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#1 Exercises » Index Laws Practice » 2007-05-07 02:19:38

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Replies: 7

To complete these questions it will be necessary to know the Index Laws:
Law 1:


Law 2:

Law 3:

Law 4:

Law 5:

And the rational index laws:

Also, we define

, where

To prove this:
, but


1: Simplify with positive indices:
a)


b)

c)

d)

e)

2: Simplify with positive indices:
a)

b)

c)

d)

e)

3: Simplify with positive indices:
a)

b)

c)

d)

e)

4: Express as a power of x:
a)

b)

c)


d)

e)

#2 Re: Introductions » Hello » 2007-03-12 22:48:19

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Well, I didn't make it up tongue I found it in "The Encyclopaedia of Music", oddly enough.

#3 Re: Maths Is Fun - Suggestions and Comments » Degree of an Expression » 2007-03-12 22:46:38

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Nice job on that page, I never knew about the fractions thing. Well... there isn't really much to talk about regarding degree apart from what you've already said... and perhaps that limit thing... so yeah up

#4 Re: Dark Discussions at Cafe Infinity » toby » 2007-03-12 18:08:06

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I must say that you, sir, are the most accomplished topic-changer I have ever met.

#5 Re: Maths Is Fun - Suggestions and Comments » forum for artists? » 2007-03-12 18:02:16

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Devantè wrote:

Actually the accent is the other way round (è). I wasn't named after DeVante Swing, no, I wasn't named after anything. But let us see who can guess what my name means. smile

I remember seeing you post about this a while ago on the forums, so I'll just try and rely on my memory for this one...

A kind of god...?

Heh, that's all that comes to mind, i think several forum members are named after gods of some kind.

#6 Re: Maths Teaching Resources » Announcement » 2007-03-12 17:57:54

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Shorten the subheadings under the forum titles so that they are nice and short like MathsIsFun's. In the MathsIsFun forum you aren't immediately freaked out by all these abstract terms you have never heard about in the forum subheading. Keeping the subheading vague, but not too vague allows catering for a larger target audience.

#7 Re: Introductions » Hello » 2007-03-12 17:49:53

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Devantè wrote:

Welcome to MathsIsFun, mathman.

It's appreciated that you like mathematics, it can be a joy for the mind (or as the statement of the wise goes 'mathematics is music for the mind' (or is it the other way round?).), even in the most strangest of places...

"Mathematics is music for the mind; music is mathematics for the soul." - Anonymous

#8 Re: Guestbook » Harry Potter » 2007-03-12 17:44:34

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lightning wrote:

if i said open sesamme a doors not gonna open is it? i dont think so

haha, I laughed at bit at that

#9 Help Me ! » Natural Number » 2007-03-11 22:15:38

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Replies: 8

How do I create equations that will only yield a natural answer number? For instance, how would I change this so that for any value of a or b (as long as b is greater than or equal to 10a), x will be a natural number?

I've seen it done with pythagorean triples, can it be done elsewhere too?

#10 Re: Guestbook » Harry Potter » 2007-03-11 21:52:02

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The spells sound are so corny:
Alo Hamora!
Wingardio Leviosum! (or something)
Expecto Patronum!
Harry Potter's all a bit too hollywood for me. I cringe every time I see an ad where Harry is screaming out "EXPECTO PATRONUM" at the top of his lungs. Can't they quieten down a bit, sheesh...

#11 Re: Maths Is Fun - Suggestions and Comments » forum for artists? » 2007-03-11 21:43:28

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Oh yeah, now I remember, I thought Devante's name was a lot like Descarte's lol

#12 Dark Discussions at Cafe Infinity » Originality. » 2007-03-11 00:08:19

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Replies: 7

Something that has worried me for a long time is that with all the different business names and trademarks, there soon will be so many different brand names that it will be virtually impossible to come up with something good, and new businesses will be left with brands with long or unusual names - the leftovers.

I have the worse concerns for books, music and art. How many unique plots are possible, how many ways can a sentence be written, without people constantly debating over who copied what etc. And for music, I have heard many melodies and harmonies in my time, and every kind of music that is pleasing to hear is based on set structures of harmony and perhaps a good melody. However, if we keep sticking to these guidelines there will be no room left for innovation, and the only place left is the avant garde world, which can really only be ingested in bite-sized portions. I think you kind of get my drift by now...

