题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032152-56724.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032153-55061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032153-86009.png)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032153-63045.png)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032153-92606.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032153-59640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032153-92606.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032154-54163.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032154-98727.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032154-22863.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032154-86430.png)
解析
试题分析:(Ⅰ)对条件
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032155-53153.png)
化简后为
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032155-11883.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032155-30674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032155-31073.png)
(Ⅱ)以C为坐标原点,射线CA为x轴正半轴建立直角坐标系,设P点坐标为(x, y),则由点到直线的距离公式可将
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032154-22863.png)
试题解析:(Ⅰ)法一、设三角形三内角A、B、C对应的三边分别为a, b, c,
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032155-53153.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032155-90173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032156-74907.png)
又由余弦定理有
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032156-32675.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032156-80756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032155-11883.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032156-42386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032156-42386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032155-30674.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032155-31073.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032157-11061.png)
法二、设三角形三内角A、B、C对应的三边分别为a, b, c,
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032155-53153.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032155-90173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032156-74907.png)
又由余弦定理有
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032156-32675.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032156-80756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032155-11883.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032156-42386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032156-42386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032155-30674.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032157-20864.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032157-28699.png)
(1)÷(2),得
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032157-96392.png)
令a="4k," b="3k" (k>0)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032158-44221.png)
(Ⅱ)以C为坐标原点,射线CA为x轴正半轴建立直角坐标系,则A、B坐标为(3,0),(0,4),直线AB方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032158-23397.png)
设P点坐标为(x, y),则由P到三边AB、BC、AB的距离为d1, d2和d3可知
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032158-49032.png)
且
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032158-20789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032158-59536.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032159-48765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032154-86430.png)
核心考点
举一反三
(1)试分别建立出厂价格、销售价格的模型,并分别求出函数解析式;
(2)假设商店每月购进这种商品m件,且当月销完,试写出该商品的月利润函数;
(3)求该商店月利润的最大值.(定义运算
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032142-72258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032132-23463.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032132-13922.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032133-95473.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032133-32890.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032133-43417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032133-18870.png)
A.2 | B.3 | C.4 | D.5 |
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032123-44232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032124-51276.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032124-65462.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032124-36359.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032124-41292.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032124-57838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032125-20799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032125-41881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032125-33544.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032125-80796.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032126-69646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032118-43099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032110-75084.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032110-34687.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032110-68078.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032111-88481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032111-59496.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032111-88270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032111-13039.png)
(Ⅰ)求角B的大小
(Ⅱ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020032112-72890.png)
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