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mathdeptv2/工具/文本文件/metadata.txt

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ans
14826
$5$
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$\dfrac 43$
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$\{1\}$
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$\pi$
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$\dfrac 14$
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$1$
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$3$
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$\dfrac 52$
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$2\pi$
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$0.9$
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$2\sqrt{2}$
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$(0,4)$
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B
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B
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C
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D
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(1) 相交; (2) $5\sqrt{5}+8$
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(1) $f(x)=\dfrac{\sqrt{2}}2\sin (2x+\dfrac\pi 4)+\dfrac 12$, 最大值为$\dfrac{1+\sqrt{2}}2$, 当且仅当$x=\dfrac\pi 8+k\pi$, $k\in \mathbf{Z}$时取得; (2) $A=\dfrac\pi 4$, $B=\dfrac\pi 3$, $AC=\sqrt{6}$
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(1) 中位数$M=42.5$, 列联表如下: \begin{tabular}{|c|c|c|}
\hline & 超过$M$& 不超过$M$\\
\hline 上班时间 & 10 & 10 \\
\hline 下班时间 & 11 & 9\\
\hline
\end{tabular}; (2) $\chi^2=0.1$, 无显著差异
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(1) $P(4a^{\frac 13},4a^{\frac 23})$; (2) $1$; (3) $2\sqrt{2}$或$\dfrac{\sqrt{2}}4$
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(1) 证明略 (2) $(\pi,\pi+3\sqrt{3}]$; (3) 证明略, 反之不一定成立, 如取$a_n$是常数$a$, 满足$a+2\sin a=\pi$(这样的$a$有三个)