某工厂用7万元钱购买了一台新机器,运输安装费用2千元,每年投保、动力消耗的费用也为2千元,每年的保养、维修、更换易损零件的费用逐年增加,第一年为2千元,第二年为3千元,第三年为4千元,依此类推,即每年增加1千元.问这台机器最佳使用年限是多少年?并求出年平均费用的最小值.(最佳使用年限佳是使年平均费用的最小的时间)
考点分析:
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如图所示,在直三棱柱ABC-A
1B
1C
1中,AB=1,AC=AA
1=
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,∠ABC=60°.
(1)证明:AB⊥A
1C;
(2)求二面角A-A
1C-B的余弦值.
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△ABC中,a,b,c分别是角A.B,C的对边,且有sin2C+
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102729743626075/SYS201311031027297436260017_ST/0.png)
cos(A+B)=0,若a=4,c=
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,求△ABC的面积.
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给定两个命题,命题p:对任意实数x都有ax
2+ax+1>0恒成立,命题q:关于x的方程x
2-x+a=0有实数根,如果p∨q为真命题,p∧q为假命题,求实数a的取值范围.
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有下列命题:
①双曲线
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102729743626075/SYS201311031027297436260015_ST/0.png)
-
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102729743626075/SYS201311031027297436260015_ST/1.png)
=1与椭圆
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102729743626075/SYS201311031027297436260015_ST/2.png)
有相同焦点;
②“-
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102729743626075/SYS201311031027297436260015_ST/3.png)
<x<0”是“2x
2-5x-3<0”必要不充分条件;
③若
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102729743626075/SYS201311031027297436260015_ST/4.png)
、
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102729743626075/SYS201311031027297436260015_ST/5.png)
共线,则
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102729743626075/SYS201311031027297436260015_ST/6.png)
、
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102729743626075/SYS201311031027297436260015_ST/7.png)
所在的直线平行;
④若
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102729743626075/SYS201311031027297436260015_ST/8.png)
,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102729743626075/SYS201311031027297436260015_ST/9.png)
,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102729743626075/SYS201311031027297436260015_ST/10.png)
三向量两两共面,则
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102729743626075/SYS201311031027297436260015_ST/11.png)
、
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102729743626075/SYS201311031027297436260015_ST/12.png)
、
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102729743626075/SYS201311031027297436260015_ST/13.png)
三向量一定也共面;
⑤∀x∈R,x
2-3x+3≠0.
其中是真命题的有:
.(把你认为正确命题的序号都填上)
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点M与点F(4,0)的距离比它到直线l:x+5=0的距离小1,则点M的轨迹方程是
.
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