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Home » \tan 30^\circ = \frac1\sqrt3 - Groen Casting

\tan 30^\circ = \frac1\sqrt3 - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Check the second derivative or evaluate \(C(t)\) at critical points and endpoints to confirm maximum:

📌 \[ C(1) = \frac{k \cdot 1}{1^2 + 1} = \frac{k}{2} \]

📌 \[ C(-1) = \frac{k \cdot (-1)}{(-1)^2 + 1} = \frac{-k}{2} \]

📌 Since \(C(t) \to 0\) as \(t \to \pm \infty\), the maximum occurs at \(t = 1\).

📌 \(\boxed{t = 1}\)

📌 An entomologist is studying the trajectory of a butterfly modeled as a line passing through \( (2, -3) \) and \( (5, 6) \). Determine the \(y\)-intercept of this line.

📌 First, compute the slope \(m\) of the line through points \((x_1, y_1) = (2, -3)\) and \((x_2, y_2) = (5, 6)\):

📌 \[ m = \frac{6 - (-3)}{5 - 2} = \frac{9}{3} = 3 \]

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