名校
1 . 对于求解方程
的正整数解
(
,
,
)的问题,循环构造是一种常用且有效地构造方法.例如已知
是方程
的一组正整数解,则
,将
代入等式右边,得
,变形得:
,于是构造出方程
的另一组解
,重复上述过程,可以得到其他正整数解.进一步地,若取初始解时满足
最小,则依次重复上述过程 可以得到方程
的所有正整数解 .已知双曲线
(
,
)的离心率为
,实轴长为2.
(1)求双曲线
的标准方程;
(2)方程
的所有正整数解为
,且数列
单调递增.
①求证:
始终是4的整数倍;
②将
看作点,试问
的面积是否为定值?若是,请求出该定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09e7065aa112872161285c5f3bfc022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3460cd2f27a53941986606734a9b479a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a79b9eaa5e7ab7a1e5c512b571914dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ca4e60aab76ce3be3b5ffb9137f163.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ef282595213e6ac1c04b09c8703e176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e62b8fca47d65828c45fc8e38fe8beb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c804f8356fa6120aa13b2d11bfea10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73f33dbb2fc073ae2d62891732e52dc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e31df193bb9a9b93b02f2daa2fb747c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1e81a0995ee5492c4281539c65bf00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18483c9c195ecd922772527fa85c0fcb.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adb4c637bd4364a8d3b8d13889befd4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba78250f4e67347c7e80c543078d02e6.png)
②将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adb4c637bd4364a8d3b8d13889befd4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b66d595bfea3722fbc56e2fdccd548.png)
您最近一年使用:0次
名校
解题方法
2 . 2023年10月11日,中国科学技术大学潘建伟团队成功构建255个光子的量子计算机原型机“九章三号”,求解高斯玻色取样数学问题比目前全球是快的超级计算机快一亿亿倍.相较传统计算机的经典比特只能处于0态或1态,量子计算机的量子比特(qubit)可同时处于0与1的叠加态,故每个量子比特处于0态或1态是基于概率进行计算的.现假设某台量子计算机以每个粒子的自旋状态作为是子比特,且自旋状态只有上旋与下旋两种状态,其中下旋表示“0”,上旋表示“1”,粒子间的自旋状态相互独立.现将两个初始状态均为叠加态的粒子输入第一道逻辑门后,粒子自旋状态等可能的变为上旋或下旋,再输入第二道逻辑门后,粒子的自旋状态有
的概率发生改变,记通过第二道逻辑门后的两个粒子中上旋粒子的个数为
.
(1)若通过第二道逻辑门后的两个粒子中上旋粒子的个数为2,且
,求两个粒子通过第一道逻辑门后上旋粒子个数为2的概率;
(2)若一条信息有
种可能的情况且各种情况互斥,记这些情况发生的概率分别为
,
,…,
,则称
(其中
)为这条信息的信息熵.试求两个粒子通过第二道逻辑门后上旋粒子个数为
的信息熵
;
(3)将一个下旋粒子输入第二道逻辑门,当粒子输出后变为上旋粒子时则停止输入,否则重复输入第二道逻辑门直至其变为上旋粒子,设停止输入时该粒子通过第二道逻辑门的次数为
(
,2,3,⋯,
,⋯).证明:当
无限增大时,
的数学期望趋近于一个常数.
参考公式:
时,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(1)若通过第二道逻辑门后的两个粒子中上旋粒子的个数为2,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a18d2bd429301b5478dcd26c572266.png)
(2)若一条信息有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef66ba6d5421383f47b4783db53bf7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8be646cd52d7f2f1714e7542e75810f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adad9633b73dfbbb3d84b4f15979e99e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ffb021aa7d5a5c2f0691e337caad624.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b930a98ed7eb5ae313050f7c97d2a16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33c5a2ba6cfa94756ac1a0f74ac9e4f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
(3)将一个下旋粒子输入第二道逻辑门,当粒子输出后变为上旋粒子时则停止输入,否则重复输入第二道逻辑门直至其变为上旋粒子,设停止输入时该粒子通过第二道逻辑门的次数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f157de581046dc6a6002f771b60ad61c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ca664b1e82da6f50064a76fe118aa80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d71b352414c4a600fc4ea827a0c64f22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c0aceee7cba466e6bf17f43d15bf25f.png)
您最近一年使用:0次
2024-03-04更新
|
1793次组卷
|
4卷引用:第2套 重组模拟卷(模块二 2月开学)
(已下线)第2套 重组模拟卷(模块二 2月开学)(已下线)专题09 计数原理与随机变量及分布列(讲义)湖南省新高考十八校联盟2024届高三下学期3月月考数学试题湖北省襄阳市第五中学2024届高三第二次适应性测试数学试题
