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【327985】广西来宾市2021年中考数学真题

时间:2025-01-20 20:55:33 作者: 字数:19976字
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广西来宾市2021年中考数学真题

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得分




一、选择题

1.下列各数是有理数的是( )
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

2.如图是一个几何体的主视图,则该几何体是( )
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

3.如图,小明从 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 入口进入博物馆参观,参观后可从 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 三个出口走出,他恰好从 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 出口走出的概率是( )
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

4.我国天问一号火星探测器于2021515日成功着陆火星表面.经测算,地球跟火星最远距离 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 千米,其中 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 用科学记数法表示为( )
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

5.如图是某市一天的气温随时间变化的情况,下列说法正确的是( )
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
A
.这一天最低温度是-4℃
B
.这一天12时温度最高
C
.最高温比最低温高8℃
D
0时至8时气温呈下降趋势

6.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/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

7.平面直角坐标系内与点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 关于原点对称的点的坐标是( )
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

8.如图, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的半径 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的长是( )
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

9.一次函数y=2x+1的图像不经过 (     )
A
.第一象限
B
.第二象限
C
.第三象限
D
.第四象限

10.《九章算术》是人类科学史上应用数学的“算经之首”,书中记载:今有三人共车,二车空;二人共车,九人步.问:人与车各几何?译文:若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 人坐一辆车,则两辆车是空的;若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 人坐一辆车,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 人需要步行.问:人与车各多少?设有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 辆车,人数为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,根据题意可列方程组为( )
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

11.如图,矩形纸片 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 分别在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 上,把纸片如图沿 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 折叠,点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的对应点分别为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 并延长交线段 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的值为( )
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

12.定义一种运算: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,则不等式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的解集是( )
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

评卷人

得分




二、填空题

13.分解因式: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ______

14.如图,从楼顶 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 处看楼下荷塘 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 处的俯角为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,看楼下荷塘 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 处的俯角为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,已知楼高 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 米,则荷塘的宽 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> __________米.(结果保留根号)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

15.为了庆祝中国共产党成立 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 周年,某校举行“党在我心中”演讲比赛,评委将从演讲内容,演讲能力,演讲效果三个方面给选手打分,各项成绩均按百分制计,然后再按演讲内容占 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,演讲能力占 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,演讲效果占 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,计算选手的综合成绩(百分制).小婷的三项成绩依次是 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,她的综合成绩是__________

16.如图,从一块边长为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的菱形铁片上剪出一个扇形,这个扇形在以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 为圆心的圆上(阴影部分),且圆弧与 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 分别相切于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,将剪下来的扇形围成一个圆锥,则圆锥的底面圆半径是__________
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

17.如图,已知点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,两点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 在抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 上,向左或向右平移抛物线后, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的对应点分别为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,当四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的周长最小时,抛物线的解析式为__________
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

评卷人

得分




三、解答题

18.计算: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

19.解分式方程: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

20.如图,四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

1)求证: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
2)尺规作图:过点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的垂线,垂足为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> (不要求写作法,保留作图痕迹);
3)在(2)的条件下,已知四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的面积为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的长.

21.某水果公司以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> / <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的成本价新进 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 箱荔枝,每箱质量 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,在出售荔枝前,需要去掉损坏的荔枝,现随机抽取 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 箱,去掉损坏荔枝后称得每箱的质量(单位: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> )如下:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>


整理数据:



分析数据:


质量( <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>


 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>


 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>


 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>


 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>


 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>


 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>



平均数


众数


中位数


数量(箱)


 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>


 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>


 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>


 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>


 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>


 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>



 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>


 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>


 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>


1)直接写出上述表格中 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的值;
2)平均数、众数、中位数都能反映这组数据的集中趋势,请根据以上样本数据分析的结果,任意选择其中一个统计量,估算这 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 箱荔枝共损坏了多少千克?
3)根据(2)中的结果,求该公司销售这批荔枝每千克定为多少元才不亏本?(结果保留一位小数)

