名校
1 . 定义:有一组对角是直角的四边形叫做“准矩形”;有两组邻边(不重复)相等的四边形叫做“准菱形”.
知图①,在四边形
中,若
,则四边形
是“准矩形”;
如图②,在四边形
中,若
,则四边形
是“准菱形”.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/17/e356ed7a-71a6-495c-a1ca-9a17df37249c.jpg?resizew=355)
(1)如图,在边长为1的正方形网格中,
在格点(小正方形的顶点)上,请分别在图③、图④中画出“准矩形”
和“准菱形”
(要求:
在格点上);
(2)如图⑤,在
中,
,以
为一边向外作“准菱形”
,且
交于点
.若
,求证:“准菱形”
是菱形;
(3)在(2)的条件和结论下,连接
,若
,请直接写出菱形
的边长为__________.
知图①,在四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/853e81b1b9606ad25244ff82c8292df6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
如图②,在四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbae18d3e3c1ba70503b7f24c6f304a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/17/e356ed7a-71a6-495c-a1ca-9a17df37249c.jpg?resizew=355)
(1)如图,在边长为1的正方形网格中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38335830b93ac4d99c28a8e209eecb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/591827e255a9a80766da16e29beb94c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22f3056f58faf7c804180dcf162c7517.png)
(2)如图⑤,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4b93d7abcfc4c3df48f03aa969c17f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca0258d74358b323e5891e7915b0b625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c791f7bf368c2efb2b49ce9dc37ad76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4b93d7abcfc4c3df48f03aa969c17f.png)
(3)在(2)的条件和结论下,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6d98dbdb2fd684ac1bcd1f16d1301c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4b93d7abcfc4c3df48f03aa969c17f.png)
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|
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2卷引用:山西省太原市杏花岭区山西省实验中学2023-2024学年九年级上学期月考数学试题
名校
2 . 综合与实践
问题情境:如图,点
为正方形
内一点,
,将
绕点
按顺时针方向旋转
,得到
(点
的对应点为点
).延长
交
于点
,连接
.
的形状,并说明理由;
(2)若
,求
的长.
问题情境:如图,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1070d38d2fea1dc88c6eb31d320b763.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1a3b94566843e92ce775ff6bdf386fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c63a1935cbb9cc5c2266cbbdb10da42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84f0ae0d8e74c9ca1708ce83c36c94df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ffd347c352296443a87197ec816fc3e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/901ac05fd87f63acf6a154d4c46052ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
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3卷引用:山西省太原市杏花岭区山西省实验中学2023-2024学年九年级上学期月考数学试题
名校
3 .
中,
,P为边
上一动点,
于E,
于F,M为
中点,则
的最小值为 _________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39132583f313bb73583c1222703ea5a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04fb30a9d07e410ac92c34b8ad0133db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca0940f5c21431c089d4f7a221df43c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0215e13a9fb5574d5194aeb9507a98aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1165830b314a0dab65ea267e82bd3f6.png)
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2023-10-14更新
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24卷引用:山西省朔州市怀仁市2021-2022学年九年级下学期期中数学试题
山西省朔州市怀仁市2021-2022学年九年级下学期期中数学试题北师大版数学上册_九年级_第一章_特殊平行四边形_单元评估测试卷北师大九年级数学上册第一章特殊平行四边形单元检测试卷广东省深圳市宝安区松岗实验学校2021-2022学年九年级上学期期中数学试题山东省青岛实验初级中学2021-2022学年九年级上学期9月月考数学试题广东省佛山市南海区沥中-海北-许海-石英-加美-中大附外学片2021-2022学年九年级上学期联考数学试题陕西省宝鸡市岐山县2021-2022学年九年级上学期期中数学试题(一模)辽宁省丹东市宽甸县第一初级中学教育集团2022-2023学年九年级上学期第一次学业质量检测数学试题黑龙江省佳木斯市第二十中学2022-2023学年九年级上学期开学考试数学试题人教版数学八年级下册第十八章 平行四边形 单元提优训练浙江省诸暨市涅浦镇中心学校2018-2019学年八年级下学期期中考试数学试题四川省南充市陈寿中学2018-2019学年八年级4月月考数学试题(已下线)专题09 特殊四边形中的最值问题-2020-2021学年八年级数学下学期期末专项复习(湘教版)江苏省常州市朝阳中学2020-2021学年八年级下学期第一次月考数学试题黑龙江省佳木斯市桦南县第三中学2021-2022学年八年级下学期期中考试数学试题江西省宜春市丰城第九中学2022-2023学年八年级上学期期末A卷数学试题.江西省宜春市丰城第九中学2022-2023学年八年级上学期期末B卷数学试题(已下线)专题18 矩形中的最值-【微专题】2022-2023学年八年级数学下册常考点微专题提分精练(浙教版)云南省昆明市五华区云南大学附属中学2022-2023学年八年级下学期期末数学试题广东省珠海市香洲区紫荆桃园中学2021-2022学年八年级下学期期中数学试题湖南省永州市京华中学2023-2024学年八年级下学期期中数学试题北京市第一零九中学2023-2024学年八年级下学期期中数学试题(已下线)八年级数学期末模拟卷(云南专用)-学易金卷:2023-2024学年初中下学期期末模拟考试(已下线)专题03 特殊的平行四边形的判定与性质(9大题型+优选提升题)-备战2023-2024学年八年级数学下学期期末真题分类汇编(湖南专用)
4 . 国家跳台滑雪中心位于北京2022年冬奥会张家口赛区古杨树场馆群,是我国首座符合国际标准的冬奥会跳台滑雪场地.外观结构与中国传统吉祥物“如意”的S形曲线完美融合,因此,被形象地称为“雪如意”,在它的身上,体现了现代建筑与自然山水、历史文化的交相辉映,在这里举行的跳台滑雪分大跳台和标准台,大跳台A点出发区海拔1771米,着陆点U点海拔1635米,大跳台与标准台水平相距
米,大跳台坡角
,标准台坡角
.求大跳台与标准台出发点落差
是多少?(参考数据:
,
,
;
,
,
,结果保留整数.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d194ea0173c3e096ffb9146a85743d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f766494b4aa7cab3c371165a9e914239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64fb264d5fed7c2293dc568d3fb6e01e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f27acebe4b2151ece74173c272a2fee9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cb722c9b6f930fa227e62da71c1a77f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/097b2e089c432375c4e5280061809b7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3c2d2db1fa8a6c703c6edecfa038d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb7e8186509333d743c128cec63d9994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59edc04822a09c8aacb12f7641c36376.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/20/9ea7a1ee-d4a7-4f18-a8a5-b6b51a1f4f02.jpg?resizew=409)
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5 . 在学习镜面反射后,小明知道了当入射光线与镜面垂直时,反射光线将与入射光线重合,沿原路返回.他利用此现象设计了一个测量物体高度的工具.
