若一个三位正整数满足十位数字大于百位数字,且个位数字等于十位数字与百位数字之和,则称这个数为“和衷共济数”.对于一个“和衷共济数”m,交换其百位和十位得到m',规定
.例如:123:∵2>1,3=2+1,∴123是一个和衷共济数,
=5
(1)判断258、369是否为“和衷共济数”?并说明理由;
(2)若F(m)的值为完全平方数,求出所有满足条件的“和衷共济数”m的值;
(3)若p、q都是“和衷共济数”,其中p=100x+10y+7,q=100+10a+b,F(p)+F(q)=20(1≤x≤3,2≤y≤6,2≤a≤8,3≤b≤9,且x,y,a,b均为整数),求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56eb5cd604f7bcb2e6f0ee169ecbe836.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbdccf10b243b64a8c6d9d302c1bfdc0.png)
(1)判断258、369是否为“和衷共济数”?并说明理由;
(2)若F(m)的值为完全平方数,求出所有满足条件的“和衷共济数”m的值;
(3)若p、q都是“和衷共济数”,其中p=100x+10y+7,q=100+10a+b,F(p)+F(q)=20(1≤x≤3,2≤y≤6,2≤a≤8,3≤b≤9,且x,y,a,b均为整数),求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a507c062709cfe2f218896247461c7d3.png)
更新时间:2021-07-28 10:16:24
|
相似题推荐
解答题-问答题
|
适中
(0.65)
名校
【推荐1】材料阅读:
如果一个四位自然数t的各个数位上的数字均不为0,且满足千位数字与十位数字的和为9,百位数字与个位数字的差为1,那么称t为“九一数”.把t的千位数字的2倍与个位数字的和记为
,百位数字的2倍与十位数字的和记为
,令
,当
为整数时,则称t为“整九一数”.
例如:5544满足:
,
,且
,
,
为整数,∴5544是“整九一数”.
又如,6231满足:
,
,
,
,
但
不为整数,∴6231不是“整九一数”.
(1)判断7221,4352是否是“整九一数”?并说明理由.
(2)若
(其中
,
,
,
且a、b、c、d均为整数)是“整九一数”,求满足条件的所有M的值.
如果一个四位自然数t的各个数位上的数字均不为0,且满足千位数字与十位数字的和为9,百位数字与个位数字的差为1,那么称t为“九一数”.把t的千位数字的2倍与个位数字的和记为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be8f69402300f6ed932697689212e91c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2feeb7462a45a01b9b9530248604063e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf83409b95cb518aa6a3d0a7b3ae8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1cd89cd4ed25371784f1d98d423024e.png)
例如:5544满足:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3859f55fde5ff24cc991093d38be20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45c435cdcff5ed51d9feafb69edbaa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2995c53924221b580f563f137eff932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cacc470ec46de91ba34567b71ff901c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca497710dd18eebbc72038234188c2f1.png)
又如,6231满足:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a78a80bebed22022d0f0026d602b0c31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/859770ecc6617c18ad66e33cc9f394fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8b2d8b0a3b4d7158d444e14268efc99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b305a99497cc9c1d16caaf4ced42608b.png)
但
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66df55a3128495cc4312ddce7da74451.png)
(1)判断7221,4352是否是“整九一数”?并说明理由.
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a20633111dc5d2285fa8c64b631ff04f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f9560f8f90d4addcf5fb6fdcc7956.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c9683c0a95aaeda96c5793b0f695d54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eef44496baeec23250f8bd229bae41de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669b9a32dbbf8810c5e9e69f28bac4d3.png)
您最近一年使用:0次
解答题-计算题
|
适中
(0.65)
【推荐2】对于有理数,定义一种新运算“
”,请仔细观察下列各式中的运算规律:1
2=
=2,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81591df917433675d91edcb677d40efe.png)
回答下列问题:
(1)计算:
=_____;
=_____.
(2)若a≠b,则
_____
(填入“
”或“
” ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
(3)若有理数a,b的取值范围在数轴上的对应点如图所示,且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3c2f679d53b91088ba6eb14c16cbc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3c2f679d53b91088ba6eb14c16cbc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f57095c078914f7e2d55fb1c9d166a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5dad7a623e378fac59df3061963855.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81591df917433675d91edcb677d40efe.png)
回答下列问题:
(1)计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df01c4658317555bef3c150523840cc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e98a5da968a8cb5789b3297c128217b9.png)
(2)若a≠b,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab9026bb4fbd8d090fc306e645442f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e9c6faf6d6311ecf38343a1dd383f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6706fe00b4e231e62d9ecbec567d526b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411837b4b3078d05b43cb0439259a362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
(3)若有理数a,b的取值范围在数轴上的对应点如图所示,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98c786e84403f922200645dd1411964e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1638b24b96dd000527cd10ae1cb62a8.png)
![](https://img.xkw.com/dksih/QBM/2019/11/13/2332897020583936/2333541150965760/STEM/475774ebb36b44f68f3a8936343e22a6.png?resizew=176)
您最近一年使用:0次
解答题-应用题
|
适中
(0.65)
【推荐1】将
克糖放入一杯水中,得到
克糖水(
).
(1)糖水的浓度为_____________;
A.
B.
C.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6ce02259a85ea191541f4a708738f1.png)
(2)再往杯中加入
克糖,生活经验告诉我们糖水更甜了,用不等式表示加糖前后的浓度关系为_________;
(3)请证明(2)中的不等式成立.
![](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/2d100c22435a23e017cfe6f535379d3c.png)
(1)糖水的浓度为_____________;
A.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd09f80733a8c98bd8c51905d15fe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2122e3f1e76a635e58e4d54aa594c552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6ce02259a85ea191541f4a708738f1.png)
(2)再往杯中加入
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f93a232c88870d213a7b74a796a1ff4b.png)
(3)请证明(2)中的不等式成立.
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
【推荐2】小杰到学校食堂买饭,看到A,B两窗口前面排队的人一样多(设为a人,
),就站在A窗口队伍的后面,过了2分钟,他发现A窗口每分钟有4人买了饭离开队伍,B窗口每分钟有6人买了饭离开队伍,且B窗口队伍后面每分钟增加5人
(2)此时,若小杰迅速从A窗口队伍转移到B窗口后面重新排队,且到达B窗口所花的时间比继续在A窗口排队到达A窗口所花的时间少,求a的取值范围.(不考虑其它因素)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23fa9f8f1c71437a141ed0eef8d1a8bc.png)
(2)此时,若小杰迅速从A窗口队伍转移到B窗口后面重新排队,且到达B窗口所花的时间比继续在A窗口排队到达A窗口所花的时间少,求a的取值范围.(不考虑其它因素)
您最近一年使用:0次