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解题方法
1 . “但有一枝堪比玉,何须九畹始征兰”,盛开的白玉兰是上海的春天最亮丽的风景线,除白玉兰外,上海还种植木兰科的其他栽培种,如黄玉兰和紫玉兰等.某种植园准备将如图扇形空地
分成三部分,分别种植白玉兰、黄玉兰和紫玉兰;已知扇形的半径为70米,圆心角为
,动点
在扇形的弧上,点
在
上,且
.
米时,求
的长;
(2)综合考虑到成本和美观原因,要使白玉兰种植区
的面积尽可能的大.设
,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a77343ecde1c2665df291761b6563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0211da37e92f915e781691296578ba0.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/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcb46b4e24ac75c20d8f0bb2548f2318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e4d476faf357f6499ff47a73a298c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(2)综合考虑到成本和美观原因,要使白玉兰种植区
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/867d00157025729b6a66380810466edc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
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2 . 设函数
,若对于任意
,都存在
,使得
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7f9b35017daa8b524c5717a355834a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc58f265c07adc6f5c9ad061e915239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a406004f851ad9b867c9ff512b20b55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d347f3cfd706ec20e2575c86251c9c7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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3 . 质点P和Q在以坐标原点O为圆心,半径为1的
上逆时针作匀速圆周运动,同时出发.P的角速度大小为
,起点为
与x轴正半轴的交点;Q的角速度大小为
,起点为射线
与
的交点.则当点
与
重合时,点
的坐标不可能是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d99ef937823db2d4d3b1ae5af609eb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059b7530c506efb568b487fb191ec080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3ea342d5ebfdfa1e0048a7738d59163.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
4 . 如图,A、C两岛相距
海里,上午9点整有一客轮在位于C岛的北偏西40°且距C岛10海里的D处,沿直线方向匀速开往A岛,在A岛停留10分钟后前往B市,上午9:30测得客轮位于C岛的北偏西70°且距C岛
海里的E处,此时小张从C岛乘坐速度为v海里/小时的小艇沿直线方向前往A岛换乘客轮去B市.
(2)若小张能乘上这班客轮,问小艇的速度至少为多少海里/小时?(由小艇换乘客轮的时间忽略不计)
(3)现测得
,
,已知速度为
海里/时
的小艇每小时的总费用为
元,若小张由岛C直接乘小艇去B市,则至少需要多少费用?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/254f942341f65547368c0206d1d748f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e4123975f257306440158659634c4a.png)
(2)若小张能乘上这班客轮,问小艇的速度至少为多少海里/小时?(由小艇换乘客轮的时间忽略不计)
(3)现测得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fffa3d9c32da53b0ea0c338012ea20c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/601db16fd0de0dc16f99302da464e8e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc13a607ac0c7f76d252d7cb1bb040fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45b82ca3f26564d127cfe81a90b1bb4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbac0fb8cc2e5eec37b63c7faddc29b.png)
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5 . 设
均为大于1的自然数,
,若存在实数
,使得
,则有序实数对
为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663a61ad241d5d874c9a9362f0ee917c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8dd0d1504fb3044e260c7cfe3c44358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ef3b1fb27cc7545208a5543a16e8184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63313f7ac7402fcb5a9a840db64c6f08.png)
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6 . 由于四边形不具有稳定性,所以求四边形面积公式需要有限制条件.我们将四个点在圆上的四边形称为圆内接四边形,圆内接四边形具有对角互补的性质.印度数学家婆罗摩笈多发现了圆内接四边形的面积公式为
,其中
、
、
、
分别为圆内接四边形的4条边,
,与海伦公式有类似之处.已知在圆内接四边形
中,
,
,
,
,则四边形
的面积为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26f9a99467e1c9715852266155be6a9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575008e0b065f0d535251a041203f99f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b515965c22d2950b592c096c6e3bdfd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bcffaa7a79cedadb925149e28e39a43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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解题方法
7 . 已知函数
.
(1)若不等式
对任意
时恒成立,求实数
的取值范围;
(2)将函数
的图象向左平移
个单位,然后保持图象上点的纵坐标不变,横坐标变为原来的
,得到函数
的图象,若存在非零常数
,对任意
,有
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f0e855911b392669d0ef75556bbed8b.png)
(1)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6309b008a64c796c953e7738fc0a33e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf97222c1fd4b67b7afaba2ca897289.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aeb076bad84890e24dbdc945ad543cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a60e77043cfa243c212f9e340c5f46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f0ae4918f9f84f6e54e257c85375a79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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8 . 如下图,
是线段
外一点,
是线段
的垂直平分线
上的动点
,求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd2a2a843ec6b1973068444b19b0616.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbf66ad6fac34a61f1e59a7975372e52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd2a2a843ec6b1973068444b19b0616.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/288b046336f87d3529ad811eea5b075b.png)
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解题方法
9 . 已知
为钝角,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e8c744b281e2de059ad64015a6d7e6.png)
(1)求
的值
(2)求
的值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e8c744b281e2de059ad64015a6d7e6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9252a4c0d14210f580094fbfcaf65cd.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/850dba25bf0f5f13541bf9b6ec12b84d.png)
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解题方法
10 .
是平面上一定点,
,
,
平面上不共线的三个点,动点
满足
,
,则
的轨迹一定通过
的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/524d7ee6c3ba2d8b77358c7281137a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b8e5990ef4ef314941a3154457a9d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
A.外心 | B.内心 | C.重心 | D.垂心 |
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