数学Paper 1讨论专区

whyyie

回复 1620# peaceboy

(A+2I)P = P
(A+2I)PP-1 = PP-1
A+2I = I
(A+2I)^15 = I
(A+2I)^15 P = P

是这样吗? 如果 (A+2I)P = I 怎么做?

peaceboy

回复  peaceboy

(A+2I)P = P
(A+2I)PP-1 = PP-1
A+2I = I
(A+2I)^15 = I
(A+2I)^15 P = P

是这样 ...
whyyie 发表于 31-8-2010 08:11 PM

不懂，不过通常这种问题你先做(A+2I)P , 然后(A+2I)^2P , 然后(A+2I)^3P...
99.99%的答案会重复的，然后就看你要怎么弄了
（还有哪0.01%就不懂了）

Allmaths

回复  Allmaths

怎样看是(4-y^2) - (y^2-1)还是 (y^2-1)-(4-y^2)? [不以modulus为前提]
whyyie 发表于 31-8-2010 11:02 AM

那个graph是这样的...



照理来说是应该分开region算的...

Log

回复 1615# xiang911
let the center=(x,y) ,r= radius of circle
this circles passes through the points (3,2) and (6,3)
so, r²=(x-3)²+(y-2)² ,  r²=(x-6)²+(y-3)²           * --------【注：这边的 (3,2) and (6,3)不是center】
(x-3)²+(y-2)²=(x-6)²+(y-3)²
simpllify, u will get 3x+y=16
this show that the centers lie on this line  3x+y=16 ---------(1)

(find circles equation, u need to noe centers and radius,find center first)
given the line x+2y=2 touch the circle,
this also mean that,
    perpendicular distance between center and the line x+2y-2=0 and center= r
     l x+2y-2 l / {√(1²+2&#178} = √{(x-3)²+(y-2)²}     
simplify, get    4x²+y² -26x -12y-4xy+61=0   --------(2)
solve with (1) and (2),
u will get two centers (5,1) and (1,13)
each centers have their radius,  take the centers insert to the radius equation* above to get radius.
then,
circles1, center (5,1), radius=√5
circles2,  center(1,13) radius=√125
put them into circle standard form equation.

Log

show that the centre of the circles passing through the point (3,2) and (6,3) r located on the line  ...
xiang911 发表于 31-8-2010 11:55 AM

这道问题应该还有下文，determine the point on the lines x+2y=2 that the two circles pass through

peaceboy

这道问题应该还有下文，determine the point on the lines x+2y=2 that the two circles pass through: ...
Log 发表于 1-9-2010 09:11 PM

    厉害....

blazex

1.The first three terms in ascending power of x in the expansions (1+px)/(1+qx) and (1+x)^1/10 are the same. Find the value of p and q , assuming that x is so small that both expansions are valid. Use this result to show that
     (33)^1/10=651(2^1/2)/649

Allmaths

1.The first three terms in ascending power of x in the expansions (1+px)/(1+qx) and (1+x)^1/10 are t ...
blazex 发表于 2-9-2010 06:49 PM

是第二showing part的做不到吗?

blazex

回复 1628# Allmaths


   是的。

Allmaths

回复  Allmaths


   是的。
blazex 发表于 2-9-2010 08:31 PM

那就sub x=1/32...

blazex

回复 1630# Allmaths


  x 一定要在两个expansion的validity range里吗？

Allmaths

回复  Allmaths


  x 一定要在两个expansion的validity range里吗？
blazex 发表于 2-9-2010 08:53 PM

当然..如果out of range就不准了...value of x 越小越准..

hongji

2^2x-3    - 5(2^x)   +32 =0
answer is 8,32?

Allmaths

2^2x-3    - 5(2^x)   +32 =0
answer is 8,32?
hongji 发表于 3-9-2010 05:52 PM

   不对啊..是x=3,5

hongji

不对啊..是x=3,5
Allmaths 发表于 3-9-2010 07:57 PM

    u answer same my book^^
mine 不对
2^2x-3   ___>   2^2x/2^3?

Allmaths

u answer same my book^^
mine 不对
2^2x-3   ___>   2^2x/2^3?
hongji 发表于 4-9-2010 12:07 AM

    是的。。。

hongji

是的。。。
Allmaths 发表于 4-9-2010 05:07 PM

但是为什么算不到那答案
可以写出来给我看吗？

peaceboy

但是为什么算不到那答案
可以写出来给我看吗？
hongji 发表于 5-9-2010 06:45 PM

    2^x = 8
              =2^3
          x=3,

2^x=32
      =2^5
x=5

你忘了问题要求的是找x...

hongji

2^x = 8
              =2^3
          x=3,

2^x=32
      =2^5
x=5

你忘了问题 ...
peaceboy 发表于 5-9-2010 06:55 PM

    ^^dui o..
hehe xie xie

nkrealman

哈哈，關於differentiation

1.tan x = 1 + tan y,find dy/dx in term of x and y
hence show that when x=1/4pi + σx , y≈y0 +2σx where y0 is the value when x=1/4 pi

2.y=ln(sinx),find an approximation for the increase in y when x increase by σx.hence,estimate the value of ln(sin 30.05),given that ln(sin 30)=-0.6931,cot30=1.732 and 1 degree =0.01745 radian.

give your answer to 4 decimals places.