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1 . 某景区修建一栋复古建筑,其窗户设计如图所示.圆
的圆心与矩形
对角线的交点重合,且圆与矩形上下两边相切(
为上切点),与左右两边相交(
,
为其中两个交点),图中阴影部分为不透光区域,其余部分为透光区域.已知圆的半径为1
,且
,设
,透光区域的面积为
.
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787151360/STEM/1729e3fcb1944d23be9e2945be48c30e.png?resizew=151)
(1)求
关于
的函数关系式,并求出定义域;
(2)根据设计要求,透光区域与矩形窗面的面积比值越大越好.当该比值最大时,求边
的长度.
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787151360/STEM/0107eca3d1ee404d98c9405ec7ac46de.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787151360/STEM/211851f30cce45b1a2c36076c0d515c5.png?resizew=48)
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787151360/STEM/dd1a395a1bc24f4c95822c91d79d6693.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787151360/STEM/d01644a8188a4ee890e14c15ecf316d5.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787151360/STEM/0e3156b22a7742d195fdee36485e4380.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787151360/STEM/4729c2dd8a59484b811b1f33e09e4cb7.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787151360/STEM/8d3b487b5f0e48ba8ef7f0580195ac6a.png?resizew=57)
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787151360/STEM/380e2e4effa042a8bdfb79f60d5b638e.png?resizew=75)
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787151360/STEM/19f6c880ebaa481f9d6dc0bdb83fee35.png?resizew=15)
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787151360/STEM/1729e3fcb1944d23be9e2945be48c30e.png?resizew=151)
(1)求
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787151360/STEM/9c2a36e50e604d1297ff3c955a742e78.png?resizew=15)
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787151360/STEM/6666ed2450184edebd3cccfd97cd117b.png?resizew=13)
(2)根据设计要求,透光区域与矩形窗面的面积比值越大越好.当该比值最大时,求边
![](https://img.xkw.com/dksih/QBM/2017/5/6/1681346041446400/1681863787151360/STEM/bdacb3b752c64cf0a2a100b11eedb015.png?resizew=27)
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2017-05-07更新
|
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5卷引用:辽宁省沈阳市东北育才学校2018届高三上学期第二次模拟考试数学(理)试题
名校
解题方法
2 . 如图,在P地正西方向8km的A处和正东方向1km的B处各有一条正北方向的公路AC和BD,现计划在AC和BD路边各修建一个物流中心E和F,为缓解交通压力,决定修建两条互相垂直的公路PE和PF,设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f62bba61c6876520f75495b1342a342.png)
![](https://img.xkw.com/dksih/QBM/2018/12/8/2092512278085632/2094623924543488/STEM/861d651b4e8c4a2487a546e8c460acd1.png?resizew=215)
Ⅰ
为减少对周边区域的影响,试确定E,F的位置,使
与
的面积之和最小;
Ⅱ
为节省建设成本,求使
的值最小时AE和BF的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f62bba61c6876520f75495b1342a342.png)
![](https://img.xkw.com/dksih/QBM/2018/12/8/2092512278085632/2094623924543488/STEM/861d651b4e8c4a2487a546e8c460acd1.png?resizew=215)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff5ce18bd53a3c705a7c8a5bb88d2ca2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c628a08be0ec03d913fa113d981bda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9292a1dc93f6a4ac6966d7ce9f9f2b33.png)
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2016-12-03更新
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7卷引用:2019届辽宁省沈阳市东北育才学校高三上学期10月月考数学(理)试题
9-10高一下·河南·期中
名校
解题方法
3 . 某港口海水的深度
(米)是时间
(时)(
)的函数,记为:![](https://img.xkw.com/dksih/QBM/2010/5/17/1569731803963392/1569731808927744/STEM/a633767ec8f34ec988be2f249da26e89.png?resizew=59)
已知某日海水深度的数据如下:
经长期观察,
的曲线可近似地看成函数
的图象
![](https://img.xkw.com/dksih/QBM/2010/5/17/1569731803963392/1569731808927744/STEM/4c03a8ccf6ab427892793200322fde85.png?resizew=16)
(1)试根据以上数据,求出函数
的振幅A、最小正周期T和表达式;
(2)一般情况下,船舶航行时,船底离海底的距离为
米或
米以上时认为是安全的(船舶停靠时,船底只需不碰海底即可).某船吃水深度(船底离水面的距离)为
米,如果该船希望在同一天内安全进出港,请问,它至多能在港内停留多长时间(忽略进出港所需时间)?
