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newton's second law is the law of - AdVision eCommerce

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 \( x = \pm 2 \): \( 9(4) = 36 \Rightarrow 25y^2 = 189 \Rightarrow y^2 = 7.56 \) → no

📌 \( x = \pm 3 \): \( 9(9) = 81 \Rightarrow 25y^2 = 144 \Rightarrow y^2 = 5.76 \) → no

📌 \( x = \pm 4 \): \( 9(16) = 144 \Rightarrow 25y^2 = 81 \Rightarrow y^2 = 3.24 \) → no

📌 \( x = \pm 5 \): \( 9(25) = 225 \Rightarrow 25y^2 = 0 \Rightarrow y = 0 \) → 2 points

📌 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 congruent to 3 (mod 7)?

📌 Solution:** We want integers \( n \) such that \( 1 \leq n \leq 150 \) and \( n \equiv 3 \pmod{7} \).

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