数学Paper 1讨论专区

Lov瑜瑜4ever

对是这个xy=4x+36
long_sign 发表于 10-4-2011 11:42 PM

你学了mathT2的similar triangle的东西了吗？
用similar triangle就能form出这个equation了。。。

long_sign

回复 2561# Lov瑜瑜4ever


    eh?! 有用到这个???   学校还没有教....p1-chapter 5 only ;p2-chapter 2 only .....  我是先finish p1 才到p2....

Lov瑜瑜4ever

回复  Lov瑜瑜4ever


    eh?! 有用到这个???   学校还没有教....p1-chapter 5 only ;p2-chapter 2 on ...
long_sign 发表于 11-4-2011 06:46 PM

我是用similar triangle来找的。。。

vick5821

Hey guys, pls help me this ques,, URGENT.!!I need the ans by tonight or tomorrow morning before 9..pls

A circle in the first quadrant touches the x-axis, y-axis and the straight line 4y - 3x + 40 =0 . If P(4, -7) lies on the straight line, find the :
a) equation of the circle[ (x - 10)^2 + (y-10)^2 =100 ]
b) length of the tangent from P to circle [15 unit]
c) equation of the other tangent from P to the circle.  <<< how to do this?? Pls help..thanks alot

whyyie

回复 2564# vick5821

可以画出right-angled triangle with length sqrt (325), 15, 10 and point (10, 10), (x, y) and (4, -7)

然后用distance formula
(x-10)^2 + (y-10)^2 = 100 ...(1)
(x-4)^2 + (y+7)^2 = 225   ...(2)
(1) - (2) = 6x + 17y = 130

再用area of triangle = (1/2) |x1y2 + x2y3 + x3y1 - ......| = 75
17x - 6y = 260 (clockwise) - rejected  
-17x + 6y = 40 (anticlockwise)

From the anticlockwise, x = 4/13, y = 98/13
Equation of other tangent:
y + 7 = m (x - 4)
y + 7 = (-63/16)(x-4)
16y + 63x = 140

不懂有没有更短的solution

whyyie

回复 2564# vick5821

part (a) 你怎么找equation of locus of circle?

英ying

square root(x+5) - square root(x-6) = square root(x-5)

是不是Square both sides, 然后LHS要expand他？ Square root的话我表示无能啊…… 谢谢高手帮我解答

Allmaths

square root(x+5) - square root(x-6) = square root(x-5)

是不是Square both sides, 然后LHS要expand他 ...
英ying 发表于 10-5-2011 05:27 PM

   

                                √(x+5)-√(x-6)=√(x-5)
              (x+5)-2√[(x+5)(x-6)]+(x-6)=x-5
                                               x+4=2√[(x+5)(x-6)]
                                     x^2+8x+16=4(x^2-x-30)
                                  3x^2-12x-136=0
                         x=(2/3)(3+√111)   or   x=(2/3)(3-√111)  (rejected)

                        ∴x=(2/3)(3+√111)

blazex

1)express (3x+5)/((x+2)(2x-1)) as partial fractions. Hence or otherwise, find the  
  first three terms of the expansion (3x+5)/((x+2)(2x-1)) in ascending power of
  1/x.state the range of values of x for which the expansion is valid.
  p.s.我找不到range of x
2)Express (x^2+3x)/((1-x)(1+x)^2) as partial fractions.When -1<x<1, the  
  expansion of the above expression is
     a+bx+cx^2+dx^3....+ex^m+...
  Determine the values of a ,b, c,d and find e in term of m, given that m>=0.
  show that e is a positive integer when m is odd, and e is a negative integer   
  when m is even.

天空之道

consider any two event A and B let x=（P(AUB))/(P(A)+P(B))
show that
a)P(AnB)/(P(A)+P(B))=1-x
b)P(AnBlAUB)=1-x/x
c)1/2 smaller and equal than x smaller and equal than 1

blazex

回复 2570# 天空之道
A) P((AUB))/(P(A)+P(B))=x    (P(A)+P(B)-P(AnB))/(P(A)+P(B))=x
    (P(A)+P(B))/(P(A)+P(B))-(P(AnB))/(P(A)+P(B))=x
    (P(AnB))/(P(A)+P(B))=1-x


B)P((AnB)|(AUB))=(P(AnB))/(P(AUB))
                        =(P(AnB))/(P(A)+P(B)) X(P(A)+P(B))/(P(AUB))
                        =1-x X 1/x
                        =(1-x)/x
c的题目我看不懂

天空之道

回复 2571# blazex

对不起~
c is show that
1/2<x<1

huatiang

Integer subset of rational number?
How 1 express as rational number?

~搞怪男孩~

Solve the following equation,
6x^2 - 2 = |x| for x < 0
请问这题怎样做呢？
答案给的是：{2/3}

jose

The binary operation given as:
x*y=x+y-xy
Prove that * is association

x*(y*z)=x*(y+z-yz)
             x(y+z-yz)-x(y+z-yz)

做到这里就不会了

TianSang

a^(2x-1) = b^(1-3y) and a^(3x-1) = b^(2y-2)
prove that 13xy-7x-5y+3= 0

peaceboy

回复 2575# jose


   做么你的题目和你的step不一样的

peaceboy

回复 2576# TianSang



a^(2x-1) = b^(1-3y) and a^(3x-1) = b^(2y-2)

(2x-1) lg a = (1-3y) lg b ---1

(3x-1)lg a = (2y-2)lg b ----2

2/1 ,
(3x-1) / (2x-1) = (2y-2)/ (1-3y)
(3x-1)(1-3y)= (2y-2)(2x-1)
3x-9xy-1+3y = 4xy -2y-4x +2
13xy -7x -5y + 3 =0

jose

回复  jose


   做么你的题目和你的step不一样的
peaceboy 发表于 21-5-2011 09:59 AM

   其实我也不是很懂怎样做...谁可以帮帮我？

Log

回复 2574# ~搞怪男孩~
6x^2 - 2 = |x| for x < 0           lxl =  x for x≥0 and -x for x<0
so   6x^2 - 2 =-x
      6x^2  +x -2 =0
      x = 1/2 , -2/3
since x <0, so  x={-2/3}