如图,在直角三角形
中,
,动点
从点
出发,以每秒5个单位的速度沿
运动,同时动点
从点
出发,以每秒
个单位的速度沿
运动,
相遇时停止运动.过点
作
于点
,过点
作
于点
.设点
的运动时间为
秒
的长度为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/21/9fe98b9e-f8ef-4ea7-9a1f-350818f922fb.png?resizew=378)
(1)请直接写出
与
的函数关系式并注明自变量
的取值范围;
(2)在给定的平面直角坐标系中画出
与
的函数图象,并写出该函数的一条性质;
(3)当该函数图象与直线
有两个交点时,
的取值范围为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/277a7ef72a23c82b74761eda1f6a5c16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7a6be08c747b22834f1425c6253eebc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa585b9257ed0798213a9ae9b87d291.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ba837391bb4af88a9a5042248b81e2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9887e1ff61308713287d592c8e8d942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f45ffe562f631549f7a89472a5789fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65943f16e190d038cb6f41d8cb40c0cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3701b69e70fa21978b4a834e35ff98d4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/21/9fe98b9e-f8ef-4ea7-9a1f-350818f922fb.png?resizew=378)
(1)请直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)在给定的平面直角坐标系中画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)当该函数图象与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0cbc8b8572ff70d9a79e601245a6d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
更新时间:2023-12-25 06:23:49
|
相似题推荐
解答题-问答题
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名校
【推荐1】如图,在菱形
中,
,动点E从点A出发,沿A→B→C以每秒1个单位的速度运动,到达点C停止运动,过点E作
,设点E的运动时间为
,点E到
的距离
为y.
(2)在给出的平面直角坐标系中,画出函数图象,并写出这个函数的一条性质______;
(3)根据函数图象直接写出不等式
的解集是______.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67268a9d69ea306031facd555b2f8d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c672f693a7e75a7bae4936dcb1920430.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/418cb34a5390475fa6d36394282d2142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(2)在给出的平面直角坐标系中,画出函数图象,并写出这个函数的一条性质______;
(3)根据函数图象直接写出不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a583e1950f97c1c88fc322421fd1dfc.png)
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【推荐2】如图(1),在长方形
中,
,
,点P从A出发,沿A→B→C→D路线运动,到D停止;点Q从D出发,沿D→C→B→A路线运动,到A停止.若点P、点Q同时出发,点P速度为
,点Q的速度为
,a秒时点P、点Q同时改变速度,点P速度变为
,点Q速度变为
.图(2)是点P出发x秒后
的面积
与x秒的关系图象;图(3)是点Q出发x秒后
的面积
与x秒的关系图象.
根据题中的信息,解答下列问题
(1)根据图象得:
秒,
,
秒,
.
(2)连接
,当
第一次平分长方形
的面积时,求x的值;
(3)当点P、点Q在运动路线上相距的路程为
时,求x的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b79850d6b00a67110e77a33d1c46b5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432043f79e122f291c47453013042704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5631e6ec24d3d67bf4592313b6b3f4f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d989a128e30a701dfff5592476a76bab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e304742154d3ceb7767eb0e6ab29977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a37b9278b21fc0dd5e883134a2a3978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7fbd6b9f85c086ac95562fe45e8d969.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd736fbbf395fc99b5d9fa6f84940735.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfe7a785ff74d9aa4027bec2cdc06513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37b4a445e86ac65a31e55698983d7f5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/29/eb1e2c73-6db5-4e3c-a14d-205dc3a3ff89.png?resizew=457)
根据题中的信息,解答下列问题
(1)根据图象得:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d1461f3b7f2a8a65097c8de1dcbfc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4e9bb42376c12d7d21702ae8062b25a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c98c59cd4749afdd21e73529fc84323.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d1461f3b7f2a8a65097c8de1dcbfc7.png)
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(3)当点P、点Q在运动路线上相距的路程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/998ef3b9bb67d320ce30d9b453d75469.png)
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【推荐1】过中心对称图形的对称中心的任意一条直线都将其分成全等的两个部分.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/10/dfbdcc7f-5429-4719-9255-2109130e2363.png?resizew=619)
(1)如图1,两个正方形如图所示摆放,
为小正方形对角线的交点,求作过点
的直线将整个图形分成面积相等的两部分;
(2)八个大小相同的正方形如图2所示摆放,求作直线将整个图形分成面积相等的两部分(用三种方法分割);
(3)拓展:如图3,平面直角坐标系中放着5个边长为1个单位的小正方形,经过原点
的直线
恰好将5个正方形分成面积相等的两部分,则该直线的解析式为___________.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/10/dfbdcc7f-5429-4719-9255-2109130e2363.png?resizew=619)
(1)如图1,两个正方形如图所示摆放,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(2)八个大小相同的正方形如图2所示摆放,求作直线将整个图形分成面积相等的两部分(用三种方法分割);
(3)拓展:如图3,平面直角坐标系中放着5个边长为1个单位的小正方形,经过原点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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【推荐2】某商店用1000元购进某种水果销售,过了一段时间,又用2400元购进这种水果,所购数量是第一次购进数量的2倍,但每千克的价格比第一次贵了2元.
