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Chapter 16: Problem 14
Express \(2 \sin ^{2} \theta\) as a function of \(\cos 2 \theta\). a) \(\cos 2 \theta-1\) b) \(\cos 2 \theta+1\) c) \(\cos 2 \theta+2\) d) \(1-\cos 2 \theta\)
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You reach into a jelly bean bag and grab one bean. If the bag contains 30 red, 25 orange, 15 pink, 10 green, and 5 black beans, the probability that you will get a black bean or a red bean is nearest to a) \(0.6\) b) \(0.5\) c) \(0.4\) d) \(0.3\)
Calculate \(\left[\begin{array}{rr}2 & -1 \\ 3 & 2\end{array}\right]\left[\begin{array}{l}2 \\ 1\end{array}\right]\) a) \(\left[\begin{array}{l}8 \\ 3\end{array}\right]\) b) \(\left[\begin{array}{l}3 \\ 8\end{array}\right]\) c) \(\left[\begin{array}{l}-3 \\ -8\end{array}\right]\) d) \([3,8]\)
Evaluate \(2 \int_{0}^{1} e^{x} \sin x d x\) a) \(1.82\) b) \(1.94\) c) \(2.05\) d) \(2.16\)
\(\sqrt{4+x}\) can be written as the series a) \(2-\frac{x}{4}+\frac{x^{2}}{64}+\cdots\) c) \(2-\frac{x^{2}}{4}-\frac{x^{4}}{64}+\cdots\) b) \(2+\frac{x}{8}-\frac{x^{2}}{128}+\cdots\) d) \(2+\frac{x}{4}-\frac{x^{2}}{64}+\cdots\)
The shortest distance from the line \(3 x-4 y=3\) to the point \((6,8)\) is a) \(4.8\) b) \(4.2\) c) \(3.8\) d) \(3.4\)
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