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【327855】2023年内蒙古包头市中考数学真题

时间:2025-01-20 20:29:30 作者: 字数:18395字
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2023年内蒙古包头市中考数学真题

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一、选择题

1.下列各式计算结果为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的是(       
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

2.关于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的一元一次不等式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的解集在数轴上的表示如图所示,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的值为(       
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>    
A3
B
2
C
1
D
0

3.定义新运算“ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ”,规定: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的运算结果为(       
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
C
5
D
3

4.如图,直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 与直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 分别相交于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 在直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 上,且 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> .若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的度数为(       
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>    
A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

5.几个大小相同的小正方体搭成几何体的俯视图如图所示,图中小正方形中数字表示对应位置小正方体的个数,该几何体的主视图是(       
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>    
A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>    
B <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>    
C <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>    
D <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>    

6.123这三个数中随机抽取两个不同的数,分别记作 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> .若点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的坐标记作 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,则点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 在双曲线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 上的概率是(       
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

7.如图是源于我国汉代数学家赵爽的弦图,它是由四个全等直角三角形与一个小正方形拼成的一个大正方形.若小正方形的面积为1,大正方形的面积为25,直角三角形中较小的锐角为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的值为(       
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>    
A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

8.在平面直角坐标系中,将正比例函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的图象向右平移3个单位长度得到一次函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的图象,则该一次函数的解析式为(       
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

9.如图, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是锐角三角形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的外接圆, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,垂足分别为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> .若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的周长为21,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的长为(       
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>    
A8
B
4
C
3.5
D
3

10.如图,在平面直角坐标系中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 三个顶点的坐标分别为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 关于直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 对称,反比例函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的图象与 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 交于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> .若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的值为(       
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>    
A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

评卷人

得分




二、填空题

11. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 为两个连续整数,且 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ________

12. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是一元二次方程 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的两个实数根,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ________

13.如图,正方形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的边长为2,对角线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 相交于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,以点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 为圆心,对角线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的长为半径画弧,交 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的延长线于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,则图中阴影部分的面积为________
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>    

14.已知二次函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,若点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 在该函数的图象上,且 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的值为________

15.如图,在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,将 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 绕点A逆时针方向旋转 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> .连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,交 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 于点D,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的值为________
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>    

16.如图, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是正五边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的对角线, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 相交于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> .下列结论:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 平分 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>         <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>        四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是菱形;        <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
其中正确的结论是________.(填写所有正确结论的序号)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>    

评卷人

得分




三、解答题

17.1)先化简,再求值: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,其中 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
2)解方程: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

18.在推进碳达峰、碳中和进程中,我国新能源汽车产销两旺,连续8年保持全球第一.图为我国某自主品牌车企2022年下半年新能源汽车的月销量统计图.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>    
请根据所给信息,解答下列问题:
(1)
通过计算判断该车企2022年下半年的月均销量是否超过20万辆;
(2)
通过分析数据说明该车企2022年下半年月销量的特点(写出一条即可),并提出一条增加月销量的合理化建议.

19.为了增强学生体质、锤炼学生意志,某校组织一次定向越野拉练活动.如图,A点为出发点,途中设置两个检查点,分别为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 点和 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 点,行进路线为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 点在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 点的南偏东 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 方向 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 处, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 点在A点的北偏东 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 方向,行进路线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 所在直线的夹角 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>    
(1)求行进路线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 所在直线的夹角 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的度数;
(2)
求检查点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 之间的距离(结果保留根号).

20.随着科技的发展,扫地机器人已广泛应用于生活中,某公司推出一款新型扫地机器人,经统计该产品2022年每个月的销售情况发现,每台的销售价格随销售月份的变化而变化、设该产品2022年第 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 为整数)个月每台的销售价格为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> (单位:元), <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的函数关系如图所示(图中 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 为一折线).
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>    
(1) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 时,求每台的销售价格 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 之间的函数关系式;
(2)
设该产品2022年第 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 个月的销售数量为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> (单位:万台),m <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的关系可以用 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 来描述,求哪个月的销售收入最多,最多为多少万元?(销售收入 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 每台的销售价格 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 销售数量)

21.如图, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的直径, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是弦, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 上一点, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 延长线上一点,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>    
(1)求证: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ;(请用两种证法解答)
(2)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的半径为3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的长.

