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mathdeptv2/工具v2/文本文件/metadata.txt

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ans
018366
(1) $x=\dfrac{\pi}{3}+2k\pi$或$\dfrac{2\pi}{3}+2k\pi$, $k\in \mathbf{Z}$; (2) $x=\pm \dfrac{3\pi}{4}+2k\pi$, $k\in \mathbf{Z}$; (3) $x=k\pi+\dfrac{\pi}{6}$, $k\in \mathbf{Z}$
018367
(1) $\{\dfrac{\pi}{6},\dfrac{\pi}{3},\dfrac{7\pi}{6},\dfrac{4\pi}{3}\}$; (2) $\{x|x=2k\pi+\dfrac{\pi}{12}\text{或}x=2k\pi-\dfrac{5\pi}{12}, \ k\in \mathbf{Z}\}$; (3) $\{x|x=\dfrac{k\pi}{2}+\dfrac{\pi}{4}, \ k\in \mathbf{Z}\}$
018369
(1) $x=-\dfrac{\pi}{2}+2k\pi$, $k\in \mathbf{Z}$; (2) $x=\pm \dfrac{\pi}{6}+2k\pi$, $k\in \mathbf{Z}$; (3) $x=\dfrac{\pi}{4}+k\pi$, $k\in \mathbf{Z}$
009563
(1) $\{\dfrac{\pi}{2},\dfrac{11\pi}{6}\}$; (2) $\{x|x=k\pi+\dfrac{5\pi}{24}\text{或}k\pi-\dfrac{11\pi}{24}, \ k\in \mathbf{Z}\}$; (3) $\{x|x=\dfrac{k\pi}{3}+\dfrac{\pi}{6}, \ k\in \mathbf{Z}\}$
018372
$\dfrac{\sqrt{6}-\sqrt{2}}{4}$, $\dfrac{\sqrt{6}+\sqrt{2}}{4}$
018373
$-\dfrac{56}{65}$
018375
$\dfrac{\pi}{3}$
009564
(1) $\dfrac{\sqrt{2}}{2}$; (2) $\dfrac{\sqrt{3}}{2}$
009565
$-\dfrac{7\sqrt{2}}{26}$
018377
(1) $\dfrac{\sqrt{3}}{2}$; (2) $\cos 2\alpha$; (3) $-\cos 3x$
018376
$-\dfrac{4}{5}$
018378
$\dfrac{\sqrt{6}-\sqrt{2}}{4}$
018379
证明略
018380
(1) $-1$; (2) $\dfrac{1}{7}$
018381
$-\sqrt{3}$
009567
(1) $\dfrac{\sqrt{3}}{2}$; (2) $\sqrt{3}$
009568
$\dfrac{\sqrt{2}}{10}$, $7$
009569
(1) 证明略; (2) 证明略
018385
证明略
018386
$(-\dfrac{\sqrt{2}}{2},\dfrac{3\sqrt{2}}{2})$
018387
(1) $\sin(\alpha+\dfrac{\pi}{3})$; (2) $\sqrt{2}\sin(\alpha-\dfrac{\pi}{4})$; (3) $5\sin(\alpha+\varphi)$, 其中$\cos\varphi=\dfrac{3}{5}$, $\sin\varphi=\dfrac{4}{5}$; (4) $\sqrt{a^2+b^2}\sin(\alpha+\varphi)$, 其中$\cos\varphi=\dfrac{a}{\sqrt{a^2+b^2}}$, $\sin\varphi=\dfrac{b}{\sqrt{a^2+b^2}}$
024614
$\{\alpha|\alpha=2k\pi\text{或}\dfrac{2\pi}{3}+2k\pi, \ k\in \mathbf{Z}\}$
009570
$\sin C=\dfrac{220}{221}$, $\cos C=-\dfrac{21}{221}$
009571
$\sin(\alpha+\beta)=\dfrac{33}{65}$, $\cos(\alpha+\beta)=-\dfrac{56}{65}$, $\alpha+\beta$是第二象限角
009572
(1) $\sqrt{2}\sin(\alpha+\dfrac{\pi}{4})$; (2) $2\sin(\alpha+\dfrac{2\pi}{3})$
018390
$\dfrac{\sqrt{6}-\sqrt{2}}{4}$
018402
证明略
018403
证明略
018404
证明略
009576
证明略
009577
证明略
009578
证明略
018405
证明略
040387
$\dfrac{5\pi}{3}$
040388
$-1$
040389
$-\dfrac{\pi}{3}$或$\dfrac{4\pi}{3}$
040390
$-3$
040391
$-2$
040392
$-\dfrac{\sqrt{23}}{4}$
ans
041050
$2\sqrt{7}$, $(0,\pm \sqrt{7})$
040971
$2\sqrt{7}$, $(\pm \sqrt{7},0)$
041051
D
040972
