Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

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#301 Re: Help Me ! » Need help Urgently!!!!! » 2008-12-11 17:16:17

Q1

where v is in (m/s) and t is in seconds.

∴ The instantaneous velocity at 2 seconds is 4 m/s

Q2.

To prevent division by zero, the denominator must not be zero.

So solve:

Hence the domain is

Q3.

Since x = -1, 1 would cause division by zero, there are discontinuities at x = -1, 1. (These are vertical asymptotes)

#303 Help Me ! » position vector of centre of circle » 2008-12-11 13:36:59

Identity
Replies: 3

Relative to an origin, points, A, B, C, D, and E have position vectors:





Find the position vector of the centre of the circle through E, D, B and F (

).

Sorry for not having a diagram, hopefully you can work it out using the vectors themselves. Thanks!



This is actually the last part of a question so here are the other parts in case they might help:
a) Show that E lies on lines DA and BC.
b) Find

and

c) Find the position vector of point F, the intersection of lines DC and AB.
d) Show that FD is perpendicular to EA and EB is perpendicular to AF.

#304 Re: Maths Is Fun - Suggestions and Comments » Mathopolis » 2008-12-11 13:17:09

Ah I see, well... I guess you can be as generous as you like, perhaps instead of reducing the error for high numbers you could increase the error for lower numbers. Up to you I guess smile

#305 Re: Maths Is Fun - Suggestions and Comments » Mathopolis » 2008-12-11 12:05:35

Sorry I don't quite understand the system, what is PointsPer?

#306 Re: Maths Is Fun - Suggestions and Comments » Mathopolis » 2008-12-10 17:46:04

Perhaps just lessen the change in allowable error, it's just that it's quite noticeable for me at the moment.

e.g. within 4 of 80 is the same as within 1 of 10

For games with small numbers, I think the "within 1,2, or 3" system is fine.

As for the scoring, you could keep it as it is, but maybe you could also have a scoring system where it ranks firstly based on # correct and then avg. reaction time.

#307 Re: Maths Is Fun - Suggestions and Comments » Mathopolis » 2008-12-10 16:05:04

In the estimation games, it seems you get penalised WAY more for getting something wrong when the answer is small. Whereas if the answer is higher the allowable error increases. I think that this is a bit unfair, because sometimes finding the smaller answers can be just as hard as the higher answers. Maybe you could lessen the penalty?
e.g. In the estimate up to 99 shapes game, if the screen is really cluttered then you know it's in the region of 80-99, and even if you're really off, you still get points, but if there's only about 30 items on the screen and you are very close, you will still only get a few points.

Also I think the scores should have some kind of scaling in relation to the game's difficulty. For example, in Subtract Double, the scores will rarely get over 20, but in Add Single the scores can be very close to 100. I don't know how this would be implemented, but it might be a good idea

#309 Re: Help Me ! » Vector proof » 2008-12-09 23:20:49

Ah, thanks Kurre, so

Didn't see how it would follow through at first, but then realised

Nice!

#310 Help Me ! » Vector proof » 2008-12-09 20:26:03

Identity
Replies: 2

Ok, so this came about when I tried to prove:

"If the midpoints of the sides of a rectangle are joined, a rhombus is formed."

Long story short, I tried to prove that the rhombus WXYZ (formed from rectangle OABC), has equal side lengths and that led me to this hypothesis:

If

, then

Can someone please help me with this or provide a counterproof?

#311 Re: Puzzles and Games » Neat problem » 2008-10-12 18:43:57

Since

and
is positive,
.

Also,

so
.

hehe... well i guess x is somewhere in there...

#312 Re: Dark Discussions at Cafe Infinity » Debate #001: Is math a science? » 2008-10-11 02:01:24

I don't think math is a science.

The way I see it is scientists make up their theories according to empirical data and observation.

Mathematicians on the other hand make up their axioms and everything else falls in place. I don't think there is a scientific method to maths.

Scientists are 'forced' to use the scientific method because there exists no other method which will create new and more accurate theories. Hence, there is no proof in science, only evidence, and everything is potentially falsifiable.

With mathematics, you can prove something to be true and there will never be a disproof, as long as you follow the axioms you began with. We shouldn't be focusing on the process of obtaining a solution, but the strength of the solution itself.