22.如图,在菱形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 中,对角线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 相交于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 分别是边 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,线段 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 上的点,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 相交于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>    
(1)如图1,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> .当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 时,试判断点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是否在线段 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的垂直平分线上,并说明理由;
(2)
如图2,若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,且 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
求证: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 时,设 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的长(用含 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的代数式表示).

23.如图,在平面直角坐标系中,抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 轴于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 交抛物线于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 两点(点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 在点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的左侧),交 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 轴于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,交 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 轴于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>    
(1)求点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的坐标;
(2)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是线段 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 上一点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,且 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
求证: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是直角三角形;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的平分线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 交线段 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 上方抛物线上一动点,当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 时,求点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的坐标.

参考答案

1.C

【解析】
根据同底数幂的乘除法及幂的乘方运算法则即可判断.
解:A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,不符合题意;
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,不符合题意;
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,符合题意;
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,不符合题意;
故选:C

2.B

【解析】
先求出不等式的解集,然后对比数轴求解即可.
解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
由数轴得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
故选:B

3.D

【解析】
根据新定义的运算求解即可.
解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
故选:D

4.C

【解析】
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,由 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,进而可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的度数.
解:∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
故选:C

5.D

【解析】
根据各层小正方体的个数,然后得出三视图中主视图的形状,即可得出答案.
解:根据俯视图可知,这个几何体中:主视图有三列:左边一列1个,中间一列2个,右边一列2个,
所以该几何体的主视图是
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>         
故选:D

6.A

【解析】
先求出点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的坐标的所有情况的个数,然后求出其中在双曲线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 上的坐标的个数,根据随机事件概率的计算方法,即可得到答案.
解:从123这三个数中随机抽取两个不同的数,点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的坐标共有6种情况: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,并且它们出现的可能性相等.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 坐标在双曲线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 上有2种情况:  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
所以,这个事件的概率为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
故选:A

7.D

【解析】
首先根据两个正方形的面积分别求出两个正方形的边长,然后结合题意进一步设直角三角形短的直角边为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,则较长的直角边为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,再接着利用勾股定理得到关于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的方程,据此进一步求出直角三角形各个直角边的边长,最后求出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的值即可.
小正方形的面积为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,大正方形的面积为25
小正方形的边长为1,大正方形的边长为5
设直角三角形短的直角边为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,则较长的直角边为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,其中 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,其中 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
故选:D.

8.B

【解析】
根据一次函数的平移规律求解即可.
解:正比例函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的图象向右平移3个单位长度得:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
故选:B

9.B

【解析】
根据三角形外接圆的性质得出点DEF分别是 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的中点,再由中位线的性质及三角形的周长求解即可.
解:∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是锐角三角形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的外接圆, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
DEF分别是 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的中点,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的周长为21
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
故选:B

10.A

【解析】
过点B <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 轴,根据题意得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,再由特殊角的三角函数及等腰三角形的判定和性质得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,利用各角之间的关系 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,确定 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> BD三点共线,结合图形确定 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,然后代入反比例函数解析式即可.
解:如图所示,过点B <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 轴,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>    
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 关于直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 对称,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> BD三点共线,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
将其代入 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
故选:A

11.3

【解析】
根据夹逼法求解即可.
解:∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
故答案为:3

12. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ## <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【解析】
由一元二次方程的根与系数的关系得, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,然后代入求解即可.
解:由一元二次方程的根与系数的关系得, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
故答案为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

13. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【解析】
根据正方形的性质得出阴影部分的面积为扇形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的面积,然后由勾股定理得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,再由扇形的面积公式求解即可.
解:正方形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
正方形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的边长为2
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
阴影部分的面积为扇形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的面积,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
故答案为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

14.2

【解析】
将点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 代入函数解析式求解即可.
解:点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 上,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> (舍去)
故答案为:2

15.5

【解析】
过点D <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 于点F,利用勾股定理求得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,根据旋转的性质可证 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是等腰直角三角形,可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,再由 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,证明 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,再由 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,求得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,从而求得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,即可求解.
解:过点D <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 于点F
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 绕点A逆时针方向旋转 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是等腰直角三角形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
又∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是等腰直角三角形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
又∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
故答案为:5
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>    

16.①③④

【解析】
根据正五边形的性质得出各角及各边之间的关系,然后由各角之间的关系及相似三角形的判定和性质,菱形的判定依次证明即可.
解:①∵正五边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 平分 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ;正确;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,故②错误;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是平行四边形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是菱形;正确;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,正确;
故答案为:①③④

17.1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 1;(2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【解析】
1)首先利用完全平方公式和平方差公式计算,然后合并同类项,最后代入求解即可;
2)根据解分式方程的一般步骤进行求解即可.
解:(1)原式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 时,
原式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>              
2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
方程两边乘 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
检验:将 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 代入 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是原方程的根.

