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Home » x \geq 0, \quad y \geq 0 - Simpleprint

x \geq 0, \quad y \geq 0 - Simpleprint

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 = 3t^2 + 6t + 3 + 5t + 5 + 2

📌 = 3t^2 + 11t + 10

📌 The expanded expression is:

📌 \boxed{3t^2 + 11t + 10}

📌 Question:** A nanotechnologist is analyzing the behavior of a nanoparticle where the resistance \( R \) is modeled by \( R = \frac{4}{\sqrt{x} + 2} \). Rationalize the denominator of the expression for \( R \).

📌 To rationalize the denominator, multiply the numerator and the denominator by the conjugate of the denominator:

📌 R = \frac{4}{\sqrt{x} + 2} \times \frac{\sqrt{x} - 2}{\sqrt{x} - 2}

📌 R = \frac{4(\sqrt{x} - 2)}{(\sqrt{x} + 2)(\sqrt{x} - 2)}

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