$x=0(-3 \leq y \leq 3)$
040973
B
040974
$\dfrac{x^2}7+\dfrac{y^2}{16}=1$
040975
B
008878
D
008877
A
014470
$4\sqrt{3}$
040976
$\dfrac{x^2}{25}+\dfrac{y^2}{16}=1$或$\dfrac{x^2}7+\dfrac{y^2}{16}=1$
040977
(1)$\dfrac{x^2}{100}+\dfrac{y^2}{64}=1$;
(2)$\dfrac{x^2}6+\dfrac{y^2}4=1$
040978
(1)$k=7$;(2)$4<k<7$
040979
$5$,$8$,$6$,$\dfrac35$
008882
$(0,\pm5)$
021195
$20$
021196
$\dfrac{x^2}{15}+\dfrac{y^2}{10}=1$
040980
$\dfrac{x^2}{\dfrac{625}{16}}+\dfrac{y^2}{34}=1$
040981
$\dfrac35$
040982
$\dfrac{x^2}{25}+\dfrac{y^2}{16}=1$或$\dfrac{x^2}{16}+\dfrac{y^2}{25}=1$
008892
$\dfrac{x^2}9+\dfrac{y^2}{16}=1$
040983
$18$
040984
$1$
040985
(1)$10$;(2)$2$
040986
(1)$\dfrac{x^2}4+\dfrac{y^2}{8}=1$或$\dfrac{x^2}8+\dfrac{y^2}{4}=1$;\\
(2)$\dfrac{x^2}6+\dfrac{y^2}{10}=1$;\\
(3)$\dfrac{x^2}8+\dfrac{y^2}{32}=1$或$\dfrac{x^2}{68}+\dfrac{y^2}{17}=1$;\\
(4)$\dfrac{x^2}{40}+\dfrac{y^2}{4}=1$或$\dfrac{x^2}{36}+\dfrac{y^2}{40}=1$;\\
(5)$\dfrac{x^2}{10}+\dfrac{y^2}{5}=1$
021183
C
008883
D
040987
$\dfrac{x^2}{16}+\dfrac{y^2}{8}=1$
040988
$\dfrac{x^2}{10}+\dfrac{y^2}{5}=1(y\neq 0)$
040989
$2$,$\dfrac{2\pi}{3}$
008895
B
040990
$\dfrac{x^2}{4}+\dfrac{y^2}{3}=1(-2<x<0)$
040991
A
040992
$\dfrac{x^2}{36}+\dfrac{y^2}{16}=1(y \neq 0)$
008898
$\dfrac{x^2}{16}+\dfrac{y^2}{7}=1$
040993
$32-16\sqrt{3}$
008891
(1)$15$,$5$;(2)$(\dfrac{25}4,\pm \dfrac{3\sqrt{39}}{4})$
021197
$x\pm2\sqrt{6}y-5=0$
021184
$(-\sqrt{3},\sqrt{3})$
021185
$[\sqrt{2},\sqrt{3})$
021186
$[1,5)\cup(5,+infty)$
021187
$\sqrt{2}-1$
021198
$4x+9y-13=0$
021188
$(x-3)^2+(y-4)^2=4$
040994
$4$
021190
$(-\sqrt95,\sqrt15)$
021191
$k<-\sqrt{3}$或$k>\sqrt{3}$
040995
(1)$y=-\sqrt12+\sqrt34$;(2)$x+4y=0$(点在已知椭圆内);(3)$x^2+x+2y^2=0$
040996
$6\sqrt{5}$
021204
$\dfrac{\sqrt{2}}{2}$
021205
$2\sqrt{37}$,$2$
021206
$\dfrac{x^2}{25}+\dfrac{y^2}{75}=1$
021207
$\dfrac{x^2}{12}+\dfrac{y^2}{9}=1$或$\dfrac{x^2}{9}+\dfrac{y^2}{12}=1$
021208
$[-\sqrt{34},\sqrt{34}]$
021209
$\dfrac{\pi}3$
040997
$b\sqrt{a^2-b^2}$
040998
$8\sqrt{3}$
021212
$P(-6,-4)$,$d=\dfrac{22}{\sqrt{73}}$
021200
$\dfrac{x^2}{4}+y^2=1$
021201
$-\dfrac{5\sqrt{7}}{4}<x<\dfrac{5\sqrt{7}}{4}$
021202
$-\dfrac{2\sqrt{13}}{13}<m<\dfrac{2\sqrt{13}}{13}$
021203
(1)$\dfrac{x^2}{9}+\dfrac{y^2}{4}=1$;(2)$8x-9y+25=0$
040999
(1)$-6$;(2)$\dfrac{x^2}{a^2}-\dfrac{y^2}{ta^2}=1(x\neq \pm a)$;(3)$\dfrac{\sqrt{6}}{3}$;(4)$\dfrac{\sqrt{6}}{3}$或$\sqrt{6}$
041000
C,A,A
021222
(1)$\dfrac{x^2}{9}-\dfrac{y^2}{7}=1$;(2)$\dfrac{y^2}{64}-\dfrac{x^2}{36}=1(y>0)$;(3)$x^2-\dfrac{y^2}{3}=1$
021223
