To complete these questions it will be necessary to know the Index Laws:
And the rational index laws:
Also, we define, where
1: Simplify with positive indices:
2: Simplify with positive indices:
3: Simplify with positive indices:
4: Express as a power of x:
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.
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.
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.
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
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?
The spells sound are so corny:
Wingardio Leviosum! (or something)
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...
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?
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, asand 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 )
Plug in 1 and you get Approximately 2.09439510239.
Am I right?
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'
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?
I adjust my memorizing technique where it suits the number, for instance, I would remember like this:
And that also means that a number may be part of 2 groups:
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.