#313 Re: Help Me ! » Please check my reasoning » 2008-10-11 01:57:31

ok thanks mathsy

I was mostly worried about my 'reverse working' of the inequality being some kind of fallacy

#314 Help Me ! » Please check my reasoning » 2008-10-10 19:55:28

Identity
Replies: 2

Could someone please check my reasoning with this question? I'm not sure about it

Question:
Find the values of

for
for which no real solutions exist.

Let  then

.
If you look at the graph of
, it is a parabola with a minimum. You must make it so that either:
1. The graph does not touch the a-axis or
2. The graph only has non-positive roots for a.
Note that the term  translates the graph left or right.
For 1.
, so solving,
.
For 2.

Assuming
is positive (which must be true for a negative translation and hence negative roots) and considering only the right root,


Since all these steps can be done in reverse (i.e. go from

to
, then the roots will be negative if and only if
and b is positive, which is true.
Hence, the total set of values for which no solutions exist is
.

#315 Re: Dark Discussions at Cafe Infinity » LHC (Large Hadron Collider) » 2008-10-04 05:58:26

Some advanced military aircraft can cost a few billion dollars, so constructing the LHC is definitely a step in the right direction.

#316 Re: Help Me ! » how does this factor...? » 2008-10-03 11:34:39

Yeah it is! That's a good technique Jane, I'll have to remember it smile

#317 Help Me ! » how does this factor...? » 2008-10-01 11:27:03

Identity
Replies: 3

In a problem I need to find the maximum possible difference between any two variables in

The solutions give

What I don't get is how that factorises! This is a non-calculator problem and it confuses me how someone could first of all 1. See how to split up the polynomial so that just the right kind of stuff is in each place, 2. Know that the left bit actually factorises at all, 3. Factorise it.

Is there a method to the madness [other than simply inspection] or is this something you just need g0dlike intuition for?

#318 Re: Dark Discussions at Cafe Infinity » I spotted a mistake in John Wyndham’s novel » 2008-09-25 22:53:33

integer wrote:

I am enarmored of your talents.

I've spotted a frightfull mistake.

#319 Re: Help Me ! » help me with a simple pre-algebra problem please » 2008-09-18 04:37:44

In front of a number, a positive and a negative makes a negative, and a negative and a negative makes a positive. Applying this:

-10 - (-8) + (-4) - 20 = -10 + 8 - 4 - 20 = - 26

If you have trouble with this, try drawing a number line to help you picture it

#320 Re: Help Me ! » Need Someone to check my Differentiation & Integration Asgmt » 2008-08-31 23:18:39

Let

Let

You need to make u = something and dv = something, not u = something and v = something tongue
In general let u be complicated and let dv be something easy to integrate (stuff usually simplifies when u diff it)

#324 Re: Jai Ganesh's Puzzles » English language puzzles » 2008-08-05 05:39:04

ganesh wrote:

#62. What does the word 'Gestapo' (German) mean?

#325 Re: Dark Discussions at Cafe Infinity » Where to learn higher calculus? » 2008-08-05 00:51:30

An extension subject automatically becomes your 6th subject in VCE, the maximum aggregate score you can get from it is 5.5. This may not seem much but if you had another normal VCE subject in your 5th or 6th spots then the max you can get most of the time is 10% of 50 = 5. The extra 10% increments by your 5th and 6th subjects can be crucial in pushing your ENTER 99+.

http://www.vcaa.vic.edu.au/vce/studies/ … nsion.html

Melbourne, Monash, and Victoria Universities offer the courses. You need to go to the following sites and read the information. Talk to your teacher about it as well to see if it's the best idea.
e.g
http://www.monash.edu.au/study/enhancem … ation.html
http://www.services.unimelb.edu.au/umep … ation.html
[Um, I don't know why the VU link is broken, but Monash and Melbourne are more prestigious anyway]

Also on offer is Extension Physics. Perhaps if you're doing Electronic Engineering this might be more useful to you than Extension Maths, but it's your choice. Having said that, any extension study would be a great head-start into that field.
All Extension Courses cover a 1st Year University course in that particular subject. Another fantastic benefit of doing a Uni Extension is that it actually gives you Credit for if you continue to study a degree in that subject at the university! So you will reduce both the time and fees required in university to fund those 1st year Credits.
If a 1st Year Uni course sounds like a lot of hard work and intensity, don't worry. I've spoken to people on vcenotes.com and all of them say it requires the same or less work than a VCE subject. Especially Monash Maths tongue

Oh BTW, I also heard that Melbourne University Engineering is really bad. It is very theoretical and supposedly people have been demotivated by it. So if you choose to do engineering I would recommend Monash. up

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