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Home » B) $ 700 $ segundos - Midis

B) $ 700 $ segundos - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 \(\sec \frac{\pi}{4} = \sqrt{2}\), \(\csc \frac{\pi}{4} = \sqrt{2}\), sum = \(2\sqrt{2} \approx 2.828\), square ≈ 8, matches \(g(2) = 8\).

📌 But as \(x \to 0^+\), \(f(x) \to \infty\), so no maximum.

📌 Thus, the function has **no maximum value** on the open interval.

📌 But the problem likely expects a finite maximum — perhaps constraint misunderstanding.

📌 Wait — re-express:

📌 Let \(t = \sin x \cos x = \frac{1}{2} \sin 2x\), so for \(x \in (0, \frac{\pi}{2})\), \(t \in (0, \frac{1}{2}]\).

📌 f(x) = \frac{1}{t^2} + \frac{2}{t} = \frac{1 + 2t}{t^2}

📌 Let \(h(t) = \frac{1 + 2t}{t^2}\), \(t \in (0, \frac{1}{2}]\)

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Arrange the 8 units (with repeated consonants):
The number of arrangements of these 8 units, accounting for repeated B...
\frac{8!}{2!} = \frac{40320}{2} = 20160
Arrange the vowels within the block:
The vowels O, A, I, I can be arranged in:
\frac{4!}{2!} = \frac{24}{2} = 12 \text{ ways}
Total arrangements:
Multiply the number of ways to arrange the units by the vowel internal...
\times 12 = 241920
Thus, the total number of arrangements is \(\boxed{241920}\).

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