$\dfrac{x^2}{20}-\dfrac{y^2}{16}=1$
021224
$\dfrac{x^2}{33-12\sqrt{6}}-\dfrac{y^2}{12\sqrt{6}-8}=1$或$\dfrac{y^2}{16}-\dfrac{x^2}{9}=1$
021225
不正确, 正确结果为$17$
021226
$\dfrac{x^2}{115600}-\dfrac{y^2}{134400}=1$
021227
D
021228
$(-3,6)$
021229
$m<-2$
021230
$\dfrac{41}{4}$
021231
$32+2m$
021232
$|PF_1|=\dfrac{c}{a}x_0+a$,$|PF_2|=\dfrac{c}{a}x_0-a$
021233
$x^2-\dfrac{y^2}{4}=1$
041001
(1)$\dfrac{y^2}{18}-\dfrac{x^2}{18}=1$,$\sqrt{2}$;(2)$(\pm 2\sqrt{3},0)$,$\arctan{2\sqrt{2}}$
041002
A,A,B,B
041003
(1))$\dfrac{x^2}{3}-\dfrac{y^2}{5}=1$;(2))$\dfrac{y^2}{81}-\dfrac{x^2}{9}=1$或)$x^2-\dfrac{y^2}{9}=1$
021242
$\dfrac{x^2}{3}-\dfrac{y^2}{12}=1$
021243
$y=\pm \dfrac{\sqrt{2}}{4}x$
021244
证明略
041004
(1)$\dfrac{x^2}{\dfrac{81}{13}}-\dfrac{y^2}{\dfrac{36}{13}}=1$;(2)$2$或$\dfrac{2\sqrt{3}}{3}$; (3)$(\dfrac 52,\dfrac 72)$;(4)$(\pm \sqrt{7},0)$
041005
D,A,D
021251
$a^2$
021263
$\dfrac{y^2}{36}-\dfrac{x^2}{81}=1(x\neq 0)$
021252
$\dfrac{c}{a}$
021253
$y=\pm \sqrt{2}x$
021254
$0$
008917
$\dfrac{x^2}{4}-\dfrac{y^2}{5}=1$(x>0)
021255
$\dfrac{2\sqrt{3}}{3}$
021256
$\dfrac{14\sqrt{3}}{3}$
041006
$3$
021258
$x^2-4y^2=\pm \dfrac{36}{5}$
021259
$(-\dfrac{\sqrt{15}}{3},-1)$
021260
(1)椭圆:$k<4$,双曲线: $4<k<9$;(2)$\dfrac{x^2}{3}-\dfrac{y^2}{2}=1$
021261
(1)$(\sqrt{6},-\sqrt{3})\cup(\sqrt{3},\sqrt{3})\cup(\sqrt{3},\sqrt{6})$;(2)$\pm 1$
021267
(1)$e>\dfrac{\sqrt{6}}{2},e\neq \sqrt{2}$;(2)$\dfrac{17}{13}$
ans
012360
$\dfrac{\pi}{3}$
009305
(1)$x^15$,$-15x^14$,$105x^13$,$-455x^12$\\
(2)$-2099520a^9b^14$
009306
(1)$\dfrac{105}{8}$;(2)$-252$
009309
$120$
009308
证明略
009317
(1)第$18$,$19$项; \\
(2)$\mathrm{C}_{35}^{27}3^{27}x^{27}$
009319
证明略
021093
(1)$\dfrac{1}{45}$;(2)$\dfrac{7}{10}$
022919
(1)$\dfrac{1}{36}$;(2)$\dfrac{1}{18}$;(3)$\dfrac{5}{12}$
021095
(1)$\dfrac{1}{68880}$;(2)$\dfrac{1}{11480}$
021096
$\dfrac37$
021097
$\dfrac{1}{12}$
021098
$\dfrac{18}{25}$
021099
$\dfrac{2}{5}$
021101
$\dfrac{11}{12}$
021102
$\dfrac{3439}{10000}$
021103
$\dfrac{n!}{n^n}$
021104
$\dfrac{1}{15}$
021105
$\dfrac15$
021106
(1)$\dfrac{11}{42}$;(2)$\dfrac{31}{42}$
021107
(1)$\dfrac{1279}{1785}$;(2)$\dfrac{59049}{139075300}$
021108
(1)$\{5,7,9\}$;(2)$\{0,2,4,5,6,7,8,9\}$;(3)$\emptyset$
021109
B
021110
(1)$\{1,2,3,4\}$;(2)A
021111
(1)$\{1,2,3,4\}$;(2)A
021112
充分非必要
021113
(1)$A\cup B$;(2)$A \cap \overline{B}$;(3)$(A \cap \overline{B}) \cup(\overline{A} \cap B) $
021114
$B\subseteq \overline{A}$,$\overline{A}\cup \overline{B}=\omega$
021116
(1)$\dfrac12$;(2)$\dfrac56$;(3)$\dfrac23$;(4)$\dfrac56$
