泰语网友交流区

jimy

原帖由 turyoonai 于 19/01/2005 02:24 发表


sawadee krup,khun pood thai kheng chang leaw krup, phom mai dai son krup.

mai mi ....phom ru nit noi

jimy

原帖由 turyoonai 于 19/01/2005 02:24 发表


sawadee krup,khun pood thai kheng chang leaw krup, phom mai dai son krup.

mai mi la....phom put thai ru nit noi,

yin di ti dai ru jak

dugong

原帖由 jimy 于 22-1-2006 01:45 发表
sawahti krup......phom yak rian pra-sa thai,son pra-sa thai dai mai?
khop khun krup     la gon....

wadee khrab khun jimy~
yin dee ton rab su tii nii khrab~
pom yak rian pasa thai meun kan, son mai dai, pom kao zai nid noi duey na khrab~
rao ja rian cha cha na~

jimy

原帖由 dugong 于 19/01/2005 14:39 发表

wadee khrab khun jimy~
yin dee ton rab su tii nii khrab~
pom yak rian pasa thai meun kan, son mai dai, pom kao zai nid noi duey na khrab~
rao ja rian cha cha na~

sawahti krup khun dugong,yin di ti dai ru jak
rao jak rian meun kan na,dai mai?khun put thai kheng kheng ...
mai put dang dang na,phom ko mai ru!

chucky

wa dee jao..........
haha.."i think i"..很好听的歌哦。。。
有人有这首歌吗？？

akaki

dugong,我不会做的数学都在这里了，尽快帮我解答。

1.
The co-ordinates of P,Q,R, the vertices of the triangle PQR,are(1,1),(5,4),(4,0).if the altitude through P meets QR in X,find
(a)the equation of PX
(b)the co-ordinate of X
(c)the length PX


2.
The co-ordinate of the vertices of a triangle are (0,4),(2,0),(4,2).
Prove that the triangle is isosceles and find its area.

3.
Find the equation of the lines passing through the point A(3,4),and (i)parallel,(ii)perpendicular to the line 4x+3y=8.If these lines meet the line 2x+y=1 in points B and C,find the area of triangleABC.

4.
The co-ordinate of the pointA,B,C are (-3,-1),(11,13),(-1,-3),find the  equation of the sides AB and BC.Deduce the co-ordinates of the centre
of the circumcircle of the triangle.

5.
Find the radius and centre of the circumcircle of the triangle whose
vertices are (-1,8),(-1,-2),(2,4) .

6.
Prove that the quadrilateral whose vertices are (1,3),(1,-1),(3,1),
(-1,1)is cyclic.

7.
Show that the points (1,3),(3,4),(4,-3)are three vertices of a triangle and find the co-ordinate of the fourth vertex.

8.
Find the points of intersection of the line y=x-2 and the curve  
y2(y square)=4x.Write down the equation of the perpendicular bisector
of the line joining these points and find where it meets the axis of x.

9.
Find the points of intersection of the curve x2+y2+10(x+y)+25=0 with  
the co-ordinate axes.Explain the result.

就这9题，如果可以的话，请用英文回答
用华文也可以。thanks...

akaki

原帖由 siokae0422 于 20-1-2006 06:10 PM 发表




最近玩失踪吗？？？

我没有，最近很忙，所以。。。哈哈

akaki

原帖由 dugong 于 20-1-2006 08:56 PM 发表

嗯，星期六我有去新坛的足球网聚，
之后要去新坛两位会员的生日的派对。
要的话星期天？

累的话就要多多照顾身体，不然生病的话就不好了。不要让我当心啦

我还以为很轻松，没想到读这系。。很耗体力。。。。
星期天，也不知道，想着数学想到要疯了。。。:@


你也一样，好好照顾自己。

akaki

原帖由 siokae0422 于 9-1-2006 05:55 PM 发表
哈哈，我也来。。。。。。
有dugong的出现我也要出现！

有你出现的地方，我也会出现。哈哈

akaki

原帖由 siokae0422 于 6-1-2006 12:23 AM 发表
你们真的吵架了吗？？？发生什么事了？

我们没有吵架啊。奇怪，你怎么会觉得。。？？

akaki

原帖由 dugong 于 12-1-2006 07:25 PM 发表
来顶一下。。针对你们楼上的话题，应该先问Khun Akaki一下哦。。

问我什么？？跟我有关？？

akaki

963--966楼,你们在说什么？？

akaki

原帖由 chucky 于 13-1-2006 11:40 PM 发表
sa wa dee jao........
很久没来了。。。
大家碜样了。。？

哦。。。欢迎你回来～～

akaki

原帖由 siokae0422 于 16-1-2006 01:48 AM 发表




奇怪为什么我的看到空空的？

我也一样。哈哈

akaki

原帖由 turyoonai 于 16-1-2006 02:37 AM 发表


呵呵～～没什么就好～～

因为看她这么久没上来，就关心一下啦～～

祝她学业进步！！呵呵～～

谢谢。

不过我想我的成绩是退步，不是进步。。。。
显。。。明天又要留校。

akaki

原帖由 siokae0422 于 21-1-2006 02:44 AM 发表
哈哈，终於看到你们恢复以前温馨的日子了！

难道以前dugong还没来到这里，这里不够温馨？？哈哈哈

听我爸爸说，泰国的女生都很美，是真的吗？？＇
快点给我看你老婆的照片吧。

dugong

1.
The co-ordinates of P,Q,R, the vertices of the triangle PQR,are(1,1),(5,4),(4,0).if the altitude through P meets QR in X,find
(a)the equation of PX
(b)the co-ordinate of X
(c)the length PX

