![](https://img.xkw.com/dksih/QBM/2014/12/17/1573772356730880/1573772362997760/STEM/c4ce07bd-478f-44d5-b644-90cdbdc74814.png?resizew=173)
相似题推荐
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f8f01137e92c0f2e63467036ae9cce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932c1e7b8e4167bda4c7b2b9123fac0c.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/595631ff0eed928133d584b57c66e015.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d1293596a28b5b0eaeaad7e72ae714.png)
![](https://img.xkw.com/dksih/QBM/2020/11/19/2596296435728384/2598616531279872/STEM/07c19166ef104c3eb670c022afb5562b.png?resizew=196)
【推荐2】如图,为
的直径,以
为边作等边三角形
与
交于点D,E,过点E作
于点F,下面是两位同学的对话:
|
|
(1)请你选择一位同学的说法,并进行证明.
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a9fd76d8997e3b2db7d9cb9b72d0f80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3e9ef3e849788645552cfb0735d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fffa3d9c32da53b0ea0c338012ea20c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/13/c6c67c75-4591-457f-a908-1109e0b924e4.png?resizew=186)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
(2)求图中阴影部分的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4ab7e657f01bdfa235f8c4d6681d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b9d0c688e55286443c9974797fc647f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://img.xkw.com/dksih/QBM/2021/1/10/2633057351671808/2634004426907648/STEM/ce83f1c5-22e9-4f4a-8599-c0099ee81464.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23dc2d2dd56fcc67698c45a6e0e48f80.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4d3d4307b9f64d8c99f864941f37874.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df049f15adb6667113ceee3a6638cd0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd0763b031b7e6b6d87ce3554ac482d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/ec977099-166b-424f-935d-570689ddb2eb.png?resizew=194)
(1)求证:PB是⊙O的切线.
(2)若PB=3,tan∠PDB=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://img.xkw.com/dksih/QBM/2021/4/16/2701197573750784/2704623992619008/STEM/e1545a04-1d3f-4812-8c4b-e1896499ba51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9874ccd4e42a0c5323d929bb47482870.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febc9a89d0d1c97b88c0f4acd32b4e67.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3839ab58dabbf4c12ee69770bdbf8dac.png)
【推荐2】【发现问题】
“速叠杯”是深受学生喜爱的一项运动,杯子的叠放方式如图1所示:每层都是杯口朝下排成一行,自下向上逐层递减一个杯子,直至顶层只有一个杯子.爱思考的小丽发现叠放所需杯子的总数随着第一层(最底层)杯子的个数变化而变化.
【提出问题】
叠放所需杯子的总数y与第一层杯子的个数x之间有怎样的函数关系?
【分析问题】
小丽结合实际操作和计算得到下表所示的数据:
第一层杯子的个数 | ||||||
杯子的总数 |
然后在平面直角坐标系中,描出上面表格中各对数值所对应的点,得到图2,小丽根据图2中点的分布情况,猜想其图象是二次函数图象的一部分;为了验证自己的猜想,小丽从“形”的角度出发,将要计算总数的杯子用黑色圆表示(如图3),再借助“补”的思想,补充相同数量的白色圆,使每层圆的数量相同,进而求出与
的关系式.
【解决问题】
(1)直接写出与
的关系式;
(2)现有个杯子,按【发现问题】中的方式叠放,求第一层杯子的个数;
(3)杯子的侧面展开图如图4所示,,
分别为上、下底面圆的半径,
所对的圆心角
,
.将这样足够数量的杯子按【发现问题】中的方式叠放,但受桌面长度限制,第一层摆放杯子的总长度不超过
,求杯子叠放达到的最大高度和此时杯子的总数.(提示:杯子下底面圆周长与AB的长度相等)