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Home » Solution: Use identity $\sin(2z) = 2\sin z \cos z$. So: - Dyverse

Solution: Use identity $\sin(2z) = 2\sin z \cos z$. So: - Dyverse

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 × 3 / 8 = 90 / 8 = 11.25 → but since wolves, round down?

📌 However, math olympiad problems may accept fractional in calculation only if logical

📌 But better: check if 75 × 0.4 = 30 is correct — yes

📌 30 × 3 / 8 = 11.25 → but 8 × 11 = 88, 8 × 12 = 96 → none divisible

📌 But in such contexts, the problem likely expects 11.25? Unlikely

📌 Alternative: perhaps "3/8" is exact — answer should be 11.25? But not valid

📌 Wait: maybe 40% of 75 is exactly 30, and 3/8 of 30 is 11.25 — but in real observation, could be 11 or 12

📌 But for math problem, we compute mathematically:

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\( x = \pm 3 \): \( 9(9) = 81 \Rightarrow 25y^2 = 144 \Rightarrow y^2...
\( x = \pm 4 \): \( 9(16) = 144 \Rightarrow 25y^2 = 81 \Rightarrow y^2...
\( x = \pm 5 \): \( 9(25) = 225 \Rightarrow 25y^2 = 0 \Rightarrow y =...
Total lattice points: \( (0, \pm3), (\pm5, 0) \) → 4 points.
Thus, the number of lattice points is \( \boxed{4} \).
Question:** How many of the 150 smallest positive integers are congrue...
Solution:** We want integers \( n \) such that \( 1 \leq n \leq 150 \)...
Such numbers are of the form \( n = 7k + 3 \).
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