(1)该商店第一次购进水果多少千克?
(2)已知该水果的日销售量
(千克)与售价
(元)是一次函数关系.若售价为13元,则每天可以卖出50千克;若售价为15元,则每天可以卖出40千克.求
与
之间的函数表达式.
(1)该商店第一次购进水果多少千克?
(2)已知该水果的日销售量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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【推荐1】如图,直线
与x轴交于点A,直线
(k、b为常数,且
)与x轴交于点
,直线
与
交于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/26/d747af52-d183-4add-9e48-0d880d2f5f3b.png?resizew=197)
(1)求点C的坐标及直线
的函数表达式;
(2)若点D是线段
上一个动点,点D的横坐标是m,
的面积是S,请求出S与m之间的函数关系式;
(3)在y轴上是否存在点P,使得
的值最小?若存在,求出点P的坐标及这个最小值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9be9a7157db756c4536495e5698cf405.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a01e2e3d40112fdeeb464f81eaac1c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69fff64ee6ea236550185efc7ed1b598.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/283d55dc61b813675e92bd4062b78d6f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/26/d747af52-d183-4add-9e48-0d880d2f5f3b.png?resizew=197)
(1)求点C的坐标及直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(2)若点D是线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f517953a21c2a45fd8465072c44bfc.png)
(3)在y轴上是否存在点P,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4d1d99eab930cef884e01b97d4d56f1.png)
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【推荐2】如图,一条直线经过点A(5,0),B(1,4).
![](https://img.xkw.com/dksih/QBM/2020/5/19/2466195531456512/2466857349808128/STEM/e5e9d902-9a6a-4ea2-a7a4-dce8f34e4fb8.png?resizew=191)
(1)求直线AB的解析式;
(2)若直线
与直线AB相交于点C(3,
),与
轴相交于点D,求
、
的值以及△ACD的面积.
![](https://img.xkw.com/dksih/QBM/2020/5/19/2466195531456512/2466857349808128/STEM/e5e9d902-9a6a-4ea2-a7a4-dce8f34e4fb8.png?resizew=191)
(1)求直线AB的解析式;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bebb3b7f47e0decd48e64cb32aaa5903.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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【推荐1】如图,在
中,
,
,过点C作
交AB于点D,动点P,Q同时出发,点P从点A出发沿AC运动到终点C,速度为每秒5个单位长度,点Q从点B出发沿BC运动到终点C,速度为每秒
个单位长度,连接PQ,过点P作
,
,点E在PQ的下方,设点P的运动时间为
秒.
![](https://img.xkw.com/dksih/QBM/2023/7/29/3291328675790848/3291559246462976/STEM/e2aed6046b724569adde092a9967da3e.png?resizew=276)
(1)
______,
______;
(2)求
的长(用含
的代数式表示);
(3)连接
,若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c07cdfa2304ed56b88d2eded4fdc89f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dab6b7f0d88caf738cc0648a9cbb87ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4056761b8f826eeb6ad8c9a151d3c9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd4db790b5abe169c1551edb1add746.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa4e186c7669178f61dfff97b0ea2559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf4b43b6792b9ae78a1c8cae4e60524.png)
![](https://img.xkw.com/dksih/QBM/2023/7/29/3291328675790848/3291559246462976/STEM/e2aed6046b724569adde092a9967da3e.png?resizew=276)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ec5d678ec42846e1d28301e3bfd4be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ca90e8a784f990c4097eec9219908d.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e430f13f42cf2d44aa0f0e20b959684f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6c6e7c025362c46a64a8956761f08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105068b25f5a63af32f4082cfe08691e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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【推荐2】如图,在
中,
米,
米.M点在线段
上,从C向A运动,速度为1米/秒;同时N点在线段
上,从A向B运动,速度为2米/秒.运动时间为t秒.
(1)当t为何值时,
?
(2)当t为何值时,
的面积最大?并求出这个最大值.
(3)当t为何值时,
与
相似?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c76c6b05c18bdf6f74e69697daf0df5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd0763b031b7e6b6d87ce3554ac482d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/30/c1fbbe40-f1b1-4ee7-a163-9a63729f03d7.png?resizew=246)
(1)当t为何值时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c48401a9609dc72f87f59a53ade4671d.png)
(2)当t为何值时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
(3)当t为何值时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
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