数学Paper 1讨论专区

Allmaths

回复 1202# Lov瑜瑜4ever


经过peaceboy的解释...我终于明白了....给那个题目炸到...
Leo has RM60. With the amount of money, he can buy 25 more Type B pens than Type A pens. If a Type A pen is RM0.20 more expensive than a Type B pen, what are the prices of the Type A pen and the Type B pen respectively?



Let X= quantity pen Type A that can be bought
     B= Price of pen Type B


(25+X)B=60   -------------eq 1
X(B+0.2)=60  -------------eq 2


From eq 2, X=60/(B+0.2)  ---------------eq 3


Sub eq 3 into eq 1,
[25+60/(B+0.2)]B=60
25B+[60B/(B+0.2)]=60
25B(B+0.2)+60B=60(B+0.2)
25B^2+5B+60B=60B+12
25B^2+5B-12=0
(B-0.6)(B+0.8)=0


B=0.60   or   B=-0.80(Rejected)


Price of pen Type B = RM0.60
Then price of pen Type A = RM0.80

walrein_lim88

回复  Lov瑜瑜4ever


经过peaceboy的解释...我终于明白了....给那个题目炸到...
Leo has RM60. With  ...
Allmaths 发表于 15-6-2010 11:22 PM

    haha...厉害

Allmaths

回复 1207# walrein_lim88


是不是很炸到？

Lov瑜瑜4ever

回复  Lov瑜瑜4ever


经过peaceboy的解释...我终于明白了....给那个题目炸到...
Leo has RM60. With  ...
Allmaths 发表于 15-6-2010 11:22 PM

真的是炸到了咯
这种题目之前还真的是没看过><
现在学到了
哈哈

JianWen

solve the simultaneous equations

   a log 4 _128 - b log8_2 = 6
   log2_a + 1/3 log2_(b^3) = 2 log4_6


ans: a=2,b=3

yingchin

帮忙下。谢谢
surd75 + 3/surd27

HanQing

帮忙下。谢谢
surd75 + 3/surd27
yingchin 发表于 16-6-2010 01:01 PM

是simplify 吗?
√75 +3 √27
=  (√25 x √5) + (3 x √9 x √3)
=5√5+ 9√3

Lov瑜瑜4ever

solve the simultaneous equations

   a log 4 _128 - b log8_2 = 6
   log2_a + 1/3 log2_(b^3) = 2 l ...
JianWen 发表于 16-6-2010 12:51 PM

这题应该不难吧
给你个暗示
log(a^y)_(b^x)=(x/y)(loga_b)

HanQing

solve the simultaneous equations

   a log 4 _128 - b log8_2 = 6
   log2_a + 1/3 log2_(b^3) = 2 l ...
JianWen 发表于 16-6-2010 12:51 PM

After simplifying  a log 4 _128 - b log8_2 = 6
you will get (7/2)a- b/3=6-----(1)

After simplifying  log2_a + 1/3 log2_(b^3) = 2 log4_6
you will get ab=6------(2)
b = 6/a-----(2)'

substituting (2)' into (1)

(7/2)a-(6/a)(1/3) = 6
(7/2)a - 2/a = 6
7a^2-4 = 12a
7a^2 - 12a -4 = 0
(7a  + 2)( a  -  2) =0
a = 2  ( a=-2/7 is rejected as a >0 )

substituting a =2 into (2) b = 3

dcyeo

to Lov瑜瑜4ever

it must be calculated in the condition buying the pens separately with rm 60
because the question state"With the amount of money, he can buy 25 more Type B pens than Type A pens."
the answer which is given by allmaths is true.

If the question didnt have "can"
thet means he are buying the both types of pens in a time with rm 60.
let say he used up rm 60 to buy the pens,
then the solution is

sorry cant reply in same time because pc got problems

dcyeo

Let amount of pen A=x
amount of pen B=x+25
price of A=0.20+y , price of B=y

(x+25)(y)+(a)(0.20+y)=60
2xy+0.2x+25y=60----eq1

from basic statement we know that,
if pens A with amount of x discount by rm0.20,
the amount of pens with cost rm y will increase by 25. so:

25y=0.2x
x=25y/0.2
x=125y-----eq2

subs eq2 into eq1,
250y^2+50y-60=0
25y^2+5y-6=0
y=0.40 or y=-0.60 (rejected)

then pen A=rm 0.60, B=rm 0.40

Lov瑜瑜4ever

to Lov瑜瑜4ever

it must be calculated in the condition buying the pens separately with rm 60
be ...
dcyeo 发表于 16-6-2010 01:51 PM

我已经说过很多次了
allmath的那个答案是对的(for 分开来买)
可是我的解释也没错吖(for 一起买)><

dcyeo

我已经说过很多次了
allmath的那个答案是对的(for 分开来买)
可是我的解释也没错吖(for 一起买)>
Lov瑜瑜4ever 发表于 16-6-2010 01:59 PM

i mean exactly used up rm 60

qwer0909

given that I(W)=RE(1/W)=1/2.find the complex number W in the form of a+bi.
I=imaginary part, RE=real part
这题怎样做呢?

Lov瑜瑜4ever

i mean exactly used up rm 60
dcyeo 发表于 16-6-2010 08:48 PM

对呀
我的eqn不是exact用完RM60吗？？？
要不然用了多少？你说。。。

Lov瑜瑜4ever

given that I(W)=RE(1/W)=1/2.find the complex number W in the form of a+bi.
I=imaginary part, RE=rea ...
qwer0909 发表于 16-6-2010 10:20 PM

Let w=a+bi
1/w=1/(a+bi)=(a-bi)/(a^2+b^2)=[a/(a^2+b^2)-bi/(a^2+b^2)]
so, I(w)=b=1/2
     Re(1/w)=a/(a^2+b^2)=1/2-----eqn 1

from eqn 1, a/(a^2+1/4)=1/2 when b=1/2
                 a^2+1/4=2a
                 4a^2-8a+1=0
                 b^2-4ac=(48)^1/2=4(3)^1/2
       Hence, a=[8+4(3)^1/2]/8        or          a=[8-4(3)^1/2]/8
                   =[2+(3)^1/2]/4                        =[2-(3)^1/2]/4

so, w=[2+(3)^1/2]/4+1/2(i) or w=[2-(3)^1/2]/4+1/2(i)

不懂对不对><

dcyeo

对呀
我的eqn不是exact用完RM60吗？？？
要不然用了多少？你说。。。
Lov瑜瑜4ever 发表于 16-6-2010 10:40 PM

do you know what is the meaning of " exactly used up" ?
that means dont have any remainder or change you will get back.
understand what i mean?

Lov瑜瑜4ever

do you know what is the meaning of " exactly used up" ?
that means dont have any remainder or cha ...
dcyeo 发表于 17-6-2010 02:07 PM

我明白你在说什么
我的也是没有remainder啊
只是我没用分数来表示答案
我有round off小数点

好像你在pasar malam买3件10块的衣服
一件衣服多少钱呢？
RM3.33333333333333333333333333333333333333333
以分数表示就是RM3 1/3
可是你3件一起买
还是exactly used up 10块钱不是吗？
因为你是用3xRM3 1/3=RM10
而不是RM3.33333333333333333333333333333333333333333x3=RM9.999999999999999999999999999999999
你也不可能给老板RM9.999999999999999999999999999999999999999
还是要给RM10不是吗？

我的eqn只是没有以分数来表示答案
如果用分数来标示的话
那么RM60块就可以exactly used up了
你没必要抓这些pasar malam出现的东西吧><

结论：
我这个eqn并不是要表达你要知道的东西
而是要说一起买的话
会很多个答案(很多个价钱)
就犹如Walrein_Lim的结论~

海涵

这题怎么做?
If (x+iy)^2 = i , find all the real values of x and y.

Lov瑜瑜4ever

这题怎么做?
If (x+iy)^2 = i , find all the real values of x and y.
海涵 发表于 19-6-2010 01:54 PM

expand那个eqn
(x+iy)^2=x^2-y^2+2ixy
so x^2-y^2+2ixy=i=0+i
compare,
x^2-y^2=0
       x^2=y^2
           x=y

2ixy=i
2xy=1
2x^2=1,when y=x
  x^2=1/2
      x=[(2)^1/2]/2 or x=-[(2)^1/2]/2
and y=[(2)^1/2]/2 or y=-[(2)^1/2]/2 ,as y=x

不懂答案对不对