Mathematics Thread

What is the hardest math you learned?

  • Calculus (specify in comments)

    Votes: 69 35.0%
  • Trigonometry

    Votes: 27 13.7%
  • (Enriched) Geometry

    Votes: 18 9.1%
  • Equations (specify)

    Votes: 7 3.6%
  • Graphing Equations (specify)

    Votes: 5 2.5%
  • Basic Algebra (specify)

    Votes: 9 4.6%
  • I can do better!

    Votes: 49 24.9%
  • What kind of math is that?!

    Votes: 13 6.6%

  • Total voters
    197
Also, it might be useful to note that \( \frac{1}{2}(n^2 + n + 2) = \frac{1}{2}n(n+1) + 1 \)

I was going to ask a group theory question here, but then I realised that if G is a group, and H is cyclic subgroup of G, then the fact that H is abelian does not imply that H is a normal subgroup of G.
 
can someone figure this out? iv tried like 6 times and still cant get it right.

A runner runs 7.03 km in 21.9 min and then takes 37.0 min to walk back to the starting point.What is the magnitude of the average velocity for the total trip?
 
That seems trivial. What results did you get, and what's the supposed correct answer? And why ask for the "magnitude"?
I got 4.28 m/s, 3.97 m/s both twice and my other 2 answers were ridiculously wrong. unfortunately I don't know, it's part of an assignment for university. I'm not quite sure because in the question they ask for the average speed for the total trip? which turned out to be 3.97m/s
 
What do you not know? Their answer? Then how do you know that you "cant get it right"?

I'd say 3.98 m/s, but I'm still confused by the "magnitude" thing and that this is a university level question.
 
What do you not know? Their answer? Then how do you know that you "cant get it right"?

I'd say 3.98 m/s, but I'm still confused by the "magnitude" thing and that this is a university level question.

I don't know their answer :( because its online, so basically they give u the question online and u work it out however you want then type your answer in a box on the website and you can click "check answer" or "submit" if you click submit it locks the correct answers if you click check answers it just says which ones are correct and which are in correct.

Yeah and we only just started university (1st years :P )
 
Just a simple, quick question on circle geometry:
Lets say I'm given 4 points on a circle: A, B, C and D. If I were to draw the perpendicular bisector of A and B, and the perpendicular bisector of C and D, is the point of intersection of these two lines always the centre of the circle?
 
Just a simple, quick question on circle geometry:
Lets say I'm given 4 points on a circle: A, B, C and D. If I were to draw the perpendicular bisector of A and B, and the perpendicular bisector of C and D, is the point of intersection of these two lines always the centre of the circle?

No. It's possible that the two lines are the same, and then there's no "the point of intersection" but infinitely many, and only one of them is the center of the circle.
 
No. It's possible that the two lines are the same, and then there's no "the point of intersection" but infinitely many, and only one of them is the center of the circle.

I understand. But is the intersection the centre of the circle if the two lines don't have the same equation?

Edit: Maybe this question is more relevant: Is the perpendicular bisector of two points on a circle always a diameter of that circle?
 
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I got 4.28 m/s, 3.97 m/s both twice and my other 2 answers were ridiculously wrong. unfortunately I don't know, it's part of an assignment for university. I'm not quite sure because in the question they ask for the average speed for the total trip? which turned out to be 3.97m/s

can someone figure this out? iv tried like 6 times and still cant get it right.

A runner runs 7.03 km in 21.9 min and then takes 37.0 min to walk back to the starting point.What is the magnitude of the average velocity for the total trip?
youve asked 2 different questions. average velocity is 0, average speed i get 3.98 m/s
 
Ah, thanks... now I understand what they mean with "magnitude". In German, I don't think we have two separate words for velocity and speed, and I only knew "magnitude" as in "order of magnitude".

Magnitude of velocity is speed, but they asked for "magnitude of the average velocity" and not "average magnitude of velocity", so I'd say you're right and it's zero.
 
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ok so don't open the spoiler if you're offended by some harmless words

@mods, I warned people. you can't ban me for that.

