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teres minor and major - Nurtured Nest

📅 May 8, 2026 👤 scraface

May 08, 2026

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📌 So, \( x = 4 \) or \( x = -2 \).

📌 Since \( x > 2 \) for the logs to be defined, \( x = 4 \).

📌 A right triangle has legs of length 9 and 12. A circle is inscribed in the triangle. What is the radius of the circle?

📌 The area \( A = \frac{1}{2} \cdot 9 \cdot 12 = 54 \).

📌 The semi-perimeter \( s = \frac{9 + 12 + 15}{2} = 18 \), where 15 is the hypotenuse (via Pythagoras).

📌 The inradius \( r = \frac{A}{s} = \frac{54}{18} = 3 \).

📌 The function \( f(x) = 2^{x} + 2^{-x} \) has a minimum value. What is this minimum value?

📌 Let \( y = 2^x \), so \( f(x) = y + \frac{1}{y} \).

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