三潭印月,是浙江杭州西湖十景之一,被誉为"西湖第一胜境".景区内有三座石塔,它们的分布呈等边三角形,边长约为60米.为了保护石塔,文物保护单位计划以每座塔为圆心,沿半径6米的圆周设置保护桩,在三座塔所在三角形的内切圆圆周设置灯光,既符合三潭印月的景致,又起到警示作用.为评估保护方案对观赏性的影响,试问在整个保护水域(三角形和保护桩区域内部),天上圆月投影到灯光区的概率为( )
![](https://img.xkw.com/dksih/QBM/2021/1/28/2645902740742144/2647841434001408/STEM/492fc03ae4494996b582c53c572b9f7a.png?resizew=171)
![](https://img.xkw.com/dksih/QBM/2021/1/28/2645902740742144/2647841434001408/STEM/0c23cad5511a485788cce3e4829295c8.png?resizew=112)
![](https://img.xkw.com/dksih/QBM/2021/1/28/2645902740742144/2647841434001408/STEM/492fc03ae4494996b582c53c572b9f7a.png?resizew=171)
![](https://img.xkw.com/dksih/QBM/2021/1/28/2645902740742144/2647841434001408/STEM/0c23cad5511a485788cce3e4829295c8.png?resizew=112)
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更新时间:2021-01-31 09:50:05
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【推荐1】如图,长方形的四个顶点为
,
,
,
,曲线
经过点
.现将一质点随机投入长方形
中,则质点落在图中阴影区域的概率是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/c69074bf-6538-47c8-84ac-fcb794aefbc0.png?resizew=198)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1a9821a00b71f6b7d7a76d91b3f810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4fd4da08956db1f206c8ea026f4e52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f3cd3027a533dd07220f161c958602.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e62dfe60e2f098c466a048b982151365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aef469c7b7cb9945b984222381b9c000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/c69074bf-6538-47c8-84ac-fcb794aefbc0.png?resizew=198)
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【推荐2】利用随机模拟方法计算
和
所围成图形的面积.首先利用计算机产生两组
之间的随机数:
,
;令
;若共产生了
个样本点
,其中落在所围图形内的样本点数为
,则所围成图形的面积可估计为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50866229ec5a3640fb250f9bd2192b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
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