[17:59:39] 5BLD: okay soe
[17:59:52] 5BLD: if x(!)=log(sin(1/!))
[17:59:59] Fluttershy: lol
[17:59:59] 5BLD: and ! is a function of +
[18:00:01] 5BLD: then
[18:00:05] 5BLD: theres no variable
[18:00:07] 5BLD: just funxions
[18:00:10] 5BLD: its riek sayin
[18:00:12] Fluttershy: and
[18:00:14] Fluttershy: no
[18:00:16] Fluttershy: nonono
[18:00:17] 5BLD: d/dx of sin
[18:00:21] Fluttershy: sin is a variable
[18:00:25] 5BLD: lol
[18:00:37] 5BLD: but then ! is a function?
[18:00:38] Fluttershy: s*n*√-1
[18:00:58] Fluttershy: sin(1/!) = sn*i/!
[18:01:06] 5BLD: aha
[18:01:08] 5BLD: okay...
[18:01:16] 5BLD: impricit with 4 variabelles letsgoo
[18:01:20] Fluttershy: i/! is of course a function too
[18:01:21] 5BLD: *3
[18:01:26] Fluttershy: and of quorce its an odd function
[18:01:30] 5BLD: wut
[18:01:37] Fluttershy: because

i/!

pi radiance rotational simmatry
[18:01:41] Fluttershy: i/!

