1 . 疫情无情,人间有情.为了有效解决疫情发生以来市民群众因管控带来的出门买菜难等生活不便问题,某市在全市范围内组织开展“送菜上门、便民利民”工作.如图,运送物资的车辆已装车完毕,运送人员小赵计划从
处出发,前往
,
,
,
4个小区运送生活物资,已知
,
,
,
与
的交点为
,且
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/28/b9f20d54-4973-47b2-b4a9-5fda0f5e73f3.png?resizew=170)
(1)分别求
,
的长度.
(2)假设
,
,
,
,
,
,
,
均为平坦的直线型马路,小赵开着货车在马路上以
的速度匀速行驶,每到1个小区,需要10分钟的卸货时间,直到第4个小区卸完货,小赵完成运送生活物资的任务.若忽略货车在马路上损耗的其他时间(例如:等红绿灯,货车的启动和停止……),求小赵完成运送生活物资任务的最短时间(单位:min).
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52e46d6aebfd3439eaa959b09a611da8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6049355da8406aac9ba285838e3d7a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94237bbb1e77e6beb12fd8e82c235e79.png)
![](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/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/28/b9f20d54-4973-47b2-b4a9-5fda0f5e73f3.png?resizew=170)
(1)分别求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)假设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2d980c1eb675aa10eb9368e83961aaa.png)
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2022-06-27更新
|
772次组卷
|
9卷引用:天津市第四中学2022-2023学年高二上学期入学摸底考试数学试题
天津市第四中学2022-2023学年高二上学期入学摸底考试数学试题湖北省十堰市2021--2022学年高一下学期期末数学试题河北省承德高中2021~2022学年高一下学期六月联考数学试题江西省上饶市四校2021-2022学年高一下学期第四次联考数学试题 吉林省白山市2021-2022学年高一下学期期末数学试题(已下线)6.4.3第3课时余弦定理、正弦定理应用举例(精练)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)第六章 平面向量及其应用(单元测试)-2022-2023学年高一数学同步精品课堂(人教A版2019必修第二册)(已下线)模块四 专题3 期末重组综合练(湖北)江苏省南京航空航天大学附属高级中学2022-2023学年高一下学期6月月考数学试题
名校
解题方法
2 . 如图,某公园拟划出形如平行四边形
的区域进行绿化,在此绿化区域中,分别以
和
为圆心角的两个扇形区域种植花卉,且这两个扇形的圆弧均与
相切.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/24/81b7720d-9243-42e8-88b5-20e7d7732db9.png?resizew=240)
(1)若
,
,
(长度单位:米),求种植花卉区域的面积;
(2)若扇形的半径为10米,圆心角为
,则
多大时,平行四边形绿地
占地面积最小?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3702b5620dbee356a8e560c78d223ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4189a0821a0ffab9dc171ecd279ba442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/24/81b7720d-9243-42e8-88b5-20e7d7732db9.png?resizew=240)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64756816485784ee017b03ec7574f75b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6848ef9be4dd05447bdecbc3f5eebd7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b50b8c699f9dac858f5f5df565313db4.png)
(2)若扇形的半径为10米,圆心角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1cde7aace5b888a1a1c26fb911e2f49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60b47abcacc10f90489c0d52a9e269ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2022-06-23更新
|
1444次组卷
|
8卷引用:湖南省长沙市长郡中学2022-2023学年高二上学期第一次月考数学试题
湖南省长沙市长郡中学2022-2023学年高二上学期第一次月考数学试题江西省赣州市赣县第三中学2022-2023学年高二上学期开学考试数学试题上海市虹口区2022届高三二模数学试题(已下线)专题13 解三角形-备战2023年高考数学母题题源解密(全国通用)(已下线)第06讲 任意角三角函数、诱导公式及恒等式-2(已下线)专题04三角函数必考题型分类训练-2上海市位育中学2023届高三下学期开学考试数学试题(已下线)模块四 专题3 三角函数与解三角形
名校
解题方法
3 . 已知函数
.
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3a948a5eaf678b7107b938be3a56d8e.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7f9b35017daa8b524c5717a355834a.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3a948a5eaf678b7107b938be3a56d8e.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cdea634b07c580a1497e518c3c7ef84.png)
您最近一年使用:0次
4 . 如图,在
中,
分别是
的中点.从条件①
;②
中选择一个作为已知条件,完成以下问题:
![](https://img.xkw.com/dksih/QBM/2022/5/19/2983014030344192/2984836545576960/STEM/db9265e4f85c430a9a51e7a05f27492f.png?resizew=220)
(1)求
的余弦值;
(2)若
相交于点
,求
的余弦值.
