1 . 某市政府欲在如图所示的矩形
的非农业用地中规划出一个休闲娱乐公园(如图中阴影部分),形状为直角梯形
(线段
和
为两条底边),已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e33ccc70b853067d184dcc5b8459de04.png)
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/300eaf6cba3b91d8c09db611e11582dd.png)
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ff404c218faa8101298309554c53757.png)
,其中曲线
是以
为顶点、
为对称轴的抛物线的一部分.
![](https://img.xkw.com/dksih/QBM/2016/1/6/1572421473067008/1572421479448576/STEM/2ca0ee604ec24c10a4ea48a7ff78acfb.png)
(1)以
为原点,
所在直线为
轴建立直角坐标系,求曲线
所在抛物线的方程;
(2)求该公园的最大面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34b0c4c783dd55685bd3e88bb31c6696.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a256acc1953e3cfe36343a9375169fa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82c9ef70f8fa5a0effb5ddd3ec3201a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b77eb3e3dd6bf9a4e637e98ec2ddccc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e33ccc70b853067d184dcc5b8459de04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5fe30c67ac20cd4e8b9cc2d0d420a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/300eaf6cba3b91d8c09db611e11582dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5fe30c67ac20cd4e8b9cc2d0d420a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ff404c218faa8101298309554c53757.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5fe30c67ac20cd4e8b9cc2d0d420a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7382071f035087d3c35e3ffb741d981.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa5694373bd78b1ca2180f831bf1c8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b693717f525facc79b9a500ed998b109.png)
![](https://img.xkw.com/dksih/QBM/2016/1/6/1572421473067008/1572421479448576/STEM/2ca0ee604ec24c10a4ea48a7ff78acfb.png)
(1)以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa5694373bd78b1ca2180f831bf1c8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d86a0a3e867a448094f74a54a1fee64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7382071f035087d3c35e3ffb741d981.png)
(2)求该公园的最大面积.
您最近一年使用:0次
2014·全国·一模
名校
2 . 某地需要修建一条大型输油管道通过240公里宽的沙漠地带,该段输油管道两端的输油站已建好,余下工程是在该段两端已建好的输油站之间铺设输油管道和等距离修建增压站(又称泵站).经预算,修建一个增压站的工程费用为400万元,铺设距离为
公里的相邻两增压站之间的输油管道费用为
万元.设余下工程的总费用为
万元.
(1)试将
表示成
的函数;
(2)需要修建多少个增压站才能使
最小,其最小值为多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/749d0e03dc286f2a835768d4ac5f07a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)试将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)需要修建多少个增压站才能使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
您最近一年使用:0次
2016-12-03更新
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8卷引用:山西省朔州市应县第一中学2020-2021学年高一上学期第四次月考数学试题
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