1 . 如图,OA,OB为扇形湖面OAB的湖岸,现欲利用渔网和湖岸在湖中隔出两个养殖区
区域I和区域Ⅱ,点C在
上,
,
,其中
,半径OC及线段CD需要用渔网制成
若
,
,则所需渔网的最大长度为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b700fa9aeb1016aa71f76e4b6bb212e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/266e7cc4ba2a8c8b220dbf25bf4a8fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe27fa32d136b72c390fa2960ec21650.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaf36687e3790e160f02f17eccb2472b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d34f7238f70f7a7c4d3e993c0f05970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d120188b2543fbcad46353413b1b062.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b68963a152bb8afd1639340ef0b654a5.png)
![](https://img.xkw.com/dksih/QBM/2018/5/28/1955075714433024/2020720319078400/STEM/9a9f9e039b014ba4a641a74e0cab7667.png?resizew=283)
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2018-08-29更新
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599次组卷
|
2卷引用:辽宁省六校协作体2020-2021学年高二下学期第三次联考数学试题
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2 . 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
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解题方法
3 . 某工厂有甲、乙两个生产车间,其污水瞬时排放量
(单位:
)关于时间
(单位:
)的关系均近似地满足函数
,其图象如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/23/26d08519-def2-4de0-a24a-c37a31e041f7.png?resizew=162)
(1)根据图象求函数解析式;
(2)若甲车间先投产,1小时后乙车间再投产,求该厂两个车间都投产
时刻的污水瞬时排放量;
(3)由于受工厂污水处理能力的影响,环保部门要求该厂的两个车间任意时刻的污水排放量之和不超过
,若甲车间先投产,为满足环保要求,乙车间比甲车间至少需推迟多少小时投产?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ff4266515b801477248b32e10f3ac4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f42a97e3ae09c48e1d587f59af3621bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/795ea8d61f4e4e138231819356f4073b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/23/26d08519-def2-4de0-a24a-c37a31e041f7.png?resizew=162)
(1)根据图象求函数解析式;
(2)若甲车间先投产,1小时后乙车间再投产,求该厂两个车间都投产
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16dca1f69db5d45d7e0195b60f546a40.png)
(3)由于受工厂污水处理能力的影响,环保部门要求该厂的两个车间任意时刻的污水排放量之和不超过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d18b1b3fa4bc1f8e48a68b9f77e37e3b.png)
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9-10高一下·河南·期中
名校
解题方法
4 . 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
5 . 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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585次组卷
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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