名校
解题方法
1 . 某处有一块闲置用地,如图所示,它的边界由圆O的一段圆弧
和两条线段
,
构成.已知圆心O在线段
上,现测得圆O半径为2百米,
,
.现规划在这片闲置用地内划出一片梯形区域用于商业建设,该梯形区域的下底为
,上底为
,点M在圆弧
(点D在圆弧
上,且
)上,点N在圆弧
上或线段
上.设
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/c6222bb9-a391-4a91-8406-21126f998d5d.png?resizew=173)
(1)将梯形
的面积表示为
的函数;
(2)当
为何值时,梯形
的面积最大?求出最大面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49a4c11d41372175ba3541a44c3376b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d900531973c546625694146fa1509ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6f9353ca110c8b81561455b232dbc15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/719d071fa86799218653af756956b7aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd6ffb78dad3375efa3b08ab518553d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fb35158a52a23a6e57ff890cef8c7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/c6222bb9-a391-4a91-8406-21126f998d5d.png?resizew=173)
(1)将梯形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e22545a765af9563ea7c8db75c16df6.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/6e22545a765af9563ea7c8db75c16df6.png)
您最近一年使用:0次
2 . 设函数
和
都是定义在集合
上的函数,对于任意的
,都有
成立,称函数
与
在
上互为“互换函数”.
(1)函数
与
在
上互为“互换函数”,求集合
;
(2)若函数
(
且
)与
在集合
上互为“互换函数”,求证:
;
(3)函数
与
在集合
且
上互为“互换函数”,当
时,
,且
在
上是偶函数,求函数
在集合
上的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfc595518cf752e1c7903dfff93dbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/298b861acdad2f218a882319c1a3280a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d761c4444f5eac17133caaf19d6b9ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588bbf780d49cf4d29802c2e4126f112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95ff35f3b50966a5e3cbb0b5977af7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0ba94c781da05ac6ca38261904b40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
(3)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c395237799431ccbd691c17d5c78ac3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a7a292b39ec75214652cb000bfa8310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f96bafcae32d0b273c95d1bd70fa01c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05486718d0f498abca5c2c21912bb26d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1be9a7177c28cc52018fddf300e5b37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc30165c18de623d0a3efb961e606d1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2020-02-01更新
|
1542次组卷
|
3卷引用:上海市嘉定区封浜高级中学2016-2017学年高一下学期期末数学试题
上海市嘉定区封浜高级中学2016-2017学年高一下学期期末数学试题上海市嘉定区2016-2017学年高一下学期期末数学试题(已下线)第五章 三角函数(选拔卷)-【单元测试】2021-2022学年高一数学尖子生选拔卷(人教A版2019必修第一册)
3 . 对于函数
,如果存在常数
,使得对
取D内每一个值时,都有等式
,那么这个函数
称为“过周期函数”,常数
叫做函数
的“过周期”.
(1)若记
为
的所有过周期组成的集合,求集合
;
(2)猜想
是否为过周期函数?若是,写出它的一个过周期:若不是,请说明理由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f2ab09ce6ffc17ccbe9d4b203009d4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/444103f2411981d89ee755fe64c1233b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/574e568c0faa283942a9fffd0a8efce1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb788ae88e457017bb81120b6a2e5ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb788ae88e457017bb81120b6a2e5ee.png)
(1)若记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ffce595318f7bb0e2d7d048cb4c96d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)猜想
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318a16f1950d06e5500c76d8f81a507f.png)
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4 . 如图,在
中,D为BC的中点,G为AD的中点,过点G任作一直线MN分别交AB,AC于M,N两点,若
,
,试问:
是否为定值?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a398a79942d381cab12d13bf4028d5ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17b84e1b1028bc6b7432d4262251aa29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f0b84ee4ed90face0993d4f4dda379.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/11/5c2830df-cb47-4b61-9e58-cc79a39552db.png?resizew=149)
您最近一年使用:0次
2019-05-17更新
|
431次组卷
|
2卷引用:步步高高一数学暑假作业:作业24 平面向量基本定理及坐标表示
名校
5 . 习近平总书记在十九大报告中指出,必须树立和践行“绿水青山就是金山银山”的生态文明发展理念,这将进一步推动新能源汽车产业的迅速发展.以下是近几年我国新能源乘用车的年销售量数据及其散点图:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/17/b42a1d56-2a4c-4971-90fa-08406c593ae6.png?resizew=268)
(1)请根据散点图判断,
与
中哪一个更适宜作为年销售量
关于年份代码
的回归方程类型? (给出判断即可,不必说明理由)
(2)根据(1)的判断结果及表中数据,建立
关于
的回归方程,并预测
年我国新能源乘用车的销售量(精确到
).
附: 1.最小二乘法估计公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50be0ffb7fcaff347a8764eab60c4985.png)
年份 | 2013 | 2014 | 2015 | 2016 | 2017 |
年份代码 | |||||
新能源乘用车年销量 |
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/17/b42a1d56-2a4c-4971-90fa-08406c593ae6.png?resizew=268)
(1)请根据散点图判断,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e136e7637543c8ae92c8dcd55b31924.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1449e6e0d5478519a1131b25cc2bc818.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)根据(1)的判断结果及表中数据,建立
![](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/6567511bb9486b2ca7452b870abd2a1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a87796ee30e6c5d5e6b6285b32abe10c.png)
附: 1.最小二乘法估计公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50be0ffb7fcaff347a8764eab60c4985.png)
其中 |
您最近一年使用:0次
2018-05-09更新
|
4057次组卷
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2卷引用:【全国市级联】福建省泉州市2018届高三第二次(5月)质量检查数学文试题