数学弱。。请教几道数学题~

qiongyue0312

1. If the sequence X1,X2,X3,Xm...is such that X1=3 and X(n+1)=2Xn -1 for n=1,then X20-X19=?

A 2^19

B 2^20

C 2^21

D 2^20-1

E 2^21-1

2. A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly. Measurements on the R-scale of 6 and 24 correspond to the measurements on the S-scale of 30 and 60, respectively. What measurement on the R-scale corresponds to a measurement of 100 on the S-scale?(看不懂题)

A 20

B 36

C 48

D 60

E 84

3. If a code word is defined to be a sequence of different letters chosen from the 10 letters A,B,C,D,E,F,G,H,I, and J, what is the ratio of the number of 5-letter code words to the number of 4-letter code words?

A 5 to 4

B 3 to 2

C 2 to 1

D 5 to 1

E 6 to 1

answer: 1a2c3e

sqsouare

1、如果论证过程复杂，想不出来，带入前几个数推理即可，x2-x1=2^1,x3-x2=2^2,x4-x3=2^3,……,x20-x19=2^19。

2、关键是R和S线性关系，则设S=aR+b,带入已知条件求得a=5/3,b=20,则S=100时R=48。

3、实际上为无重复的排列问题。所问的比例即P10:5/P10:4。

qiongyue0312

谢谢。呵呵，说得很清楚。懂了~

还有一道题：

This year Henry will save a certain amount of his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he saves this year, he will have 1+r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year?

答案是：1/(2r+3)

sqsouare

设今年总的收入是X，用于存钱的百分比为Y（即问题所问的Fraction）。

则根据题目所给信息列出方程：XY（1+r）（用于明年花的钱）=X(1-Y)/2(今年花的钱），求得Y即得答案。

sqsouare

说得有点失误，应该设Fraction为Y（分数表示），不应该说“百分比”。

qiongyue0312

谢谢sqsouare！一讲就懂了，可自己做就没有思路。~