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\[ A \approx 5000 \times 1.195618 \] - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 A right triangle has legs of lengths \( \sqrt{5} \) and \( \sqrt{11} \). Find the length of the altitude to the hypotenuse.

📌 Hypotenuse: \( c = \sqrt{(\sqrt{5})^2 + (\sqrt{11})^2} = \sqrt{5 + 11} = \sqrt{16} = 4 \).

📌 Area: \( rac{1}{2} \cdot \sqrt{5} \cdot \sqrt{11} = rac{1}{2} \sqrt{55} \).

📌 Also: \( rac{1}{2} \cdot 4 \cdot h = 2h \).

📌 Set equal: \( 2h = rac{1}{2} \sqrt{55} \) â \( h = rac{\sqrt{55}}{4} \).

📌 #### \(rac{\sqrt{55}}{4}\)Question: Let $ f(u) = u - rac{u^4}{4} $ for every real number $ u $. If $ b_1 = 2 $ and $ b_{n+1} = f(b_n) $ for $ n \geq 1 $, find $ b_3 $.

📌 Solution: Compute $ b_2 = f(2) = 2 - rac{2^4}{4} = 2 - rac{16}{4} = 2 - 4 = -2 $. Then $ b_3 = f(-2) = -2 - rac{(-2)^4}{4} = -2 - rac{16}{4} = -2 - 4 = -6 $. Thus, $ b_3 = oxed{-6} $.

📌 Question: A science communicator designs an exhibit where the number of interactive stations $ S $ at time $ t $ (in hours) satisfies $ S(t) = t^2 - 5t + 6 $. Find all times $ t $ when $ S(t) = 0 $.

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\[ inom{17}{2} = rac{17 imes 16}{2} = 136 \]
Il y a 136 solutions entiÃ¨res.
#### 136
Un train parcourt 150 km Ã 50 km/h puis 200 km Ã 100 km/h. Quelle es...
Temps pour la premiÃ¨re partie : \( rac{150}{50} = 3 \) heures.
Temps pour la deuxiÃ¨me partie : \( rac{200}{100} = 2 \) heures.
Distance totale : \( 150 + 200 = 350 \) km.
Temps total : \( 3 + 2 = 5 \) heures.
\[ rac{350}{5} = 70 ext{ km/h} \]
La vitesse moyenne est de 70 km/h.

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