如图,在平面直角坐标系中,直线
与x轴相交于点A,与y轴相交于点B,直线
与直线
相交于点C,点P是线段OA上一动点(点P不与点O,A重合),过点P作
轴交AB于点Q,以OP,PQ为邻边作矩形OPQR,点R在OB上.设
,矩形OPQR与
重叠部分的面积为S.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/30/b0d660b3-1b75-47cc-abd2-ca22b11f301f.png?resizew=222)
(1)求点C的坐标;
(2)求S关于t的函数解析式,并直接写出自变量t的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e434a6fc177990ab7f2b604c111e1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e434a6fc177990ab7f2b604c111e1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2784a52c4da98dc9df661fc152fc29e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8070045849428341cc37653339f3713.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/173bc7a36757d77f01213411edd25241.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/30/b0d660b3-1b75-47cc-abd2-ca22b11f301f.png?resizew=222)
(1)求点C的坐标;
(2)求S关于t的函数解析式,并直接写出自变量t的取值范围.
更新时间:2022-08-29 06:01:09
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【推荐1】如图,已知长方形相邻两边的长分别是xcm和3cm,设长方形的面积为ycm2.
(1)试写出长方形的面积y与x之间的关系式;
(2)利用(1)中的关系式,求当x=5cm时长方形的面积;
(3)当x的值由4cm变化到12cm时,长方形的面积由 cm2变化到 cm2.
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(2)利用(1)中的关系式,求当x=5cm时长方形的面积;
(3)当x的值由4cm变化到12cm时,长方形的面积由 cm2变化到 cm2.
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【推荐2】2018年5月14日川航3U863航班挡风玻璃在高空爆裂,机组临危不乱,果断应对.正确处置,顺利返航,避免了一场灾难的发生,创造了世界航空史上的奇迹!下表给出了距离地面高度与所在位置的温度之间的大致关系.根据下表,请回答以下几个问题:
(1)上表反映的两个变量中,________是自变量,________是因变量?
(2)若用h表示距离地面的高度,用y表示表示温度,则y与h的之间的关系式是:________;当距离地面高度5千米时,所在位置的温度为:________
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如图是当日飞机下降过程中海拔高度与玻璃爆裂后立即返回地面所用时间关系图.根据图象回答以下问题:
(3)返回途中飞机再2千米高空水平大约盘旋了几分钟?
(4)飞机发生事故时所在高空的温度是多少?
距离地面高度(千米) | 0 | 1 | 2 | 3 | 4 | 5 |
所在位置的温度(![]() | 20 | 14 | 8 | 2 | ![]() |
(2)若用h表示距离地面的高度,用y表示表示温度,则y与h的之间的关系式是:________;当距离地面高度5千米时,所在位置的温度为:________
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如图是当日飞机下降过程中海拔高度与玻璃爆裂后立即返回地面所用时间关系图.根据图象回答以下问题:
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【推荐1】如甲、乙两家草莓采摘园的草莓品质相同,销售价格也相同。“五一期间”,两家均推出了优惠方案,甲采摘园的优惠方案是:游客进园需购买60元的门票,采摘的草莓六折优惠;乙果摘园的优惠方案是:游客进园不需购买门票,采摘园的草莓超过一定数量后,超过部分打折优惠。优惠期间,设某游客的草莓采摘量为x(千克),在甲采摘园所需总费用为
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表示
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![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/29/0ee0f728-ae6b-4a60-89e8-1c60fca07a8a.png?resizew=180)
(1)甲、乙两采摘园优惠前的草莓销售价格是每千克___________元;
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、
与x的函数表达式;
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/29/0ee0f728-ae6b-4a60-89e8-1c60fca07a8a.png?resizew=180)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
(3)在图中画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
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【推荐2】如图所示,平面直角坐标系中,直线
与直线
相交于点
,直线
与
轴相交于点
.过直线
上的一点
作
轴的垂线,交直线
于点
,连接
.
