📅 May 8, 2026 👤 scraface

May 08, 2026

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📌 Now, substitute into the formula for the inradius:

📌 Question: A science communicator demonstrates a circular gear with a diameter of 10 cm rotating inside a triangular frame. If the triangle is equilateral and each side is tangent to the gear, what is the area of the triangle?

📌 Solution: Since the circle is inscribed in an equilateral triangle and has diameter 10 cm, its radius is:

📌 In an equilateral triangle, the radius $ r $ of the inscribed circle is related to the side length $ s $ by:

📌 Now compute the area $ A $ of the equilateral triangle using the formula:

📌 Solution: Let the rectangle have width $ 2x $ and height $ y $, inscribed in a semicircle of radius 5, with its base on the diameter. The top corners lie on the semicircle, so by the Pythagorean theorem:

📌 To maximize $ A $, take the derivative and set it to zero:

📌 Question: A paleobotanist compares a fossilized spherical seed with radius $ 2x $ to a modern hemispherical fruit with radius $ 3x $. What is the ratio of the volume of the seed to the volume of the fruit?

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