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Home » The shortest altitude is the one to the hypotenuse: \(\boxed4.8\) cm. - Portal da AcÃºstica

The shortest altitude is the one to the hypotenuse: \(\boxed4.8\) cm. - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 #### 93.15

📌 Peter studies algorithm efficiency and compares two sorting methods. Method A runs in O(n²) time and takes 0.01n² seconds for n elements. Method B runs in O(n log n) time and takes 0.05n log₂(n) seconds. For what minimum value of n does Method B become faster than Method A?

📌 We need to solve: 0.05n log₂(n) < 0.01n².

📌 Divide both sides by n (n > 0): 0.05 log₂(n) < 0.01n → log₂(n) < 0.2n.

📌 We test values:

📌 n = 10: log₂(10) ≈ 3.32, 0.2×10 = 2 → 3.32 > 2 → A faster

📌 n = 20: log₂(20) ≈ 4.32, 0.2×20 = 4 → 4.32 > 4

📌 n = 25: log₂(25) ≈ 4.64, 0.2×25 = 5 → 4.64 < 5 → B faster

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