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Home » An equilateral triangle with perimeter 36 cm has side length: - American Beagle Club

An equilateral triangle with perimeter 36 cm has side length: - American Beagle Club

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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f(x) = 1 + \frac{1}{\sin^2 x} + \frac{1}{\cos^2 x}
Let $ a = \sin^2 x $, $ b = \cos^2 x $, so $ a + b = 1 $, and $ a, b >...
f(x) = 1 + \frac{1}{a} + \frac{1}{b}
We now minimize $ \frac{1}{a} + \frac{1}{b} $ under the constraint $ a...
\frac{1}{a} + \frac{1}{b} \geq \frac{4}{a + b} = 4
Equality occurs when $ a = b = \frac{1}{2} $, i.e., when $ \sin^2 x =...
Substituting back:
f\left(\frac{\pi}{4}\right) = 1 + \frac{1}{\frac{1}{2}} + \frac{1}{\fr...
Thus, the minimum value of $ f(x) $ is:
Question: A science policy analyst is modeling the growth of renewable...

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