解题方法
1 . 为保护森林公园中的珍稀动物,采用某型号红外相机监测器对指定区域进行监测识别.若该区域有珍稀动物活动,该型号监测器能正确识别的概率(即检出概率)为
;若该区域没有珍稀动物活动,但监测器认为有珍稀动物活动的概率(即虚警概率)为
.已知该指定区域有珍稀动物活动的概率为0.2.现用2台该型号的监测器组成监测系统,每台监测器(功能一致)进行独立监测识别,若任意一台监测器识别到珍稀动物活动,则该监测系统就判定指定区域有珍稀动物活动.
(1)若
.
(i)在该区域有珍稀动物活动的条件下,求该监测系统判定指定区域有珍稀动物活动的概率;
(ii)在判定指定区域有珍稀动物活动的条件下,求指定区域实际没有珍稀动物活动的概率(精确到0.001);
(2)若监测系统在监测识别中,当
时,恒满足以下两个条件:①若判定有珍稀动物活动时,该区域确有珍稀动物活动的概率至少为0.9;②若判定没有珍稀动物活动时,该区域确实没有珍稀动物活动的概率至少为0.9.求
的范围(精确到0.001).
(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8be646cd52d7f2f1714e7542e75810f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adad9633b73dfbbb3d84b4f15979e99e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522e9d7b8144a9a6aae2e105f987284c.png)
(i)在该区域有珍稀动物活动的条件下,求该监测系统判定指定区域有珍稀动物活动的概率;
(ii)在判定指定区域有珍稀动物活动的条件下,求指定区域实际没有珍稀动物活动的概率(精确到0.001);
(2)若监测系统在监测识别中,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03d18ac829394977153b4a4cbb0d621a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adad9633b73dfbbb3d84b4f15979e99e.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585df9acf845b8da7324c21c79a57b72.png)
您最近一年使用:0次
2 . 设函数
.
(1)当
时,求函数
的单调区间;
(2)若对定义域内任意的实数
,恒有
,求实数
的取值范围.(其中
是自然对数的底数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/749dc66e9e0d6112b8fed4be89957827.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若对定义域内任意的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5931095eb29d9d6b55ed9fa32a4ef1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594663e98b797cdc4efbd098cc15854f.png)
您最近一年使用:0次
名校
解题方法
3 . 如图,三棱锥
中,
为线段
的中点.
平面
;
(2)设
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b2b1992c9847cbbffd0da8c2d904bbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f5ba965420dfd5aa4da211682df096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8abf4ad9c679afd53a496a5a4866a8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2024-04-17更新
|
1071次组卷
|
2卷引用:2024届浙江省丽水、湖州、衢州三地市二模数学试卷
名校
解题方法
4 . 已知抛物线
,点
在抛物线
上,且
在
轴上方,
和
在
轴下方(
在
左侧),
关于
轴对称,直线
交
轴于点
,延长线段
交
轴于点
,连接
.
(1)证明:
为定值(
为坐标原点);
(2)若点
的横坐标为
,且
,求
的内切圆的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f4fb72e39d79b7a0cd892fa5fa34bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098a3e7d1f1890863b7483a98b618119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf25e032b5599ac49383de06e776365.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f07ef98b19a4b2040d0a2674210a0d07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8313752eac999238a713688ec5dd94ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3111eb07acf36e3c08e8f72789ffd220.png)
您最近一年使用:0次
2024-04-12更新
|
1339次组卷
|
3卷引用:2024届浙江省丽水、湖州、衢州三地市二模数学试卷
5 . 设等差数列
的公差为
,记
是数列
的前
项和,若
,
.
(1)求数列
的通项公式;
(2)若
,数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9640394bcbf52c435bdfa5e108002e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1959cec7b14403c2b839111c5e15bdb1.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/065b4c79e7a73cc0b1a2d444e0cf13f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c630ae094545da6da659feb70ef0ca.png)
您最近一年使用:0次
2024-04-12更新
|
1962次组卷
|
3卷引用:2024届浙江省丽水、湖州、衢州三地市二模数学试卷