1. Right Triangle PQR is to be constructed in the xy plane so that the right angle is at P and PR is parallel to the x-axis. The x-and y- coordinates of P,Q, and R to be integers that satisfy the inequality -4<=x<=5 and 6<=y<=16. How many different triangles with these properties could be constructed?
answer: 9900
2. If n is a positive integer less than 200 and (14n)/60 is an integer, then n has how many different positive prime factors?
answer: 3 (除了一个一个算,还有什么简单快速的方法吗?)
再请教,做数学时,一题大约分配多长时间。1分种?2 分钟?
多谢
1,直角三角形PQR,P是直角,PR平行x轴.
P,Q,R的横坐标范围是-4到5的整数,也就是有10种选择.纵坐标范围是6到16的整数,有11种选择.
P的坐标选择有10*11种选择.
当P的横纵坐标确定以后,R的纵坐标和Q的横坐标也相继确定.(根据直角和平行的关系).R的横坐标还有还有9种选择,Q的纵坐标还有10种选择.
总共就是10*11*9*10=9900了.
这道是以几何的方式考组合.
2.通过(14n)/60是整数可以看出,n至少有2,3,5这三个质因数.
如果有一个更大的质因数存在,比如7,那么n至少是2*3*5*7=210>200了.所以不可能.
那么n就只有三个质因数.
欢迎光临 国际顶尖MBA申请交流平台--TOPWAY MBA (http://forum.topway.org/) | Powered by Discuz! 7.2 |