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Home » x = \frac-50 \pm \sqrt37968 - AMAZONAWS

x = \frac-50 \pm \sqrt37968 - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 \boxed{\frac{2x\sqrt{6}}{3}}

📌 Question: A marine biologist is designing a conical fish shelter with a base radius of $ 2x $ units and a slant height of $ 5x $ units. What is the total lateral surface area of the cone in terms of $ \pi $ and $ x $?

📌 The lateral surface area of a cone is given by:

📌 where $ r = 2x $ and $ l = 5x $. Substituting:

📌 A = \pi (2x)(5x) = 10\pi x^2

📌 \boxed{10\pi x^2}

📌 Question: A quantum algorithm designer is modeling a 3D lattice where each node is a cube of side $ x $. A diagonal connects two opposite vertices of the cube. What is the length of this space diagonal in terms of $ x $?

📌 The space diagonal $ d $ of a cube with side length $ x $ is given by the 3D Pythagorean theorem:

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