名校
解题方法
1 . 在新农村建设中,某村准备将如图所示的
内区域规划为村民休闲中心,其中
区域设计为人工湖(点D在
的内部),
区域则设计为公园,种植各类花草.现打算在
,
上分别选一处E,F,修建一条贯穿两区域的直路
,供汽车通过,设
与直路
的交点为P,现已知
米,
,
,
米,
,
段的修路成本分别为100万元/百米,50万元/百米,设
,修路总费用为关于
的函数
,(单位万元),则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5157b42da58d55daad27d98b2fec15ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4189a0821a0ffab9dc171ecd279ba442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfaa4beac0c303da8ea298b7effce1fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9680bd6f250acb8b568510419b59d3e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/731ac94d7d7af196a74d9aa5021cbb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21f808404463c108bea981ca900c15a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfc513822ba6e34a16a468450ce282b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fd7229922fbb3ce09dada883f74fbb1.png)
A.![]() | B.![]() |
C.修路总费用最少要400万元 | D.当修路总费用最少时,![]() |
您最近一年使用:0次
2024-01-07更新
|
537次组卷
|
4卷引用:广东省珠海市第一中学2024届高三上学期期末模拟数学试题(三)
广东省珠海市第一中学2024届高三上学期期末模拟数学试题(三)2024年普通高等学校招生全国统一考试模拟试题数学试题(一)(已下线)6.4.3 第3课时 余弦定理、正弦定理应用举例【第三练】“上好三节课,做好三套题“高中数学素养晋级之路(已下线)解三角形-综合测试卷B卷
解题方法
2 . 某街道规划建一座口袋公园.如图所示,公园由扇形
区域和三角形
区域组成.其中
三点共线,扇形半径
为30米.规划口袋公园建成后,扇形
区域将作为花草展示区,三角形
区域作为亲水平台区,两个区域的所有边界修建休闲步道.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/b1bb7ad3-ee63-4f58-8211-0d81d9483eaa.png?resizew=167)
(1)若
,
,求休闲步道总长(精确到米);
(2)若
,在前期民意调查时发现,绝大部分街道居民对亲水平台区更感兴趣.请你根据民意调查情况,从该区域面积最大或周长最长的视角出发,选择其中一个方案,设计三角形
的形状.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ed01d1ff5a7f21a68fb3a1e5c7f393e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf126cfed85fa9b7720ec6f7b0008dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d322efb382f7cc7a9bb242bcd706d649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ed01d1ff5a7f21a68fb3a1e5c7f393e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf126cfed85fa9b7720ec6f7b0008dc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/b1bb7ad3-ee63-4f58-8211-0d81d9483eaa.png?resizew=167)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3925e45d83a5383e492cdb1666493cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/718db7266fcd1f56a5992783235ab720.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7df59d622d4b375f2e811020babf06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf126cfed85fa9b7720ec6f7b0008dc.png)
您最近一年使用:0次
解题方法
3 . 2023年杭州亚运会首次启用机器狗搬运赛场上的运动装备. 如图所示,在某项运动赛事扇形场地
中,
,
米,点
是弧
的中点,
为线段
上一点(不与点
,
重合).为方便机器狗运输装备,现需在场地中铺设三条轨道
,
,
.记
,三条轨道的总长度为
米.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/9eb07001-5f34-48ab-b0c2-346e89c60147.png?resizew=148)
(1)将
表示成
的函数,并写出
的取值范围;
(2)当三条轨道的总长度最小时,求轨道
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f788fb0059b7356dc6c7811f46057e66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85f0a31ea2b1a279e1d50c3fba77d061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ada3bf3a5bd0b858fea04c4d77a720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/9eb07001-5f34-48ab-b0c2-346e89c60147.png?resizew=148)
(1)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)当三条轨道的总长度最小时,求轨道
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
您最近一年使用:0次
2023-12-13更新
|
404次组卷
|
2卷引用:上海市徐汇区2024届高三上学期一模数学试卷
名校
4 . 如图,已知
,M,N分别为
两边上的点,
,过M,N做圆弧,Q为
的中点,且
,则线段AQ长度的可能值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b7310796c09a69c44d6290056f2b287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69b0dfa6898f9560ab8a5e5905c1f81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ae728c7be0f0cf78711f3fa5ccccf30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b891a9c85312ba0be38b6813d1af78de.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/15/02c4360c-8b17-4d71-bc3e-818adb7117f1.png?resizew=205)
A.2 | B.![]() | C.5 | D.![]() |
您最近一年使用:0次
解题方法
5 . 某单位为端正工作人员仪容,在单位设置一面平面镜.如图,平面镜宽
为
,某人在
点处观察到自己在平面镜中所成的像为
.当且仅当线段
与线段
有异于
,
的交点
时,此人能在镜中看到自己的像.已知
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/9/643e3e4d-a5c1-4d5a-9754-e5e3b3e62f7c.png?resizew=153)
(1)若在A点处能在镜中看到自己的像,求
的取值范围;
(2)求某人在A处与其在平面镜中的像的距离
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f71a41641aa0d0e45a3c03d3d2c1196b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6024fd4532f5f981deac4582c799a6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.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/1371fe98a65d8ebd840c8d98346b6d15.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/9/643e3e4d-a5c1-4d5a-9754-e5e3b3e62f7c.png?resizew=153)
(1)若在A点处能在镜中看到自己的像,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/746853ea6d76bd7cccc6bdd6c739aed7.png)
(2)求某人在A处与其在平面镜中的像的距离
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6024fd4532f5f981deac4582c799a6ef.png)
您最近一年使用:0次
解题方法
6 . 为方便居民休闲娱乐,某市计划在一块三角形空地上修建一个口袋公园,如图所示.在公园内部计划修建景观道路
(道路的宽度忽略不计),已知
把三角形空地分成两个区域,
区域为儿童娱乐区,
区域为休闲健身区.经测量,
米,
米.若儿童娱乐区每平方米的造价为
元,休闲健身区每平方米的造价为
元,景观道路每米的造价为
元.