021117
(1)不是;(2)$0.94$
021125
(1)$(A\cap B \cap \overline{C})\cup (A \cap \overline{B} \cap C)\cup (\overline{A} \cap B \cap C)\cup (A \cap B \cap C)$;
(2)$\overline{A\cap B \cap C }$;
(3)$(A\cap B \cap \overline{C})\cup (A \cap \overline{B} \cap C)\cup (\overline{A} \cap B \cap C)$
021118
$\dfrac47$,$\dfrac27$,$\dfrac17$,$\dfrac67$,$\dfrac67$,$\dfrac57$
019932
(1)$\dfrac34$;(2)$\dfrac1{13}$;(3)$\dfrac12$;(4)$\dfrac{51}{52}$
021119
$\dfrac45$
021120
$\dfrac35$
021121
$\dfrac14$,$\dfrac16$,$\dfrac14$
021122
$0.9$,$0.1$
018762
证明略
021126
大数定律
021127
$\dfrac{73}{75}$
021128
$\dfrac34$,$\dfrac{9}{44}$,$\dfrac{9}{220}$.$\dfrac{1}{220}$
021129
(1)$0.46$;(2)$0.51$;(3)$0.97$
021130
(1)$0.852$;(2)$25560$;(3)$5869$
021131
(1)$0.1,0.06,0.025,0.02,0.02,0.02$;(2)$0.02$;(3)$40$
021132
(1)$30\%$;(2)$53\%$;(3)$73\%$;(4)$14\%$;(5)$90\%$;(6)$10\%$;
021133
(1)$\dfrac13$;(2)$\dfrac14$
021134
C
021135
(1)$\dfrac56$;(2)$\dfrac16$;(3)$\dfrac23$;(4)$\dfrac12$
021136
(1)$0.995$;(2)$0.095$
021137
(1)$7:1$;(2)$11:5$
021138
$0.328$
021139
$(\dfrac23,1)$
021140
(1)$\dfrac38$,$\dfrac23$;(2)$\dfrac{21}{32}$
021141
D
021142
D
021143
A
021144
A
021145
\textcircled{2}
021146
总体是$2487$万人的年龄, 样本是$24000$个常住居民的年龄, 样本量是$24000$
021147
观测, 观测, 实验
021148
不可靠, 样本容量太小, 样本不一定具有代表性
021149
$2$
021150
$122$
021151
$a=b=10.5$
021152
平均值是$17$,方差是$27$
021153
平均数是$72.0$, 中位数是$70$, 方差是$74.9$
021154
$\dfrac{n}{N}$
021155
B
021156
20
021157
C
021158
$4467$
021159
(1)抽签法;(2)分层抽样
021160
$49,04,40,36,16,08,06,55,33,69$
021161
样本容量为$92$, 抽样人数为$31$
021162
021163
分层抽样, 高一抽$18$人, 高二抽$22$人, 高三抽$10$人
021164
C
021165
$4$,$5.14$
021166
$0.32$,$96$
021167
$300$
021168
集中, 分散, $6.88$,$12.43$
021169
\begin{tabular}{c|ccccccc}
8 & 9 \\
9 & 3 & 4 & 6 & 7 \\
10 & 0 & 0 & 1 & 1 & 3 & 5 & 8\\
11 & 0 & 2
\end{tabular}
021170
021171
021172
D
021173
$35$
021174
$12$
021177
C
021179
\textcircled{1},\textcircled{2}
021180
A
021175
甲更准, 乙更稳定
021176
(1)$3.47$,(2)$2773$
021178
$100$
021181
(1)$9.5$;(2)不能
021182
平均成绩是$89.6$, 总体方差是$12.09$
023356
$A\subset C\subset B \subset E \subset D \subset G$;$E \subset F \subset G$
023357
全错
023358
$\dfrac{72\sqrt{21}}7$
023359
(1)$\dfrac16$;(2)
023360
$2\sqrt{15}$或$4\sqrt{6}$
023361
023362
$\frac{b^2-a^2}{\sqrt{a^2+b^2} \cdot \sqrt{a^2+b^2+c^2}}$.
023363
(1) $\frac{1}{2}$; (2) $\frac{\pi}{3}$.
023364
(1) 略; (2) $\arcsin{\frac{3\sqrt{2}}{10}}$; (3) $\frac{24\sqrt{41}}{41}$
023365
023366
$\sqrt{41}$
023367
(1) 略; (2) $\frac{\pi}{4}$.
023368
$8\sqrt{3}$.