22.(阅读理解)如图1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的面积与 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的面积相等吗?为什么?
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
解:相等,在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 中,分别作 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,垂足分别为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 是平行四边形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
(
类比探究)问题①,如图2,在正方形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的右侧作等腰 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的面积.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
解:过点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
请将余下的求解步骤补充完整.
(
拓展应用)问题②,如图3,在正方形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的右侧作正方形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 在同一直线上, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,直接写出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的面积.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

23.2022年北京冬奥会即将召开,激起了人们对冰雪运动的极大热情.如图是某跳台滑雪训练场的横截面示意图,取某一位置的水平线为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 轴,过跳台终点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 作水平线的垂线为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 轴,建立平面直角坐标系.图中的抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 近似表示滑雪场地上的一座小山坡,某运动员从点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 正上方 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 米处的 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 点滑出,滑出后沿一段抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 运动.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

1)当运动员运动到离 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 处的水平距离为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 米时,离水平线的高度为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 米,求抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的函数解析式(不要求写出自变量 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的取值范围);
2)在(1)的条件下,当运动员运动水平线的水平距离为多少米时,运动员与小山坡的竖直距离为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 米?
3)当运动员运动到坡顶正上方,且与坡顶距离超过 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 米时,求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的取值范围.

24.如图①,在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 上一动点(不与点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 重合),在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 内作矩形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 上,点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 上,设 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

1)当矩形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 是正方形时,直接写出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的长;
2)设 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的面积为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,矩形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的面积为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,令 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 关于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的函数解析式(不要求写出自变量 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的取值范围);
3)如图②,点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 是(2)中得到的函数图象上的任意一点,过点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 分别与 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 轴正半轴, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 轴正半轴交于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 两点,求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 面积的最小值,并说明理由.

25.如图,已知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的直径, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的边 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 分别交于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 并延长,与 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的延长线交于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
1)求证: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的切线;
2)若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的值;
3)在(2)的条件下,若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的平分线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的值.

参考答案

1.D

【解析】
利用有理数和无理数的定义判断即可.
解:四个选项的数中: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 是无理数, 0是有理数,
故选项D符合题意.
故选:D

2.C

【解析】
主视图、左视图、俯视图是分别从物体正面、左面和上面看,所得到的图形.依题意,由几何体的主视图即可判断该几何体的形状.
解:由该几何体的主视图可知,该几何体是选项C中的图形.
故选:C

3.B

【解析】
此题根据事件的三种可能性即可确定答案
当从A口进,出来时有三种可能性即:BCD;恰好从C口走出的可能性占总的 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,故概率为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
故答案选:B

4.C

【解析】
科学记数法的表示形式为a×10n的形式,其中1≤|a|10n整数.确定n值时,要看把原数a,小数点移了多少位,n绝对值与小数点移的位数相同.
解:将 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 个数用科学数法表示 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
C

5.A

【解析】
根据气温变化图逐项进行判断即可求解.
解:A. 这一天最低温度是 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,原选项判断正确,符合题意;
B.
这一天14时温度最高,原选项判断错误,不合题意;
C.
这一天最高气温8℃,最低气温-4℃,最高温比最低温高 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,原选项判断错误,不合题意;
D.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 时至 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 时气温呈先下降在上升趋势,原选项判断错误,不合题意.
故选:A

6.A

【解析】
分别根据同底数幂的乘法、同底数幂的除法、幂的乘方、整式的加减法则进行计算,即可求解.
解:A.  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,原选项计算正确,符合题意;
B.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,原选项计算错误,不合题意;
C.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,原选项计算错误,不合题意;
D.
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,不是同类项,无法相减,原选项计算错误,不合题意.
故选:A

7.B

【解析】
根据关于原点对称的点的坐标特点:两个点关于原点对称时,它们的坐标符号相反,可以直接得到答案.
解:∵P34),
关于原点对称点的坐标是(-3-4),
故选B

8.C

【解析】
根据圆周角定理求出∠COB的度数,再求出OBD的度数,根据30°角所的直角等于斜的一半求出OD度.
BAC=30°
∴∠COB=60°
∵∠ODB=90°
∴∠OBD=30°
OB=4
OD= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> OB= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> =2
C

9.D

【解析】
根据一次函数的系数判断出函数图象所经过的象限,由k=20b=10可知,一次函数y=2x+1的图象过一、二、三象限.另外此题还可以通过直接画函数图象来解答.
∵k=2
0b=10
根据一次函数图象的性质即可判断该函数图象经过一、二、三象限,不经过第四象限.
故选D.

