一个四位正整数
满足百位上的数字比千位上的数字小5.个位上的数字比十位上的数字小5,则称
为“队伍数”,将“队伍数”
的千位和十位数字组成的两位数与百位和个位数字组成的两位数的和记为
,将“队伍数”
的千位和百位数字组成的两位数与十位和个位数字组成的两位数的差记为
.
例如:四位正整数
,∵
,
,∴
是“队伍数”,此时,
,
.
(1)判断:8361,5322是否是“队伍数”,并说明理由,如果是,求
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17b0d3d00ada7d3f06452d16bc97eabe.png)
(2)若A是“队伍数”,且满足
是一个正整数的平方,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e01f11f9361a48ad480e079a2216354c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17b0d3d00ada7d3f06452d16bc97eabe.png)
例如:四位正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821ccaf9e755dc9ee988ad41fa1a71b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89976415fc4ceab880632a5f6703fadb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/064b57fb422e5cb6e12a8dc0c7610dea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821ccaf9e755dc9ee988ad41fa1a71b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e840c7d93b329706d0e4063055f5b6cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/097d1025cdf15737705ecf977d3d3b8f.png)
(1)判断:8361,5322是否是“队伍数”,并说明理由,如果是,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e01f11f9361a48ad480e079a2216354c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17b0d3d00ada7d3f06452d16bc97eabe.png)
(2)若A是“队伍数”,且满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a7a23f29cb63ee49769ffd16b93e74d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e01f11f9361a48ad480e079a2216354c.png)
更新时间:2022-11-22 13:07:46
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【推荐1】定义:若分式M与分式N的和等于它们的积,即
,则称分式M与分式N互为“关联分式”.如
与
,因为
,所以
与
互为“关联分式”,其中一个分式是另外一个分式的“关联分式”.
(1)试说明分式
与分式
互为“关联分式”;
(2)若分式
是分式
的“关联分式”,
,求分式
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa89218855dabf0c50047f80cce5338.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6fef2ef5023639ab69d2f109ce7868.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6fef2ef5023639ab69d2f109ce7868.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bbd4ca146e35e8e8c68fcfc674b5aba.png)
(1)试说明分式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45465ed1443900739ab5ffd9947965c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d63bba4f970e4668a49ae2da47af6c01.png)
(2)若分式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e98d981663460ffd504a9fc9dd6f47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2daf8685a27af3c225a71e86b98d98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eae9ba258299eb489b490594397e23c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11026ff13d31cad5f4d053e82931690f.png)
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【推荐2】对于一个三位自然数;各数位上的数字互不相等且均不为0;若百位数字与个位数字的和与1的差等于十位数字;则称这个三位自然数为“和差一数”;若百位数字与个位数字和的两倍与1的差等于十位数字;则称这个三位自然数为“倍差一数”.例如:自然数463;满足各数位数字互不相等且均不为0;且
;所以463是“和差一数”;自然数392;满足各数位数字互不相等且均不为0;且
;所以392是“倍差一数”.
(1)请写出最小的“和差一数”为______;最大的“倍差一数”为______;
(2)若“和差一数”s的百位数字为3;“倍差一数”t的个位数字为1;且
能被7整除;请求出满足条件的s.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f97c63ed0cd50f859a8e8e07bf2de107.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfeb8f92c266cc75324400d76af17df5.png)
(1)请写出最小的“和差一数”为______;最大的“倍差一数”为______;
(2)若“和差一数”s的百位数字为3;“倍差一数”t的个位数字为1;且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd300aec74c91ac86e43265abacc49ad.png)
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【推荐1】将5张相同的小长方形纸片(如图1所示)按图2所示的方式不重叠的放在长方形
内,未被覆盖的部分恰好被分割为两个长方形,面积分别为
和
已知小长方形纸片的长为a,宽为b,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/5943fddc-7a89-468a-8dc2-3ffa6387cc05.png?resizew=251)
(1)当
时,长方形
的面积是 ,
的值为 ;
(2)当
时,请用含a、b的式子表示
的值;
(3)若
长度为定值,
的长度不确定,将这5张小长方形纸片还按照同样的方式放在新的长方形
内.当
的长度改变时(
),
的值总保持不变,则a、b 满足的什么关系?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/5943fddc-7a89-468a-8dc2-3ffa6387cc05.png?resizew=251)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4a17ec9398bf1291533c1e24d3c9c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a38c43d922840f5f7693007beeb62b34.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b03bb56c7e76954b192bd8595a0865a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a38c43d922840f5f7693007beeb62b34.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ab5d9cbc71de38d53e4e1abe988389f.png)
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【推荐2】某种圆珠笔的售价是每支2元,甲、乙两家文具店均有促销活动:甲文具店全部九折,乙文具店20支及以下不打折,超过20支的部分打八折.设小明需要购买的圆珠笔的数量为x,根据题意回答下列问题:
(1)若购买超过20支的圆珠笔,则在甲文具店需要花费 元,在乙文具店需要花费 元.(用含x的代数式表示)
(2)当x=25时,选择哪家文具店更优惠?当x=50呢?
(3)随着x的变化,试说明选择哪家文具店更优惠.
(1)若购买超过20支的圆珠笔,则在甲文具店需要花费 元,在乙文具店需要花费 元.(用含x的代数式表示)
(2)当x=25时,选择哪家文具店更优惠?当x=50呢?
(3)随着x的变化,试说明选择哪家文具店更优惠.
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【推荐3】阅读下面的材料:如图1,如果线段
在数轴上,
,
点所表示的数分别为
,
(
),则线段
的长(点
到点
的距离)可表示为
.
请用上面材料中的知识解答下面的问题:
如图2,1个单位长度表示
,一个点从数轴上的原点开始,先向左移动
到达
点,再向左移动
到达
点,然后向右移动
到达
点.
(1)请直接写出
、
、
三点表示的数,并求出线段
的长度;
(2)若数轴上有一点
,且
,则点
表示的数是什么?
(3)若点
以每秒
的速度向左移动至点
,同时点A,点C分别以每秒
和
的速度向右移动至点
,点
,,设移动时间为t秒,求:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.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/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3b4c102ae0e48d1a26964c466461800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/7819f6e7447bbe91baac7eb439940d72.png)
请用上面材料中的知识解答下面的问题:
如图2,1个单位长度表示
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9568e24f4e1f3efea3b74066cc8b508d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9568e24f4e1f3efea3b74066cc8b508d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5992036c739557714bc05e08a93bdd3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c30220a034d64f889eaf8931735176dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/22/4e9a5ed6-547d-4a3a-994d-21d8a13feefa.png?resizew=574)
(1)请直接写出
![](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/e1a9c6a736e6eac98a676fa3232db5a5.png)
(2)若数轴上有一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43312c559441f02b4ba51d248e85def.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5992036c739557714bc05e08a93bdd3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9568e24f4e1f3efea3b74066cc8b508d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce781fcab3b08eb3baafbca4a01bb8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6dddf9d2cd95ea148d36206330338a5.png)
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