003494
(1) 略; (2) $3$; (3) $108\sqrt{3}$.
023369
(1) $48$; (2) $16\sqrt{3}+8\sqrt{21}+40$
023370
(1) 略; (2) $\frac{1}{3}$; (3) $\frac{\sqrt{2}}{2}+\frac{\sqrt{6}}{2}$.
023108
C
023109
1; 4.
023110
8; 4.
023111
$M \in a$,$M \notin \alpha$.
023112
$\{1,4,6\}$.
023113
$D$.
023114
$C$.
023115
$A$.
023116
1个或者无数个
023117
平行四边形
023118
10
023119
\textcircled{1}, \textcircled{2} ,\textcircled{4}, \textcircled{5}.
023120
$D$.
012345
$D$.
023124
$\frac{5(\sqrt{6}-1)}{2} $.
023125
$\sqrt{2}+2\sqrt{13}$.
023126
(1) F ; (2) F; (3) F; (4) T; (5) T; (6) T; (7) T; (8) F.
023127
(1) T ; (2) F; (3) F; (4) F; (5) F.
023128
异面或者平行.
023129
(1) 平行; (2) 异面.
023130
相交或者平行.
023131
充分不必要.
023132
4个.
023133
$45^{\circ}$; $30^{\circ}$或$60^{\circ}$.
023134
(1) $\frac{\pi}{3}$; (2) $\arccos \frac{\sqrt{10}}{10}$; (3) $\arccos \frac{\sqrt{10}}{5}$.
023135
\textcircled{1} \textcircled{4}.
023136
$\frac{a}{3}$.
012345
D
023137
B
023140
$\frac{\pi}{4}$或$\frac{\pi}{3}$.
023141
(1) 点 $P$ 在$C$点; (2) 点 $P$ 在距离$C$点$\frac{16}{5}$.
023142
$\frac{\sqrt{39}}{2}$.
016740
1.
016731
8.
023143
$\arctan\frac{1}{5}$或者$\arctan\frac{4}{5}$.
023144
$\arctan\frac{2\sqrt{5}}{5}$.
017767
2
023145
$\sqrt{6}$.
023146
$\frac{\sqrt{3}}{3}$.
023147
$[ 30,90 ]$.
023148
(1) $\frac{\sqrt{15}}{5}$; (2) $\frac{\pi}{6}$.
023149
$\frac{\sqrt{3}}{2}$.
023150
$\frac{2}{3}$.
023151
(1) $\arctan \frac{\sqrt{5}}{5}$; (2) $\arccos \frac{\sqrt{30}}{10}$; (3) 在 $BC$ 边上存在一点 $G$, $BG$的值为1.
023152
(1) 略; (2) $\arcsin \frac{\sqrt{21}}{7}$; (3) 存在 $P$, 使得 $DE \parallel $ 平面 $BMP$, $\dfrac{AP}{DP}$ 的值3.
031552
$\frac{\sqrt{10}}{5}$
003489
(1) $\arcsin \frac{\sqrt{6}}{3}$; (2) $\arcsin \frac{\sqrt{3}}{3}$; (3) $\frac{\pi}{4}$.
023153
(1) $\frac{\sqrt{6}}{3}$; (2) $\frac{\sqrt{6}}{6}$; (3) $\frac{\sqrt{6}}{6}$.
003456
$\frac{3\sqrt{5}}{5}$.
003457
$\frac{\pi}{3}$或$\frac{2\pi}{3}$.
023154
1或3.
023155
$\frac{\pi}{3}$.
023156
\textcircled{1}\textcircled{2}\textcircled{3}\textcircled{5}.
023157
B
023158
B
023159
A
023160
$\frac{\pi}{3}$.
023161
4.3
023162
(1) 略; (2) $\frac{\sqrt{3}}{2}$; (3) $\arcsin \frac{2\sqrt{5}}{5}$.
023163
(1) $\frac{\pi}{2}$; (2) $\frac{\pi}{3}$.
023164
(1) 四边形 $MNDC$为矩形; (2) $\arctan \frac{\sqrt{2}}{2}$; (3) $\frac{\sqrt{2}}{2}$.
023165
(1) 异面直线 $D_1E$ 与 $A_1D$ 所成角的大小不会随点 $E$ 的移动而改变, 所成角为$\frac{\pi}{2}$; \\(2) 点 $E$距离点 $A$ 为$2-\sqrt{3}$, 二面角 $D_1-EC-D$ 的大小为 $\dfrac{\pi}{4}$; \\(3) 直线 $AD_1$ 平行于 平面 $B_1DE$.
