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Home » The possible residues modulo 3 are 0, 1, and 2: - Groen Casting

The possible residues modulo 3 are 0, 1, and 2: - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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x = \frac{-2 \pm \sqrt{4 + 44}}{2} = \frac{-2 \pm \sqrt{48}}{2}
x = \frac{-2 \pm 4\sqrt{3}}{2} = -1 \pm 2\sqrt{3}
Valid solution (since \(x > 1\)):
x = -1 + 2\sqrt{3}
A company's profit function is modeled by \(P(x) = -5x^2 + 150x - 1000...
Use the vertex formula \(x = -\frac{b}{2a}\):
x = -\frac{150}{2(-5)} = \frac{150}{10} = 15
Evaluate the limit \(\lim_{x \to \infty} \frac{3x^2 - 2x + 1}{2x^2 + x...
Divide numerator and denominator by \(x^2\):
\lim_{x \to \infty} \frac{3 - \frac{2}{x} + \frac{1}{x^2}}{2 + \frac{1...

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