1 . 2020年春节期间,新型冠状病毒引起的肺炎疫情席卷武汉,一方有难八方支援,全国各地医疗队伍紧急支援武汉,我市某医院决定从8名医生中选派4名分别支援武汉四家医院,每家医院各派去1名医生,其中甲和乙不能都去武汉,甲和丙只能都去或都不去武汉,则不同的选派方案有( )种
A.240 | B.360 | C.600 | D.120 |
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2 . 现有一块半径为
,圆心角为
的扇形
铁皮废料,现在准备利用这块铁皮制作一些图形模型.已知点P在弧
上,设
.
![](https://img.xkw.com/dksih/QBM/2021/6/26/2751508277264384/2759699972161536/STEM/35fff90f4a5448609d9be3ca0f528c4a.png?resizew=429)
图1 图2
(1)方案1:过点P裁剪一个扇形内接矩形
(如图1),点Q在
上,点M,N在
上,
①若
,求矩形
的面积;
②若矩形
是正方形,求
的值;
(2)方案2:从P点处分别向
作两条垂线
和
,垂足为S,T,(如图2)这样可以裁剪出两个直角三角形
和
,为了提高废料的利用率,我们希望这两个直角三角形面积和最大,试问此时点P应在何处?请说明你的理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d42a77bf2a9be342e532da4bf2463af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/259728433d68902065408fb6a34c6d4d.png)
![](https://img.xkw.com/dksih/QBM/2021/6/26/2751508277264384/2759699972161536/STEM/35fff90f4a5448609d9be3ca0f528c4a.png?resizew=429)
图1 图2
(1)方案1:过点P裁剪一个扇形内接矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ac79e422ba4876949f0514c44539b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/734a6a1d319648bb969845a9159cdba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/389bc3f29c058067e06e0d0d2be399da.png)
②若矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ac79e422ba4876949f0514c44539b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43660b1543b3a2b46185f7629d28a963.png)
(2)方案2:从P点处分别向
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5a5e484dfef494d27bc35ae7b8cf75d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d4aca03910382accfe738520daf689c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d583183429b6b31aa9742eefc67d3181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d5a832611462e8ae0c890eece6bfaeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be3d778ca15706a4c9c327f3eae9f1b5.png)
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