【纪念当年的帖子（2010）】Add Maths功课讨论区

leenyiam

我也有问题想问大家。。
那个请问那个m+怎样用？
为什么我按了还是不能记得之前的m value的？

_韩_

想问看这题怎样prove
(1-tan^2  x) / (1+tan^2  x)=1-2 sin^2  x

menglee90

回复 838# josser


   

menglee90

回复 842# _韩_

_韩_

回复 844# menglee90

如何变成 cos^2  x -sin^2  x

menglee90

回复 845# _韩_

(1- tan^2 x) / sec^2 x = 1/sec^2 x - tan^2 x / sec^2 x = cos^2 x - sin^2 x

josser

find the values of k for which line  x+y=k  is a tangent to the curve  x^2 + y^2 = 8.

menglee90

回复 847# josser

x + y = k is the tangent to circle x^2 + y^2 = 8 when they intersect at only one point, means the following simultaneous equation has only one solution.

x + y = k    ---> y = k-x
x^2 + y^2 = 8
   
x^2 + y^2 = 8
x^2 + (k-x)^2 = 8
....
2x^2 - 2kx + k^2 - 8 = 0

2x^2 - 2kx + k^2 - 8 = 0 has only one solution, means
b^2-4ac = 0
(-2k)^2 - 4(2)(k^2 - 8) = 0
...
16-k^2=0
k = 4 or -4

josser

这题...
y=x^n ,  where n is an integer. given that the curve passes between the points (2,200) and (2,2000) determine the value of n .

menglee90

回复 849# josser


   问题不明确，这是完整的问题？答案是n=8,9,10？

josser

(i) sketch the graph of the curve y=3sin x , for -π < x < π

The straight line  y=kx , where k is a constant, passes through the maximum point of this curve for -π < x < π.
  
(ii) find the value of k in terms of π

(iii) state the coordinates of the other point , apart from the origin , where the line and the curve intersect.

menglee90

回复 851# josser


     

josser

回复  josser


   问题不明确，这是完整的问题？答案是n=8,9,10？
menglee90 发表于 27-7-2011 02:40 PM

    问题还有个graph 的，只是我不知道如何post 上来 。。 答案是9

josser

还有一题。。。
prove  (1/sin x  +  1/tan x )^2 = (1+cos x)/( 1-cos x)

menglee90

回复 854# josser

(1/sin x  +  1/tan x )^2=1/(sin^2 x) + 1/(tan^2 x) + 2/(sin x tan x)

=1/(sin^2 x) + (cos^2 x)/(sin^2 x) + 2 cos x /(sin^2 x)
=(1 + 2 cos x + cos^2 x) / sin^2 x
= (1 + cos x)^2 / (1 - cos^2 x)
= (1 + cos x)^2 / (1 - cos x)(1+cos x)
=
(1 + cos x)/ (1 - cos x)

josser

the sum of the first hundred terms of an ap with first term a and common difference d is T . The sum of the first 50 odd-numbered terms is 1/2T-1000. Find the value of d .

menglee90

回复 856# josser


问题不明确。The sum of the first 50 odd-numbered terms is 1/2T-1000很模糊。

Allmaths

the sum of the first hundred terms of an ap with first term a and common difference d is T . The sum ...
josser 发表于 10-8-2011 10:48 PM

    你的1/2T-1000是:

(1/2)T-1000?
1/(2T-1000)?
1/(2T)-1000?

brackets 很重要啊。。

josser

回复 858# Allmaths


    很不好意识，是 (1/2) T - 1000  ><  ... 但这一题已solve 到了。。。
这里有另一题我不会做，  
the sum of the first n term of a series is given by the expression ( 6- (2^(n+1))/(3^(n-1))). by defining an expression for the nth term of the series, or otherwise , show that this is a GP , and state the values of the first term and the common difference .

josser

*common ratio ... 不是common difference ><