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【327658】2022年广西北部湾经济区中考数学真题

时间:2025-01-20 19:56:09 作者: 字数:20922字
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2022年广西北部湾经济区中考数学真题

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得分




一、选择题

1. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 的相反数是(  )
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
C
3
D
-3

2.2022北京冬残奥会的会徽是以汉字“飞”为灵感来设计的,展现了运动员不断飞跃,超越自我,奋力拼搏,激励世界的冬残奥精神下列的四个图中,能由如图所示的会徽经过平移得到的是(       
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>

3.空气是混合物,为直观介绍空气各成分的百分比,最适合用的统计图是(  )
A
.折线图
B
.条形图
C
.直方图
D
.扇形图

4.如图,数轴上的点A表示的数是 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,则点A关于原点对称的点表示的数是(       
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
B
0
C
1
D
2

5.不等式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 的解集是(       
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>

6.如图,已知a∥b,∠1=55°,则∠2的度数是(        )
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
A
35°
B
45°
C
55°
D
125°

7.下列事件是必然事件的是(       
A
.三角形内角和是180°
B
.端午节赛龙舟,红队获得冠军
C
.掷一枚均匀骰子,点数是6的一面朝上
D
.打开电视,正在播放神舟十四号载人飞船发射实况

8.如图,某博物馆大厅电梯的截面图中,AB的长为12米,ABAC的夹角为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,则高BC是(       
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>

9.下列运算正确的是(       
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>

10.《千里江山图》是宋代王希孟的作品,如图,它的局部画面装裱前是一个长为2.4米,宽为1.4米的矩形,装裱后,整幅图画宽与长的比是813,且四周边衬的宽度相等,则边村的宽度应是多少米?设边衬的宽度为x米,根据题意可列方程(       
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>

11.如图,在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,将 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 绕点A逆时针旋转 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 并延长交AB于点D,当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 的长是(       
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>

12.已知反比例函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 的图象如图所示,则一次函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 和二次函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 在同一平面直角坐标系中的图象可能是(       
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>

评卷人

得分




二、填空题

13.化简:(1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> =_____

14. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ______时,分式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 的值为零.

15.如图,一个质地均匀的正五边形转盘,指针的位置固定,当转盘自由转动停止后,观察指针指向区域内的数(若指针正好指向分界线,则重新转一次),这个数是一个奇数的概率是________
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>

16.古希腊数学家泰勒斯曾利用立杆测影的方法,在金字塔影子的顶部直立一根木杆,借助太阳光测金字塔的高度.如图,木杆EF2米,它的影长FD4米,同一时刻测得OA268米,则金字塔的高度BO________米.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>

17.阅读材料:整体代值是数学中常用的方法.例如“已知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,求代数式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 的值.”可以这样解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> .根据阅读材料,解决问题:若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 是关于x的一元一次方程 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 的解,则代数式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 的值是________

18.如图,在正方形ABCD中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,对角线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 相交于点O.点E是对角线AC上一点,连接BE,过点E <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,分别交 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 于点FG,连接BF,交AC于点H,将 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 沿EF翻折,点H的对应点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 恰好落在BD上,得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 若点FCD的中点,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 的周长是_________
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>

评卷人

得分




三、解答题

19.计算: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>

20.先化简,再求值 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,其中 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>

21.如图,在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 中,BD是它的一条对角线,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
(1)
求证: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
(2)
尺规作图:作BD的垂直平分线EF,分别交ADBC于点EF(不写作法,保留作图痕迹);
(3)
连接BE,若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 的度数.

