[求助]PP3的4道题(2天就考了,拜托了!谢谢!)

深谷幽兰

1. Which of the following inequlities has a solusion set that when graphed on the number line, is a single segment of finite length?
a. x^4>=1
b. x^3<=27
c. x^2>=16
d. 2<=I1I<=5
e. 2<=3x+4<=6
ANS: E
我觉得BCDE都可以呀, 都是有限的.

2.IF r and s are intergers and rs+s is odd, which of the following must be even?
a.r
b.s
c, r+s
d. rs-r
e. r^2+s
ANA: C
RS+S 是偶数, 则RS和S必须都是偶数=> S是偶数或R是偶数或都是ODD. => R+S不一定是偶数呀?

3. IF the operation is defined for all integers a and b by a@b=a+b-ab, which of the following statement must be true for all a, b,c,
ANS: (A@B)@C=A@(B@C)
不明白这是如何得来的?

4.a certain library accesses fines for overdue books as follows. on the first day that book is overdued, the total fine is $0.1, for each additional day that the book is overdue, the total fine is either increased by $0.30 or doubled,whichever results in the lesser amount. What is the total fine for a book on the fourth day it is overdue?
ANS: $0.7
我算了半天都是0.6.

还有两天考了, 那位帮忙回答一下.谢谢!

scujean

1. Which of the following inequlities has a solusion set that when graphed on the number line, is a single segment of finite length?
a. x^4>=1
b. x^3<=27
c. x^2>=16
d. 2<=I1I<=5
e. 2<=3x+4<=6
ANS: E
我觉得BCDE都可以呀, 都是有限的.

   a. x^4>=1 →(x^4-1)>=0→(x^2-1)(x^2+1)>=0→(x+1)(x-1) (x^2+1)>=0

→因为(x^2+1)>0，所以(x+1)(x-1)>=0→x<-1,x>1

b. x^3<=27→(x^3-3^3)<=0→(x-3)(X^2+3x+3^2)<=0→用判别式d=b^2-4ac→得知(X^2+3x+3^2)没有实根，但(X^2+3x+3^2)=[(x+3/2)^2+27/4]>0→所以(x-3)<=0→x<=3

c. x^2>=16→[x^2-4^2]>=0→(x-4)(x+4)>=0→x>4,x<-4

d. 2<=I1I<=5--- 2<=I1I，2小于觉对值1，是否抄错？

深谷幽兰

d. 2<=I1I<=5--- 2<=I1I，2小于觉对值1，是否抄错？

谢谢. 是2<=IXI<=5

深谷幽兰

b.
x^3<=27→(x^3-3^3)<=0→(x-3)(X^2+3x+3^2)<=0→用判别式d=b^2-4ac→得知(X^2+
3x+3^2)没有实根，但(X^2+3x+3^2)=[(x+3/2)^2+27/4]>0→所以(x-3)<=0→x<=3

问题是X应该在-3<=X<=3呀?考试时什么时候需要象你这样分解什么时候就直接看呢?谢谢.

scujean

4.a certain library accesses fines for overdue books as follows. on the first day that book is overdued, the total fine is $0.1, for each additional day that the book is overdue, the total fine is either increased by $0.30 or doubled,whichever results in the lesser amount. What is the total fine for a book on the fourth day it is overdue?
ANS: $0.7
我算了半天都是0.6.

那么第一天是0.1，第二、第三天显然是double比较合算，到第四天是+$0.3合算，也就是这样的一个罚款变化，0.1->0.2->0.4->0.7

scujean

以下是引用深谷幽兰在2006-4-23 13:11:00的发言：

b.
x^3<=27→(x^3-3^3)<=0→(x-3)(X^2+3x+3^2)<=0→用判别式d=b^2-4ac→得知(X^2+
3x+3^2)没有实根，但(X^2+3x+3^2)=[(x+3/2)^2+27/4]>0→所以(x-3)<=0→x<=3

问题是X应该在-3<=X<=3呀?考试时什么时候需要象你这样分解什么时候就直接看呢?谢谢.

你的想法应是→觉对值X<a→-a<x<a

这种的，我只会这样算，无法贪快..看看其他人有没其他办法..

2<=IXI<=5

用数字想，要分成x>0或X<0讨论

当x>0，把X想成3→2<=X(=3) <=5

X<0→X想成-3→X(=-3) <-2

3. IF the operation is defined for all integers a and b by a@b=a+b-ab, which of the following statement must be true for all a, b,c,
ANS: (A@B)@C=A@(B@C)
不明白这是如何得来的?

a@b=a+b-ab

其运算为前+后-前*后

(A@B)@C=A@(B@C)

(a@b)=a+b-ab

(a@b)@c=(a+b-ab)+c-(a+b-ab)*c---1式

(b@c)=b+c-bc

a@(b@c)=a+(b+c-bc)-a*(b+c-bc)----2式

1式=2式

[此贴子已经被作者于2006-4-23 13:48:36编辑过]

深谷幽兰

非常感谢!

salvador

2.IF r and s are intergers and rs+s is odd, which of the following must be even?
a.r
b.s
c, r+s
d. rs-r
e. r^2+s
ANA: C
RS+S 是偶数, 则RS和S必须都是偶数=> S是偶数或R是偶数或都是ODD. => R+S不一定是偶数呀?

lz，题目说RS+S 是奇数，是敲错了还是看错了？

深谷幽兰

2.IF r and s are intergers and rs+s is odd, which of the following must be even?
a.r
b.s
c, r+s
d. rs-r
e. r^2+s
ANA: C
RS+S 是偶数, 则RS和S必须都是偶数=> S是偶数或R是偶数或都是ODD. => R+S不一定是偶数呀?

lz，题目说RS+S 是奇数，是敲错了还是看错了？

.

没错, 我看了半天

深谷幽兰

.IF r and s are intergers and rs+s is odd, which of the following must be even?
a.r
b.s
c, r+s
d. rs-r
e. r^2+s
ANA: C
RS+S 是偶数, 则RS和S必须都是偶数=> S是偶数或R是偶数或都是ODD. => R+S不一定是偶数呀?

lz，题目说RS+S 是奇数，是敲错了还是看错了？

.

明白了. 看的时候把RS+S看成了EVEN.如果是奇数就好做了. 做题真是要仔细呀!