请教几道数学题

stephie

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 are to be integers that satisfy the inequalities -4〈=X〈=5 and 6<=y<=16. How many different traingles with these properties could be constructed?


2, A square countertop has a square tile inlay in the center, leaving an untiled strip of uniform width around the tile.If the ratio of the tiled are to the untiled area is 25 to 39, which     of the following could be the width , in inches ,of the strip?


I. 3/2;     II.3;     III. 9/2.

3、n=ABCD(A-D均大于1的质数)，问n除了1之外有几个因子？

4，N是一个正整数，且N^2可以让72整除，问可以给N整除的最大正整数是多少？

为什么是12呢？

    

可以说说上面的题的思路吗？特别是3和4那两道题，我每次做涉及因子的题都错。可以请问一下一般的对于这种题的思路吗？

    

pcpcpcpcpc

1. C(11,2)*9*10=4950


2. No sufficient data---no any distance told in inches, so I II III all could be the width.


3. there are a b c d ab ac ad bc bd cd abc abd acd bcd abcd, so total 14


4. because 72=8*9, and N^2 is divisible by 8*9, so N is divisible by 4*3=12

stephie

第一题答案是9900。但是不知道怎么算


可不可以说说第二题什么意思，想不出图形


可不可以说一下第三题的思路呢？我觉得每次做因子题都会错，都用列举法吗？

kokomi

1 p(11,2)*p(10,2) ?


2 读不懂ing...





3 将N写成N=(a1^b1)*(a2^b2)*(a3^b3)*...(an^bn) (1式)的形式,其中a1~an都是不为1的质数N一共有含1和本身在内的 (b1+1)*(b2+1)*...(bn+1)个因子.
对于每一个ai,都有bi+1种取法,(不取,取1个,取2个,...取bi个),根据乘法原理,共有(b1+1)*(b2+1)*...(bn+1)种取法,故共有这些因子


4 N^2=72*a=6^2*2*a,当a=2时可以写成x^2的形式,x=6*a=12

[此贴子已经被作者于2004-2-22 23:15:44编辑过]

pcpcpcpcpc

第一题 P(11,2)*9*10=9900

stephie

第一题为什么这样呢？