22.综合与实践
(
问题情境)数学活动课上,老师带领同学们开展“利用树叶的特征对树木进行分类”的实践活动,
(
实践发现)同学们随机收集芒果树、荔枝树的树叶各10片,通过测量得到这些树叶的长y(单位:cm),宽x(单位:cm)的数据后,分别计算长宽比,整理数据如下:


1

2

3

4

5

6

7

8

9

10

芒果树叶的长宽比

3.8

3.7

3.5

3.4

3.8

4.0

3.6

4.0

3.6

4.0

荔枝树叶的长宽比

2.0

2.0

2.0

2.4

1.8

1.9

1.8

2.0

1.3

1.9


(
实践探究)分析数据如下:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>


平均数

中位数

众数

方差

芒果树叶的长宽比

3.74

m

4.0

0.0424

荔枝树叶的长宽比

1.91

2.0

n

0.0669


(
问题解决)
(1)
上述表格中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ________ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ________
(2)①
A同学说:“从树叶的长宽比的方差来看,我认为芒果树叶的形状差别大.”
B同学说:“从树叶的长宽比的平均数、中位数和众数来看,我发现荔枝树叶的长约为宽的两倍.”
上面两位同学的说法中,合理的是________(填序号)
(3)
现有一片长 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,宽 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 的树叶,请判断这片树叶更可能来自于芒果、荔枝中的哪种树?并给出你的理由.

23.打油茶是广西少数民族特有的一种民俗,某特产公司近期销售一种盒装油茶,每盒的成本价为50元,经市场调研发现,该种油茶的月销售量y(盒)与销售单价x(元)之间的函数图像如图所示.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
(1)
yx的函数解析式,并写出自变量x的取值范围;
(2)
当销售单价定为多少元时,该种油茶的月销售利润最大?求出最大利润.

24.如图,在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,以AC为直径作 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> BC于点D,过点D <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,垂足为E,延长BA <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 于点F
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
(1)
求证:DE <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 的切线
(2)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 的半径.

25.已知抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> x轴交于AB两点(点A在点B的左侧).
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
(1)
求点A,点B的坐标;
(2)
如图,过点A的直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 与抛物线的另一个交点为C,点P为抛物线对称轴上的一点,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,设点P的纵坐标为m,当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 时,求m的值;
(3)
将线段AB先向右平移1个单位长度,再向上平移5个单位长度,得到线段MN,若抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 与线段MN只有一个交点,请直接写出a的取值范围.

26.已知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,点AB分别在射线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 上运动, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
(1)
如图①,若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,取AB中点D,点AB运动时,点D也随之运动,点ABD的对应点分别为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> .判断OD <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 有什么数量关系?证明你的结论:
(2)
如图②,若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,以AB为斜边在其右侧作等腰直角三角形ABC,求点O与点C的最大距离:
(3)
如图③,若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,当点AB运动到什么位置时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 的面积最大?请说明理由,并求出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 面积的最大值.

参考答案

1.A

【解析】
试题根据相反数的意义知: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 的相反数是 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> .
故选:A
(
考点)

2.D

【解析】
根据平移的特点分析判断即可.
根据题意,得
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 不能由 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 平移得到,
A不符合题意;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 不能由 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 平移得到,
B不符合题意;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 不能由 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 平移得到,
C不符合题意;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 能由 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 平移得到,
D符合题意;
故选D

3.D

【解析】
解:由分析可知,要求直观反映空气的组成情况,即各部分在总体中所占的百分比,结合统计图各自的特点,应选择扇形统计图.故选D

4.C

【解析】
根据数轴上表示一对相反数的点关于原点对称即可求得答案.
数轴上的点A表示的数是1
A关于原点对称的点表示的数为1
故选:C

5.B

【解析】
先移项,合并同类项,再不等式的两边同时除以2,即可求解.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
故选:B

6.C

【解析】
根据两直线平行,同位角相等可得∠3=∠1=55°,再根据对顶角相等即可求得答案.
∵a//b

∴∠3=∠1=55°

∴∠2=∠3=55°

故选C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>

7.A

【解析】
根据事件发生的可能性大小判断相应事件的类型即可.
解:A、三角形内角和是180°是必然事件,故此选项符合题意;
B
、端午节赛龙舟,红队获得冠军是随机事件,故此选项不符合题意;
C
、掷一枚均匀骰子,点数是6的一面朝上是随机事件,故此选项不符合题意;
D
、打开电视,正在播放神舟十四号载人飞船发射实况是随机事件,故此选项不符合题意;
故选:A

