1 . 某城市在进行规划时,准备设计一个圆形的开放式公园.为达到社会和经济效益双丰收.园林公司进行如下设计,安排圆内接四边形
作为绿化区域,其余作为市民活动区域.其中
区域种植花木后出售,
区域种植草皮后出售,已知草皮每平方米售价为
元,花木每平方米的售价是草皮每平方米售价的三倍. 若
km ,
km
(1)若
km ,求绿化区域的面积;
(2)设
,当
取何值时,园林公司的总销售金额最大.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db5e1441a49e782ff0ef46e776cde06a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df6d51738ac1bc8b9530ea4a55745c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07160f14b3b453bebb64cb2bf96dc85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89c41757ae282475fb29ec1e8e02045d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adce79579360c94699123b74bb2795ea.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1950345548fe750b80ce79b168969ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://img.xkw.com/dksih/QBM/2018/12/19/2100386859679744/2101590403235840/STEM/7c17c3d7af5640c7afd8cbb0d18e997d.png?resizew=153)
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2 . 如图,有一块半径为20米,圆心角
的扇形展示台,展示台分成了四个区域:三角形
,弓形
,扇形
和扇形
(其中
).某次菊花展分别在这四个区域摆放:泥金香、紫龙卧雪、朱砂红霜、朱砂红霜.预计这三种菊花展示带来的日效益分别是:50元/米2,30元/米2,40元/米2.为使预计日总效益最大,
的余弦值应等于__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49a4c11d41372175ba3541a44c3376b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3201d3796ed9a29338aac25245a7c8e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc775691cd03e1abed66100c942eb3a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ed01d1ff5a7f21a68fb3a1e5c7f393e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/564743a1fe463a981f06914e3cb5e03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3da02b38bc1ab163a7471711b9b1427e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed66570f697459aba9daa2eaf9460bcb.png)
![](https://img.xkw.com/dksih/QBM/2018/5/10/1942255375106048/1943667288367104/STEM/e867a1919ca3494fbdac10a2143aa363.png?resizew=149)
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2018-05-12更新
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839次组卷
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5卷引用:【全国市级联考】2018年江西省南昌市高三第二次理科数学模拟试题
【全国市级联考】2018年江西省南昌市高三第二次理科数学模拟试题【全国市级联考】江西省南昌市2018届高三第二次文科数学模拟试题2019届湖南省永州市祁阳县高三下学期第二次模拟考试理科数学试题江西省南昌市师大附中2019届高三数学(文科)二模试题(已下线)1.4 生活中的优化问题举例-2020-2021学年高二数学(理)课时同步练(人教A版选修2-2)
3 . 如图所示,在一半径等于1千米的圆弧及直线段道路
围成的区域内计划建一条商业街,其起点和终点均在道路
上,街道由两条平行于对称轴
且关于
对称的两线段EF、CD,及夹在两线段EF、CD间的弧组成.若商业街在两线段EF、CD上收益为每千米2a元,在两线段EF、CD间的弧上收益为每千米a元.已知
,设
,
(1)将商业街的总收益
表示为
的函数;
(2)求商业街的总收益的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f788fb0059b7356dc6c7811f46057e66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae7d29d4928c427ce72379eb0202678.png)
(1)将商业街的总收益
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd288d4152caf5fc8187a1a901c8949f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)求商业街的总收益的最大值.
![](https://img.xkw.com/dksih/QBM/2017/4/22/1671142035128320/1719208170930176/STEM/97ee320817af40d8b66620db77a1e8a4.png?resizew=189)
![](https://img.xkw.com/dksih/QBM/2017/4/22/1671142035128320/1719208170930176/STEM/fc1daec7aadd417285ff1238ce3593ff.png?resizew=189)
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