18.(1)该车企2022年下半年的月均销量超过20万辆
(2)2022
年下半年月销量的特点:月销量呈递增趋势;12月的销量最大;有三个月的销量超过了20万辆;中位数为20.5万辆;月均销量超过20万辆等
建议:充分了解客户需求,及时处理客户反馈,提供优质的售后服务

【解析】
1)根据平均数的定义求解即可;
2)利用条形统计图中的数据进行阐述即可.
1)解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> (万辆),
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
该车企2022年下半年的月均销量超过20万辆.
22022年下半年月销量的特点:月销量呈递增趋势;12月的销量最大;有三个月的销量超过了20万辆;中位数为20.5万辆;月均销量超过20万辆等.
建议:充分了解客户需求,及时处理客户反馈,提供优质的售后服务.

19.(1)行进路线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 所在直线的夹角为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
(2)
检查点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 之间的距离为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【解析】
1)根据题意得, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,再由各角之间的关系求解即可;
2)过点A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,垂足为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,由等角对等边得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,再由正弦函数及正切函数求解即可.
1)解:如图,根据题意得, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
答:行进路线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 所在直线的夹角为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
2)过点A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,垂足为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>       
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 中,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
答:检查点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 之间的距离为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

20.(1) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
(2)
5个月的销售收入最多,最多为3375万元

【解析】
1)利用待定系数法即可求解;
2)根据销售收入 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 每台的销售价格 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 销售数量求得销售收入为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 万元与销售月份 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 之间的函数关系,再利用函数的性质即可求解.
1)解:当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 时,设每台的销售价格 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 之间的函数关系式为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
图象过 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 两点,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 时,每台的销售价格 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 之间的函数关系式为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
2)设销售收入为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 万元,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> (万元).                    
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的增大而增大,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> (万元).                           
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,∴第5个月的销售收入最多,最多为3375万元.

21.(1)证明见解析
(2)8

【解析】
1)证法一:连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ;证法二:连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,根据 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,即可得到结果;
2)连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,根据角度间的关系可以证得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 为直角三角形,根据勾股定理可得边 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的长,进而求得结果.
1)证法一:如图,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的直径,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>    
证法二:如图,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的内接四边形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的直径,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>    
2)解:如图,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的半径为3
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>    

22.(1) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 在线段 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的垂直平分线上
(2)①
证明见解析,② <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【解析】
1)根据菱形的性质及垂直平分线的判定证明即可;
2)①根据菱形的性质得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,再由各角之间的关系得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,由含30度角的直角三角形的性质求解即可;③连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> .利用等边三角形的判定和性质得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,再由正切函数及全等三角形的判定和性质及勾股定理求解即可.
1)解:如图,点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 在线段 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的垂直平分线上.
理由如下:连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是菱形,对角线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 相交于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 在线段 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的垂直平分线上.                    
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>    
2)①证明:如图,∵四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是菱形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>    
如图,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是等边三角形.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
由勾股定理得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>                            
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>    

23.(1) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
(2)①
证明见解析,②点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的坐标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【解析】
1)根据一次函数与坐标轴的交点及一次函数与二次函数的交点求解即可;
2)①设 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 然后利用勾股定理求解, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,过点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 轴,垂足为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> .再由等腰三角形及各角之间的关系即可证明;②根据题意得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,设点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的坐标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,根据题意得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> .分两种情况(i)当点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 在直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的左侧抛物线上时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> .(ii)当点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 在直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的右侧抛物线上时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> .求解即可.
1)解:∵直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 轴于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,交 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 轴于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 交抛物线于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 两点,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 在点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的左侧,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的横坐标为3
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
2)如图,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>       
抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 轴于点A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
由勾股定理得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是等腰直角三角形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
过点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 轴,垂足为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是等腰直角三角形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是直角三角形.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 平分 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 轴.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
设点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的坐标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,根据题意得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
i)当点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 在直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的左侧抛物线上时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
过点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 轴,垂足为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 中,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> (舍去).
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
ii)当点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 在直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的右侧抛物线上时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
过点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 轴,垂足为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 中,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> (舍去).
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的坐标为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>