8.A

【解析】
RtACB中,利用正弦定义,sinα= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,代入AB值即可求解.
解:在RtACB中,∠ACB=90°
∴sin
α= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
BC= sinα <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> AB=12 sinα(米),
故选:A

9.D

【解析】
根据各自的运算,依据法则计算判断即可.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 不是同类项,
无法计算,不符合题意;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
计算错误,不符合题意;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
计算错误,不符合题意;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
符合题意;
故选D

10.D

【解析】
设边衬的宽度为x米,则整幅图画宽为(1.4+2x), 整幅图画长为(2.4+2x),根据整幅图画宽与长的比是813,列出方程即可.
解:设边衬的宽度为x米,根据题意,得
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
故选:D

11.B

【解析】
先证 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,再求出AB的长,最后根据弧长公式求得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 绕点A逆时针旋转 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 得到,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 的长= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
故选:B

12.D

【解析】
先由反比例函数图象得出b0,再分当a0a0时分别判定二次函数图象符合的选项,在符合的选项中,再判定一次函数图象符合的即可得出答案.
解:∵反比例函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 的图象在第一和第三象限内,
b0
a0,则- <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 0,所以二次函数开口向下,对称轴在y轴右侧,故ABCD选项全不符合;
a0,则- <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 0时,所以二次函数开口向上,对称轴在y轴左侧,故只有CD两选项可能符合题意,由CD两选图象知,c0
又∵a0,则-a0,当c0,a0时,一次函数y=cx-a图象经过第二、第三、第四象限,
故只有D选项符合题意.
故选:D

13. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>

【解析】
根据 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,计算出结果即可.
解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
故答案为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>

14.0

【解析】
根据分式值为零,分子等于零,分母不为零得2x=0x+2≠0求解即可.
解:由题意,得2x=0,且x+2≠0,解得:x=0
故答案为:0

15. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>

【解析】
由题意知,一个质地均匀的正五边形转盘被分成5个形状大小相同的三角形,标有奇数的三角形有3个,用奇数的个数除以数字的总数即为这个数是一个奇数的概率.
解:一个质地均匀的正五边形转盘被分成5个形状大小相同的三角形,上面分别标有奇数的三角形有3个,当转盘自由转动停止后,观察指针指向区域内的数,这个数是一个奇数的概率是: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
故答案为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>

16.134

【解析】
在同一时刻物高和影子成正比,即在同一时刻的两个物体,影子,经过物体顶部的太阳光线三者构成的两个直角三角形相似,根据相似三角形的性质即可得.
解:∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
故答案为:134

17. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>

【解析】
先根据 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 是关于x的一元一次方程 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 的解,得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,再把所求的代数式变形为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,把 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 整体代入即可求值.
解:∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 是关于x的一元一次方程 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 的解,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
故答案为:14

18. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ## <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>

【解析】
过点EPQ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ADAB于点P,交DC于点Q,得到BP=CQ,从而证得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,得到BE=EF,再利用 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> F为中点,求得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,从而得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,再求出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,再利用AB <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> FC,求出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,求得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,从而得到EH=AH-AE= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,再求得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,求得EG= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> OG=1, 过点FFMAC 于点M,作FNOD于点N,求得FM=2MH= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> FN=2,证得Rt <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> Rt <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,从而得到ON=2NG=1  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,从而得到答案.
解:过点EPQ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ADAB于点P,交DC于点Q
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
AD <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> PQ
AP=DQ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
BP=CQ
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
BP=CQ=EQ
EFBE
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>    
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
BE=EF
又∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> F为中点,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
又∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>    
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
AE=AO-EO=4-2=2
AB <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> FC
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>    
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
EH=AH-AE= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
又∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>    
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
EG= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> OG=1
过点FFMAC 于点M
FM=MC== <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
MH=CH-MC= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>    
FNOD于点N
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
Rt <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> Rt <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
∴Rt
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ≌Rt <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
ON=2NG=1
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
故答案为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>