Solution
(a)Q and R->(5,4)(4,0)=(x1,y1)(x2,y2)

Standard Formula: (x1-x2)/(y1-y2)=(x-x1)/(y-y1)
Sub-in coordinates of Q and R: (5-4)/(4-0)=(x-5)/(y-4)
1/4=(x-5)/(y-4)
(1/4)(y-4)=x-5
1/4y-1=x-5
y=4(x-4)
y=4x-16-->Equation of PX (general form is y=mx+c)

(b) coordinate of X (x,1) --> given that y=1, to find x.

sub in equation from part (a)
y=4x-16
1=4x-16
4x=17
x=4.25

(c)忘记了oops~

Khun Akaki，我的中学是酱教的。不知道跟你的学校一样吗？一题一题来～

dugong

2.
The co-ordinate of the vertices of a triangle are (0,4),(2,0),(4,2).
Prove that the triangle is isosceles and find its area.

Isosceles的意思是三角型的三边，两边是相同长短的。（1 triangle have two sides with same length）
我这里没有办法画那个形状出来，所以我用数学方程式作出来ok？以下我用英文解释给你，搀华文的话会很乱。大概用我生锈的英文跟你讲解，千万不要写进答案卷，不然老师看了满头雾水。

Firstly, you plot the triangle on rough paper. You have 3 points right? Sub in the 3 points and you will know what i mean by "三角型的三边，两边是相同长短的"。After you plot, you will know the 2 sides are the same length. So, you will have to find the length of that 2 sides....

you use the method i used before in qn 1a

Khun Akaki以下的可以照抄。。。。

Solution
2.Let be X, Y and Z be the points of (0,4),(2,0),(4,2) respectively.
X=(0,4)
Y=(2,0)
Z=(4,2)

To prove that this triangle is an isosceles triangle, we have to prove that the distance between X and Y is equals to the distance between X and Z.

Firstly, find the distance (length) between point X and point Y.

X=(0,4) and Y=(2,0) --> (x1,y1) and (x2,y2)

x2-x1=2-0=2 ---> representing by a
y2-y1=0-4=-4 ---> representing by b

Using Pythygoras Theorem

a^2+b^2=c^2
(2^2)+(-4^2)=c^2
4+16=c^2
20=c^2
c=4.47

Therefore, distance between X and Y is 4.47.

Secondly, find the distance (length) between point X and point Y.

X=(0,4) and Z=(4,2) --->(x1,y1) and (x2,y2)

x2-x1=4-0=4 ---> representing by a
y2-y1=2-4=-2 ---> representing by b

Using Pythygoras Theorem

a^2+b^2=c^2
(4^2)+(-2^2)=c^2
16+4=c^2
20=c^2
c=4.47

Therefore, distance between X and Z is 4.47. Comparing with the distance between X and Z, its also 4.47. Distance between points X and Y, and distance between X and Z made up the two sides of the isosceles triangle with the same length. Thus, we can conclude that this triangle is a isosceles.

Finding the area:
By cutting the triangle into half and rearrange, we can see that this triangle is a rectangle. Thus, we can use the "length x breadth" way to find its area.

Area
= a x b
= 4 x 2
= 8 square units

dugong

3. Find the equation of the lines passing through the point A(3,4),and (i)parallel,(ii)perpendicular to the line 4x+3y=8.If these lines meet the line 2x+y=1 in points B and C,(iii)find the area of triangle ABC.

Solution

(i)Given equation of the line 4x+3y=8, we rearrange into the standard format of y=mx+c.

4x+3y=8
3y=-4x+8
y=-1/3(4x+8) --> equation actual line
m=-4/3

To find equation of paralle line:

Since both lines are parallel, we can conclude that they have the same gradient.
y=mx+c
4=(-4/3)(3)+c
4=-4+c
c=4+4
c=8

Therefore, equation of parellel line is y=-4/3x+8

(ii) To find new gradient of perpendicular line, use m x -1/2

-4/3 x -1/2
= 4/3 x 1/2
= 2/3 --->new gradient

y=mx+c
4=(2/3)3+c
4=2+c
c=4-2
c=2

Therefore, equation of perpendicular line is y=2/3x+2/3

dugong

Khun Akaki,我暂时就跟你做三题。

原帖由 akaki 于 23-1-2006 16:43 发表

我还以为很轻松，没想到读这系。。很耗体力。。。。
星期天，也不知道，想着数学想到要疯了。。。:@

你也一样，好好照顾自己。

消耗不少脑细胞。慢慢来，是很困难，但没问题。

原帖由 akaki 于 23-1-2006 17:13 发表

问我什么？？跟我有关？？

当然跟你有着很大关系。

原帖由 akaki 于 23-1-2006 17:17 发表
963--966楼,你们在说什么？？

等我们出来见面时才我跟跟你讲，现在讲没有用，讲了你应该也不会相信，不会明白。