名校
1 . 杭州,作为2023年亚洲运动会的举办城市,以其先进的科技和创新能力再次吸引了全球的目光.其中首次采用“机器狗”在田径赛场上运送铁饼等,迅速成为了全场的焦点.已知购买
台“机器狗”的总成本为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ca9e0ec002a3d42ac87f66f7e498c2.png)
.
(1)若使每台“机器狗”的平均成本最低,问应买多少台?
(2)现安排标明“汪1”、“汪2”、“汪3”的3台“机器狗”在同一场次运送铁饼,且运送的距离都是120米. 3台“机器狗”所用时间(单位:秒)分别为
,
,
. “汪1”有一半的时间以速度(单位:米/秒)
奔跑,另一半的时间以速度
奔跑;“汪2”全程以速度
奔跑;“汪3”有一半的路程以速度
奔跑,另一半的路程以速度
奔跑,其中
,
,且
则哪台机器狗用的时间最少? 请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ca9e0ec002a3d42ac87f66f7e498c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89f36551fee6d6dffb8dfe01c7c052eb.png)
(1)若使每台“机器狗”的平均成本最低,问应买多少台?
(2)现安排标明“汪1”、“汪2”、“汪3”的3台“机器狗”在同一场次运送铁饼,且运送的距离都是120米. 3台“机器狗”所用时间(单位:秒)分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275bd8ce17fcc4a786510b008414ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/155c5f3a5c55e0c95191c5a893f63062.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e4109d38a447a8925a10cf442752f68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1dcd75e97ee60339d6c4831796d5e15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c21242ae7ab734ea9678948abb188dc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/763fdfc9a96cf11bc805e236f9c4860e.png)
您最近一年使用:0次
2023-12-27更新
|
226次组卷
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3卷引用:湖北省重点高中智学联盟2023-2024学年高一上学期12月联考数学试题
湖北省重点高中智学联盟2023-2024学年高一上学期12月联考数学试题山东省德州市万隆中英文高级中学2023-2024学年高二下学期6月月考数学试题(已下线)福建省部分学校教学联盟2023-2024学年高一下学期开学质量监测数学试题
2 . 已知数列
,
满足
,
,
,
.
(1)求证:
;
(2)求证:
;
(3)设数列
的前n项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fc336b4a83bf6d66c4afcc431597f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad6d8a8a57db1c2fc7f465d2cfd2aa78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b71406c902e2bfb15f5b84ea419611e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5530b78617f9a9976adc605a71fe0d48.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25528980b648e76c63bedf345e95a713.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e970038ed20d95a45c228ee5572861.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362832fa3d3c13c1eafd565349d66dce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e637fe1df3fffd9330e03f91626dbce.png)
您最近一年使用:0次
名校
解题方法
3 . 如图所示为一个半圆柱,
为半圆弧
上一点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/a4bf1bc1-bee0-46d6-83c9-71497aa77f09.png?resizew=124)
(1)若
,求四棱锥
的体积的最大值;
(2)有三个条件:①
;②直线
与
所成角的正弦值为
;③
.请你从中选择两个作为条件,求直线
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2395720e6d6aeb7efdcd8e921849acf4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/a4bf1bc1-bee0-46d6-83c9-71497aa77f09.png?resizew=124)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a65b94de267eb6858634181642c65c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
(2)有三个条件:①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b0f78a8003789a66fa4cb38a84858c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411f35f7181f79573bbfab44ea77ff1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62871bb0dff211fc3bd80f9066c25b29.png)
您最近一年使用:0次
2021-01-02更新
|
1635次组卷
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5卷引用:T8联考八校2020-2021学年高三上学期第一次联考数学试题
T8联考八校2020-2021学年高三上学期第一次联考数学试题山东省济宁市育才中学2022-2023学年高二上学期第一次学情检测数学试题江苏省南京市秦淮中学2021届高三下学期期初学情调研数学试题(已下线)专练11 空间向量与立体几何综合检测(A卷)-2021-2022学年高二数学上册同步课后专练(人版A版选择性必修第一册)2023版 湘教版(2019) 选修第二册 过关斩将 第2章 空间向量与立体几何
4 . 已知
.
(1)求证:
;
(2)若
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077a31bd2b8e26c35bfd855e42b5d7a9.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1862e609668e42e0cd6f753c178eeea9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d499e8ca8a0c2c810507e34456181577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58ca64e2ff48c3562312ebc331a4790d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d93c567736dc0f56e0da4101e298352.png)
您最近一年使用:0次
2019-09-20更新
|
785次组卷
|
6卷引用:江西省上饶市“山江湖”协作体2019-2020学年高二上学期第一次联考数学(文)试题