023166
\textcircled{2}\textcircled{3}
023167
$75^{\circ}$
010502
arctan$\frac{\sqrt{5}}{5}$
023168
arccos$\frac{2}{3}$
023169
$\frac{\pi}{4}$
023170
$\sqrt{41}$或$13$
023171
$6$或$1.5$
023172
$30^{\circ}$
023173
$3.5cm$
023174
$\frac{\sqrt{2}}{2}$
023175
B
023176
$A$
023177
$D$
023178
$(1)$略; $(2)\frac{\sqrt{14}}{14}$
023179
$(1)\frac{\pi}{6};(2)arccos\frac{\sqrt{3}}{3}$
023180
$(1)$略; $(2)arctan\frac{\sqrt{6}}{2}$;$(3)$略; $(4)\frac{\sqrt{2}}{6}$
023181
011402
A
023182
B.
023183
2.
023184
5.
023185
$\sqrt{29}$.
023186
$\frac{\pi}{6}$.
023187
$\frac{15\sqrt{3}}{2}$
017677
$DM\perp PC$(或$BM\perp PC$)
023188
\textcircled{1}\textcircled{2}\textcircled{4}
023189
(1)略; (2)$arccos\frac{\sqrt{15}}{5}$
023190
(1)略; (2)6.
023191
$S=\begin{cases}\frac{1}{2cos\alpha},\quad\alpha\in(0,arctan\sqrt{2}]\\ \frac{\sqrt{2}-cot\alpha}{sin\alpha},\alpha\in(arctan\sqrt{2},\frac{\pi}{2}]\end{cases}$
023192
(1)略; (2)$\frac{2\sqrt{6}}{3}$.
023193
$8$.
023194
$arctan\frac{\sqrt{3}}{2}$.
023195
$64.$
023196
$arctan\sqrt{2}$.
023197
$10.$
023198
$(1)$外心; $(2)$内心; $(3)$垂心.
023199
$\sqrt{3}$
023200
$48$.
023201
$\frac{6}{7}$.
023202
A.
023203
$S=32,V=16$.
023204
$\frac{2\sqrt{11}}{11}$.
023205
$(1)$略; $(2)\frac{5}{3}$.
023206
$(1)V=a^2;(2)$\textcircled{1}$\frac{\sqrt{51}}{9}$;\textcircled{2}$\frac{\sqrt{30}}{3}$.
023207
$\sqrt{29}$.
023208
$\frac{\sqrt{6}}{3}$.
023209
$arctan\frac{\sqrt{5}}{5}$.
023210
$arccos\frac{2}{3}$.
023211
$\frac{\pi}{6}$.
023212
$\frac{15\sqrt{3}}{2}$.
023213
$3\pi^2$或$\frac{9}{2}\pi^2$.
023214
$\frac{\sqrt{3}}{2}a$.
023215
$\pi$.
023216
$\sqrt{2}:1$.
023217
$1:4:9$.
023218
$\frac{8}{3}\pi$.
023219
$12:15:20$.
023220
$576$.
023221
$\theta_{min}=\pi-arctan\frac{4}{3}$,此时$P$ 在线段 $A_1C_1$ 的中点.
023222
略.
023223
$(1)$略; $(2)arctan\sqrt{2}$;$(3)$是, $\frac{\sqrt{6}}{24}$.
023224
$P^{6}_{20-m}$.
023225
$60$.
023226
$48$.
023227
$6$.
023228
$6$.
023229
$156$.
023230
$103$.
023231
$48$.
023232
$(\frac{2}{3},1)$.
023233
$a_{n}=\begin{cases}2-a,n=1 \\2^{n-1},n\geq2
\end{cases}$.
023234
(1)$m=9$;(2)$k_{n}=3^{n+1}+2$.
023235
$(-\frac{1}{11},-\frac{1}{19})$.
023236
(1)略; (2)$S_{n}=\frac{2}{3}-(n+\frac{2}{3})(\frac{1}{4})^{n}$;(3)$(-\infty,-5]\cup[1,+\infty)$.
023237
$1716$.
023238
5或8.
023239
$x=15,y=5$.
023240
21.
023241
6.
016908
12.
023242
540.
023243
2880.
023244
200.
023245
$-1$.
023246
$2^{n-1},n\in \mathbf{N}$且$n\ge1$.
023247
$2^{n-1},n\in \mathbf{N}$且$n\ge1$.
023248
$7(\frac{1}{3})^{n-1}-6,n\in \mathbf{N}$且$n\ge1$.
023249
$765$.
023250
(1)58409520;(2)6275430;(3)64684945;(4)64682995.
023251
$92$.
023256
$\frac{3}{5}$
023257
$\frac{3}{7}$
023258
$\frac{1}{35}$
031430
$\frac{14}{33}$
017716
$\frac{3}{10}$
017041
$\frac{3}{4}$
023259
$\frac{2}{7}$
023260
$\frac{2}{27}$
023261
$\frac{9}{10}$
023262
$-49$
023263
$12$
023264
$\frac{5}{6}$
023265
(1) $d_1, d_2, d_3$ 的值分别为2,3,6;\\
(2) 略; (3) 略.
