求助大家，帮我分析下这两个数学上的比较的含义吧～

aimeedoudou · 发表于 2011-4-29 09:02:57

og12上两道数学题目跟比较有关，我就懵啦～大家帮我看看第39题：
有图我画不出来，但是题目大意是有个点（假设A），the point A on segment PQ that is twice as far from P as from Q is?? 问A的位置。
我想知道这里A在PQ上的比例是多少？我自己理解的是2PA＝AQ，答案也是这样的。

但是当我看到第52题时
In a certain population, there are 3 times as many people aged 21 or under as there are people over 21, the ratio of those 21 or under to the total population is????

我以为还是 3倍的21岁以下的＝21岁以上的。所以ratio不应该是 1：4？？？但是答案是3：4

我的疑惑是这两个比较表达方式有什么不一样么？还是我对题目理解错了？

aimeedoudou · 发表于 2011-4-29 09:21:36

顶一下～大家帮我看看呗～

aimeedoudou · 发表于 2011-4-29 21:22:37

再顶一下，请大家帮帮我啊

红红的云 · 发表于 2011-4-30 04:05:30

第一题和第二题是一样的意思。你double check 第一题的理解

twice as far/long/many+x as y

means 2x=y

the point A on segment PQ that is twice as far from P as from Q is?

2ap=aq

The point on segment PQ that is twice as far from P as from Q is: Q=(3,2)

=(0,-1)
A) (3,1)
B) (2,1)
C) (2, -1)
D) (1.5, 0.5)
E) (1,0)

the point A on segment PQ that is twice as far from P as from Q is?

if any point O(x,y) divides distance between two point A(x1,y1) and B(x2,y2) in the ratio m1:m2
co ordinates of the point O is

x=(m1x2+m2x1)/(m1+m2) and y=(m1y2+m2y1)/(m1+m2)

here A(x1,y1)=P(0,-1) ..B(x2,y2)=Q(3,2) and m1:m2=2:1

so the coordinate of the point on segment PQ that is twice as far from P as from Q is
x=(2*3+0*1)/3=2 y=(2*2+(-1)*1)/3 =1
or(2,1)

aimeedoudou · 发表于 2011-4-30 07:49:41

第一题和第二题是一样的意思。你double check 第一题的理解

twice as far/long/many+x as y

means 2x=y

the point A on segment PQ that is twice as far from P as from Q is?

2ap=aq

The point on segment PQ that is twice as far from P as from Q is: Q=(3,2)

=(0,-1)
A) (3,1)
B) (2,1)
C) (2, -1)
D) (1.5, 0.5)
E) (1,0)

the point A on segment PQ that is twice as far from P as from Q is?

if any point O(x,y) divides distance between two point A(x1,y1) and B(x2,y2) in the ratio m1:m2
co ordinates of the point O is

x=(m1x2+m2x1)/(m1+m2) and y=(m1y2+m2y1)/(m1+m2)

here A(x1,y1)=P(0,-1) ..B(x2,y2)=Q(3,2) and m1:m2=2:1

so the coordinate of the point on segment PQ that is twice as far from P as from Q is
x=(2*3+0*1)/3=2 y=(2*2+(-1)*1)/3 =1
or(2,1)

-- by 会员红红的云 (2011/4/30 4:05:30)

太谢谢你啦
我上面写错了一个地方应该是2AP＝AQ

但是我不太理解你后面给出的这个式子～那个m1：m2不应该是1：2？应该是点O到Q的距离是点O到P的两倍啊？所以O的坐标不应该是（1，0）？？不懂啦不懂啦
还有我上面的第2题（那个按年龄分人群）那个不是跟第一题说法一样么，为什么结果不是我理解的那样呢？
拜托你再帮我看看好不好？特别特别感谢

红红的云 · 发表于 2011-5-2 12:30:41

网上查一查线段定点分点的理论。

红红的云 · 发表于 2011-5-2 12:33:12

问题不是出在你对句子的理解上，可能是你解此题的方法有误。网上查一查线段定点分点的理论。

lesezeichen · 发表于 2011-5-2 13:29:11

你分明是看错了，显然AP=2AQ，两道题的表达方式是一样的，意思也完全一样。

X is twice（3 times。。。）as adj as Y, or twice ( 3 times...) as adj X as Y, 均表示X是Y的倍数。

所以第二题，21以下是21以上的三倍，21以下：总人数=3:4

求助大家，帮我分析下这两个数学上的比较的含义吧～

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