(1)若
,求景观道路
的长度;
(2)求
为何值时,口袋公园的造价最低?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/523b97f957da879ef8a7c946316aefde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d52c4612c289ce6e84aa4635de75f6a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6f1af4b44b2e97e8f319bab4ae9010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11884ea468894d9cc30eddc09b4a39ab.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/4/e8dbdffc-7d67-4655-8f68-22975f166ea3.png?resizew=160)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11cff497834dca6d39a6f64b93197949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3981e7286d41960daf4e110c1c84e03a.png)
您最近一年使用:0次
2023-11-14更新
|
297次组卷
|
2卷引用:山东省潍坊市2024届高三上学期期中考试数学试题
7 . 已知向量
,
,以下结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed98b448838aece15a0be7ce8ed42d1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aceeb82a28fd8fc6eb07aa0324eabb36.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() |
您最近一年使用:0次
名校
8 . 某城市平面示意图为四边形
(如图所示),其中
内的区域为居民区,
内的区域为工业区,为了生产和生活的方便,现需要在线段
和线段
上分别选一处位置,分别记为点
和点
,修建一条贯穿两块区域的直线道路
,线段
与线段
交于点
,
段和
段修建道路每公里的费用分别为10万元和20万元,已知线段
长2公里,线段
和线段
长均为6公里,
,设
.
(单位:万元)与
的关系式(不用求
的范围);
(2)求修建道路的总费用
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e57a13c665af88f326c9890072bf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663dc9f276fc4c86d9165533f9045dc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575025a5b31355d27edaffa3df1fc310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)求修建道路的总费用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
您最近一年使用:0次
2023-11-12更新
|
1000次组卷
|
7卷引用:湖北省武汉市华中师范大学第一附属中学2023-2024学年高三上学期期中数学试题
湖北省武汉市华中师范大学第一附属中学2023-2024学年高三上学期期中数学试题四川省南充市南充高级中学2024届高三上学期第四次月考数学(文)试题四川省南充高级中学2023-2024学年高三上学期第四次月考数学(理科)试题(已下线)考点16 解三角形实际应用问题 --2024届高考数学考点总动员【练】(已下线)第12讲 6.4.3 第3课时 余弦定理、正弦定理应用举例-【帮课堂】(人教A版2019必修第二册)(已下线)6.4.3.3 余弦定理、正弦定理应用举例——课堂例题(已下线)专题1 以实际问题为背景的解三角形问题【讲】(高一期末压轴专项)
9 . “特种兵式旅游”,是年轻游客中兴起的一种新的旅游方式,即用尽可能少的时间、费用,游览尽可能多的景点.某景点示意图如下:
为景点入口,
、
、
为景点出口,且
、
、
均在圆
上,阴影部分为草地,其中
,
分别为
,
街道上的标志性建筑,且
.
为“特种兵”通道,已知
.
(1)若
,求
;
(2)记
为“特种兵通道”的总长,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/c5db41a1f31d6baee7c69990811edb9f.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c7ce7b83d2a1d30e7cf668a0e436b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de22cf0e953a9ad14f30f8a2b5383c13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe4ae0d6f2782a490c990e8499cd7436.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/19/0dae78d9-952a-4ab6-9ecf-8e526ea86ab7.png?resizew=210)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf1ddb449c6faa34ca3c5e4a83ec368a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c866e0116428eda716a173d7194aed8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
您最近一年使用:0次
10 . 如图,已知两质点A,B同时从点P出发,绕单位圆逆时针做匀速圆周运动,质点A,B运动的角速度分别为3rad/s和5rad/s,设两质点运动
时这两质点间的距离为
.
(1)求
的解析式;
(2)求这两质点从点P出发后第n次相遇的时间
(单位:s).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c39a3be176eadd348d2130c3922005f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/16/05428e8f-adf3-4ef1-af4f-6f7d3f8129ce.png?resizew=163)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求这两质点从点P出发后第n次相遇的时间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
您最近一年使用:0次
2023-09-30更新
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223次组卷
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3卷引用:江西省部分高中学校2024届高三上学期9月大联考数学试题
江西省部分高中学校2024届高三上学期9月大联考数学试题河南省2023-2024学年高三上学期一轮复习阶段性检测(三)数学试题(已下线)专题05 三角函数(5大易错点分析+解题模板+举一反三+易错题通关)