数学Paper 1讨论专区

happy=]

回复 2880# Allmaths


   thx =]

happy=]

a computer program has an error that causes the program not to function perfectly, n programmer are assigned seperately to detect the error. the probability that each programmer will detect the error is 0.875. determine the value of n if the probability that at least one programmer detects the error is 0.998

happy=]

A married couple is taking driving tests. If the probability that either the husband or the wife passes the test each time is taken, is 0.8,
a) Find the probability that the husband or the wife passes the test after taking the test exactly two times,
b) Find the probability that both the husband and the wife pass the test after taking the test more than two times.
Ans: a) 0.294 b) 0.00107
i need working...

苑静

回复 2882# happy=]

n= unknown, p= 0.875, q =1-0.875 = 0.125

express in binomial distribution to find n,
P(X≥ 1）= 0.998
1-P(X＜1）=0.998
P(X=0）=1-0.998 = 0.002
nC0 (0.875)^0 (0.125)^n = 0.002
(1)(1)(0.125)^n = 0.002
nlg0.125 = lg0.002
n = 3


答案对吗？

苑静

第六课我不太会做，最大问题在于怎么 sketch graph
该怎么sketch呢？ 我会找asymptotes，但对于那个function应该是怎样的形状就完全摸不着了 （单纯的直线和quadratic还是可以的)

strawb3rry94

这个是function的题目><
f(x)= x/2x-1 ,x is not equal to 1/2
g(x)= ax^2+bx+c
Find the values of a,b and c if g。f = -3x^2+4x-1/(2x-1)^2
**想问下这类的题目是不是要用comparison?
可是如果拿来compare的话我的答案跟老师给的答案就不一样了
帮帮忙><

peaceboy

回复 2886# strawb3rry94

f(x)= x/2x-1 ,x is not equal to 1/2
g(x)= ax^2+bx+c
Find the values of a,b and c if g。f = -3x^2+4x-1/(2x-1)^2

没错是用compare
你的step写来看下

btw下次写题目的时候该放括号的地方级的要放，不然我们看不懂题目很难帮你做

strawb3rry94

回复  strawb3rry94

f(x)= x/2x-1 ,x is not equal to 1/2
g(x)= ax^2+bx+c
Find the values of a,b  ...peaceboy 发表于 6-6-2012 08:33 PM

    我做到了^^
不过不懂steps对吗~
帮我看下我有没有写错~谢谢啊^^

gof=gf(x)
      =g(x/2x-1)
      =a(x/2x-1)^2 + b(x/2x-1) + c
      =a[x^2/(2x-1)^2] + bx/2x-1 +c
      =ax^2/(2x-1)^2 + bx(2x-1)/(2x-1)^2 + c(2x-1)^2/(2x-1)^2
      =ax^2/(2x-1)^2 + bx(2x-1)/(2x-1)^2 + c(4x^2-4x+1)/(2x-1)^2
      =(ax^2 + 2bx^2 - bx + 4cx^2 - 4cx + c)/(2x-1)^2
      =(ax^2 + 2bx^2 + 4cx^2 - bx - 4cx + c)/(2x-1)^2
      =[(a+2b+4c)x^2 + (-b-4c)x + c]/(2x-1)^2
By comparisons:
(-3x^2 + 4x - 1)/(2x-1)^2 = [(a+2b+4c)x^2 + (-b-4c)x + c]/(2x-1)^2
c= -1 ,  -b-4c= 4            , a+2b+4c= -3
             -4(-1)-4= b          a+2(0)+4(-1)= -3
              4-4= b                 a-4= -3
                 b= 0                 a= -3+4
                                          a= 1

strawb3rry94

还有一题>< 不过是polynomial的~

When P(x)=x^3+px^2+qx+16 is divided by x^2+x-6 it leaves a remainder of 6x-8.
(a)Find the values of p and q.
(b)Find the quotient.

