解题方法
1 . 截面惯性矩
是衡量截面抗弯能力的一个几何参数,若截面图形为矩形,则
,其中
为矩形的宽,
为矩形的高.某木器厂要加工如图所示的长方体实木梁,已知该实木梁的截面图形为矩形
,且矩形
外接圆的直径为
,要使该截面的惯性矩最大,则矩形
对应的高应为______
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910c6cc1a6e5f6f601f9336d5f08c7a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe9f7abf7bcf4e1aa2579cd191d7761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
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2 . 甲、乙、丙、丁四位同学坐在一排
个座位上,由于某种原因,甲旁边要留一个空座位,则共有______ 种坐法.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
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3 . 已知函数
.
①当
时,
,记
前
项积为
,若
恒成立,整数
的最小值是______________ ;
②对所有n都有
成立,则
的最小值是_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/227c3613c9bdafd6f258c53dbf49776b.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bef2639f7d9950f9481a5ddd92334be7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40c16b5df55ae677b721c5401ca1a8f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
②对所有n都有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f791e32e2606e39c024f26c7a02feb08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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4 . 天道酬勤,勤能补拙,努力的人得到的结果也许不尽如人意,虽然问心无愧的他们往往能平静看待生活中的点点滴滴,后悔这个词离他们似乎很遥远,但面对不顺时,他们有时候也会反思一些细节,情不自禁的流下悔恨的泪水.其实每个人在生活中都曾有过后悔的经历,即便是懒惰成性,不思进取的人,遇到挫折时,他们中也会有人会反思过去的不足,即使明知悔之晚矣,也往往会流下悔恨的泪水.某位经验丰富的班主任老师,从高一开始,一直在反复告诫自己的学生:珍惜当下,积极进取,争做高考后无怨无悔的人,不做高考后如祥林嫂般的悔恨者.一晃三年过去了,这位班主任老师结合学生三年的表现,调查发现,自己任教的班级勤懒生人数之比为
,结合自己对以前毕业于自己班的学生高考后的表现发现,勤生高考后流下悔恨的泪水的概率为0.001,而懒生高考后流下悔恨的泪水的概率为0.020.展望本届学生高考,他清楚地知道,自己班上一定有学生会在高考后流下悔恨的泪水,若真如该老师所料,有一位学生流下了悔恨的泪水,则这个学生恰好是一名懒生的概率为________ (结果用既约分数表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69ab63040717ef57816edc448ceedc82.png)
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5 . 已知A,B两个袋子中有除了颜色外完全相同的黑球,白球若干.其中A袋子有2只黑球,1只白球,B袋子中有2只黑球,2只白球.现从A,B两袋中随机选一只球交换,则交换后A袋中黑球个数的数学期望为______ .
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6 . 某高三班主任老师结合学生三年的表现,调查发现班级勤懒生人数之比为
,结合以前的学生高考后的表现,勤生高考后流下悔恨的泪水的概率为0.001,而懒生高考后流下悔恨的泪水的概率为0.491.展望今年高考,他清楚地知道,自己班上一定有学生会在高考后流下悔恨的泪水。若真如该老师所料,有一位学生流下了悔恨的泪水,则这个学生恰好是一名懒生的概率为________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69ab63040717ef57816edc448ceedc82.png)
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7 . 已知
表示数
,其中数列
单调递增,且
为正整数.当
时,记所有满足条件的
的个数为
当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec28b5d6e3263275d38599aed15ccd2.png)
______ ;当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b79bd8fd7c11f7ee3f42c409a632b4e.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27effd133986a687e5928c1eb1d27b9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3a8c295c6019e7b2517a0f6320f4ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef7ca2b3e8061384501f668e59696a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891c0cae5388125948b70ea4ebc4d9a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31cdbb0647b2b452f47a95dcf736bae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec28b5d6e3263275d38599aed15ccd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c8e6b35ef78852d6a39d8eca26847e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b79bd8fd7c11f7ee3f42c409a632b4e.png)
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8 . 在锐角
中,
,它的面积为10,
,
,
分别在
、
上,且满足
,
对任意
,
恒成立,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/345078b37bdf02f53100140507c85bde.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6168bceb8119e8e2290ccc35b6ccc0e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc57614c316ede4c0a0ab3d533e21bd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/721fc29059eafb153d24020dbaefee29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd59a5621e55f43dd7e78aa7cbfaffae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f370a1d4dd341e5ab1774a66c66c1204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/345078b37bdf02f53100140507c85bde.png)
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9 . 我国许多地方都有风格迥异的古塔.现在在某塔底共线三点
处分别测得塔顶P点的仰角为
,
,
,且
,设该塔高为
,示意图如图,则该塔高![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5516a7ad03e49c26d9a6303365664fb.png)
________ m.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de303eb9ff8ccfc0b6ebdf8380456fd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5516a7ad03e49c26d9a6303365664fb.png)
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10 . 设
.若曲线
上一点
不满足
,则曲线
在点
处的切线方程为
.则曲线
过点
的切线方程为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/896021fc6c5bd4fc7fb58cc894ff81a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bbbf52d1f9d61b41bdd4acfc9fac268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b4f86e48e2b0d63c1865c60ed1e4d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/928bbbe3bdcda7bd6af53da4b1ee340d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bbbf52d1f9d61b41bdd4acfc9fac268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b4f86e48e2b0d63c1865c60ed1e4d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d6a72ab261df207cbbc3b58db5c4312.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ede062e00b14e9e1604c8174c59942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa482d7bcaa385bfc3548b42a4bfb60.png)
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