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Home » \( \textRemaining contaminants = 10,000 \times (1 - 0.05)^10 \). - Groen Casting

\( \textRemaining contaminants = 10,000 \times (1 - 0.05)^10 \). - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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Note $ s = \frac{1}{2} \sin 2x $, and since $ 0 < x < \frac{\pi}{2} $,...
Define $ g(s) = 1 + 2s + \frac{1}{s} $, for $ 0 < s \leq \frac{1}{2} $...
g'(s) = 2 - \frac{1}{s^2}
Set $ g'(s) = 0 \Rightarrow 2 = \frac{1}{s^2} \Rightarrow s^2 = \frac{...
So minimum occurs at endpoint $ s = \frac{1}{2} $:
g\left( \frac{1}{2} \right) = 1 + 2 \cdot \frac{1}{2} + \frac{1}{\frac...
Thus, the minimum value is $ \boxed{4} $.
Question: A philosopher of science considers three unit vectors $ \mat...
Solution: Since $ \mathbf{a}, \mathbf{b}, \mathbf{c} $ are unit vector...
\|\mathbf{a} + \mathbf{b} + \mathbf{c}\|^2 = \|\mathbf{a}\|^2 + \|\mat...

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