(注:若两个条件都选择作答,则按第一个条件作答内容给分)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efe0fa00b1e1523a0f1cec2ca5eafc91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cca04b2a2b61d62a809776670a60c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d8332bf70ea360b452b85e20a7d081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f25a13423cebb3b19c9b9bbd21a7286.png)
![](https://img.xkw.com/dksih/QBM/2022/5/19/2983014030344192/2984836545576960/STEM/db9265e4f85c430a9a51e7a05f27492f.png?resizew=220)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/268544817735d20ffbceef3b26db5dde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7d6902c8862bd2616be038549f77aff.png)
(注:若两个条件都选择作答,则按第一个条件作答内容给分)
您最近一年使用:0次
2022-05-22更新
|
1112次组卷
|
4卷引用:云南省昆明市第二十四中学2021~2022学年高二下学期期末统考数学模拟试题
云南省昆明市第二十四中学2021~2022学年高二下学期期末统考数学模拟试题重庆市巴蜀中学校2022届高三下学期适应性月考(十)数学试题(已下线)专题4-5 解三角形大题归类 -1(已下线)专题12 解三角形综合-1
5 . 如图,有一个圆锥形花篮,母线长为20cm,在花篮口的点P处用一根绳子将花篮挂在墙面上,当绳子的长度最短时,可以紧紧箍住花篮,不会上下滑动,已知绳子的长度是20cm.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/11/6f38cc38-b8e5-4ffe-bcfe-37d7919ce014.png?resizew=77)
(1)求花篮的底面半径;
(2)求母线OQ与水平地面所成角的大小.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/11/6f38cc38-b8e5-4ffe-bcfe-37d7919ce014.png?resizew=77)
(1)求花篮的底面半径;
(2)求母线OQ与水平地面所成角的大小.
您最近一年使用:0次
名校
解题方法
6 . 对于数列
,若存在正整数M,同时满足如下两个条件:①对任意
,都有
成立;②存在
,使得
.则称数列
为
数列.
(1)若
,
,判断数列
和
是否为
数列,并说明理由;
(2)若
数列
满足
,
,求实数p的取值集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bade4623a0b3c76e2b0447501f389a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee632cfe1cc460fbcd32b9e8a630a543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c18d0bc4997e313bc272ddc5a566221.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ab9017f0c3eefa1f5f27179586713a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63c9c1617a0b6a253652713676791ac8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943c93c27edb900ad23df19fb24185de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239016a408e2b0de90c20b5c7b3ec59c.png)
![](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/63c9c1617a0b6a253652713676791ac8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63c9c1617a0b6a253652713676791ac8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/613915e81a8eaf5363040516a6e27cfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab6aca864ee6207c4e8aefcd0972e7ce.png)
您最近一年使用:0次
2022-04-27更新
|
499次组卷
|
3卷引用:北京市八一学校2021-2022学年高二下学期期中考试数学试题
解题方法
7 . 老李的手机被人偷了,而手机中有企业的重要数据.情急之下,他向A派出所报了案.为了帮助老李找到那部重要的手机;A派出所联系了与其相距
米的B派出所.这时,小偷正好用老李的那部手机与人通话.A、B两个派出所的监听仪器听到手机发声的时间差为6秒,且B处的声强是A处声强的4倍(设声速为
米/秒,声强与距离的平方成反比),试确定持手机者的位置P(即确定P到AB中点M的距离以及
的正切值)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa9a1b2bc186d78fd4370dd15fa542a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/635b829d01436b1de5f9218a2e8ca226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/471fd32f4bf526fb00d05331d56a85ed.png)
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8 . 一颗人造卫星在地球上空1630千米处沿着圆形轨道匀速运行,每2小时绕地球一周,将地球近似看作一个球体,半径为6370千米,卫星轨道所在圆的圆心与地球球心重合,已知卫星在中午12点整通过卫星跟踪站点A的正上空
,12:03时卫星通过点C,如图所示.(卫星接收天线发出的无线电信号所需时间忽略不计)
![](https://img.xkw.com/dksih/QBM/2022/4/20/2962142816968704/2963101690200064/STEM/d914a2d6-a9f3-46dc-871c-abfde0aed8bc.png?resizew=209)
(1)求人造卫星在12:03时与卫星跟踪站A之间的距离;(精确到1千米)
(2)求此时天线方向AC与水平线的夹角.(精确到1分)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://img.xkw.com/dksih/QBM/2022/4/20/2962142816968704/2963101690200064/STEM/d914a2d6-a9f3-46dc-871c-abfde0aed8bc.png?resizew=209)
(1)求人造卫星在12:03时与卫星跟踪站A之间的距离;(精确到1千米)
(2)求此时天线方向AC与水平线的夹角.(精确到1分)
您最近一年使用:0次
9 . 若两条异面直线a、b所成的角为
,它们的公垂线段
,长为d,E、F两点分别在直线a、b上,且线段AE长为m,线段
长为n.求线段EF的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6024fd4532f5f981deac4582c799a6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d71fe246270d1277f9eb2bf15af22e83.png)
您最近一年使用:0次
解题方法
10 . 如图,已知扇形AOB的半径为a,中心角为
.从A向半径OB作垂线,垂足为
,由
作弦AB的平行线,与OA交于
,反复如此做,得到
,
,…,
,…,它们的面积分别为
,
,
,…,求所有这些面积的和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c897ad1992d7aeca35ee9b83061d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce1de41fb9bd93a1f40ead5995f346e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e15ad72ffe1329e115bbd7e23eb0169.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f08d49452177c235b67a73a9917b03f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://img.xkw.com/dksih/QBM/2022/4/19/2961622817325056/2962088015781888/STEM/1af05329-b511-4d34-8017-3e02ef06b3b5.png?resizew=148)
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