2023·全国·模拟预测
解题方法
1 . 在
中,内角A,B,C所对的边分别为a,b,c,且满足
.若
的内切圆面积为
,则
的面积最小值为__________ ,此时周长为__________ .
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2 . 已知
的内角
的对边分别为
,若
,
,
为
的中点,
为
的中点,
,则
的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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名校
3 . 一家商店使用一架两臂不等长的天平称黄金.一位顾客到店里购买10g黄金,售货员先将5g的砝码放在天平左盘中,取出一些黄金放在天平右盘中使天平平衡;再将5g的砝码放在天平右盘中,再取出一些黄金放在天平左盘中使天平平衡;最后将两次称得的黄金交给顾客.你认为顾客购得的黄金________ 10g.(填“大于”“小于”“等于”“不确定”)
附:依据力矩平衡原理,天平平衡时有
,其中
,
分别为左右盘中物体质量,
,
分别为左右横梁臂长.
附:依据力矩平衡原理,天平平衡时有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/182777973733f762bed550fdf648cb4f.png)
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解题方法
4 . 已知正实数
,
满足
,那么
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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5 . 将基本不等式
推广可得正确结论
,当且仅当
时,等号成立.利用此结论解决问题:已知一个矩形的周长为
,将矩形围绕其一边旋转形成一个圆柱,当矩形的长是________
时,旋转形成的圆柱体积最大,其最大值是________
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4baf6044ad9ec71f9715451151b9f3.png)
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6 . 已知定义在
的不恒为0的函数
,对于任意正实数
满足
,且
时
,若正实数a,b满足
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
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解题方法
7 . 某经销商计划购进一批产品,并租借库房用来储存.经过调研,每月的房租费用
(单位:万元)与储存库到门店的距离
(单位:
)成反比,每月从储存库运送到门店费用
(单位:万元)与
成正比.若储存库租在距离门店
处,则
和
分别为1万元和4万元.为降低成本,经销商应该把储存库租在距离门店______ 千米处,才能使两项费用之和最小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
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2023-11-19更新
|
49次组卷
|
2卷引用:海南省琼中黎族苗族自治县琼中中学2023-2024学年高一上学期阶段性教学检测(一)数学试题
8 . 若直角三角形两条直角边的和为10,则其斜边的最小值是___________ .
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9 . 中国宋代的数学家秦九韶曾提出“三斜求积术”,即假设在平面内有一个三角形,边长分别为
,
,
,三角形的面积
可由公式
求得,其中
为三角形周长的一半,这个公式也被称为海伦-秦九韶公式,现有一个三角形的边长满足
,则此三角形面积的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
10 . 已知实数
满足
,则
的最大值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1358c3e799d533c9b36a3b9728b26853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cf99adccc80f28343fedd8d0aad7429.png)
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