若一个四位正整数m满足前两个数字组成的两位数是后两个数字组成的两位数的2倍,则把这个四位数m称为“Double数”.
例如:2010的前两个数字组成的两位数是:20,后两个数字组成的两位数是:10,
∵
,∴2010是“Double数”;
9246的前两个数字组成的两位数是:92,后两个数字组成的两位数是:46,
∵
,∴9246是“Double数”;
7525的前两个数字组成的两位数是:75,后两个数字组成的两位数是:25,
∵
,∴7525不是“Double数”.
(1)判断7035,3814是否是“Double数”?并说明理由;
(2)记一个“Double数”m各个数位数字之和为
,令
.当
能被8整除时,求出所有符合条件的“Double数”m.
例如:2010的前两个数字组成的两位数是:20,后两个数字组成的两位数是:10,
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eff0216631c3f203699f16afa6ea39d.png)
9246的前两个数字组成的两位数是:92,后两个数字组成的两位数是:46,
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7f04f26434420c3542bc463fff15bbe.png)
7525的前两个数字组成的两位数是:75,后两个数字组成的两位数是:25,
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75e5e830481f3ce128cbdd2746ea8cd9.png)
(1)判断7035,3814是否是“Double数”?并说明理由;
(2)记一个“Double数”m各个数位数字之和为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366de99698b6ffdb68aebc918485f3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a89352986c9fc3f960ce41e7b45ad41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d5408842cf8095d3b0a4e1bef10226.png)
更新时间:2022-04-14 21:37:44
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相似题推荐
解答题-问答题
|
较难
(0.4)
名校
【推荐1】规定:若
是以
为未知数的二元一次方程
的整数解,则称此时点
为二元一次方程
的“理想点”.请回答以下关于
的二元一次方程的相关问题.
(1)已知
,请问哪些点是方程
的“理想点”?哪些点不是方程
的“理想点”?并说明理由;
(2)已知
为非负整数,且
,若
是方程
的“理想点”,求
的平方根;
(3)已知
是正整数,且
是方程
和
的“理想点”,求点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16fe8d6ceb1175bdbf6936ff67fa2990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16fe8d6ceb1175bdbf6936ff67fa2990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce17494e52cc29acb63658db69a5569b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f30e59c3c2a6538f463a78481bd006d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f30e59c3c2a6538f463a78481bd006d8.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/502e0dfa3f0e38017cd23a3d55b84840.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f8437f913a9f6cb98484b83ba08d7ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20b8d3564d7ae5687f69b64b150c4b35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55db12bc9a3b7bd2e6decaaea6ba387e.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ceec4b56e0743426ce72c3fc50c0333.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14ec64732ac023f079acf497571c26e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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【推荐2】一个多位数m(数位大于等于4)的末三位数与末三位数以前的数字所组成的数之差记为
,
如果能被
整除,则这个多位数就一定能被
整除.例如:判断
能不能被
整除,这个数的末三位数字是
,末三位以前的数字所组成的数是
,则
,
能被
整除,因此,
也一定能被
整除.反之,若一个多位数m(数位大于等于4)能被
整除,则m的末三位数与末三位数以前的数字所组成的数之差
一定能被
整除.
(1)
= ,
(能或不能)被
整除.
(2)若两个四位数m,n均为
的倍数,且
,n的千位数字为
,百位数字为5,十位数字为5,个位数字为
.规定
,当
时,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ff8085a11ffdf501fe34cb5616c4ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ff8085a11ffdf501fe34cb5616c4ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5453184e251cfe787b5965cd38426962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5453184e251cfe787b5965cd38426962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afcbb6f6312221078c05ceda4a5fd369.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5453184e251cfe787b5965cd38426962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d34592355573c5de6b0c4ab311956d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cda3540d6125b1522037703329355fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76ccd492d8633849dcff83a787862d1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c696d722e1b4b938c7a956ff83f733bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5453184e251cfe787b5965cd38426962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afcbb6f6312221078c05ceda4a5fd369.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5453184e251cfe787b5965cd38426962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5453184e251cfe787b5965cd38426962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ff8085a11ffdf501fe34cb5616c4ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5453184e251cfe787b5965cd38426962.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a493f06b12065609a9887577ef0db44a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833f2d49e3713fcd4f3352195e9e936b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5453184e251cfe787b5965cd38426962.png)
(2)若两个四位数m,n均为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5453184e251cfe787b5965cd38426962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d8296d04535e20965309b1b593300d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edf6dfee4181b3df1eb44e754df4861a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb3da37c982b8447b530199f28c7cf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73edb643c66fd70b642117a0424e5ada.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d830a61edce928c134b2d4007dd226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e4900f502fd6587bcee8d564ee9f9d2.png)
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(0.4)
【推荐1】我们把以O为圆心,1,2,3,…,n为半径的圆:
,
,
,…,
称为“纬线”,过O的三条“数轴”被点O分成六条射线,分别记:
,
,…,
称为“经线”,“经线”与“纬线”的交点称为“格点”(O为特殊的格点),把所有整数按下图位方式放在格点上(整数0放在“原点”O处).如:把整数1摆放到
与
交点位置,记作:
;又如,格点A表示的数是
,则A点的位置可记作:
或
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/28/f29d767a-ab69-470e-8953-7ed91c0bb8b7.png?resizew=384)
(1)若
,则
______,
______;
(2)已知:格点
、
、
分别在“经线”
、
、
上,并在同一“纬线”
上.
