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The Mathematics Club ~ *ΜΑΘ* ~

NurseBarbra said:
Spoiler:
Click to expand...
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.
 
smile! said:
Eh...? Explain. :P
Click to expand...
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....
Click to expand...
How so?

I swear I'd have given that stuff a try if I came to the club earlier.
 
ShinyMeowth said:
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.
Click to expand...

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)
 
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
 
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.
Click to expand...

...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?
 
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
Click to expand...
-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
 
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?
Click to expand...
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
 
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
Click to expand...

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.
 
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.
Click to expand...

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

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.
Click to expand...

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.
 
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.
Click to expand...

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.
 
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 :(
 
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?
 
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.
 
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.
Click to expand...
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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