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#1 Help Me ! » Factor and Remainder Theorem » 2005-09-07 20:00:54

ahgua
Replies: 2

Given that (2x + 1)(x  1) are factors of a cubic expression g(x).  When g(x) is divided by x²  − 2x  3 ,  it leaves a remainder (31x + 33).  Find the expression g(x).

#2 Re: Help Me ! » the formulas for sine, cosine and tangent » 2005-09-05 00:03:06

It is better to remember "TOA CAH SOH". It means "fat old woman" in hokkien (If I remember correctly ).

#3 Re: Jokes » Clean Jokes » 2005-09-03 16:32:44

Because his maths teacher says it was a piece of cake

#4 Jokes » Clean Jokes » 2005-09-02 16:04:06

ahgua
Replies: 63

Why does a boy eat up his maths homework?

#5 Re: Guestbook » Rebel (65) » 2005-08-31 00:59:18

God says "Never use my name in vain"

Anyway, I am Maester of Yevon.

#6 Re: Help Me ! » Maths Olympiad » 2005-08-30 23:57:03

Oh i haven't learn that, thank ganesh, i have just gain a new knowledge....

How noe u

#8 Help Me ! » Maths Olympiad » 2005-08-30 18:43:18

ahgua
Replies: 5

Which is bigger? Prove without a calculator.

2000¹¹¹¹¹         2000³³³³³
------------ or    ---------------
2000²²²²²         2000^44444

#9 Re: This is Cool » Remembering sin and cos values » 2005-08-30 15:55:03

To remember the trigo ratio:

1. Draw a table

Trigo/Angle  30        45        60

sin               1          2          3        [write 1,2,3 in the first row(sin)]

cos              3          2           1       [reverse the order of values]

tan              3           1          3       [write 3,1,3 in the third row(tan)]

2. Square root every no. in the table

Trigo/Angle  30        45        60

sin               1        √2        √3

cos           √3        √2           1

tan            √3        1          √3

*** √1 = 1. So, need not square root 1!

3. Divide value in first 2 rows by 2

Trigo/Angle  30        45        60

sin            1/2        √2 /2   √3 /2

cos           √3 /2    √2 /2     1 /2

tan            √3        1          √3

4. Reciprocate the first value in the tan row.

Trigo/Angle  30        45        60

sin            1/2        √2 /2   √3 /2

cos           √3 /2    √2 /2     1 /2

tan           1/ √3      1          √3

Easy right.

For angle of 0°, 90°, 180°, 270° and 360°

1. Draw a table.

Start with the sin row: write 0 and 1, alternating each value, starting with 0

SO:

0          90          180          270            360

sin      0            1           0              1               0

cos

tan

2. Reverse the order of value of cos with reference to sin

0          90          180          270            360

sin      0            1           0              1               0

cos     1            0           1              0               1

tan

3. Copy down the value for tan with reference to sin, substituting all "1"s with undefined "∞"s

SO:

0          90          180          270            360

sin      0            1           0              1               0

cos     1            0           1              0               1

tan     0            ∞          0              ∞              0

4. Make the second "1" negative for the first and second row

SO:

0          90          180          270            360

sin      0            1           0             -1               0

cos     1            0          -1              0               1

tan     0            ∞          0              ∞              0

That's all

#10 Re: This is Cool » I'm cracking up » 2005-08-27 13:42:45

How do you solve it?

I am lousy in these kinds of things

Well, i get the same answer, but i was unable to prove that z=y

Please tell me how to prove

#11 Re: Dark Discussions at Cafe Infinity » Venting. Do not read if you; are under 13 or; have a heart condition. » 2005-08-26 22:22:22

Your grades doesn't matter, you can't bring it with you when you die, and I won't feel VERY happy even if I top in class.

I feel that happiness is important. You can only ENJOY life if you are happy. Life is short, but death is eternal, so always feel happy, even if you did not do well for your exams.

#12 Re: Jokes » Mathematics jokes » 2005-08-26 19:14:37

Haha! I haven't heard of something like that!

#13 Re: Introductions » To introduce myself. » 2005-08-26 19:08:52

Wow! You are a good programmer!!!

I only know a little bit on VB and C++

#14 Re: Help Me ! » Determining the zeros... » 2005-08-26 15:54:31

Another way is by the "completing the square".

x² - 8x + 5 = 0

x² - 8x = -5

x² - 8x + 4² = -5 + 4² [When LHS = x² - ax, adding (a/2)² to both sides enables it to be factorise to (x - b)² form]

(x - 4)² = 11

x - 4 = ± √11

x = 4 ± √11

#15 Re: Maths Teaching Resources » EqWorld - The World of Mathematical Equations » 2005-08-26 13:49:37

But, it is always good to know a little more.

so ...

http://eqworld.ipmnet.ru is a GOOD WEBSITE

#16 Re: Help Me ! » Determining the zeros... » 2005-08-26 13:35:02

Use the formula:

x = -b ± √(b² - 4 ac)
--------------------- for ax² + bx + c
2a
a = 1, b = -8 and c = 5

x = 8 ± √(8² - 4 x 1 x 5)
-------------------------
2(1)

x = 8 ± √(4 x 11)
-----------------
2

x = 8 ± 2 √(11)
---------------
2

x = 4 ± √(11)

∴ x = 4 + √(11) or 4 - √(11)

= 4 + 11^½ or 4 - 11^½

#17 Re: Guestbook » cool stuff » 2005-08-26 03:53:45

I think playing games, studying and rugby is cool!

Of course, cycling and shopping are cool too.

#18 This is Cool » Strange formula » 2005-08-26 01:47:40

ahgua
Replies: 3

There is a formula to find area of any polygon drawn on a graph.

Suppose the vertices of the polygon are (x1,y1) ; (x2,y2) ; (x3,y3) ; (x4,y4).

Area of the polygon on the graph = 1/2 x | x1y2 + x2y3 + x3y4 + x4y1 - x2y1 - x3y2 - x4y3 - x1y4 |

| | is the absolute sign.

How do you prove that this formula is true?

P.S. The textbook didn't teach me this!

#19 Re: Help Me ! » Hep with Trig. please :) » 2005-08-26 01:32:33

Prove that (sec^2 x + 2 tan x)/ (1 - tan^2 x) = (cos x + sin x)/(cos x - sin x)
Hence solve the equation (sin x +cos x)/(sin x - cos x) = tan x for 0 < x < 2pi.

#20 Re: Puzzles and Games » What next? » 2005-08-25 23:03:59

maybe, after ATCG is U.

Uracil is another nitrogenous base of a nucleic acid (RNA, not DNA)

There are only two possible combinations of these nitrogenous base:

AT and CG

Other than that, there is no possible combination as T cannot form hydrogen bond with C and G and A cannot form hydrogen bond with C and G

#21 Help Me ! » Variations » 2005-08-25 22:50:04

ahgua
Replies: 3

I got stumbled by a question on variations. So pls help me!!!

5 men are hired to complete a certain job. If one more man were hired, the job can be completed 8 days earlier. Given that the no. of days required to complete the job is inversely proportional to the mo. of the men hired, find how many additional men must be hired in order for the job to be completed 28 days earlier.

#22 Re: Help Me ! » Hep with Trig. please :) » 2005-08-25 22:41:34

thanks ajp3. But I got another question on trigo...

Given cosec A + cot A = 3

and thus evalute cosec A -cot A

and find cos A