10.B

【解析】
设有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 辆车,人数为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,根据“如果每3人坐一辆车,那么有2辆空车;如果每2人坐一辆车,那么有9人需要步行”,即可得出关于xy的二元一次方程,此得解.
解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 辆车,人数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 人,依意得:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
B

11.A

【解析】
根据折叠性质则可得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的垂直平分线,则由直角三角形性质及矩形性质可得∠AEO=AGDFHED90°,根据相似三角形判定推出EFH∽△GAD,再利用矩形判定及性质证FHAB,即可求得果.
解:如FFHAD于点H
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 对应点分别为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
EFAA'的垂直平分线
∴∠AOE=90°
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 是矩形,
∴∠BADBD90°
∴∠OAEAEO=OAEAGD
∴∠AEO=AGD
FHAD
∴∠FHED90°
∴△EFH∽△GAD
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
∵∠AHFBADB90°
ABFH是矩形.
FHAB
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
A

12.C

【解析】
根据新定义运算规则,分别从 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 两种情况列出关于x的不等式,求解后即可得出结论
解:由意得,当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
原不等式的解集 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
原不等式的解集 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
上所述,不等式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的解集是 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
C

13. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

【解析】
利用平方差公式进行因式分解即可.
解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
故答案为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

14. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

【解析】
由三角函数分别求出BCBD,即可得出CD
解:由意知:BAC=90°-45°=45°ABC是直角三角形,
RtABC中,tanBAC = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> AB=30米,
BC=AB•tan45°=30米,
∵∠BAD=90°-60°=30°tanBAD = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
BD=AB•tan30°= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> (米),
CD=BC-BD= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> (米);
故答案 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

15.89

【解析】
根据加权平均数的定义列式计算可得.
解:选手甲的综合成绩为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> (分 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
故答案为:89分.

16. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

【解析】
先利用菱形的性质得到含30°角的直角三角形,再利用勾股定理求出AE,最后利用弧长公式求出弧长,弧长即为圆锥底面圆的周长,再利用周长公式即可求半径.
解:如图,连接AE,由切线性质可知:AE⊥BC,即∠AEB=90°
菱形铁片上∠BAD=120°
∴∠B=180°-120°=60°

∴∠BAE=30°

∴AB=2BE=2

∴BE=1

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
扇形的弧长为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
所以圆锥底面圆半径为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
故答案为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

17. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

【解析】
先通过平移和轴对称得到当BE <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 三点共线时 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 最小,再通过设线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的解析式并将三点坐代入,当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,求出a,最后将四形周 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的周长进行比,确定a的最,即可得到平移后的抛物线的解析式.
解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
由平移的性可知: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的周长为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
要使其周最小,则应使 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 最小;
抛物线平移了a位,当a0,抛物线向右平移,当a0,抛物线向左平移;
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 向左平移2位得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 由平移的性可知: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 关于x称点记为E <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,由轴对称性可知, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
BE <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 三点共线时 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 最小,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的解析式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
E点坐代入解析式可得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的周长为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的周长为
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,其周最小,
所以抛物线向右平移了 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 位,
所以其解析式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
故答案 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

18.-2

【解析】
先分别计算出有理数的乘方及括号内的有理数加减,再计算乘除,即可求得结果.
解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

19. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

【解析】
分式方程去分母转化为整式方程,求出整式方程的解得到x经检验即可得到分式方程的解.
解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
去分母,得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
解此方程,得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
经检验 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 是原分式方程的根.

