1 . 某湿地公园内有一条河,现打算建一座桥将河两岸的路连接起来,剖面设计图纸如下:
![](https://img.xkw.com/dksih/QBM/2017/3/19/1647033146163200/1647946590740480/STEM/30f0c34163754a4a9e5609184b23ac76.png?resizew=489)
其中,点
为
轴上关于原点对称的两点,曲线段
是桥的主体,
为桥顶,且曲线段
在图纸上的图形对应函数的解析式为
,曲线段
均为开口向上的抛物线段,且
分别为两抛物线的顶点,设计时要求:保持两曲线在各衔接处(
)的切线的斜率相等.
(1)求曲线段
在图纸上对应函数的解析式,并写出定义域;
(2)车辆从
经
倒
爬坡,定义车辆上桥过程中某点
所需要的爬坡能力为:
(该点
与桥顶间的水平距离)
(设计图纸上该点处的切线的斜率),其中
的单位:米.若该景区可提供三种类型的观光车:①游客踏乘;②蓄电池动力;③内燃机动力.它们的爬坡能力分别为
米,
米,
米,又已知图纸上一个单位长度表示实际长度
米,试问三种类型的观光车是否都可以顺利过桥?
![](https://img.xkw.com/dksih/QBM/2017/3/19/1647033146163200/1647946590740480/STEM/30f0c34163754a4a9e5609184b23ac76.png?resizew=489)
其中,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/974bc22aed322f940bdd8a83de869edf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e04a5b59cced25ab7057d03fe3c0ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e04a5b59cced25ab7057d03fe3c0ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fed19e09b52266a544aebf9077a1270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3a1008494918681c42448ebef61dea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/974bc22aed322f940bdd8a83de869edf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc96ce462f6a456c6993588e8edb0af2.png)
(1)求曲线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
(2)车辆从
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b237a5e4df47a0a2cf6c468d39085bce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1452ad51bc851e39fb45acb2825089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b418f716e6ea876faa7b003b8af56044.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/742145c3bfb5281e2e583e6405a3d4ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67f08d5e69543f99644ac3c8974c5b58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
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2017-03-20更新
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5卷引用:2020届江苏省南京市第二十九中高三下学期3月期初数学试题