023266
$0.54$
023267
$\dfrac{5}{36}$; $\dfrac{5}{12}$
023268
$\dfrac{3}{8}$; $\dfrac{7}{8}$
023269
$0.88$
023270
$0.9$
023271
$7$或$8$
002651
$7$
023272
(1) F; (2) F; (3) T; (4) F.
023273
(1) $\dfrac{4}{15}$; (2) $\dfrac{11}{15}$
023274
(1) $\dfrac{70}{323}$; (2) $\dfrac{728}{969}$; (3) $\dfrac{27}{128}$
023275
(1) $\dfrac{211}{3456}$; (2) $\dfrac{7}{10}$; (3) $\dfrac{1}{15}$
023276
(1) $c_n=2n-1$; (2) $S_n=1+(n-1)3^n$
023277
$18$
023278
B
023279
A
023280
C
023281
B
023282
C
023283
$55$
023284
$50$; $1015$
023285
$3$
023286
$n=1$时, $a_n=5$; $n \geq 2$时, $a_n=2n-2$
023287
$2^n+3$
023288
$1049410$
023289
$19$
023290
(1) $0.5$; (2) $\frac{3}{16}$; (3) 略
023291
(1) $\{a_n\}-3n+15$; (2) $T_n=\frac{1}{6}(\frac{3}{2}-\frac{1}{n+1}-\frac{1}{n+2})$
023292
(1) $P_3=-2p^3+3p^2$; $P_4=4p^3-3p^4$; (2) 当$0<p<\frac{1}{2}$时,做一道且及格的概率最大; 当$p=\frac{1}{2}$时,做一道或者三道且及格的概率最大; 当$\frac{1}{2}<p<1$时,做三道且及格的概率最大.
023294
(1) 略; (2) $\sqrt{2}$
023295
(1) $\frac{2}{3}$; 在 $BC$ 边上存在一点 $G$, 使得点 $D$ 到平面 $PAG$ 的距离为 $\sqrt{2}$, $|BG|=1$; (3) $|HB|=\frac{\sqrt{5}}{3}$.
023296
A
023297
B
023298
C
023299
D
023300
C
023301
C
023302
$0.325$; $81.5$
017209
$0.98$
023303
4; $\sqrt{3}$
023304
$1$
023305
(1) $0.04$; (2) $440$.
023306
\textcircled{1}\textcircled{4}
023307
$100$ 名观众的样本平均数和方差分别约为$19.9$ 和$15.1$, 估计所有观众新闻类节目收看时长的总体方差约为$15.1$.
023308
(2) 二级; (3) $4400$
023309
$36\pi$
023285
$3$
023310
$[\frac{\pi}{3},\frac{\pi}{2}]$
023311
$3$
023312
$\frac{\sqrt{2}a}{2}$
023313
C
023314
B
023315
(1) $\frac{\sqrt{6}}{3}$; (2) $\frac{3\sqrt{2}}{2}$; (3) $\frac{\sqrt{6}}{3}$
023316
$1047.2$立方厘米
023317
(1) $S_n=2^n-1$; (2) $T_n=2^{n+1}-2-n$
023318
$10$
023319
$\frac{2}{5}$
023320
$19$
023321
$\dfrac{6}{\pi}$
023322
$84$
023323
$480$
023324
$a$
023325
$2\pi$
023326
$2$
023327
$\frac{33}{40}$
023328
$2$
023329
$1440$
023330
$\frac{8}{15}$
023331
$6\sqrt{3}$
023332
$8:27$
023333
$27$
014424
$13$
023334
$28$
023335
$\frac{5}{12}$
023336
$56-\frac{40\pi}{3}$
023337
$64$
023338
$\frac{\sqrt{3}}{4}$
023339
D
023340
A
023341
B
023342
C
023343
C
023344
D
023345
(1) $\frac{2}{3}$; (2) $\frac{1}{6}$
023346
(1) $-32$; (2) $-17$; (3) $-5$
023347
(1) $a, b$ 的值分别为$0.005,0.025$; (2) 估计这个 100 名候选者面试成绩的平均数和第 60 百分位数分别约为$69.5$和$71.7$; (3) $\frac{3}{5}$.
