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1 . 明朝科学家徐光启在《农政全书》中用图画描绘了筒车的工作原理(如图).假定在水流量稳定的情况下,筒车上的每一个盛水筒都做逆时针匀速圆周运动,筒车转轮的中心O到水面的距离h为1.5m,筒车的半径r为2.5m,筒转动的角速度
为
,如图所示,盛水桶M(视为质点)的初始位置
距水面的距离为3m,则3s后盛水桶M到水面的距离近似为( )(
,
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ea20ecbd481884949b6378230040c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a929d0d84e3654f03694adc8d1a326e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8a7ff6bb8000946da9599d7d903ac9a.png)
A.4.5m | B.4.0m | C.3.5m | D.3.0m |
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2024-06-14更新
|
445次组卷
|
2卷引用:重庆市沙坪坝区部分学校2023-2024学年高一下学期4月阶段检测数学试题
解题方法
2 . 已知
,
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17413ca9b1286ed354edc6c20ba09a2b.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787379f7ff8d24be7eebfea1cfe956d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ff265969988f1f138700129e5d7a6d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/030a7a7d9b57f46855b70778578eff3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17413ca9b1286ed354edc6c20ba09a2b.png)
您最近一年使用:0次
解题方法
3 . 已知正数
满足
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9defa23d2a9b88f4dd10e0ea4bef2189.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/131ac7eb1e911c9a40e84235bf3742ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/273b63fc788388fab8b4f685fdb83230.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 命题“
,
”的否定是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8ef1b97418352325952246b43f84d38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41449d0bfb64876573d9732cc9abd7d.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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解题方法
5 . 如图,在三棱锥中,
,
,
,二面角
的大小为
,则三棱锥
的外接球表面积为
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解题方法
6 . 正弦波是频率成分非常单一的信号,其波形是数学上的正弦曲线,任何复杂信号,如光谱信号,声音信号等,都可由多个不同的正弦波复合而成,现已知某复合信号由三个振幅、频率相同的正弦波
,
,
叠加而成,即
,设
,
,
,
,若图中所示为
的部分图象,则下列描述正确的是( )
A.![]() |
B.![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() |
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解题方法
7 . 已知函数,若对任意
都有
,则实数a的取值范围是( )
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
8 . 已知函数,
.
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fd7af568e3d9f444beb0ff41426477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23d71715e6c2b6ccefb4161d9e3641d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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9 . 设集合、
为正整数集
的两个子集,
、
至少各有两个元素.对于给定的集合
,若存在满足如下条件的集合
:
①对于任意,若
,都有
;②对于任意
,若
,则
.则称集合
为集合
的“
集”.
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a4c458e37238547c09a481eb0ca295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
(2)若三元集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275bd8ce17fcc4a786510b008414ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275bd8ce17fcc4a786510b008414ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21edab576db2b4f56237ad687957a913.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380cc5e32580ddf29206ebb596336151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea5867fde790c54e6a931c5d1d22b049.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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10 . 在平面直角坐标系中,已知
,动点
到
轴的距离为
,且
.
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63caa7e958f171d9dbc9424fc4ea4339.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6619883500131ca27c672a58bc213672.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b556b1a9944719cf423e90f8df16c773.png)
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