20.1)证明见详解;(2)作图见详解;(3CE=4

【解析】
1)根据 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,得到BAC=DCA <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> AC=CA,利用AAS”即可明;
2)如,延AB,任意取一点H,使H和点CAB,以C为圆心,CH半径画弧,交ABFG,分FG为圆心,以大于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> FG长为半径画弧,两弧交于I,作直线CI,交AB长线ECDABE
3明四ABCD平行四形,根据平行四形面公式即可求解.
解:(1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
∴∠BAC=DCA
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> AC=CA
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
2)如,延AB,任意取一点H,使H和点CAB,以C为圆心,CH半径画弧,交ABFG,分FG为圆心,以大于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> FG长为半径画弧,两弧交于I,作直线CI,交AB长线ECDABE
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
AB=CD
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
ABCD平行四形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,
5CE=20
CE=4

21.1a=6b=4.7c=4.75;(2500kg;(310.5元.

【解析】
1)用20减去各数据的频数即可求出a,根据众数、中位数的意即可求出bc
2用平均数行估算,用每箱坏数量乘以2000即可求解;
3)用购买总费用除以没有坏的数量即可求出解.
解:(1a=20-2-1-7-3-1=6
20个数据中,4.7数最大,所以众数b=4.7
20个数据排序,第1011个数据分别为4.74.8,所以中位数c= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
2用平均数行估算,(5-4.75×2000=500kg
答:用平均数行估算, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 箱荔枝共坏了500千克;
3)(10×2000×5÷4.75×200010.5
答:公司批荔枝每千克定10.5元才不本.

22. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ;② <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

【解析】
过点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,根据材料可知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,再由等腰三角形性质可知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,即可求出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
连接CE,证明 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,即可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,由此即可求解.
解:①过点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
在正方形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
在正方形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
过程如下:如解图3,连接CE
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
在正方形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 、正方形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 中,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
在正方形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

23.1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ;(212米;(3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

【解析】
1)根据题意可知:点A04)点B48),利用待定系数法代入抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 即可求解;
2)高度差为1米可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 可得方程,由此即可求解;
3)由抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 可知坡顶坐标为  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,此时即当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 时,运动员运动到坡顶正上方,若与坡顶距离超过 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 米,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,由此即可求出b的取值范围.
解:(1)根据题意可知:点A04),点B48)代入抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 得,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的函数解析式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
2)∵运动员与小山坡的竖直距离为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 米,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> (不合题意,舍去),  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
故当运动员运动水平线的水平距离为12米时,运动员与小山坡的竖直距离为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 米;
3)∵点A04),
抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
坡顶坐标为  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
当运动员运动到坡顶正上方,且与坡顶距离超过 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 米时,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

24.1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ;(2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ;(36

【解析】
1)直接根据等腰直角三角形性质及正方形性质可以得出: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,进一步计算即可;
2)先根据等腰直角三角形以及直角三角形得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,代入 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 化简即可;
3)设l <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的最小,两个函数有一个交点,列出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的表达式求解即可.
解:(1)根据意:可知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
等腰直角三角形, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
DC=8
AC= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
2EFGH矩形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
3)由(2)得P <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 上,
l <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的最小,两个函数有一个交点,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

25.1)见解析;(2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ;(3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>

【解析】
1)连接DF,由周角性可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 利用平行线的判定与性可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,再根据等腰三角形性及直角三角形性可推出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,即可结论
2)由相似三角形的判定可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 推出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,由 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,可利用勾股定理求得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,即可求出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
3MN,并延COAF <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 相交于点P,点QAQ,利用(2)所得结论及已知分求得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,再由相似三角形的判定及性可推出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ,代入求后即可求得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
1明:如DF
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的直径,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
DFAE
ABCD是平行四形,
AEOC
DFOC
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 的切线
2)解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
由勾股定理得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> (不合意,舍去).
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
3)解:MN,并延COAF <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 相交于点P,点QAQ
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
ABCD是平行四形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> ABOC
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a> 平分 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
ABOC
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
RtAPO中,由勾股定理得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
RtAPH中,由勾股定理得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1014/" title="广西" class="c1" target="_blank">广西</a> <a href="/tags/1904/" title="来宾" class="c1" target="_blank">来宾</a>