如图,在四棱锥P-ABCD中,底面ABCD为平行四边形,∠ADC=45°,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231744316319811/SYS201311012317443163198017_ST/0.png)
,O为AC中点,PO⊥平面ABCD,M为PD中点.
(Ⅰ)证明:PB∥平面ACM;
(Ⅱ)证明:平面ADP⊥平面PAC.
考点分析:
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以下茎叶图记录了甲、乙两组各三名同学的植树棵数.乙组记录中有一个数据模糊,无法确认,在图中以X表示.
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(Ⅱ)如果X=9,分别从甲、乙两组中随机选取一名同学,求这两名同学的植树总棵数为19的概率.
(注:方差
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,其中
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为x
1,x
2,…,x
n的平均数)
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在△ABC中,内角A,B,C的对边分别是a,b,c,cos(C+
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)+cos(C-
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)=
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.
(I)求角C的大小;
(II)若c=
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,sinA=2sinB,求a,b.
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选做题:(考生可以在以下三个题任选一道题作答,如果多做以考生所作的第一道题为准)
(a) 不等式|x-4|-|x-2|>1的解集为
.
(b) 已知直线l的极坐标方程为:
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,圆C的参数方程为
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(θ为参数),那么直线l与圆C的位置关系为
.
(c) 如图已知圆中两条弦AB与CD相交于点F,E是AB延长线上一点,且
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.若CE与圆相切,则CE的长为
.
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已知向量
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=(
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,1),
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=(0,-1),
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=(k,
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).若
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与
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共线,则k=
.
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执行如图所示的程序框图,若输入A的值为2,则输出P的值为
.
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