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Home » Probability of rolling a prime: $\frac36 = \frac12$ - Coaching Toolbox

Probability of rolling a prime: $\frac36 = \frac12$ - Coaching Toolbox

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 x = -1 + 2\sqrt{3}

📌 A company's profit function is modeled by \(P(x) = -5x^2 + 150x - 1000\), where \(x\) is the number of units sold. Find the number of units that maximizes profit.

📌 Use the vertex formula \(x = -\frac{b}{2a}\):

📌 x = -\frac{150}{2(-5)} = \frac{150}{10} = 15

📌 Evaluate the limit \(\lim_{x \to \infty} \frac{3x^2 - 2x + 1}{2x^2 + x - 4}\).

📌 Divide numerator and denominator by \(x^2\):

📌 \lim_{x \to \infty} \frac{3 - \frac{2}{x} + \frac{1}{x^2}}{2 + \frac{1}{x} - \frac{4}{x^2}} = \frac{3}{2}

📌 A projectile is launched with velocity \(v_0 = 30 \, \text{m/s}\) at an angle of \(45^\circ\). Find the maximum height reached.

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