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📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 The arc length \( L \) is given by \( L = r\theta \), where \( \theta \) is in radians.

📌 Convert 45 degrees to radians:

📌 \[ \theta = \frac{45 \times \pi}{180} = \frac{\pi}{4} \]

📌 Then, calculate the arc length:

📌 \[ L = 10 \times \frac{\pi}{4} = \frac{10\pi}{4} = \frac{5\pi}{2} \approx 7.85 \text{ cm} \]

📌 A function is defined by \( f(x) = x^3 - 6x^2 + 11x - 6 \). Find the x-values where the function crosses the x-axis.

📌 To find the roots, solve \( x^3 - 6x^2 + 11x - 6 = 0 \).

📌 By trial or synthetic division, find \( x = 1 \) is a root. Factorize:

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Find intersection with \(y = 2x + 1\):
2x + 1 = -\frac{1}{2}x + \frac{11}{2}
Multiply both sides by 2:
4x + 2 = -x + 11
\Rightarrow 5x = 9 \Rightarrow x = \frac{9}{5}
y = 2 \cdot \frac{9}{5} + 1 = \frac{18}{5} + \frac{5}{5} = \frac{23}{5...
Thus, the closest point is \(\boxed{\left( \frac{9}{5}, \frac{23}{5} \...
Compute the maximum value of \((\sec x + \csc x)^2\) for \(0 < x < \fr...
Let \(f(x) = (\sec x + \csc x)^2 = \left(\frac{1}{\cos x} + \frac{1}{\...
Let \(u = \sin x + \cos x\). Then:

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