The Mathematics Club ~ ΜΑΘ ~

ShinyMeowth · Feb 20, 2011

NurseBarbra said:
Spoiler:

ii)2x/[x^2]-1 = 3
(answer in the form "a+b(sqrt10)", equation: [Ax^2 + Bx + C])
∴ 2x = 3(x^2-1)
∴ 2x = 3x^2 -3
∴ 3x^2 -2x-3 = 0
∴ 3+2(sqrt10)

The part where you solve the quadratic equation is mistaken. Everything up to that is correct.

Spoiler:

But from what I have seen, that was probably done due to a "5²=20"-type mistake.

I like Pokemon (...) · Feb 20, 2011

smile! said:
Eh...? Explain. :P

x-1 = 1/x
and
y+1 = 1/y
When x = ([FONT=&quot]√5 +1)/2
and when y = ([/FONT][FONT=&quot]√5 -1)/2[/FONT][FONT=&quot][/FONT]

And when you get the fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21, etc. where you take the previous number and add it to the last number to get the next number) and put it as a fraction (1/1, 1/2, 2/3, 3/5, 5/8, 8/13, etc.) the fraction converges to ([FONT=&quot]√5-1)/2. When you flip the fraction (1/1, 2/1, [/FONT]3/2, 5/3, 8/5, 13/8, etc.) the fraction converges to ([FONT=&quot]√5 +1)/2. Which is also the golden ratio, which is supposed to be related to beauty or something like that. [/FONT]

smile! said:
The quote kinda contradicts what you're saying....

How so?

~~I swear I'd have given that stuff a try if I came to the club earlier.~~

MeerFall · Feb 20, 2011

who like algabra?! (puts hand up)

NurseBarbra · Feb 20, 2011

ShinyMeowth said:
The part where you solve the quadratic equation is mistaken. Everything up to that is correct.

Spoiler:

The quadratic formula is x=(-b+√(b²-4ac))/2a.
a=3, b=-2, c=-3.
By substituting the values,
x=(-(-2)+√((-2)²-4*3*(-3))/(2*3)
x=(2+√(4+36))/6
x=(2+√40)/6
x=(2+√10√4)/6
x=(2+2√10)/6
x=(1+√10)/3
x=1/3+√10)/3

But from what I have seen, that was probably done due to a "5²=20"-type mistake.

sorry, i looked at the wrong equation, the next question was the equation of a line and the formulas are on top of eachother. (Fail on my regard)

ShinyMeowth · Feb 20, 2011

NurseBarbra said:
sorry, i looked at the wrong equation, the next question was the equation of a line and the formulas are on top of eachother. (Fail on my regard)

Don't worry about it, as long as you don't do it on a test.

NurseBarbra · Feb 20, 2011

Well the formulas arent labeled and there like this in order of the questions(the test was 40 questions long):
-b+-√(b²-4(a)(c))
2a
ax²+bx+c
(x+h)² = (x+xh+h)
4/3πr³

Spinor · Feb 20, 2011

MeerFall said:
who like algabra?! (puts hand up)

I'm too busy dealing with Manly stuff like Analysis and Topology to deal with Algebra ^____^

smile! · Feb 21, 2011

I like Pokemon (...) said:
x-1 = 1/x
and
y+1 = 1/y
When x = ([FONT=&quot]√5 +1)/2
and when y = ([/FONT][FONT=&quot]√5 -1)/2[/FONT][FONT=&quot][/FONT]

And when you get the fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21, etc. where you take the previous number and add it to the last number to get the next number) and put it as a fraction (1/1, 1/2, 2/3, 3/5, 5/8, 8/13, etc.) the fraction converges to ([FONT=&quot]√5-1)/2. When you flip the fraction (1/1, 2/1, [/FONT]3/2, 5/3, 8/5, 13/8, etc.) the fraction converges to ([FONT=&quot]√5 +1)/2. Which is also the golden ratio, which is supposed to be related to beauty or something like that. [/FONT]

How so?

~~I swear I'd have given that stuff a try if I came to the club earlier.~~

...I'll get back to you on that during a convo. XD

How so? Err.. The way I understood your sentence is that Maths = everything but then you limited to physics is just maths. What about Biology and Chemistry?

Regeneration · Feb 21, 2011

NurseBarbra said:
Well the formulas arent labeled and there like this in order of the questions(the test was 40 questions long):
-b+-√(b²-4(a)(c))
2a
ax²+bx+c
(x+h)² = (x+xh+h)
4/3πr³

-b+-√(b²-4(a)(c)) - Quadratic formula
2a

ax²+bx+c - General form of a linear equation in 2 variables.

(x+h)² = (x+xh+h) - Aren't x and h supposed to be squared and isn't xh supposed to be 2xh? o.o

4/3πr³ - Volume of a sphere

I like Pokemon (...) · Feb 21, 2011

smile! said:
How so? Err.. The way I understood your sentence is that Maths = everything but then you limited to physics is just maths. What about Biology and Chemistry?

~~I guess I didn't make it clear, that Biology was just Chemistry, and Chemistry was just Physics~~

And on my test papers, I have all of those as well as:
Volume of a pyramid/cone: [base]*[perpendicular height]/3
Volume of a prism: [Area of cross section]*[length]
Area of a trapezium: h(a+b)/2

NurseBarbra · Feb 22, 2011

Regeneration said:
(x+h)² = (x+xh+h) - Aren't x and h supposed to be squared and isn't xh supposed to be 2xh? o.o

Yeah but my teacher is kinda derp when it comes to equations. can't actually believe that he became a maths teacher. in class he put down 5(10)=510 one time.

