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Home » The expression is positive in \( (-\infty, -3) \) and \( (4, \infty) \) - Appfinity Technologies

The expression is positive in \( (-\infty, -3) \) and \( (4, \infty) \) - Appfinity Technologies

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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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
n = 24: log₂(24) ≈ 4.58, 0.2×24 = 4.8 → 4.58 < 4.8 → B faster
n = 23: log₂(23) ≈ 4.52, 0.2×23 = 4.6 → 4.52 < 4.6 → B faster
n = 22: log₂(22) ≈ 4.46, 0.2×22 = 4.4 → 4.46 > 4.4 → A faster
So, the smallest n where B is faster is 23.
#### 23
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First, calculate the score for the 5th game:
S(5) = 2(5)^2 + 3(5) + 1 = 2(25) + 15 + 1 = 50 + 15 + 1 = 66
Next, calculate the score for the 3rd game:
S(3) = 2(3)^2 + 3(3) + 1 = 2(9) + 9 + 1 = 18 + 9 + 1 = 28
The score difference between the 5th and 3rd games is:
S(5) - S(3) = 66 - 28 = 38
Thus, the score difference is:

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