19.3

【解析】
先计算括号内的,并计算乘方,再计算乘法,最后计算加减即可.
解:原式=1×3+4-4
=3+4-4
=3

20.x3-2xy+x1

【解析】
首先运用平方差公式计算,再运用单项式乘以多项式计算,最后合并同类项,即可化简,然后把xy值代入计算即可.
解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
=
x(x2-y2)+xy2-2xy+x
=x3-xy2+xy2-2xy+x
=x3-2xy+x
x=1y= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 时,原式=13-2×1× <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> +1=1

21.(1)见解析
(2)
见解析
(3)50°

【解析】
1)由平行四边形的性质得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,可利用“SSS证明三角形全等;
2)根据垂直平分线的作法即可解答;
3)根据垂直平分线的性质可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,由等腰三角形的性质可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,再根据三角形外角的性质求解即可.
(1)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 四边形ABCD是平行四边形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
(2)
如图,EF即为所求;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
(3)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> BD的垂直平分线为EF
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>

22.(1)3.752.0
(2)②
(3)
这片树叶更可能来自于荔枝,理由见解析

【解析】
1)根据中位数和众数的定义求解即可;
2)根据方差的定义,方差越小,形状差别越小,根据树叶的长宽比的平均数、中位数和众数来看,即可判断荔枝树叶的长宽比;
3)计算该树叶的长宽比即可判断来自哪颗树.
(1)
芒果树叶的长宽比中数据从小到大排序处在第56位的两个数的平均数为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,因此中位数m=3.75
荔枝树叶的长宽比中数据出现次数最多的是2.0,因此众数n=2.0
故答案为:3.752.0
(2)
合理的是②,理由如下:从树叶的长宽比的方差来看,芒果树叶的长宽比的方差较小,所以芒果叶形状差别更小;从树叶的长宽比的平均数、中位数和众数来看,荔枝树叶的长宽比为2,所以荔枝树叶的长约为宽的两倍;
故答案为:②;
(3)
这片树叶更可能来自荔枝,理由如下:
这片树叶长 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,宽 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,长宽比大约为2.0
根据平均数这片树叶可能来自荔枝树.

23.(1)y= -5x+50050x100
(2)75
元,3125

【解析】
1)设直线的解析式为y=kx+b,根据题意,得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,确定解析式,结合图像,确定自变量取值范围是50x100
2)设销售单价为x元,总利润为w元,根据题意构造二次函数,根据函数的最值计算即可.
(1)
设直线的解析式为y=kx+b,根据题意,得
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
函数的解析式为y= -5x+500
y=0时,-5x+500=0
解得x=100
结合图像,自变量取值范围是50x100
(2)
设销售单价为x元,总利润为w元,根据题意,得:
W=x-50(-5x+500)
=
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
∵-5
0
w有最大值,且当x=75时,w有最大值,为3125
故销售单价定为75元时,该种油茶的月销售利润最大;最大利润是3125元.

24.(1)见解析
(2)13

【解析】
1)连接OD,只要证明ODDE即可;
2)连接CF,证ODABC的中位线,得CF=2DE,再证DEFBC的中位线,得CF=2DE,AE=2xDE=3k,则CF=6kBE=EF=AE+AF=2k+10AC=BA=EF+AE=4k+10,然后在RtACF中,由勾股定理,得 (4k+10)2=102+(6k)2
解得:k=4,从而求得AC=4k+10=4×4+10=26,即可求得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 的半径OA长,即可求解.
(1)
证明:连接OD
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
OD=OC
∴∠
C=∠ODC
AB=AC
∴∠
B=∠C
∴∠
B=∠ODC
OD <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> AB
∴∠
ODE=∠DEB
DEAB
∴∠
DEB=90°
∴∠
ODE=90°
DEOD
DE是⊙O的切线.
(2)
解:连接CF
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
由(1)知ODDE
DEAB
OD <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> AB
OA=OC
BD=CD,即ODABC的中位线,
AC <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 的直径,
∴∠
CFA=90°
DEAB
∴∠
BED=90°
∴∠
CFA=∠BED=90°
DE <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> CF
BE=EF,即DEFBC的中位线,
CF=2DE,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
AE=2xDE=3kCF=6k
AF=10
BE=EF=AE+AF=2k+10
AC=BA=EF+AE=4k+10
RtACF中,由勾股定理,得
AC2=AF2+CF2,即(4k+10)2=102+(6k)2
解得:k=4
AC=4k+10=4×4+10=26
OA=13,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 的半径为13