Do you think this is a major concern?

#13 Re: Maths Is Fun - Suggestions and Comments » forum for artists? » 2007-03-10 23:50:49

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Who's applying the pressure here? I'm rather confused.

#14 Re: Guestbook » times tables » 2007-03-10 23:45:46

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Study hard at maths then you can P4\/\/lV ur friends at it.

#15 Re: Dark Discussions at Cafe Infinity » Attention: The Arctic is to melt mostly by the summer of 2040 » 2007-03-10 14:39:28

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Mass exodus of polar bears... wouldn't that be kinda hard?

#16 Re: Help Me ! » Whats the perimeter? » 2007-03-10 03:11:18

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Ok, lemme have a go at this *IT MAY NOT BE CORRECT*

I hope I have interpreted this correctly and the coloured part of the diagram is the length you've asked me to find.

You might wanna look at the attached diagram first:

Double theta to find the angle needed for one half of the total perimeter:

Then, make it a fraction of the whole circle then multiply by pi and the diameter :

As the two halves of the perimeter are in fact equal, simply multiply this by 2 too, and you will get the total perimeter:

And, as

and cos(60) = 1/2, therefore arccos(1/2) = 60. Simplify the rest and you will get

(I am always amazed at how you can reduce something so complex to something so simple and workable smile)

Plug in 1 and you get Approximately 2.09439510239.

Am I right? big_smile

#17 Re: Maths Is Fun - Suggestions and Comments » forum for artists? » 2007-03-10 02:20:21

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When I first came to this forum you reminded me of Deviantart (LoL), but now it's the other way round wink

#18 Re: Dark Discussions at Cafe Infinity » Bullying-reasons or whims? » 2007-03-10 02:19:07

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Oh yea I've had those white rabbits, aren't they just condensed sugar?

#19 Re: Help Me ! » Small Math Grammar Question » 2007-03-10 01:03:08

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Ok thanks all, what I was trying to explain was, that as F*D=F, F=/=0, then D = 1

"Or more generally, as the multiplied number doesn't equal zero and did not change, the number it was multiplied by must equal 1."

Or perhaps I should simply stick to using F and D instead of 'number' or 'term' tongue

#20 Re: Help Me ! » Small Math Grammar Question » 2007-03-10 00:29:24

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Oh, so would the following passage be correct?

"Or more generally, as the multiplied term did not change, the term it was multiplied by must equal 1."

#21 Help Me ! » Small Math Grammar Question » 2007-03-10 00:03:03

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Replies: 6

I know that if you have an equation...
a + b = c
...a, b, and c are terms.

However, if you have the equation...
a × b = c
...would you still be able to call a, b, and c terms? Would the product of a and b mean that they are the same term?

Also, are variables ANY pronumerals representing unknown values or are they only pronumerals which constantly change.
i.e. For y=mx+c, are all variables?
i.e. For a+b=c, where Each Letter Has 1 Possible Value, are any or all variables?


Thanks.

#22 Re: Dark Discussions at Cafe Infinity » Continue the story » 2007-03-09 18:33:29

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he completely ignored it, seeing as two threads are better than one...

#23 Re: Help Me ! » What is 7+9? » 2007-03-09 16:29:24

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lil_tomboysk8 wrote:

How can you solve 7+9, since 7 8 9???

Huh? This must explain why you can't divide by zero or find the square root of negative numbers. WE HAVE A HOLE IN OUR MATHS!!!

#24 Re: Puzzles and Games » Words words words! » 2007-03-09 03:45:39

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lightning wrote:
Zach wrote:

lightning #3: That's not even a real word.

yes it is you know like a tigers terrortory

I think you probably meant territory up

#25 Re: This is Cool » 2424[b]2[/b]4242 in [math]\pi[/math] » 2007-03-09 03:33:36

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I adjust my memorizing technique where it suits the number, for instance, I would remember like this:

6406286208998628

And that also means that a number may be part of 2 groups:

3.1415926

For me 5 is part of the 3.1415, as it progresses up from 3 to 4 to 5, but it is also a necessary part of 5-9 and 2-6 to keep a difference of 4 between each of the two which is how i've remembered them.

-.- maybe i should just learn in groups of five.

Yes.

Nevermind.

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