这个要怎么做啊？
我懂P(x)=D(x).Q(x)+R(X)
可是不懂这个要怎样><

peaceboy

回复 2889# strawb3rry94


    When P(x)=x^3+px^2+qx+16 is divided by x^2+x-6 it leaves a remainder of 6x-8.
(a)Find the values of p and q.
(b)Find the quotient.


x^2 +x -6 =0
(x+3)(x-2)=0
x=2,-3

P(2) = 6(2)-8
8+4p+2q+16 = 4
4p+2q= -20
2p+q = -10 ---------(1)  

P(-3)= 6(-3)-8
-27+9p-3q+16 = -26
9p-3q = -15
3p-q = -5-----------------(2)

剩下的自己来

上面那题step没有错

strawb3rry94

回复  strawb3rry94


    When P(x)=x^3+px^2+qx+16 is divided by x^2+x-6 it leaves a remainder of ...
peaceboy 发表于 7-6-2012 11:36 AM

真的是太感谢你了^^ 哈哈err..不过我想问下这题有原理的吗？

peaceboy

回复 2891# strawb3rry94


    P(x)=D(x).Q(x)+R(X)

when, D(x) = 0
P(x)=0*Q(x)  + R(X)
P(x)= R(x)

strawb3rry94

回复  strawb3rry94


    P(x)=D(x).Q(x)+R(X)

when, D(x) = 0
P(x)=0*Q(x)  + R(X)
P(x)= R(x)
peaceboy 发表于 8-6-2012 12:17 PM

哦哦原来如此
谢谢你啊^^

strawb3rry94

Given α and β are the roots of the equation 2x^2+3x+4=0.Form the equation which has roots：
α^3β,αβ^3.
这题怎么做？

Allmaths

Given α and β are the roots of the equation 2x^2+3x+4=0.Form the equation which has roots：
α^3β ...
strawb3rry94 发表于 16-6-2012 01:45 PM

    2x^2+3x+4=0
x^2+(3/2)x+2=0

α+β=-3/2
αβ=2


New equation:


x^2-(α^3β+αβ^3)x+(α^3β)(αβ^3)=0
x^2-αβ(α^2+β^2)x+(αβ)^4=0
x^2-αβ[(α+β)^2-2αβ]x+(αβ)^4=0


Substitute α+β=-3/2 and αβ=2 into x^2-αβ[(α+β)^2-2αβ]x+(αβ)^4=0 就可以了

strawb3rry94

2x^2+3x+4=0
x^2+(3/2)x+2=0

α+β=-3/2
αβ=2


New equation:


x^2-(α^3β+αβ ...
Allmaths 发表于 17-6-2012 10:34 AM

做到了^^谢谢啊
想问下这题：By writing y=x^2+6x,solve the equation x^2+6x+2square root x^2+6x =24
我把y sub进去可是做不出答案><

Allmaths

做到了^^谢谢啊
想问下这题：By writing y=x^2+6x,solve the equation x^2+6x+2square root x^2+6x =2 ...
strawb3rry94 发表于 17-6-2012 07:31 PM

   
x^2+6x+2(x^2+6x)^(1/2)=24

Let y=x^2+6x,

y+2(y)^(1/2)-24=0

Let y=z^2,

z^2+2z-24=0
z=4 or -6

然后继续做下去找x， 注意x必须符合 x^+6x>=0, x<=-6 or x>=0

clc

Ivanlsy 发表于 22-2-2009 12:37 PM
log_4 N = p
N = 4^p
(log_12 N) = q

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log_3&#8289; 48=log_N&#8289; 48/log_N &#8289;3  
log_3&#8289; 48=(log_N &#8289;4+log_N &#8289;12)/(log_N&#8289; 12-log_N &#8289;4 )
log_3 &#8289;48=(1/p+1/q)/(1/q-1/p)=(p+q)/(p-q)

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genji

请问谁有past year maths T 2011 P1 的答案呢？ 题目我找到了，但是就是找不到答案，请各位帮帮忙

plouffle0789

oxford fajar ace ahead volume 1 chapter 1:numbers and sets

quick check 1.5
pages 26
第一题的（e）



答案有简略掉一个STEP.我弄不明白怎么会是- π /2

-Pi/2