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#202 Re: Help Me ! » Modulus Function Question » 2009-07-05 21:00:23

To solve an inequality like that, one way is to graph

and
and find where the first graph is below the second graph.

can be written as

So the turning point is at

.

However, due to the modulus sign, we must reflect every negative y-value about the x-axis, so the turning point of

is

So when you sketch the graph it should look like a normal parabola except the part between the x-intercepts has been reflected about the x-axis. This graph should cross the line y=2 at 4 points, and if you graph you will see there are two sections below the line y = 2.

To find the intercept between the two graphs,

So for

and

,

#203 Re: Help Me ! » Remainder Theorem/Factor Theorem/Partial Fractions Question » 2009-07-05 20:44:12

The cubic equation can be written as:

Since if you sub in the roots of x you get zeros.

Now use the remainder theorem to find the value of a, and long divide for the final answer.

#206 Re: Dark Discussions at Cafe Infinity » How would you move Mnt. Fuji? » 2009-07-02 07:11:53

Ricky wrote:
Ricky wrote:
Identity wrote:

A lever 100000000000 miles long

You'd need to build a ship for it, something like an ark immediately.

In hindsight, perhaps this was a bit to obscure, but I believe Identity was referencing to Archimedes' lever, hence the "ark immediately".

I don't know how an ark fits in with the lever ? tongue

#207 Re: Dark Discussions at Cafe Infinity » How would you move Mnt. Fuji? » 2009-07-01 16:09:29

Create a wormhole, pushing it into the fourth dimension!

#208 Re: Dark Discussions at Cafe Infinity » Eerie facts » 2009-06-30 22:56:42

Stephen Hawking was born on the same day as Galileo Galilei, exactly 300 years later!

I also remember there was another cool birthday/deathday coincidence but not sure which was it was, maybe it was:
Einstein died 100 years after Gauss.
But I think it involved Ramanujan... alas I have not been able to find it.

Oh yeah and I forgot to say, I saw star trek and it wasn't what I expected but it was still awesome! I have to get the DVD!

#211 Re: Dark Discussions at Cafe Infinity » How would you move Mnt. Fuji? » 2009-06-27 18:48:47

- Run past it, watching it as it moves by.

- My name is not "mount Fuji"!

- I would not move it very well.

- Wait for the earth to rotate.

- Pick a small rock from mount Fuji and take it back to me on my flight home. The centre of mass of mount Fuji should have moved.

big_smile

#212 Re: Dark Discussions at Cafe Infinity » Star Trek » 2009-05-21 00:13:48

Oh stop making me jealous rolleyes

lol I really want to see it after I get my exams done with

#213 Help Me ! » Integral » 2009-05-14 22:09:06

Identity
Replies: 2

Please

How many ways are there to do this integral?

#214 Re: Help Me ! » Division Method: Reciprocal Multiplication » 2009-05-12 20:42:43

What is Reciprocal Multiplication? Can you give an example?

#215 Re: Maths Is Fun - Suggestions and Comments » New "Manipulative" called "Smart Blocks" » 2009-05-09 16:12:31

If you do
12x+=

or something like that it comes up with 0... maybe just call it 'incorrect expression' or something

#216 Re: Dark Discussions at Cafe Infinity » Star Trek » 2009-05-02 22:32:17

Harry Potter, whenever it comes out big_smile

#217 Dark Discussions at Cafe Infinity » Star Trek » 2009-04-29 21:57:57

Identity
Replies: 12

Wow, the trailers for Star Trek look amazing! Anyone else really excited about the movie?

Here are the trailers:
http://www.youtube.com/watch?v=7w4vk5OZmn8
http://www.youtube.com/watch?v=fdneFmLn0Sg

I haven't been that big of a fan of Star Trek but judging by the trailer and reviews it looks like it will a masterpiece.

Here are the reviews on rottentomatoes:
http://au.rottentomatoes.com/m/star_trek_11/

#218 Re: Help Me ! » A proof I'm looking for » 2009-04-25 00:25:13

Thanks Kurre, I'll try to find it in the list. However, it is not Ceva's theorem or Menelaus's theorem.

I remember seeing a wikipedia page on it - it was a very advanced proof I think, but still uses Euclidean geometry somehow

#219 Help Me ! » A proof I'm looking for » 2009-04-24 23:41:33

Identity
Replies: 2

I'm looking for a geometric theorem which can be only proven using logical contraposition. I can't remember what it's called, but I faintly recall it involving a triangle and some lines.... thanks

#221 Re: Introductions » proving inequalities » 2009-04-21 20:30:28

That is a great proof, thanks bobbym, I learnt a lot from that.

However, is there a way to find the minimum of

without calculus?

Thanks also nurshodiq, I'm not that familiar with AMGM but it's interesting.

#223 Re: Help Me ! » Percentage question - Has been very confusing me since I know maths. » 2009-04-18 21:38:35

Do you mean 19 percent of 137?

This is a rough analogy, but here it goes:

Imagine $137 is all (100%) of the money I have, and it is somehow evenly scattered throughout 100 boxes (it is composed of 1 cent coins)
If you want to take 19% of the money, then it would make sense that you need to take 19 out of the 100 boxes.

So you now have

of the boxes and
of the money. The total amount of money is $137, so you actually have:

In general, if you want to find x% of y, then it will be

#224 Re: Exercises » find all positive integers to » 2009-04-16 20:14:00

tony123 wrote:

find all positive integers to


Since this must be a cube,

No solution? hmm

#225 Re: This is Cool » The square roots of recurring '1's » 2009-04-13 15:03:08

Hmm that is pretty cool!

Are there any other numbers whose square root has interesting properties?

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