ans

13512
$2$

13513
$x=\mu$

13514
可能异面, 可能相交

13515
$\dfrac{y^2}{15}+\dfrac{x^2}{16}=1$, $x\ne 0$

13516
$[1,15]$

13517
$-\dfrac 13$

13518
$\dfrac 43$

13519
$(-\infty,-1]\cup [3,+\infty)$

13520
$\sqrt{3}$

13521
$\pi$

13522
A

13523
D

13524
B

13525
(1) $\dfrac{5}{12}\text{h}$; (2) 能, $v$的取值范围为$(\dfrac{9\sqrt{3}}2,\dfrac{\sqrt{559}}3]$

13526
(1) 证明略; (2) $\dfrac{a_1}{a_2}\le \dfrac{a_1+a_3+\cdots+a_{2n-1}}{a_2+a_4+\cdots+a_{2n}}$, 当且仅当$n=1$或$d=0$时成立等号; (3) $2023^2$

13527
$\{(0,1),(2,5)\}$

13528
$x>1$且$y>1$

13529
$\sqrt{2}$

13530
$(-\infty,-8]\cup [2,+\infty)$

13531
$[-2,2]$

13532
$\dfrac 13$

13533
$\dfrac{4\pi}{3}$

13534
$20$

13535
\textcircled{3}\textcircled{4}

13536
\textcircled{1}\textcircled{3}\textcircled{4}

13537
B

13538
C

13539
D

13540
(1) 甲与乙的平均数分别为$7$和$7$; (2) 甲与乙的方差分别为$3$和$1.2$; (3) 两人射击水平相当, 甲的发挥更稳定

13541
(1) $\dfrac 12$; (2) $\dfrac{4\sqrt{5}}5$


13542
$3.5$

13543
$\dfrac{20}{11}$

13544
$a=\pm 1$

13545
$-17$

13546
$0.7$

13547
$5$

13548
$6\sqrt{3}$

13549
$0.6$

13550
$2\pi^2+16\pi$

13551
$\dfrac 83$

13552
C

13553
C

13554
B

13555
(1) $f(x)=\begin{cases}2^x-1+\log_2 (x+1), & x\ge 0, \\ 1-2^{-x}-\log_2(-x+1), & x<0;\end{cases}$ (2) $f(x)=-2^{x-2}+1-\log_2(x-1)$, $1<x\le 3$

13556
(1) $6$; (2) $-4$

13557
$(-\infty,-1)\cup (1,+\infty)$

13558
$240$

13559
$\dfrac 92$

13560
$(-\dfrac 32,+\infty)$

13561
$x+3y=0$或$x+y-4=0$

13562
$\dfrac 52$

13563
$\dfrac{\sqrt{5}+1}4$

13564
$\dfrac{1}{15}$

13565
$4$

13566
$\dfrac{3\sqrt{5}}5$

13567
B

13568
D

13569
D

13570
(1) $\chi^2=24>6.635$, 有$99.9\%$的把握认为患该疾病群体与为患该疾病群体的卫生习惯有差异; (2) 证明略, $R$的估计值为$6$

13571
(1) $y=2x$; (2) $(-\infty,-1)$

13572
$-\dfrac 12$

13573
$2\pi$

13574
$\dfrac{\sqrt{6}}2a^2$

13575
$3x-y-2=0$

13576
$-\dfrac{3}{25}\overrightarrow{b}$

13577
$-2$

13578
$\dfrac{2\sqrt{5}}5$

13579
$[\dfrac 54,\dfrac{3\sqrt{17}}4]$

13580
$77$

13581
$4$

13582
A

13583
B

13584
D

13585
(1) $0.89$; (2) $0.0014$

13586
(1) $x^2-\dfrac{y^2}{3}=1$; (2) 证明略

13587
$\{1,2\}$

13588
$2$

13589
$6$

13590
$3$

13591
$5$

13592
$-\sqrt{2}$

13593
$\dfrac 16$

13594
$-28$

13595
$0.14$

13596
$2$

13597
$\ln 2$

13598
$\dfrac{\sqrt{13}}2$

13599
A

13600
C

13601
C

13602
B

13603
(1) $\dfrac\pi 6$; (2) $6+6\sqrt{3}$

13604
(1) 证明略; (2) $\dfrac{\sqrt{6}}8$

13605
(1) $X\sim \begin{pmatrix} 0 & 20 & 100\\ 0.2 & 0.32 & 0.48\end{pmatrix}$; (2) 应选择先回答B类问题

13606
(1) $\dfrac{x^2}{25}+\dfrac{y^2}{9}=1$; (2) $2\sqrt{2}+\sqrt{17}$; (3) 定值为$34$