25.(1)A-10),B30
(2)-3
(3)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>

【解析】
1)令 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,由抛物线解析式可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,解方程即可确定点A,点B的坐标;
2)由抛物线解析式确定其对称轴为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,可知点P1m),再将直线l与抛物线解析式联立,解方程组可确定点C坐标,由 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 列方程求解即可;
3)根据题意先确定点M05)、N45),令 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,整理可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,根据一元二次方程的根的判别式为可知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,然后分情况讨论 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 时以及 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 结合图像分析a的取值范围.
(1)
解:抛物线解析式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,令 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
故点AB的坐标分别为A-10),B30);
(2)
对于抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,其对称轴为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
P为抛物线对称轴上的一点,且点P的纵坐标为m
P1m),
将直线l与抛物线解析式联立,可得
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,可解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
故点C坐标为(4-5),
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 时,可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
(3)
将线段AB先向右平移1个单位长度,再向上平移5个单位长度,得到线段MN
结合(1),可知M05)、N45),
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,整理可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
其判别式为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 时,解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,此时抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 与线段MN只有一个交点;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 即时,解方程 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 时,如图1
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,可解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
此时有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,且 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 时,如图2
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,可解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
此时有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,且 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
综上所述,当抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 与线段MN只有一个交点时,a的取值范围为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>

26.(1) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,证明见解析
(2)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
(3)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 的面积最大;理由见解析, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 面积的最大值为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>

【解析】
1)根据“直角三角形斜边中线等于斜边一半”可得OD= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ABOD′= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> AB,进而得出结论;
2)作AOB的外接圆I,连接CI并延长,分别交⊙IOD,当O运动到O时,OC最大,求出CD和等边三角形AOB上的高OD,进而求得结果;
3)作等腰直角三角形AIB,以I为圆心,AI为半径作⊙I,取AB的中点C,连接CI并延长交⊙IO,此时AOB的面积最大,进一步求得结果.
3)以AB为斜边在其右侧作等腰直角三角形ABC,连接OCAB于点T,在OT上取点E,使OE=BE,连接BE,由(2)可知,当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 时,OC最大,当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 时,此时OT最大,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 的面积最大,由勾股定理等进行求解即可.
(1)
解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,证明如下:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> AB中点为D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> 的中点, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
(2)
解:如图1
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
AOB的外接圆I,连接CI并延长,分别交⊙IOD
O运动到O时,OC最大,
此时AOB是等边三角形,
BO′=AB=6
OC最大=CO′=CD+DO′= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> AB+ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> BO′=3+3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
(3)
解:如图2,作等腰直角三角形AIB,以I为圆心,AI为半径作⊙I
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
AI= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> AB=3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ,∠AOB= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> AIB45°
则点O在⊙I上,取AB的中点C,连接CI并延长交⊙IO
此时AOB的面积最大,
OC=CI+OI= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> AB+3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> =3+3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>
SAOB最大= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> ×6×(3+3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a> )=9+9 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/108/" title="西北" class="c1" target="_blank">西北</a> <a href="/tags/159/" title="经济" class="c1" target="_blank">经济</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1017/" title="北部湾" class="c1" target="_blank">北部湾</a>