解题方法
1 . 某公园为了美化环境和方便顾客,计划建造一座圆弧形拱桥,已知该桥的剖面如图所示,共包括一段圆弧形桥面ACB和两段长度相等的直线型桥面AD、BE,拱桥ACB所在圆的半径为3米,圆心O在DE上,且AD和BE所在直线与圆O分别在连结点A和B处相切.根据空间限制及桥面坡度的限制,桥面跨度DE的长要不大于18米,不小于12米.已知直线型桥面的修建费用是每米0.6万元,弧形桥面的修建费用是每米2.5万元,设
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/30/fcbe57a7-c0af-45b8-91a8-8e9440d54eb9.png?resizew=204)
(1)若桥面(线段AD,BE和弧ACB)的修建总费用为W万元,求W关于
的函数表达式,并写出
的取值范围;
(2)当
为何值时,桥面修建总费用W最低?(角
的取值精确到
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc464e9a543e2995cd64ad444f0bf340.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/30/fcbe57a7-c0af-45b8-91a8-8e9440d54eb9.png?resizew=204)
(1)若桥面(线段AD,BE和弧ACB)的修建总费用为W万元,求W关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ea6771d7581e9bfff5f7fa9d43f221d.png)
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解题方法
2 . 甲乙丙三人计划本周六去桃花源景区游玩.现有甲、乙两人都住在
地,打算同时徒步从
地出发赶往
地,甲不经
地直接匀速前往
地,他的速度(单位:千米/小时)范围由函数
,
决定:由于丙不认识路,所以乙经
地接到丙后前往
地,速度为
千米/小时,此间乙在
地停留
分钟,其中
千米,
千米,
千米,如图.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/8849596c-56f0-4629-942a-3fc9ea40d363.png?resizew=138)
(1)求
的取值范围;
(2)甲、乙到达
地后原地等待,为使在
处互相等待的时间不超过
小时,甲的速度
中
应控制在什么范围内?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/9944fa15265c94ab4b62d9482c50cf12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e08a9f03807728b902a8b4486550e370.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/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b184c94e38f1e5dbe750b2168c2a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1682d306c38087d9e6f7efb9cec596a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a927a294d3d7119b54427b195b6dac8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/8849596c-56f0-4629-942a-3fc9ea40d363.png?resizew=138)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e256ffedf7b1835be1b2d949b2f3d12f.png)
(2)甲、乙到达
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e256ffedf7b1835be1b2d949b2f3d12f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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