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ancient greece drama and theatre - SUpost

📅 July 6, 2026 👤 scraface

Jul 06, 2026

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📌 f(x) = 1 + rac{1}{2}(\cos 4x - \cos 2x)

📌 Now, use the identity for $ \cos 4x - \cos 2x $:

📌 \cos A - \cos B = -2 \sin\left(rac{A+B}{2}

📌 ight)\sin\left(rac{A-B}{2}

📌 Let $ A = 4x $, $ B = 2x $:

📌 \cos 4x - \cos 2x = -2 \sin(3x)\sin(x)

📌 f(x) = 1 + rac{1}{2}(-2 \sin 3x \sin x) = 1 - \sin 3x \sin x

📌 We now seek the minimum value of $ f(x) = 1 - \sin 3x \sin x $. Since $ -1 \leq \sin 3x \sin x \leq 1 $, the maximum of $ \sin 3x \sin x $ is 1, so the minimum of $ f(x) $ is:

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Salt in 20% solution: \(0.20 \times 3 = 0.6\) liters.
Salt in 50% solution: \(0.50 \times 2 = 1.0\) liter.
Total salt: \(0.6 + 1.0 = 1.6\) liters.
Total volume: \(3 + 2 = 5\) liters.
Concentration: \(\frac{1.6}{5} \times 100 = 32\%\).
If \(x^2 - 5x + 6 = 0\), what are the values of \(x\)?
Factor the quadratic: \((x - 2)(x - 3) = 0\).
So, \(x = 2\) or \(x = 3\).
A cylindrical tank with radius 3 meters and height 5 meters is filled...
Volume of a cylinder: \(V = \pi r^2 h\).

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