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sst question paper class 9 half yearly - AdVision eCommerce

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 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?

📌 Solution: The volume $ V $ of a sphere of radius $ r $ is:

📌 The volume of a hemisphere of radius $ 3x $ is half the sphere volume:

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é¢æ° \(f(x) = 3x^3 - 5x^2 + 2x - 7\) ã®å°é¢æ°ãæ±ãã\(x = 2...
f'(x) = rac{d}{dx}(3x^3 - 5x^2 + 2x - 7) = 9x^2 - 10x + 2
f'(2) = 9(2)^2 - 10(2) + 2 = 36 - 20 + 2 = 18
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