某工厂C发生爆炸出现毒气泄漏,已知毒气以圆形向外扩散,且半径以每分钟
的速度增大. 一所学校A,位于工厂C南偏西
,且与工厂相距
.消防站B位于学校A的正东方向,且位于工厂C南偏东
,立即以每分钟
的速度沿直线
赶往工厂C救援,同时学校组织学生P从A处沿着南偏东
的道路,以每分钟
的速度进行安全疏散(与爆炸的时间差忽略不计).要想在消防员赶往工厂的时间内(包括消防员到达工厂的时刻),保证学生的安全,学生撤离的速度应满足什么要求?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1890f0b4e81634bb7e013412698640f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0017113f394bc42d821adeb220857cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7337fa5b5771eb878925b70e68d51827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a4c9b697e3df2b5469b71d3b5e47a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83adce2b89e0f610ac9fdff945eda7ec.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/29/74eda439-0548-47c0-ad21-656dd1f93608.png?resizew=176)
更新时间:2020-04-17 19:33:41
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【推荐1】为了美化环境,某公园欲将一块空地规划建成休闲草坪,休闲草坪的形状为如图所示的四边形
,已知
,
,
是以
为直角顶点的直角三角形.拟修建两条小路
、
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米.
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(1)若
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(2)设
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的内切圆还是
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45233580092f1d2e3c166ec26a6424a.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/6f0b3df3-fbb4-4048-8134-095823e3bdcc.png?resizew=139)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db3565e9c55354622c65421ee4393a79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c44ce799d9835933017b9cac05ed6077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8419015c50f805216e1c95c2911f7d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
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【推荐2】为进行科学实验,观测小球A、B在两条相交成60°角的直线型轨道上运动的情况,如图所示,运动开始前,A和B分别距O点3m和1m,后来它们同时以每分钟4m的速度各沿轨道l1、l2按箭头的方向运动.问:
(1)运动开始前,A、B的距离是多少米?(结果保留三位有效数字).
(2)几分钟后,两个小球的距离最小?
![](https://img.xkw.com/dksih/QBM/2011/10/14/1570316457115648/1570316462505984/STEM/0a017b68ff524d49ab7281033eeb1abc.png?resizew=175)
(1)运动开始前,A、B的距离是多少米?(结果保留三位有效数字).
(2)几分钟后,两个小球的距离最小?
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解题方法
【推荐1】已知函数
是定义在
上的奇函数,当
时,
,且
的图象与函数
(
且
)的图象相交于定点
.
(1)求函数
的解析式,并写出
的单调递减区间(不用证明);
(2)若对
,不等式
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeafb473e48cf58533d681a51f345604.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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(1)求函数
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30e736012e694acdb6785783eed63d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9053377a15517eac574306d4a8cd44c.png)
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解题方法
【推荐2】已知关于的x不等式
.
(1)若
,解这个关于
的不等式;
(2)
恒成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64e5aca417107465d488c35e5c1dbbc2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5f421939ee855f25927e7570d82c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/947c9286632a2f501c6703f1b7c9b511.png)
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【推荐3】已知
.
(1)若对任意
,
恒成立,求实数
的最小值;
(2)若
,且
,
为任意角,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80027540415bd2b98c9be19e21b5f8d8.png)
(1)若对任意
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
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