OG11-PS 248不明白

AlphaBeta

这道题不懂什么意思，请大家指教：

248、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 triangles with these properties could be constructed?

C. 9900

elitist

6<=y<=16,y共有11个值可以取，也就是说三角形的一条直角边的两个顶点P和Q的纵坐标取值有11种可能性。C¹₁₁ 

-4<=x<=5,意思是说三角形的一条直角边P和Q取值必须在这个范围内，有P²₁₀种可能性。

而一旦P的坐标固定后，R的横坐标也固定了，而纵坐标有（C¹₁₁ －1）种可能性。

所以答案是 C¹₁₁ x P²₁₀ （C¹₁₁ －1）

AlphaBeta

明白拉，多谢拉。

麻烦看看247（不好意思），就是题干第一句话看不懂也：

p，r，s，t，u。An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant. If th list of numbers shown above is an arithmetic sequence, which of the following must also be an arithmetic sequence?

"OG11解An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant." 释说是r-p=s-r=t-s=u-t=c,不明白,是我阅读这句话有问题?

thanks a lot

meimei5656

An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant.

这句话有什么不懂的？

还记得高中时学过的等差数列罢，上面的那句就说的是等差数列。

each term after the first 是指第一项之后的每项。

我给你把上面的那句翻译成汉语：

一个算术数列是一个这样的数列，第一项之后的每项等于前一项和一个常数的和

AlphaBeta

恍然大悟! 看来对数学术语的阅读还不熟悉阿.还有阿，decimal是专指小数吗，它还有十进制数的意思,那不是还包括整数?真是个菜菜问题,但是做题时确实受了影响的。比如：“the tenths digit in the decimal”是指小数点后面的十分位数，还是整个数（我理解为十进制数）的十位数，那可不一样啊。

再啰嗦一道简单的题目：

OG11-173 the probability is 1/2 that a certain coin will turn up heads on any given toss. if the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?

A 1/8    D 7/8  答案是D， 我一开始选了A。我是这样理解的：一次1/2，三次就是（1/2）的三次方1/8，不就行了？为啥要先考虑heads 的1/8，再1减去1/8？heads和tails的几率是一样的呀？不知道我是不是又钻牛角尖了。

elitist

如果遇到类似这样的问法 “at least one of the ********” ，都是先取非得到一个值，然后用1去减那个值。

例如本题 at least one of the tosses the coin will turn up tails，这里包涵了好多种情况，如果你考虑每种情况，然后加和，那就麻烦了。

先取非，none of the tosses the coin will turn up tails, namely all of the tosses the coin will turn up heads.

(1/2)*(1/2)*(1/2) = 1/8

然后1－1/8 = 7/8