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If \(n\) is even, \(n\) is divisible by 2. - AMAZONAWS
If \(n\) is even, \(n\) is divisible by 2. - AMAZONAWS
📅 March 11, 2026
👤 scraface
Mar 11, 2026
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📌 Solution: For a right triangle with legs $ a $ and $ b $, and hypotenuse $ z $, the inradius is given by $ c = rac{a + b - z}{2} $. The area $ A $ of the triangle is $ rac{1}{2}ab $. The area of the incircle is $ \pi c^2 $. Using the identity $ a^2 + b^2 = z^2 $, and expressing $ a + b $ in terms of $ z $ and $ c $, we find $ a + b = z + 2c $. Also, the semiperimeter $ s = rac{a + b + z}{2} = rac{2z + 2c}{2} = z + c $. The area can also be written as $ A = r \cdot s = c(z + c) $. Therefore, the ratio becomes:
📌 Solution: The volume of a sphere of radius $ x $ is $ V_{ ext{particle}} = rac{4}{3}\pi x^3 $. The volume of a hemisphere of radius $ 3x $ is half the volume of a full sphere:
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