LOL!!!!!!
[18:01:42] 5BLD: rol
[18:01:51] 5BLD: wait
[18:01:55] 5BLD: log is also a variable right?
[18:02:02] 5BLD: so...
[18:02:04] 5BLD: log(sin(1/!)) is
[18:02:14] Fluttershy: no
[18:02:26] Fluttershy: log is a function of dx
[18:02:34] 5BLD: l.o. g((sqrt(-1).(s.n))/!)
[18:02:39] 5BLD: where . means tiems ofc
[18:02:44] Fluttershy: lol
[18:02:49] 5BLD: and g is a funxion of s, n and !
[18:03:04] Fluttershy: and g(i.s.n/!) is a function where i.s.n/! = x
[18:03:07] 5BLD: and where sqrt(-1).(s.n)
[18:03:10] Fluttershy: l.o.g(x)
[18:03:17] 5BLD: (s.n) is part of the module sqrt(-1)
[18:03:19] Fluttershy: lo*g(x)
[18:03:24] 5BLD: it's
[18:03:25] 5BLD: like math.sqrt(1)
[18:03:29] Fluttershy: also
[18:03:31] 5BLD: sqrt(-1).(sn)
[18:03:39] 5BLD: so basically the Tin function
[18:03:43] 5BLD: of module sqrt(-1)
[18:03:47] 5BLD: cuz Sn is tin
[18:03:53] Fluttershy: 1 is a function of e^pi*arcsec(!)
[18:04:02] 5BLD: lol
[18:04:10] Fluttershy: sin(x) is the imaginary tin function
[18:04:18] 5BLD: but theres no e, pi, or a, r , c, or s in the funxion 1
[18:04:22 | Edited 18:04:31] Fluttershy: where function is a variable containing the string "variable";.
[18:04:31] 5BLD: so 1(e,pi,a,r,c,s,e,c)=?
[18:04:38] Fluttershy: = 1/cot(!)
[18:04:48] Fluttershy: LOL 1/cot = TAN ! ! !! ! ! !! LOL O!¬O !O !O !O OW)AGF{S)GIPR OTPlrg
[18:05:05] Fluttershy: where ! ! !! ! ! !! LOL O!¬O !O !O !O OW)AGF{S)GIPR OTPlrg is a function of Li
[18:05:05] 5BLD: I sang " 'Applejack' jugs of cider on the wall, 'Applejack' jugs of cider," Applejack got one less.
[18:05:22] Fluttershy: oh ??????????????????
[18:05:33] 5BLD: and where tan is actually the Ta rithmic integral
[18:05:36] Fluttershy: art thou listenizing to the smilesmilesmilewremicks??? ?? ??
[18:05:41] 5BLD: like Li is the logarithmic integral
[18:05:45] Fluttershy: Ta = tantalum
[18:05:48] Fluttershy: Li = lithium
[18:05:50] 5BLD: ah
[18:05:55] 5BLD: so Li is the Lithium funxion
[18:05:57] Fluttershy: MATHS = CHEMISTRY OMFG NEW DISCOVERY
[18:06:18 | Edited 18:06:28] Fluttershy: CoS = COBALT SULFIDE OMFGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG
[18:06:36] 5BLD: SIN= SULPHUR NITRIDERATE
[18:06:47] Fluttershy: LOL ! ! !
[18:06:51] 5BLD: THARFOR
[18:06:54] Fluttershy: SIN = SULFUR INDIUMIDE
[18:06:56] 5BLD: COSINE IS
[18:07:09] 5BLD: (COS)i (N)e
[18:07:11] Fluttershy: COS = CSO = CSO4 BECAUSE 4 = 1 = CARBON SULFATE
[18:07:27] 5BLD: which is i lots of Cobalt Sulphide
[18:07:29] Fluttershy: SIN = INDIUM SULFIDE
[18:07:29] 5BLD: and e lots of nitrogen
[18:07:42] Fluttershy: TAN = TANTALUM NITRIDE
[18:07:57] Fluttershy: DIVIDE BY TAN AND YOU GET TALUM NITRIDE/TAN = 1
[18:08:08] 5BLD: AND W IS THE TUNGSTENIAL INTEGWAL
[18:08:13] Fluttershy: LOL ! ! !
[18:08:14] 5BLD: NOT THE LAMBERT FUNXION
[18:09:03] Fluttershy: INVERSE X^X = LN(X)/TUNGSTEN(LN(X)) = LITHIUM NITRIDE(X)/TUNGSTEN(LITHIUM NITRIDE(X))
[18:09:23] 5BLD: LOL YOU FORGOT TO BALANCE YOU'R IQUASHUN NUB
[18:09:31] Fluttershy: NO
[18:09:36] Fluttershy: OWAIT YEAH I DID
[18:09:38] Fluttershy: BOOSHIT
[18:09:40] 5BLD: AND LUL ^ IS NOT AN ELEM'NT
[18:10:00] Fluttershy: REPLACE ALL THE LITHIUMS WITH LITHIUM.3 BECAUSE . = *
[18:10:13] 5BLD: WHERE . = and * ARE FUNXIONS
[18:10:22] Fluttershy: AND LITHIUM PROLLABY HATH A VALEN'T'CY OF 1 AND NITTRIJJEN HATH A VALEN'T'CY OF 3
[18:10:25] Fluttershy: 3LI = N
[18:10:35] Fluttershy: OWEIGHT
[18:10:42] Fluttershy: LITHIUM = LI, NOT L
[18:10:54] Fluttershy: REPLACE LITHIUM WITH 3/i (LITHIUM)
[18:11:06] Fluttershy: BUT 1/i = -i
[18:11:13] 5BLD: BUT NOW SUB IN LOGARITH'MIC INTEGWAL FOR LITHIUM
[18:11:19] Fluttershy: REPLACE LITHIUM WITH -LITHIUM√-9
[18:11:19] 5BLD: AND CANCEL YOUR FRAXIONS FURVER
[18:11:28] 5BLD: WIT PARCIAL FRAXXIONES
[18:12:03] Fluttershy: BREST = BREAST = BoOB = BOOSHIT BORON OXIDE
[18:13:02] 5BLD: BUT BUT BUT Bo(x) IS THE Booshit FUNXION
[18:13:08] Fluttershy: OH ****
[18:13:18] 5BLD: AND ITS OXYGEN BORONIDE YOU MORON
[18:13:19] Fluttershy: OK SO
[18:13:23] Fluttershy: OH YEAH BOOSHIT
[18:14:41] Fluttershy: THE INTEGRAL OF E^X/X IS Ei(X) WHERE Ei(X) IS THE INTEGRAL OF E^X/X
[18:14:48] Fluttershy: http://www.wolframalpha.com/input/?i=integrate+e^x+/x
[18:16:18] Fluttershy: = E^X (SUMFROM1TO∞ (N-1)!/X^N)
[18:16:39] 5BLD: it's the Eileen funxion
[18:16:58] Fluttershy: oh
[18:18:56] Fluttershy: (24ln2 + 19)/(17 - 4√2) squiggly equals pi
[18:19:19] Fluttershy: = 3.14159168164etc.
[18:20:56] Fluttershy: ln√2 = arccoth(3)
[18:21:16] Fluttershy: trouxdat