名校
3 . 抛物线
与椭圆
有相同的焦点,
分别是椭圆的上、下焦点,P是椭圆上的任一点,I是
的内心,
交y轴于M,且
,点
是抛物线上在第一象限的点,且在该点处的切线与x轴的交点为
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16231e127f8a00b343c1986f65f0ab56.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8516f71467b419293fa27df70bdaed74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/332f0dc7afc21adbab48acae2eaf875b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede935419d69a161bb22fd513647da06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3900190c901795456d20b1939916dafd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcc675d3c35af2425ec134743250ceae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c153922d3e1fec7dcb99c1713459547.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57aa9c9b0ab417c0b952809669f6161b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16231e127f8a00b343c1986f65f0ab56.png)
您最近一年使用:0次
2024-02-27更新
|
906次组卷
|
5卷引用:重庆市开州中学2024届高三下学期高考模拟考试(二)数学试题
4 . 一般地,
元有序实数对
称为
维向量.对于两个
维向量
,定义:两点间距离
,利用
维向量的运算可以解决许多统计学问题.其中,依据“距离”分类是一种常用的分类方法:计算向量与每个标准点的距离
,与哪个标准点的距离
最近就归为哪类.某公司对应聘员工的不同方面能力进行测试,得到业务能力分值
、管理能力分值
、计算机能力分值
、沟通能力分值
(分值
代表要求度,1分最低,5分最高)并形成测试报告.不同岗位的具体要求见下表:
对应聘者的能力报告进行四维距离计算,可得到其最适合的岗位.设四种能力分值分别对应四维向量
的四个坐标.
(1)将这四个岗位合计分值从小到大排列得到一组数据,直接写出这组数据的第三四分位数;
(2)小刚与小明到该公司应聘,已知:只有四个岗位的拟合距离的平方
均小于20的应聘者才能被招录.
(i)小刚测试报告上的四种能力分值为
,将这组数据看成四维向量中的一个点,将四种职业
的分值要求看成样本点,分析小刚最适合哪个岗位;
(ii)小明已经被该公司招录,其测试报告经公司计算得到四种职业
的推荐率
分别为
,试求小明的各项能力分值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086eb439f6a1578fdba904825340772d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/728f740c8ad3983bf2e51b1a7dc42c36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a556a8011e12f1dcd7cd458a4b35ece9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e260b088f071983f254ce8f5163fcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e260b088f071983f254ce8f5163fcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b216d768026fa703c4a84ae2a8df0449.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a872e033a5bee216ecf0b656fe122742.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83a60c26f1979ea77bdb59cd85342bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa556d0a8348ebac5888d9381a74cad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b1dbff69a597a3f9aa8783a4c174153.png)
岗位 | 业务能力分值 | 管理能力分值 | 计算机能力分值 | 沟通能力分值 | 合计分值 |
会计(1) | 2 | 1 | 5 | 4 | 12 |
业务员(2) | 5 | 2 | 3 | 5 | 15 |
后勤(3) | 2 | 3 | 5 | 3 | 13 |
管理员(4) | 4 | 5 | 4 | 4 | 17 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629da762b7571611670f5b6f22cf2f7c.png)
(1)将这四个岗位合计分值从小到大排列得到一组数据,直接写出这组数据的第三四分位数;
(2)小刚与小明到该公司应聘,已知:只有四个岗位的拟合距离的平方
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eab58b13ac4379f8aef381f54eeaacca.png)
(i)小刚测试报告上的四种能力分值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5915cbb31d1cd4dc188b97e4354cf04f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17e60233c2784b997e48546af6dbac3e.png)
(ii)小明已经被该公司招录,其测试报告经公司计算得到四种职业
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17e60233c2784b997e48546af6dbac3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c809f18069c13e373486308339e4f9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b51cc86cca36bac13e309cfea252fc00.png)
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2024-02-23更新
|
1217次组卷
|
4卷引用:第1套 重组模拟卷(模块二 2月开学)
(已下线)第1套 重组模拟卷(模块二 2月开学)单元测试B卷——第九章?统计浙江省L16联盟2023-2024学年高三下学期返校适应性测试数学试题福建省泉州市第七中学2023-2024学年高一下学期期中考试数学试题
解题方法
5 . 数列
满足
且
,
,
,
构成等差数列.
(1)试求出所有三元实数组(α,β,γ),使得
为等比数列.
