数学Paper 1讨论专区

peaceboy

divides externally new things ma..If got ratio like -2:3 how ar???
vick5821 发表于 3-8-2010 08:14 PM

    没看过ratio有negative 的...

vick5821

really no de ??

peaceboy

really no de ??
vick5821 发表于 3-8-2010 08:18 PM

    我长这么大都没看过

vick5821

A square ABCD with A(0,-2) and C (5,1). AC is the diagonal of the square. Find the coordinates of B and D...

peaceboy

A square ABCD with A(0,-2) and C (5,1). AC is the diagonal of the square. Find the coordinates of B  ...
vick5821 发表于 3-8-2010 09:36 PM

D________________ C (5,1)
l                          l
l                          l
l                          l
l                          l
l                          l
l_______________ l
A(0,-2)                  B


然后我们知道D的x和A一样，B的x和C一样
还有D的y和C一样，B的y和A一样

所以D (0,1) , B (5,-2)

题目不是很美...

vick5821

the diagram is not like that?? is like senget de square

peaceboy

回复 1486# vick5821


    assume B = (x,y ) and D = ( a,b )

distance of AB = distance of BC ,
(y+2)^2 + (x-0)^2 = (y-1)^2 + (x-5)^2
y^2+4y+4+x^2 = y^2 -2y +1 +x^2 -10x +25
6y + 10x - 22 = 0
3y+5x-11=0

y = (11-5x)/3-----------1

mid pnt of AC = BD

(x+a)/2 = (5+0)/2
a=(5-x)  ----2

(y+b)/2 = (1-2)/2
b=(-1-y) -------3

distance of AC = distance of BD ,

(y-b)^2+(x-a)^2 = (1+2)^2 + (5+0)^2
y^2 - 2by + b^2 + x^2 - 2ax + a^2 = 34

sub 2 and 3

y^2 - 2(-1-y)y + (-1-y)^2 + x^2 - 2(5-x)x + (5-x)^2 = 34
y^2 +2y +2y^2 +y^2 +2y+1 +x^2 -10x+2x^2 +25 - 10x +x^2 =34
4y^2 + 4y + 4x^2- 20x - 8 =0
y^2 +y +x^2 -5x -2 =0
sub 1 into this equa
[(11-5x)/3]^2 +[(11-5x)/3]+x^2 -5x -2 =0
(121 -110x +25x^2) /9 +(11-5x)/3 + x^2 -5x -2 =0
34x^2 / 9 - 170x/9  +136/9 =0
34x^2 - 170x  + 136 =0
x=4, 1
y=(11-5x)/3
y=-3, 2

所以B = (4,-3)
D = (1,2)

长到....

之前不小心加减弄错

vick5821

I dun think the answer will have decimal leh

peaceboy

I dun think the answer will have decimal leh
vick5821 发表于 3-8-2010 11:35 PM

    修改了

vick5821

get the 2 value d straight know the coordinates of two points?? I thought we are finding for B first?? Get a quadratic, then solve, the get 2 values of x, then  one is for B one is for D ar?? why??

peaceboy

get the 2 value d straight know the coordinates of two points?? I thought we are finding for B first ...
vick5821 发表于 4-8-2010 06:40 PM

不信的话你sub回去，你会发现其实都一样的
   
from 2,a=(5-x)
x=4 , a=1
x=1 , a=4

from 3, b=(-1-y)
y=-3 , b=2
y=2 , b=-3

为什么会一样？
因为如果一开始你用
distance of CD = distance of DA ,
也是等于
(b+2)^2 + (a-0)^2 = (b-1)^2 + (a-5)^2
所以其实只不过是换个symbol罢了...

然后如何知道哪个是B和D
方法就是看问题给的graph = =

(4,-3) , 是在x-axis的下面，如果问题说它是B,就是B

(1,2) , 是在y-axis的下面，如果问题说它是D,就是D

如果问题什么都没给
这样的话随便放都没差 ...

vick5821

The perpendicular distance from (4,-3) to a line is 2 units. The line has a negative gradient and cuts the axis at (0,-5/2). Determine the equation of the line.thanks

Log

回复 1492# vick5821
let the line be y=mx+c
at (0,-5/2),  c=-5/2
thus, y=mx -5/2
    mx-y-5/2=0
given perpendicular distance from (4 ,-3)= 2
       l {m(4)-(-3)-5/2)} / √(m²+1) l = 2
         l (4m+ 1/2) / √(m²+1) l  = 2
           (4m+1/2)²/(m²+1) =2²
           (4m+1/2)²=4（m²+1)
solve, u will get 2 m values, take the -ve sign as the question required
substitute back to the equation line and get the equation.
(4y+3x+10=0)

kelfaru

用代数来做应该可以吧...
找出四个information就可以了吧...

kelfaru

Prove [a(ab)^n] / b >= 0 by using binomial expansion.

Allmaths

Prove [a(ab)^n] / b >= 0 by using binomial expansion.
kelfaru 发表于 8-8-2010 02:10 AM

可以不要用 binomial expansion吗?

kelfaru

回复 1496# Allmaths


不要的话就很容易可以解出来...

yingchin

Find the numbers A,B and C such that 2x^4 +2x^3 +5x^2 + 3x + 3 =(x^2 + x+ C)(Ax^2+ Bx + 3)

要用Long Division吗？ 还是什么？

Lov瑜瑜4ever

Find the numbers A,B and C such that 2x^4 +2x^3 +5x^2 + 3x + 3 =(x^2 + x+ C)(Ax^2+ Bx + 3)

要用Lo ...
yingchin 发表于 8-8-2010 01:03 PM

2x^4+2x^3+5x^2+3x+3 =(x^2+x+C)(Ax^2+Bx+3)
用long division的话或许会有点慢
我觉得啦
用compare的方法会比较快
先观察
发现到Cx3=3,C=1
还有(x^2)(Ax^2)=2x^4,A=2
最后就到B了...
B的我compare x^3term的
(x^2)(Bx)+(x)(Ax^2)=2x^3
Bx^3+2x^2=2x^3
              B=0
遇到这种问题
先观察power最高的那个term，然后再观察constant term
最后才观察其他的term
这样比较节省时间。。。

yingchin

回复 1499# Lov瑜瑜4ever


   哦，原来是这样。谢谢