![](https://img.xkw.com/dksih/QBM/2022/2/18/2919121217118208/2920758474539008/STEM/86905c4a-1946-409e-bb7f-cc5487895103.png?resizew=222)
(1)求点
的坐标;
(2)求
的面积;
(3)将直线
向下平移4个单位长度得到直线
,设直线
与
轴相交于点
,则直线
上是否存在一点
,使得
是以
为腰的等腰三角形?若存在,请直接写出
的坐标,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f60525565ec28ec944b0793395f7aef1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b7526e0cde0ca10ce6ce5954caefc26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.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/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3efe64291ba2d93e7e5532cac16cfb87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2022/2/18/2919121217118208/2920758474539008/STEM/86905c4a-1946-409e-bb7f-cc5487895103.png?resizew=222)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(3)将直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
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【推荐1】如图,一个正比例函数与一个一次函数的图象交于点A(3,4),其中一次函数与y轴交于B点,且OA=OB.
(1)求这两个函数的表达式;
(2)求△AOB的面积S.
(1)求这两个函数的表达式;
(2)求△AOB的面积S.
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【推荐2】如图,已知直线
的解析式为
,直线
的解析式为:
,
与
轴交于点
,
与
交于点
.
(1)求k,b的值;
(2)求三角形
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70510f3e0e82927f7987a41ed2c1f0ab.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f99ce0fdd3a34df8d5e913b7b9f6f3fa.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/4/82eec603-7a66-4a17-8e8c-153b9d43f614.png?resizew=138)
(1)求k,b的值;
(2)求三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
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【推荐1】如图,在矩形
中,
,
.
为
的中点,动点
从点
出发,沿折线
运动,当它到达点
时停止运动,设点
运动的路程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e646b2fa9e633d201810109ccfbedc58.png)
,连接
,设
的面积为
.
与
的函数关系式为:______.
(2)在给出的平面直角坐标系中画出
的函数图象,并写出这个函数的一条性质:______.
(3)如图2,
的图象如图所示,根据函数图象,直接写出当
时
的取值范围是______.(结果保留一位小数,误差不超过0.2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e646b2fa9e633d201810109ccfbedc58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72fb378d6bf91902efa15881985c5e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b4dcc093218443f71a046b6df94bbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)在给出的平面直角坐标系中画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
(3)如图2,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/424be0f19cb65f984169be8f8ec362e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/421a7d6f54bf58a7a4f4ce61e06aefa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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【推荐2】【阅读】已知平面直角坐标系中有两点
,
,根据勾股定理,可知两点间的距离
.特别地,如果点
,
所在的直线与坐标轴重合或平行于坐标轴或垂直于坐标轴时,那么这两点间的距离公式可简化为
或
.例如:已知点
,
,则这两点间的距离
.
根据以上材料,解决下列问题:
(1)已知
,
,则A,B两点间的距离为________.
(2)已知点M,N在同一条平行于y轴的直线上,点M的纵坐标为-2,点N的纵坐标为3,则M,N两点间的距离为________.
(3)如图,在平面直角坐标系中,已知点
,
,试探究在x轴上是否存在一点P,使得
的值最小?若存在,请求出此时点P的坐标及
的最小值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c43b758b519150de45cc852c24144373.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b7e35faab6d74fa0c36599c39d1698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06b8ae26c446d54f456a4f9b2f28d091.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b225d772013d021cf1bfe7b9421fa5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b7e35faab6d74fa0c36599c39d1698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfbc79d4aafa7c8ad068e2cf1b73ba72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0761e63cb3a4113d50f6bf808cdc031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac5225ff6aa3c06ff5c8437f88093f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b08a6fec15e862872c978203fd49968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6a0f6f7ef1ed1236b5a7ffb2398caf.png)
根据以上材料,解决下列问题:
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f1e95fb519f59c46f40e4ab44660073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfa7486b5644f884e8282bf23079e3ed.png)
(2)已知点M,N在同一条平行于y轴的直线上,点M的纵坐标为-2,点N的纵坐标为3,则M,N两点间的距离为________.
(3)如图,在平面直角坐标系中,已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c8c39de4d7d1277da346b51b5bd2499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f3cd3027a533dd07220f161c958602.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a13ec9a812274ad0839f20ba17348687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a13ec9a812274ad0839f20ba17348687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/20/6da9725b-8e72-4965-a178-04fbe883d6ae.png?resizew=173)
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