题目列表(包括答案和解析)
已知关于
的方程
有实根
,复数
,则复数
在复平面内的对应点到原点的距离为
A.2 B.4 C.
D. 8
如图所示,竖直平面内的3/4圆弧形光滑轨道半径为R,A端与圆心O等高,AD为与水平方向成45°角的斜面,B端在O的正上方,一个可看成质点的小球在A点正上方由静止开始释放,自由下落至A点后进入圆形轨道并恰能到达B点。求:
(1)到达B点的速度大小;
(2)释放点距A点的竖直高度;
(3)小球落到斜面上C点时的速度大小。
![]()
如图所示,竖直平面内的3/4圆弧形光滑轨道半径为R,A端与圆心O等高,AD为与水平方向成45°角的斜面,B端在O的正上方,一个可看成质点的小球在A点正上方由静止开始释放,自由下落至A点后进入圆形轨道并恰能到达B点。求:
(1)到达B点的速度大小;
(2)释放点距A点的竖直高度;
(3)小球落到斜面上C点时的速度大小。
![]()
(一)根据下列句子所给汉语意思写出空缺处单词,或根据所给词写出正确形式。
【小题1】If you want to go to the party with me, you should (表现好) well.
【小题2】There were several new (arrive) at the hotel last night.
【小题3】It's illegal to read people's private letters without (允许).
【小题4】You are only (稍微) underweight for your height.
【小题5】The Prime Minister has formed a new (内阁).
(二)根据下列句子所给汉语意思完成句子。
【小题6】It’s going to rain. Xiao Feng, will you please help me (收衣服) on the line?
【小题7】 (已经确认)that the 31st Olympic Games will be held in Brazil.
【小题8】Is it __________(在步行距离内)or do I need to take a bus?
【小题9】Firstly, we should life. (养成对…的好态度)
【小题10】In recent years, many of my friends have come to big cities to .(追求幸福与成功)
阅读下面短文,根据以下提示:1)汉语提示,2)首字母提示,3)语境提示,在每个空格内填入一个适当的英语单词,并将该词完整地写在右边相对应的横线上。所填单词要求意义准确,拼写正确。
People often don’t do what they really want to for fear
of failure. You don’t apply for a job ______ case you don’t
get it. You don’t perform at the school concert b others
might laugh at you. A lack of confidence can l to a lot
of suffering. The key to o this problem is to believe in
yourself. This might be (容易)said than done, but there
are many w to help you do this. Talk about your problem
with a friend or look advice on the Internet. Imagine
yourself being (成功) and practise breathing techniques
to keep you calm when you get nervous. And the important
thing is: believe you can do it. When you’ve ______(学会)to do
that, you are well on your way.
1.C 2.A 3.B 4.D 5.C 6.B 7.D 8.C 9.B 10.A
11.120° 12.3x+y-1=0 13.
14.10 15.100 16.(1),(4)
17.解:(1)设抛物线
,将(2,2)代入,得p=1. …………4分
∴y2=2x为所求的抛物线的方程.………………………………………………………5分
(2)联立
消去y,得到
. ………………………………7分
设AB的中点为
,则
.
∴ 点
到准线l的距离
.…………………………………9分
而
,…………………………11分
,故以AB为直径的圆与准线l相切.…………………… 12分
(注:本题第(2)也可用抛物线的定义法证明)
18.解:(1)在△ACF中,
,即
.………………………………5分
∴
.又
,∴
.……………………
7分
(2)


. ……………………………14分
(注:用坐标法证明,同样给分)
19.
解法一:(1)连OM,作OH⊥SM于H.
∵SM为斜高,∴M为BC的中点,∴BC⊥OM.
∵BC⊥SM,∴BC⊥平面SMO.
又OH⊥SM,∴OH⊥平面SBC.……… 2分
由题意,得
.
设SM=x,
则
,解之
,即
.………………… 5分
(2)设面EBC∩SD=F,取AD中点N,连SN,设SN∩EF=Q.
∵AD∥BC,∴AD∥面BEFC.而面SAD∩面BEFC=EF,∴AD∥EF.
又AD⊥SN,AD⊥NM,AD⊥面SMN.
从而EF⊥面SMN,∴EF⊥QS,且EF⊥QM.
∴∠SQM为所求二面角的平面角,记为α.……… 7分
由平几知识,得
.
∴
,∴
.
∴
,即所求二面角为
. ……………… 10分
(3)存在一点P,使得OP⊥平面EBC.取SD的中点F,连FC,可得梯形EFCB,
取AD的中点G,连SG,GM,得等腰三角形SGM,O为GM的中点,
设SG∩EF=H,则H是EF的中点.
连HM,则HM为平面EFCB与平面SGM的交线.
又∵BC⊥SO,BC⊥GM,∴平面EFCB⊥平面SGM. …………… 12分
在平面SGM中,过O作OQ⊥HM,由两平面垂直的性质,可知OQ⊥平面EFCB.
而OQ
平面SOM,在平面SOM中,延长OQ必与SM相交于一点,
故存在一点P,使得OP⊥平面EBC. ……………………… 14分
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