Impo · Feb 23, 2011

NurseBarbra said:
Yeah but my teacher is kinda derp when it comes to equations. can't actually believe that he became a maths teacher. in class he put down 5(10)=510 one time.

..i think you should take his place.

and my teacher decided to give the class a directed investigation, and he's giving us a whole week. the questions are really hard (for me, anyway), and i've only managed to solve 3 out of 5 the first day. i wanna see how people here fair, i'm expecting for all of you to get it in like 5 seconds and make me feel stupid :P , but here they are;

A girl thinks of 3 numbers. She adds these numbers in pairs, getting 11, 17 and 22.
What are the three numbers?
(This took me so long to get, it was like a sudden brain wave and i got the answer. i then spiraled into a 10 minute victory dance with my friend, because we conquered the maths)

The sum of two numbers is 8 and the difference between their squares is 34.
Find their difference.
(This one annoyed me alot, took me a while to realise the seemingly obvious, but i got it)

and the other ones a calendar one that i can't be bothered typing.
as soon as i finish the others im going to post them and see if others can solve them too :)

Pokemon Trainer Touko · Feb 23, 2011

Oh my god~! My classmates are doing trigonometry and they don't even know what's the sine and cosine rules~?!?! :O Unbelievable~!

smile! · Feb 23, 2011

I like Pokemon (...) said:
~~I guess I didn't make it clear, that Biology was just Chemistry, and Chemistry was just Physics~~

~~Oh, okay. XD~~

Impo said:
A girl thinks of 3 numbers. She adds these numbers in pairs, getting 11, 17 and 22.
What are the three numbers?

The sum of two numbers is 8 and the difference between their squares is 34.
Find their difference.

~~I miss doing these kinds of questions. XD~~

Basically, it's how you manipulate the algebra. For the first one, just assign the numbers as x, y and z. Then make an equation for each and solve them accordingly.

For the second, it's about factorization. As long as you know that x² - y² = (x+y)(x-y), you should be able to do it.

Impo · Feb 23, 2011

smile! said:
~~Oh, okay. XD~~

~~I miss doing these kinds of questions. XD~~

Basically, it's how you manipulate the algebra. For the first one, just assign the numbers as x, y and z. Then make an equation for each and solve them accordingly.

For the second, it's about factorization. As long as you know that x² - y² = (x+y)(x-y), you should be able to do it.

hehe, i've done them already. it took me a while, i forgot about difference of two squares for a while. i wanted to see how fast you could do it, and im guessing it took two seconds.

how are you so good at maths? i'm so jealous.

Dude22376 · Feb 23, 2011

Uh, those questions aren't really that hard, unless you don't know algebra.

1) Let the numbers be x, y and z.
x + y = 11 (1)
x + z = 17 (2)
y + z = 22 (3)
As there are 3 unknowns and 3 equations we should be able to solve it.
(1) + (3): x + 2y + z = 33
Subtract (2): 2y = 16 thus y = 8
The rest is just basic manipulation, x = 3 and z = 14.

2) Let the numbers be x and y, x > y.
x + y = 8 (1)
x^2 - y^2 = 34 (2)
Again we have 2 equations and 2 unknowns, so it should be solvable.
Rearranging (1): y = 8 - x
Substituting into (2): x^2 - (8 - x)^2 = 34
Expanding: x^2 - 64 + 16x - x^2 = 34
Cancelling x squared and shifting -64 over: 16x = 34 + 64, thus x = 6.125
Then y = 1.875

If you want to get past your mental block at doing maths, just remember that if there are n equations and n unknowns, you should be able to solve for every unknown. Write down equations representing everything that is given to you in the question. Then solve those equations for the answers.
At your level, only substitution and elimination are needed. My answers for the two questions you provided display both techniques (eliminating x + z in the first and substituting 8 - x in the second).
If there are more unknowns than there are equations, then the question can't be solved!
If there are 2 equations which mean the same thing (like x + y = 3 and 2x + 2y = 6), then you can totally ignore one of those equations. If this puts you in a situation where there are more unknowns than equations, then the question can't be solved.

Oh, and if you want your equations to be displayed nicely on forums, try using Texify. It'll take some time to learn how to use, but you'll be able to display superscripts, subscripts, Greek letters, differential/integral signs, etc. Sadly I can't use it because I don't have 15 posts yet :(

Impo · Feb 23, 2011

ahhh, imma try all the harder ones now :) ,

Regeneration · Feb 23, 2011

This thread needs more manly trigonometry questions. I have one if anybody is bored:
If sinθ + cosθ = √2cos(90° - θ), find cot θ.

It's not really difficult, anyone wants to try?

Dude22376 · Feb 23, 2011

Let theta=x, it's easier than entering Greek characters.
cos(90-x) is sin x, substitute that in:
sin x + cos x = sqrt(2) sin x
Divide by sin x on both sides (assuming sin x is not 0):
1 + cos x/sin x = sqrt(2)
cos x/sin x is cot x, which is sqrt(2) - 1.

Regeneration · Feb 23, 2011

Dude22376 said:
Let theta=x, it's easier than entering Greek characters.
cos(90-x) is sin x, substitute that in:
sin x + cos x = sqrt(2) sin x
Divide by sin x on both sides (assuming sin x is not 0):
1 + cos x/sin x = sqrt(2)
cos x/sin x is cot x, which is sqrt(2) - 1.

Nice, that is the correct answer. I need to think of tougher questions now! >:D

My final examinations are fast approaching, so gotta practise lots of math. XD

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