13607
(1) $y=x$; (2) 在$[0,+\infty)$上是严格增函数; (3) 证明略

13608
$1$

13609
$[\dfrac 12,1]$

13610
$2\sqrt{3}$

13611
$x\le \dfrac{a+b}{2}$, 等号成立当且仅当$a=b$


13612
$2x-y+1=0$

13613
$\dfrac{3\pi}{4}$

13614
$115$

13615
$-1$

13616
如$x^2+(y-2)^2=1$等(答案不唯一)

13617
$(0,-4)$

13618
$72$

13619
$\dfrac 78$

13620
B

13621
A

13622
C

13623
C

13624
(1) $\dfrac 13$; (2) 证明略

13625
(1) $a_n=3n-1$; (2) $S_n=\dfrac{21}{4}-\dfrac{6n+7}{4\cdot 3^{n-1}}$

13626
(1) $V=x(3-2x)^2$, $x\in (0,\dfrac 32)$; (2) 当$x=\dfrac 12$时, $V$取到最大值$2$

13627
(1) 最小正周期为$\pi$, 取值范围为$[-1,2]$; (2) $\sqrt{3}$

13628
(1) $2$; (2) 双曲线方程为$x^2-\dfrac{y^2}{3}=1$, 过顶点$(2,0)$与$(-1,0)$


13629
$4$或$-6$

13630
$(\dfrac\pi 6,\dfrac{5\pi}6)$

13631
$44$

13632
$41$

13633
$1$

13634
$24$

13635
$\dfrac{7\sqrt{3}}3\pi$

13636
$20$

13637
$2.5$

13638
$76$元

13639
$p_1$,$p_4$

13640
$\dfrac 34$

13641
D

13642
B

13643
C

13644
B

13645
证明略

13646
(1) $\dfrac\pi 3$; (2) $(6,12]$

13647
(1) $0.6$; (2) $x\sim \begin{pmatrix}0 & 10 & 20 & 30\\0.16 & 0.44 & 0.34 & 0.06\end{pmatrix}$, $E[X]=13$

13648
(1) $\dfrac{x^2}3+y^2=1$; (2) $\sqrt{6}$; (3) $1$

13649
(1) 在$(-1,1)$上是严格增函数, 在$(1,+\infty)$上是严格减函数; (2) $(-\infty,0]$; (3) 证明略

13650
$\{(0,0),(1,0),(-1,0)\}$

13651
$7$

13652
$-2$

13653
$0$

13654
$\dfrac{6\pi}{5}$

13655
$0.75$

13656
$(-6,2)$

13657
$\dfrac{2\sqrt{3}}3$

13658
$\dfrac{16}3$

13659
$\dfrac\pi 6$

13660
\textcircled{1}\textcircled{2}\textcircled{4}

13661
$12120$

13662
B

13663
B

13664
D

13665
D

13666
(1) $1$; (2) $\arcsin\dfrac{\sqrt{3}}4$

13667
(1) $\sqrt{7}$; (2) $-1-\dfrac{\sqrt{3}}2$

13668
(1) $(x-2)^2+y^2=\dfrac{12}7$; (2) $\dfrac{3\sqrt{2}}2$或$\dfrac{\sqrt{2}}2$

13669
(1) $\dfrac 25$; (2) $X\sim \begin{pmatrix} 0 & 1 & 2 \\ \dfrac{6}{25} & \dfrac{13}{25} & \dfrac{6}{25}\end{pmatrix}$; (3) 不认为人数有变化, 理由略

13670
(1) $y=x-1$; (2) $(-\infty,\dfrac{3}{2}]$; (3) $(-\infty,\dfrac{\sqrt{2}}2)$

13671
$1$

13672
$3$

13673
$\dfrac 12$

13674
$(0,2)$

13675
$2$

13676
$0.57$

13677
$\dfrac 72+\sqrt{6}$

13678
$\dfrac\pi 3$或$\dfrac{2\pi}3$

13679
$\sqrt{5}$

13680
$\dfrac{7\sqrt{3}}3$

13681
$\dfrac 83$

13682
$\dfrac 32$

13683
A

13684
C

13685
A

13686
B

13687
(1) 证明略; (2) $\dfrac\pi 6$

13688
(1) 证明略; (2) $(\dfrac 94,\dfrac{15}4)$

13689
(1) $l=\dfrac{1}{\sin \theta}+\dfrac{1}{\cos\theta}+\dfrac{1}{\sin\theta\cdot \cos\theta}$, $\theta\in (\dfrac\pi 6,\dfrac\pi 3)$; (2) $2+2\sqrt{2}$, 此时$\theta=\dfrac\pi 4$

13690
(1) $\dfrac{\sqrt{2}}2$; (2) $t=\dfrac{\sqrt{6}}3b$

13691
(1) $a=1$, $b=0$; (2) $3$; (3) 证明略