[18:21:27 | Edited 18:21:29] Fluttershy: oops
[18:21:48] Fluttershy: arctanh(1/3) = ln√2
[18:22:01] 5BLD: sqrt(6 zeta(2)) is about pie
[18:22:01] 5BLD: *pi
[18:22:05] 5BLD: closar than yours atreast
[18:22:16] Fluttershy: lol
[18:22:22] Fluttershy: its exactry pie/e
[18:22:29] Fluttershy: L.O.L. !
[18:22:30] 5BLD: ik
[18:22:31] 5BLD: amazing huh
[18:22:34] 5BLD: how did i doit
[18:23:00] Fluttershy: riemannzeta2=(pi^(e^ln2))/6 LOL ! ! ! ! !
[18:23:31] Fluttershy: iwannafind d exac valeux of zeta(3)
[18:23:46] Fluttershy: it annoys me sometimes
[18:24:21] 5BLD: maek prouxgram
[18:24:28] Fluttershy: butbut not egg-sact
[18:24:34] Fluttershy: zeta3 = 1.20205690315959428539973816151144999076498
[18:24:37] Fluttershy: etc.
[18:24:46] Fluttershy: but noboooooooodeeh knows what the exac valeux is
[18:25:04] 5BLD: plot a graff silly
[18:25:08] Fluttershy: but but
[18:25:10] Fluttershy: not exac
[18:25:16] Fluttershy: in terms of pie n booshit rike that
[18:25:21] Fluttershy: haux to integrate x²/1+e^x
[18:25:35] 5BLD: idk why ask me for integwashion
[18:25:40] Fluttershy: lol
[18:25:42] 5BLD: btw
[18:25:55] 5BLD: I FOUND THE EXACT VALUE FOR ZETA(3)!!!!!
[18:26:04] Fluttershy: ITS ZETA(4-1) OMFG
[18:26:11] 5BLD: NO SILLY
[18:26:14] 5BLD: I AM MORE AQUARATE
[18:26:20] 5BLD: ITS APÉRY'S CONSTANT
[18:26:24] 5BLD: TROLOLOLOL
[18:26:24] 5BLD: I WIN
[18:26:25] Fluttershy: INO
[18:26:27] Fluttershy: LOL !!!!!!!!!!!!!!!!!!!!!
[18:27:03] 5BLD: btw
[18:27:05] Fluttershy: IT 2/3 INTEGRALX²/1+E^X FROM 0TOSIDEWEIGHS8
[18:27:12] 5BLD: you'r integwal cannot be done without lifium
[18:27:19] Fluttershy: ino
[18:27:33] Fluttershy: lithium is now my least favouxrite elemen't
[18:27:41] 5BLD: lol
[18:27:48] 5BLD: i hate tungsten moar
[18:28:10] Fluttershy: nah
[18:28:15] Fluttershy: i hate lithium mõar
[18:28:17] Fluttershy: cuz
[18:28:22] Fluttershy: tungsten = wolfram
[18:28:31] 5BLD: nein
[18:28:38] 5BLD: tungsten = lambert function
[18:28:46] 5BLD: cuz sum stupith math'maticians cant spell
[18:28:48] 5BLD: its not
[18:28:49] 5BLD: wambert
[18:28:51] 5BLD: siwwwy
[18:28:55] Fluttershy: lol
[18:29:17] Fluttershy: imma be like whoever the **** wambert is and invent my own function
[18:29:18] Fluttershy: ok so
[18:29:47 | Edited 18:29:55] Fluttershy: i have found the exact value of zeta(x)
[18:29:49] Fluttershy: loln
[18:29:55] 5BLD: zeta of thumb down?
[18:29:57] 5BLD: hmm
[18:30:21] Fluttershy: zeta(x) = 1/Boosack(x^sin(x))
[18:30:31] 5BLD: its the boosack funxion
[18:30:44] Fluttershy: where boosack(x) is whatever you get whenever you rearrange that equation for boosack(x)
[18:30:46] 5BLD: integwate B(2)
[18:30:51] Fluttershy: ok
[18:30:55] Fluttershy: B²+c
[18:30:56] Fluttershy: LOL ! ! ! ! ! !
[18:30:57] Fluttershy: dB
[18:31:01] Fluttershy: Dessybelle's
[18:31:04] 5BLD: lol
[18:31:05] 5BLD: but
[18:31:09] 5BLD: B is the boosack funxion
[18:31:16] 5BLD: moron
[18:31:28] Fluttershy: dB is the derivative of the Boosack function
[18:31:47] Fluttershy: ok so
[18:32:15] Fluttershy: zeta(x) = 1/(1/zeta(ln(e^x)))
[18:32:20] Fluttershy: OMFG NEW DISQUOVARREIX
[18:32:39] 5BLD: this is what i don't understand in the Wambert funxion
[18:32:44] 5BLD: you defien the funxion
[18:32:47] 5BLD: using the funxion
[18:32:50] 5BLD: its rike sayin
[18:33:00] 5BLD: i caem up with a new funxion:
[18:33:06] 5BLD: the Aluminium funxion
[18:33:10] 5BLD: okay lets call the G(x)
[18:33:31] 5BLD: G(x)=G(x)^G(x)/ln(x)
[18:33:37] 5BLD: it maek no sence
[18:34:06] Fluttershy: OK SO THE FUNCTION X! IS WIERD BECAUSE ! IS WIERD N BOOSHIT OK SO HERES MY FUNCTION. D/DX X! = BOOHAT(X) WHERE BOOHAT(X) IS THE DERIVATIVE OF X!
[18:35:03] Fluttershy: imma post this booshit in the math's thred on spidslovving
[18:35:16] 5BLD: kay
[18:35:20] 5BLD: inb4 deweated D:
[18:35:24] 5BLD: andén i repost
[18:35:26] 5BLD: http://www.youtube.com/watch?v=UA8QQZffIlM
[18:36:39] Fluttershy: ill have to put it all in a spoiler so the mods dont cry about me saying booshit
[18:37:09] 5BLD: nah
[18:37:10] 5BLD: dont
[18:37:14] 5BLD: its just boos hit
[18:37:15] 5BLD: like
[18:37:17] 5BLD: boos from marii
[18:37:19] 5BLD: *mario
[18:37:20] 5BLD: being hit
[18:37:25] Fluttershy: L.O.L. !
[18:37:34] 5BLD: you can poest that as a disclaemer if needbie
[18:37:38] Fluttershy: at the top of the post, ill just put something like
[18:37:48] Fluttershy: "dont open this spoiler if youre offended by harmless words"
[18:38:10] 5BLD: yeah
[18:38:12] 5BLD: dovat
 
