tt-2-6与2-17请教

顾风

7两个涛涛二套的数学题目，对答案有不同意见或者本人对题目阅读失败，请大家帮忙看看

Q6:
        

The figure above shows the dimensions of a semicircular cross section of a one-way tunnel.  The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel.  If vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane, what should be the limit on the height of vehicles that are allowed to use the tunnel?

 

 

A.     5½ ft

B.     7½ ft

C.     8 ½ ft

D.     9½ ft

E.      10 ft

Q17:

If a and b are positive, is (a^-1 + b^-1)^-1 less than (a^-1b^-1)^-1?

(1)     a = 2b

(2)     a + b > 1

                  

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

绿色为参考答案，本人选择的答案为灰色

hitlzc

Q6:
The figure above shows the dimensions of a semicircular cross section of a one-way tunnel.  The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel.  If vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane, what should be the limit on the height of vehicles that are allowed to use the tunnel?
 
 
A.     5½ ft
B.     7½ ft
C.     8 ½ ft
D.     9½ ft
E.      10 ft

这道题在GWD13套里有详细的讨论过，不过题号我也记不清了。

你是否能把图从你的文件里COPY过来贴上。

Q17:
If a and b are positive, is (a-1 + b-1)-1 less than (a-1b-1)-1?
(1)     a = 2b
(2)     a + b > 1
                  
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

即1/（1/a+1/b)与ab的比较

1/（1/a+1/b)＝ab/(a+b)

因为a+b>1且a,b为整数，所以ab/(a+b)>ab

littledou

Q17,比较大小一般用减法：

t=1/(1/a+1/b))-1/(1/ab))=ab(1-a-b)/(a+b)

because a, b>0, then ab>0 and a+b>0

so t的正负取决于1-a-b的正负。

Q6，你画个图就出来了。

我试着写个工式看你能不能理解：

(10^2-6^2)^(1/2)-1/2 10的平方减6的平方开根号再减1/2

顾风

哦，17题我明白了，换算的时候出错了。。。少看了一个负号

[此贴子已经被作者于2006-7-5 9:39:56编辑过]

顾风

第6题题目的中文意思是什么？

allen0018

第六题就是个直角三角形的问题

10，6，8 

然后clear the top 1/2

就是b

allen0018

一个隧道直径20

能用的是12

并且均匀分布在两侧

一个车要过去，要离最高点1/2     首先排除 10-1/2

问~~~

顾风

麻烦再说得具体一些。。。。

xjlv128

以下是引用顾风在2006-7-4 13:07:00的发言：

Q6:
  

The figure above shows the dimensions of a semicircular cross section of a one-way tunnel.  The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel.  If vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane, what should be the limit on the height of vehicles that are allowed to use the tunnel?

                               A.     5½ ft

B.     7½ ft

C.     8 ½ ft

D.     9½ ft

E.      10 ft

没看见图啊，有人说直径20是吧？

放在坐标轴里面，圆心在原点，上半圆周的方程是x2+y2=100,y>0.带入x=6,得y=8

但是，y=8得时候，货车的两边上顶角抵着隧道对不对？题目要离隧道顶1/2，所以减掉1/2啊

allen0018

同意