解题方法
1 . 如图所示,某镇有一块空地
,其中
,
km,
,当地镇政府规划将这块空地改造成一个旅游景点,拟在中间挖一个人工湖
,其中
,
都在边
,
上,且
,挖出的泥土堆放在
地带上形成假山,剩下的
地带开设儿童游乐场,为安全起见,需在
的一周安装防护网.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/19/553a0321-a5a6-4f81-9924-267d4f60f9f5.png?resizew=114)
(1)当
时,求防护网的总长度;
(2)若要求挖人工湖用地
的面积是堆假山用地
的面积的
倍,试确定
的大小;
(3)为节省投入资金,人工湖
的面积要尽可能小,问如何设计施工方案,可使
的面积最小?最小面积是多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0ecf7d59234f76e997e02e9709f1a85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3393af6d2e25ea81810c2f04c329840.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ccc37b189fa2cbc269ca0b233dac37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](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/a9b0eb72986587ffecf87c22a224bcd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0edafce95aade0386bc0d78f679dcf47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf2b5e712b42f748a3c30bb5d160c18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c29e963e1871b415c086bc600d16bd5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/19/553a0321-a5a6-4f81-9924-267d4f60f9f5.png?resizew=114)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31d3f2cfb6f2626da6a6a4cc26711114.png)
(2)若要求挖人工湖用地
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0edafce95aade0386bc0d78f679dcf47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92f279be7c8a11dcd2c0a97116bdcbb.png)
(3)为节省投入资金,人工湖
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
您最近一年使用:0次
名校
2 . “精准扶贫,修路先行”,为解决城市A和山区B的物流运输问题,方便B地的农产品运输到城市A交易,计划在铁路AD间的某一点C处修建一条笔直的公路到达B地.示意图如图所示,
千米,
千米,
.已知农产品的铁路运费为每千米1百元,公路运费为每千米2百元,农产品从B到A的总运费为
百元.为了求总运费
的最小值,现提供两种方案建立函数关系,方案1:设
千米;方案2:设
.
![](https://img.xkw.com/dksih/QBM/2021/5/25/2728844525436928/2763381872025600/STEM/da1dff13-1d5e-4a97-bcfc-47660ced5353.png?resizew=203)
(1)试将
分别表示为关于
、
的函数关系式
和
;
(2)请只选择一种方案,求出总运费
的最小值以及此时
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80739f2486099ffd39a3038c60f41825.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00eadc41339daa56623a3d3d28460936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff83a75900ae3d07bbb4eda227b449cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88bfc0387785bf3c60f75ed3d34cc98a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1950345548fe750b80ce79b168969ca.png)
![](https://img.xkw.com/dksih/QBM/2021/5/25/2728844525436928/2763381872025600/STEM/da1dff13-1d5e-4a97-bcfc-47660ced5353.png?resizew=203)
(1)试将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3634f1a6094deeafc4c3de8277d85ce6.png)
(2)请只选择一种方案,求出总运费
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
您最近一年使用:0次
2021-07-13更新
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534次组卷
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4卷引用:湖北省华中师范大学第一附属中学2020-2021学年高一下学期期中数学试题