023348
(1) $\arccos \frac{1}{3}$; (2) $4\sqrt{3}+2$
023349
(1) $\{b_n\}=n-(-1)^n \cdot n^2$;
(2) \textcircled{1} $T_{10}=0$; \textcircled{2} $2575$
023350
$2352$
023351
$25 \times 2^{100}$
023352
$18$
023353
C
023354
$2\sqrt{3}$
023355
$\frac{85}{256}$
ans
022801
$[0,1]$
022802
$\sqrt{5}$
022803
$2\sqrt{2}-1$
022804
$\pm 1$
022805
$2n-3$
022806
$1$
022807
$36$
012041
$240$
022808
若 \textcircled{1}\textcircled{3},则\textcircled{2}(或者若 \textcircled{2}\textcircled{3},则\textcircled{1})
012042
$(-1,1)$
022809
$\dfrac{4\sqrt{3}}{3}$
022810
A
022811
D
022812
A
022813
$(1)\dfrac{\pi}{4});(2)4-\sqrt{2}$
022814
(1)$\dfrac{\pi}{3}$;(2)$\arctan\dfrac{\sqrt{2}}{2}$;(3)$\dfrac{1}{2}$
004486
(1) 约为$6.7^\circ$; (2) 最小值为$256$
022815
(1) $\dfrac{x^2}{2}+y^2=1$; (2) $k=\pm\dfrac{1}{2}$
022816
(1) $\dfrac{1}{1},\dfrac{2}{1},\dfrac{1}{2},\dfrac{3}{1},\dfrac{2}{2},\dfrac{1}{3},\dfrac{4}{1},\dfrac{3}{2},\dfrac{2}{3},\dfrac{1}{4}$; (2) $1008\dfrac{28}{65}$
019810
$\{2,4\}$
019811
$x=\log_23$
031267
$4\pi$
012389
$n^2$
019814
$2$
019815
$\dfrac{\pi}{6}$
009322
$72$
019817
$\dfrac{2\sqrt{2}}{3}$
019818
$\dfrac{3}{10}$
019819
$-3$
040079
$1078$
019822
B
019823
A
004565
B
022817
(1) $\arctan\dfrac{2}{5}$; (2) $V=4$
022818
(1) $a=0$; (2) $a-\dfrac{1}{4}$
022819
(1)7小时; (2)17小时
022820
(1)$4\sqrt{2}-6$;(2)$y=-\dfrac{\sqrt{2}}{2}x$
022821
(1) $1,2,3,a_n=n$;(2)略
022822
$\sqrt{2}$
022823
3
022824
$1+\ln x$
022825
$\sqrt{5}\pi$
022826
0
022827
80
022828
$-\dfrac{1}{4}$
022829
$\dfrac{y^2}{9}-\dfrac{x^2}{1}=1$
022830
$\dfrac{9}{20}$
022831
8
022832
$\dfrac{\sqrt{5}}{2}$
022833
D
022834
A
022835
C
022836
(1) $\dfrac{16}{3}$;(2) $\arcsin\dfrac{2\sqrt{2}}{3}$
004506
(1) $1$;(2)$2$
022837
(1)$3.1$秒; (2)20米/秒, 72千米/小时
022838
(1)$\dfrac{8}{3}$;(2)略
022839
(1)$a_1=1;a_2=0$或$1$; $a_3=0$或$1$;(2)115,证明略
022840
$\{1,2\}$
022841
$\dfrac{\pi}{3}$
022842
$\dfrac{\pi}{3}$
022843
$-2$
022844
$512$
022845
$\dfrac{2\pi}{3}$
022846
$-3$
022847
$\dfrac{x^2}{9}-\dfrac{y^2}{16}=1$
022848
$(0,\dfrac{1}{3})\bigcup (\dfrac{1}{3},\dfrac{2}{3})$
022849
$2:-1:1:1$
022850
$\dfrac{\sqrt{3}}{2}$
022851
C
022852
C
022853
A
022854
(1)12;(2)略
022855
(1)$AB=\sqrt{2}$米,$BC=\dfrac{\sqrt{2}}{2}$米,面积最大为$1$平方米; (2)$AB=2\sqrt{2}$米,$BC=\dfrac{\sqrt{2}}{2}$米,面积最大为$2$平方米
022856
(1)$2020$;(2)$(-\infty,\log_2\dfrac{9}{10}]$
022857
(1)证明略; (2)关于直线$y=x$对称, $x$范围为$[-1,+\infty)$,$y$范围为$[-1,+\infty)$,证明略
022858
(1)例: $f(x)=\sin\dfrac{\pi x}{4}$,证明略; (2)证明略
022859
$(0,2)$
004512
$\sqrt{2}$
022860
$(x+\dfrac{3}{2})^2+y^2=9$
022861
$2n+1$
004558
$15$
019885
$2\pi$
022862
$0.25$
022863
$3\sqrt{3}$
022864
$[0,\dfrac{\sqrt{3}}{3}]$
004521
$(-\infty,-1]$
022865
A
022866
A
004524
C
022867
(1)证明略; (2)$ED=\dfrac{\sqrt{6}}{3}a$
004527
(1)$T=\pi $;严格增区间为$[k\pi-\dfrac{\pi}{3},k\pi+\dfrac{\pi}{6}],k\in\mathbf{Z}$;(2)$3\sqrt{3}$
022868
(1)15户; (2)$x=5$时, $f(x)$最大值为$2.12>2.1$,可以达到
022869
(1)$1$; (2)$(0,\arctan\dfrac{1}{2})$
022870
(1)$6$; (2)正确, 证明略