How do you guys solve equations like 6x^2+3xy=270

Don't care about answers, only methods

Hmmm... Let's see...

Get all x/y's on one side, factorise if possible, and then get x on its own. I'll work that one out now. Also, is there a guide to the bb-code for math tags?

Right... Here's what I did to make x the subject.

6x^2 + 3xy = 270
So, we can factorise straight away, and we get:
x(6^2 + 3y) = 270
Divide by (6^2 + 3y) and we end up with:
x = 270 / 6^2 + 3y
Simplify, and we finish with:
x = 90 / 12 + y

If we make y the subject:
6x^2 + 3xy = 270
- 6x^2
3xy = 270 - 6x^2
/ 3x
y = 270 - 6x^2 / 3x
Simplify, and we end up with:
y = 90 - 2x^2 / x
 
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Hmmm... Let's see...

Get all x/y's on one side, factorise if possible, and then get x on its own. I'll work that one out now. Also, is there a guide to the bb-code for math tags?

Right... Here's what I did to make x the subject.

6x^2 + 3xy = 270
So, we can factorise straight away, and we get:
x(6^2 + 3y) = 270
Divide by (6^2 + 3y) and we end up with:
x = 270 / 6^2 + 3y
Simplify, and we finish with:
x = 90 / 12 + y

If we make y the subject:
6x^2 + 3xy = 270
- 6x^2
3xy = 270 - 6x^2
/ 3x
y = 270 - 6x^2 / 3x
Simplify, and we end up with:
y = 90 - 2x^2 / x

he mean't finding integer solutions, not just rearranging.
 
Calculator/Math Thread

Ben speaks the truth. I forgot to mention x,y subset bold Q whoops

That's impossible with two unknowns.

No it's not.

Hmmm... Let's see...

Get all x/y's on one side, factorise if possible, and then get x on its own. I'll work that one out now. Also, is there a guide to the bb-code for math tags?

Right... Here's what I did to make x the subject.

6x^2 + 3xy = 270
So, we can factorise straight away, and we get:
x(6^2 + 3y) = 270
Divide by (6^2 + 3y) and we end up with:
x = 270 / 6^2 + 3y
Simplify, and we finish with:
x = 90 / 12 + y

If we make y the subject:
6x^2 + 3xy = 270
- 6x^2
3xy = 270 - 6x^2
/ 3x
y = 270 - 6x^2 / 3x
Simplify, and we end up with:
y = 90 - 2x^2 / x

Lol I know how to rearrange. I want all solutions in terms of, say w. Where w is any integer.

Yesterday ben and I were solving linears. Him with his program and me by hand with this silly method I came up with:

NB: yes, i did not mod the solutions down because I didn't bother. You can probably do it yourself.
NB2: in the answers, I use 'w' to represent ANY integer.

[06/10/2012 20:00:10] Fluttershy: 23x + 61y = 4068
[06/10/2012 20:24:46] fivebldcubing: x=(31-61w)
[06/10/2012 20:26:36] fivebldcubing: and y = 55+23w

23x + 61y = 4068
61y = (4068-23x)
y = (4068-23x)/61
y= 66+(42-23x)/61

r=(42-23x)/61
x=(42-61r)/23
x=1-2r + [ 19-15r ]/23

q=[ 19-15r ]/23
r=(19-23q)/15
r=1-q + [ 4- 8q ]/15

q=[ 4- 15p ]/8
q=-p + [4-7p]/8

t=[4-7p]/8
p=[4-8t]/7
p=-t+ [4-t]/7

t= [4-7w]
--

p=[8w-4]

q=[ 8- 15w]

r=(23w-11)

x=(31-61w)

--
713-1403w + 61y = 4068
61y = 3355+1403w
y = 55+23w


x=31-61w
y = 55+23w
--
 
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