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hampton inn & suites atlanta galleria atlanta ga 30339 - IQnection

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 We are given \(m + n = 7\) and \(m^2 + n^2 = 29\).

📌 First, compute \(mn\) using the identity:

📌 Now substitute into the formula:

📌 m^3 + n^3 = 7^3 - 3(10)(7) = 343 - 210 = 133.

📌 Thus, \(m^3 + n^3 = \boxed{133}\).**Question:

📌 A cube has a side length of \( a \) units. A sphere is inscribed within the cube such that it touches all six faces of the cube. What is the ratio of the volume of the sphere to the volume of the cube?

📌 The volume of the cube is given by the formula:

📌 V_{\text{cube}} = a^3

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