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📅 May 14, 2026 👤 scraface

May 14, 2026

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📌 Solution: Complete the square for both $ a $ and $ b $:

📌 Question: Let $ f(x) $ be a polynomial such that $ f(x+1) - f(x) = 6x + 4 $ and $ f(0) = 5 $. Find $ f(x) $.

📌 Solution: Since the difference $ f(x+1) - f(x) $ is linear, $ f(x) $ must be a quadratic:

📌 Solution: To find the radius $ R $ of the circumscribed circle of a triangle with sides $ a = 5 $, $ b = 6 $, and $ c = 7 $, we use the formula:

📌 where $ K $ is the area of the triangle. First, we compute the semi-perimeter $ s $:

📌 Using Herons formula, the area $ K $ is:

📌 Question: In a right triangle, the hypotenuse is $ 13 $ cm and the altitude to the hypotenuse is $ 5 $ cm. What is the area of the triangle?

📌 Solution: The area $ A $ of a triangle can be calculated using the base and height:

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