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解题方法
1 . 《孙子算经》是中国古代重要的数学著作,据书中记载,中国古代诸侯的等级从低到高分为五级:男、子、伯、侯、公.现有每个级别的诸侯各一人,共5人,要把80个橘子分完且每人都要分到橘子,级别每高一级就多分
个(
为正整数),若按这种方法分橘子,“子”恰好分得13个橘子的概率是( )
![](https://img.xkw.com/dksih/QBM/2021/5/20/2725187456753664/2734157980934144/STEM/35b3403d7b8d41b5bb047abc0947c406.png?resizew=88)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://img.xkw.com/dksih/QBM/2021/5/20/2725187456753664/2734157980934144/STEM/35b3403d7b8d41b5bb047abc0947c406.png?resizew=88)
A.![]() | B.![]() | C.![]() | D.![]() |
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2021-06-02更新
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5卷引用:福建省厦门市湖滨中学2021-2022学年高二上学期开学收心练习数学试题
(已下线)福建省厦门市湖滨中学2021-2022学年高二上学期开学收心练习数学试题辽宁省葫芦岛市2021届高三二模数学试题(已下线)6.1 等差数列(精讲)-【一隅三反】2022年高考数学一轮复习(新高考地区专用)(已下线)考点45 概率-备战2022年高考数学(文)一轮复习考点帮江苏省南京市第五中学2021-2022学年高三上学期10月月考数学试题
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2 . 《九章算术》是我国古代数学成就的杰出代表.其中《方田》章给出计算弧田面积的经验公式为:
.弧田(如图1阴影部分)由圆弧和其所对弦围成,弦”指圆弧所对弦长,“矢”等于半径长与圆心到弦的距离之差.类比弧田面积公式得到球缺(如图 2)近似体积公式:
圆面积
矢
.球缺是指一个球被平面截下的一部分,厦门嘉庚体育馆近似球缺结构(如图3),若该体育馆占地面积约为18000
,建筑容积约为340000
,估计体育馆建筑高度(单位:
)所在区间为
参考数据:
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2018/5/23/1951662548353024/1952731583913984/STEM/9ad5b79438a944e099880b6bc6da7cbb.png?resizew=171)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe4049f265a248c651b93f5aa40c47c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235006e6c09ffbdd606a5f53dff3184e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018e683996560231de4a02503790f50a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8d7b4bb12628d5ed455d814b8aafa1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36accab23dbd172687769aea43e5781c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e67a8fba0059a2d810d0d0011e0502f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b8e7bdfb42e7c5095450acbf5459570.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02f4f4d2a4158df5daa379ba327fcdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73bbc330bb9fb3bcb682e13f2262e164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5cb55c16ba23b19a9d48005145d4a4.png)
![](https://img.xkw.com/dksih/QBM/2018/5/23/1951662548353024/1952731583913984/STEM/52b047f4ffce494b90b28cdd478ccfef.png?resizew=162)
![](https://img.xkw.com/dksih/QBM/2018/5/23/1951662548353024/1952731583913984/STEM/802a1e563a79419fb78c979f408dd5de.png?resizew=157)
![](https://img.xkw.com/dksih/QBM/2018/5/23/1951662548353024/1952731583913984/STEM/9ad5b79438a944e099880b6bc6da7cbb.png?resizew=171)
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2018-05-25更新
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921次组卷
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10卷引用:2019届福建省厦门一中高三上学期返校考理科数学试题
2019届福建省厦门一中高三上学期返校考理科数学试题【全国市级联考】福建省厦门市2018届高中毕业班第二次质量检查数学(理)试题福建省厦门市双十中学2018-2019学年高一上学期12月月考数学试题河南省郑州市第一中学2020届高三名校联考数学试题(理科)河南省郑州市第一中学2020届高三名校联考数学试题(文科)河南省2020届高三毕业班高考适应性练习6月数学(理科)试题河南省2020届高三(5月份)高考数学(理科)适应性试题2021届高三高考必杀技之信息阅读题--类型9 公式的理解与应用(已下线)专题13 算法初步、推理与证明、数系的扩充与复数的引入-备战2021年高考数学(文)纠错笔记河南濮阳外国语学校2021-2022学年高三上学期限时训练二数学理科试题
3 . 阅读以下材料,并按要求完成相应的任务:莱昂哈德
欧拉
是瑞士数学家,在数学上经常见到以他的名字命名的重要常数,公式和定理,下面就是欧拉发现的一个定理:在
中,
和
分别为外接圆和内切圆的半径,
和
分别为其中外心和内心,则
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/6/b1a259a9-1a05-48e4-9259-1977e6f19620.png?resizew=136)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/6/e5af681c-00bc-49de-b2ce-e7f738fdc6c6.png?resizew=379)
如图1,
和
分别是
的外接圆和内切圆,
与
相切分于点
,设
的半径为
,
的半径为
,外心
(三角形三边垂直平分线的交点)与内心
(三角形三条角平分线的交点)之间的距离
,则有
.
下面是该定理的证明过程(部分)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa96c86a9085aeb7a57ce955200f0c80.png)
延长
交
于点
,过点
作
的直径
,连接
,
.
,
(同弧所对的圆周角相等).
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
,
,①
如图2,在图1(隐去
,
的基础上作
的直径
,
如图2,动手连接
,
,
,
.
是
的直径,所以
.
与
相切于点
,所以
,
.
(同弧所对的圆周角相等),
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
.
②
(1)观察发现:
___________,
___________(用含
,
的代数式表示);
(2)请观察式子①和式子②,并利用任务(1)的结论,按照上面的证明思路,完成该定理证明的剩余部分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c97ec04a1aa7ac6fce72d589864940a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942ed7a1f801116d70437254128e17c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95742051f1ab28e701eb18977b9cac3f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/6/b1a259a9-1a05-48e4-9259-1977e6f19620.png?resizew=136)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/6/e5af681c-00bc-49de-b2ce-e7f738fdc6c6.png?resizew=379)
如图1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79516f18a7daf0ad467a48e16d0e65f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79516f18a7daf0ad467a48e16d0e65f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79516f18a7daf0ad467a48e16d0e65f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e47d3270501173ad722523a7b91cea01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e09700a78d26bf865945ceec87bd94.png)
下面是该定理的证明过程(部分)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa96c86a9085aeb7a57ce955200f0c80.png)
延长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42774a918f52ac8aa8b1f5b78a676f17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ed609d8930e0b2135e77c79b8e0b2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f24af3580af6754589e0df654ca6735f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/840f793cf9a73e468427071e9dfecaee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d99c854e874161cd936d4d7848d4385e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66ca70b1bc18e224ba94d873219a359d.png)
如图2,在图1(隐去
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be2e2c0d4ac2bd79f6cea7a9b1a50662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6df1a193f17a78036f3a63c735f79edb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
如图2,动手连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9020059d62af7498039f091de6f005ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679165ed0b961fb0e8643fcdab64937b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1949518fc246fbd8426d08f701ade25d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd66f89184ca925f4575c26053decf2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be72ff5e7abb13db0fc8ccbb492732a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e42ab439ed525d1fd1de20bf921b831.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2516c1f30bcef258b201be137b672fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f053a7a463cc1d4b5b866dda0f71dff6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43f65029da732ae715a88074e3298d18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d6c865065e08cd749ea659ce8163271.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cd66d053fad701617e39569eb47d444.png)
(1)观察发现:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3045155183b60255854bf010b457f115.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16268d71c64f43aeeafac9900bdecfe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
(2)请观察式子①和式子②,并利用任务(1)的结论,按照上面的证明思路,完成该定理证明的剩余部分.
您最近一年使用:0次