(2)若
,求
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f390f47fa5678c9a165c50fb9dec58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be536a2097ded867adac5edebb79906b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75e6820c50fa2aa589de5331d7d5f950.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13739ca823d61005798cc3298400c6b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad28237c0f9ca65341101d9d7e73e73e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee766a75ae9ee290e403b42b3569db6.png)
(1)试求出所有三元实数组(α,β,γ),使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee766a75ae9ee290e403b42b3569db6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4623bc660145c6ff98af7b1753d5357a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee766a75ae9ee290e403b42b3569db6.png)
您最近一年使用:0次
名校
解题方法
6 . 已知
为有穷正整数数列,且
,集合
.若存在
,使得
,则称
为
可表数,称集合
为
可表集.
(1)若
,判定31,1024是否为
可表数,并说明理由;
(2)若
,证明:
;
(3)设
,若
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67905ad53186bb2908b603bc14005d10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/702dcfe2523f774f6bc4f075f3d24fe6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80566aaf96db9c785cda10dc0935c1c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84076d0854ef7c1a99a937fd50b25843.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c6985405452b5d04bd0d3305544cc2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c93e3391890fc877c761121b68cb927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54119668d2f6cbc9ce0cb92310037713.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c93e3391890fc877c761121b68cb927.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b83efe191fb8adaf89737c03ef34d1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c93e3391890fc877c761121b68cb927.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2ebfe653088b1a534d0731947db43d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/562441c2767a65f3671afa93b190126b.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffceb52b543819898a9a6fc96d7337e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7eab142f716f69be57d3f4ca2197894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2024-01-20更新
|
1474次组卷
|
7卷引用:北京市昌平区2024届高三上学期期末质量抽测数学试题
7 . 求有___________ 组
、
、
、
(
、
、
、
均为正整数),满足等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab797c5e8378285cff446f8bca5e9012.png)
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23-24高二上·全国·课后作业
8 . 设圆O的弦
的中点为M,过点M任作两弦
,弦
与
分别交
于点E,F.
的中点;
(2)如果将圆分别变为椭圆、双曲线或抛物线,你能得到类似的结论吗?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(2)如果将圆分别变为椭圆、双曲线或抛物线,你能得到类似的结论吗?
您最近一年使用:0次
名校
解题方法
9 . 如图,四边形
与
均为菱形,
,
,
,记平面
与平面
的交线为
.
;
(2)证明:平面
平面
;
(3)记平面
与平面
夹角为
,若正实数
,
满足
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f84f169e50dc59d4f7a8e1e36f5c847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf80b036459da6dcb841a4bbe3859fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d223346f234798b92bd1eaa78360b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef7ce5d5cc777ef4d5b890cc9cbb70b0.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1b6711e6dd48be6cf8fa52926924d21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(3)记平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b7195a853621ea5bebe8d2d1436732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b992104248a854e6e033c26602aff813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c7bfbdbf0f1957459f12ae149d5176e.png)
您最近一年使用:0次
2023-07-11更新
|
1977次组卷
|
5卷引用:四川省成都外国语学校2023-2024学年高二上学期10月月考数学试题
名校
解题方法
10 . 我们把和两条异面直线都垂直相交的直线叫做两条异面直线的公垂线.如图,在菱形
中,
,将
沿
翻折,使点A到点P处.E,F,G分别为
,
,
的中点,且
是
与
的公垂线.
(1)证明:三棱锥
为正四面体;
(2)若点M,N分别在
,
上,且
为
与
的公垂线.
①求
的值;
②记四面体
的内切球半径为r,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/7/36d7309a-d789-4b0d-bbdc-a09e1456bdf9.png?resizew=341)
(1)证明:三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08a9ec3b527947cad9caa4537e0cb7e7.png)
(2)若点M,N分别在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51583e34d76abf46a39b56014a536208.png)
②记四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/922b1e3f3948b044ff8f53af2aa1f038.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acf3747141ec164fcf0dff92439fd1.png)
您最近一年使用:0次
2023-07-04更新
|
2110次组卷
|
9卷引用:重庆市南开中学校2022-2023学年高一下学期期末数学试题
重庆市南开中学校2022-2023学年高一下学期期末数学试题四川省成都市2023-2024学年高二上学期九月调研考试(校级联考)数学试题四川省成都市树德中学2023-2024学年高二上学期10月阶段性测试数学试题(已下线)专题01 空间向量及其运算压轴题(5类题型+过关检测)-【常考压轴题】2023-2024学年高二数学上学期压轴题攻略(人教A版2019选择性必修第一册)(已下线)第一章 空间向量与立体几何(压轴题专练,精选20题)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第一册)(已下线)第3章 空间向量及其应用(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)(已下线)第3章 空间向量及其应用 单元综合检测(难点)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)(已下线)第三章 折叠、旋转与展开 专题一 平面图形的翻折、旋转 微点4 翻折、旋转问题中的最值(一)(已下线)第四章 立体几何解题通法 专题二 体积法 微点2 体积法(二)【基础版】