①用含n的代数式表示
、
、
,并计算:
;
②当
时,求
的值;
(3)以格点
、
、
为顶点的三角形我们称为格点三角形(
、
、
不在同一直线上),记作:
,其中
、
、![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
和的绝对值 叫
的“偏心率”,记作:
,
、
、![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
绝对值的和 叫
的“模”,记作:
;(如:以
、
、
为顶点作三角形,则
,
).
问题:在同一“纬线”是否存在三个格点
、
、
,使得“偏心率”
,如果存在,请你直接写出它的“模”
的值,如果不存在,说说你的理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c3871a062c5e0a4e009b01aa47afb48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2a14b56f7f7bb23cd4bf9041e440a46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43801f9d9826f8e3646803c915f70e8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c08273ab77c68b94446e24f0dd75e0cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdf2b5d37fa0f121e01e3c91cee9f5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fb8280885d0fd1a072039e0bbcd15a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833152435f28837221862b09009c0fa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdf2b5d37fa0f121e01e3c91cee9f5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c3871a062c5e0a4e009b01aa47afb48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018733e1242db0f5784d933494b95341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a44986287ed599f86a23cfffe788cc76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ccabd789830dd0ba2982b5c645e7324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a7c24cc4114dcda58942f5f447c87dc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/28/f29d767a-ab69-470e-8953-7ed91c0bb8b7.png?resizew=384)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5714b23172c9d87406d8db389567a822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31463b348f21711420670df9d7d03a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27ff01f54e97b5d85b34907ea1da5754.png)
(2)已知:格点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/254dd51cdedd3bef229e4efdb333c2da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8816c71000b0c376e6c34ccb43d5c267.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b059f002ad8a9cbf421e5ede083737c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b40441a571dc97d09cbb845064de396e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfee45342005b24df08c5a149670d504.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50bae0107d95c2964c862d83a78a7880.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c08273ab77c68b94446e24f0dd75e0cb.png)
①用含n的代数式表示
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ff27a22332acc887dc87b594eb1609.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d84b1e1ebf51da3e62c6e2574462ead.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)以格点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/254dd51cdedd3bef229e4efdb333c2da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8816c71000b0c376e6c34ccb43d5c267.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b059f002ad8a9cbf421e5ede083737c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/bdbb207d0375cb3cbd930649f0b1803c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdbb207d0375cb3cbd930649f0b1803c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74254e49cd586ff0b8e44d0b2ea6655c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdbb207d0375cb3cbd930649f0b1803c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aef93cba794792f95603dcd33baa7d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d2e9a50fbf326f7f9807e50d7304876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e256fd6f56bdb6aee87b7777adb376e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/715dd77318d01affb327bb344277571c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1901b3da38698414a993fbb025b8149e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657263074790d6f1750ac18b3c7e77d6.png)
问题:在同一“纬线”是否存在三个格点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/bce1a0b88197d2f43ee4e4fec77e765f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829c26a52760c048913761e19372052b.png)
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较难
(0.4)
【推荐2】同学们都知道:数轴上表示
与
的两点之间的距离可以表示为
.例如
表示7与
之差的绝对值,实际上也可理解为7与
两数在数轴上所对应的两点之间的距离.请你借助数轴进行以下
探索:
(1)数轴上表示7与
两点之间的距离是______.
(2)若
,则
______.
(3)
表示数轴上有理数
所对应的点到
和3所对应的点的距离之和,请你找出所有符合条件的整数
,使得
,这样的整数是_____.
(4)请你找出所有符合条件的整数
,使得
,这样的整数是_____.
(5)继续探索:
是否有最小值?如果有,直接写出最小值;如果没有,说明理由.
![](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/ef38de6f8993386add9b06e4a2779be1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa23be600b24025f170fe547bd2f1802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/395addb4439331615a7f220289d8b62c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/395addb4439331615a7f220289d8b62c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/25/2bc4a80a-fc84-4b76-9e78-59333b0fb321.png?resizew=371)
探索:
(1)数轴上表示7与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/395addb4439331615a7f220289d8b62c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72bd2967c563c4627572be3b9482cfe1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a4c3d7a70dbe938fcc6df0b55efa59b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29418e5014731850c55565b6bf47aa41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ea5b333a683bcd9527840904a8065e2.png)
(4)请你找出所有符合条件的整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9685f19cc978fe97f9f1e5a7f0234f4d.png)
(5)继续探索:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9832df9d4ea3203d8077cd6f64db871.png)
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