![](https://img.xkw.com/dksih/QBM/2010/5/17/1569731803963392/1569731808927744/STEM/a62d8e7e0a8c4027a77a9e888180a2e0.png?resizew=15)
![](https://img.xkw.com/dksih/QBM/2010/5/17/1569731803963392/1569731808927744/STEM/6acdd05f9a4644e8a82cdfbbc19408b2.png?resizew=9)
![](https://img.xkw.com/dksih/QBM/2010/5/17/1569731803963392/1569731808927744/STEM/1bfad8a5a2c04407a0d1dda8e62991aa.png?resizew=67)
![](https://img.xkw.com/dksih/QBM/2010/5/17/1569731803963392/1569731808927744/STEM/a633767ec8f34ec988be2f249da26e89.png?resizew=59)
已知某日海水深度的数据如下:
![]() | 0 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 |
![]() | 10.0 | 13.0 | 9.9 | 7.0 | 10.0 | 13.0 | 10.1 | 7.0 | 10.0 |
经长期观察,
![](https://img.xkw.com/dksih/QBM/2010/5/17/1569731803963392/1569731808927744/STEM/a633767ec8f34ec988be2f249da26e89.png?resizew=59)
![](https://img.xkw.com/dksih/QBM/2010/5/17/1569731803963392/1569731808927744/STEM/3fa9ea0f97b548b3be6784269fed1dac.png?resizew=104)
![](https://img.xkw.com/dksih/QBM/2010/5/17/1569731803963392/1569731808927744/STEM/4c03a8ccf6ab427892793200322fde85.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2010/5/17/1569731803963392/1569731808927744/STEM/4c03a8ccf6ab427892793200322fde85.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2010/5/17/1569731803963392/1569731808927744/STEM/309554892db3473a9ab3b2a0de6e8040.png?resizew=199)
![](https://img.xkw.com/dksih/QBM/2010/5/17/1569731803963392/1569731808927744/STEM/4c03a8ccf6ab427892793200322fde85.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2010/5/17/1569731803963392/1569731808927744/STEM/6327cf8024a94c78be0c5704ff5c0f06.png?resizew=12)
![](https://img.xkw.com/dksih/QBM/2010/5/17/1569731803963392/1569731808927744/STEM/6327cf8024a94c78be0c5704ff5c0f06.png?resizew=12)
![](https://img.xkw.com/dksih/QBM/2010/5/17/1569731803963392/1569731808927744/STEM/1320749c27884cfb9851e37c9c9b1e03.png?resizew=24)
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2013·江苏·一模
4 . 如图,摩天轮的半径为50 m,点O距地面的高度为60 m,摩天轮做匀速转动,每3 min转一圈,摩天轮上点P的起始位置在最低点处.
![](https://img.xkw.com/dksih/QBM/2014/7/8/1571813835784192/1571813841158144/STEM/c3a975c2f8e846789008b5ac73a50544.png?resizew=143)
(1)试确定在时刻t(min)时点P距离地面的高度;
(2)在摩天轮转动的一圈内,有多长时间点P距离地面超过85 m?
![](https://img.xkw.com/dksih/QBM/2014/7/8/1571813835784192/1571813841158144/STEM/c3a975c2f8e846789008b5ac73a50544.png?resizew=143)
(1)试确定在时刻t(min)时点P距离地面的高度;
(2)在摩天轮转动的一圈内,有多长时间点P距离地面超过85 m?
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2016-06-23更新
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3卷引用:2015-2016学年辽宁省沈阳二中高一4月月考数学试卷
2015-2016学年辽宁省沈阳二中高一4月月考数学试卷(已下线)2013届江苏南师附中、天一中学等五校高三下学期期初教学质量调研数学卷江苏省连云港市锦屏高级中学2017-2018学年高一下学期期中数学试题