在一次实际测量过程中,小明测得测高工具与建筑物的水平距离
米,请计算建筑物
的高度(结果精确到0.1米,参考数据:
).
项目 | 图例 | 说明 |
测量工具横截面图 |
| 直角三角形![]() ![]() ![]() ![]() ![]() ![]() |
测量示意图 |
| 在建筑物![]() ![]() ![]() |
待测数据 |
|
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3493ba3ba6a1c69ad1ab9f0039129c30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/460317e7c26f95b9b29cfe1a89b796d6.png)
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2023-09-15更新
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2卷引用:2023年山西省朔州市山阴县部分学校中考模拟数学试题
6 . 如图,已知等边
的边长为
,点
是
边上的一个动点(与点A、B不重合),直线
是经过点
的一条直线,把
沿直线l折叠,点B的对应点是点
.
(1)基础图形:如图1,当
时,若点
恰好在
边上,求
的长度;
(2)模型变式:如图2,当
时,若直线
,则
的长度为______;
(3)动态探究:如图3,点
在
边上运动过程中,点
到直线
的距离为
.
如果直线
始终垂直于
,那么
的值是否变化?若变化,求出
的变化范围;若不变化,求出
的值;
当
时,请直接写出在直线
的变化过程中,
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/17/d35c2fec-f987-4cea-b94b-47e3a65bd3ca.png?resizew=626)
(1)基础图形:如图1,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b336e518ac4ff04c6c26e4b8a15844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943712a5e96b16cc15d775cc4687237e.png)
(2)模型变式:如图2,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91ce0586aafd9bf4fb7e1be082624afc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7db6f7222557290dc8d38bfa661608a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655cc150ddc9deba2254780984d0024.png)
(3)动态探究:如图3,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1c9ae241fd78126274c65e17990c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c650fe55b7603f106c53ca2423451c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f71f070c1aa967a945113735322fae18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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7 . 如图,某“综合与实践”小组欲测量当地的一座宝塔AB的高度,他们利用高度为1米的测倾仪在点C处测得该宝塔顶部A的仰角
.由于宝塔底部B不能直接到达,于是他们将测倾仪后退60米到达点D,测得该宝塔顶部A的仰角
.点A,B,测倾仪
和
均在同一平面内,求该宝塔
的高度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0b93f41e2d30d1a48274256074143f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3323f55d5b9f7bae0a1354c3c5905806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/17/468681d8-36a8-4bce-81f9-eae0909a1aac.jpg?resizew=168)
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8 . 眼睛是人类感官中最重要的器官之一,每年的6月6日定为全国爱眼日,小林想要探究自己按照标准护眼姿势读书时书籍应离身体多远,画出如图的侧面示意图,点A为眼睛的位置,A到书籍
的距离
为40cm,
与水平方向夹角
为
,小林在书桌上方的身长
为52cm,且
垂直于水平方向,请你求出小林与书籍底端的水平距离
.(参考数据:
,
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
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2023-09-09更新
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179次组卷
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3卷引用:山西省晋城市多校2023-2024学年九年级上学期期末联考数学试题
9 . 如图,在
中,
,
,点
是
的中点,点
是
上一点,
与
交于点
.若
,则
的长为 ___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08313da7b66283d2e0b3987f3e6761f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a2d478a257a43d9b28b4105b15e0b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/15/8cff574c-8c78-48c4-a9ec-ade2455f1af3.png?resizew=123)
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10 . 随着人工智能技术的飞速发展,越来越多的智能产品进入人们的日常生活,人们足不出户就能通过远程操控处理各种事情,“智享生活、乐在其中”成为新世纪人们生活的最大变革
图
所示的是一款多功能智能语音翻译器,其侧面示意图如图
所示,
,
,底座
的长度为
,顶部
的长度为
请你分别求出该语音翻译器的后背
和前屏
的长度?(结果精确到
;参考数据:
,
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54e1d0f65817ba32a732040518f41440.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3798a74058ec4bc40b6d9b5d268c359b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c30c4bedb1189fe96828f8b2df21641.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb26c5cdef6f16f4b39cd091041b439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d04216651041ddfb04c68c93c6719a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dd58f9f2603b2a02db40ca2bf9d17a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/153df8ab54749477613adeb094dacce0.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68e8edc744d95d5d0f7f5ef505a5607e.png)
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