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hi luzbyrd
Welcome to the forum.
The one area I already knew about is the application of group theory in solving the Rubik's cube. If you're interested search for the name Singmaster.
Then I asked my pal google and came up with:
fields __ telecoms, medical imaging, navigation, power generation
complex geometry __ computer graphics, architecture, design
rings __ industrial control systems
linear algebra __ algorithms, graphics, data mining, machine learning.
At this point I decided to stop. You can complete your search by trying google yourself.
I should emphasize: I don't know the underlying theory for most of the above.
The other point that is worth making is this. Many areas of 'pure' mathematics seemed to be just there because mathematicians like to play around with ideas but who can predict when these theories might become useful in the real world? Who would have thought that a study of number bases and, in particular, base 2, would have become the basis for all computing or that prime numbers would be useful in encryption.
Bob
Meaning truncate:
1 | verb | replace a corner by a plane
2 | verb | approximate by ignoring all terms beyond a chosen one
3 | verb | make shorter as if by cutting off
4 | adjective | terminating abruptly by having or as if having an end or point cut off
That means that 6.25 truncated to 1dp is 6.2 not 6.3
Bob
Whoever wrote that answer needs to check the meaning of truncated. I'm with you on this one.
Doubt it'll come up in an exam but if it does I'm sure you'd get full marks.
Bob
We want /x^2 so factorise on the left and also take the 4 across to the RHS
Divide by x^2 and add 3
Bob
I've just thought again about my 'example' and I said it incorrectly. It's the gap that needs rounding down else a cupboard might appear to be ok but will not fit due to rounding. eg true gap is 50.6 cupboard is 50.8
I have a vague memory that a question like this did come up years ago and the mark sceme said award full marks for 14.5 or 14.4999999999...
Bob
Mostly .5 is rounded up but as its exactly halfway between the options you could make a case for rounding down.
Why is round up preferred?
(1) there only has to be one non zero digit after the 5 to tip the number over to round up.
(2) if you round down when the tenths digit is 0 1,2 3 or 4 and up if it's 6, 7 , 8, or 9 then that's 5:4 so choosing up for .5 gives even ups and downs. In a company such as an electric supplier this means bills are rounded up as often as down so the regulator is kept happy.
Example of rounding down. Various cupboards have to be pushed through a narrow gap. We know the gap is 50cm. Each cupboard is measured for width to see if it will fit through the gap. Round the widths down to the nearest cm
Why?
Bob
.
Let cuberoot(2) be c. Then c^3 = 2
Bob
If a=-5 then a^2 =25. Sqr(number) is taken to mean the positive square root which would be 5 not -5.
By writing |a| this difficulty is avoided.
Bob
For me, it's been a long day and I came home to discover you had been very rude to another member over an innocent remark and three members complaining about your behaviour.
In my haste I wrongly described your signature as offensive. I intended to edit this to inappropriate but you had already posted.
I have banned you for your failure to keep to our rules. One says that posts mustn't be promotional. Usually I delete those members from the forum
At the moment you are banned which is a lesser punishment since deleting means all posts get deleted too.
On Wednesday I will lift the ban. All future posts must be about your maths studies. The number should be moderate and you should avoid making unnecessary posts.
Bob
Factorial is only defined for whole numbers. There is a thing called the gamma function. See what wolfram says.
Bob
As both 5 and 8 go into both length and width you can put the tiles either way round and there's no half tiles needed.
Quickest is to use n times area of tile = area of floor.
Bob
Correct
Bob
A shopkeeper buys an item for C it sells it for R.
Their profit is the difference.
Bob
You can rewrite this as 2 times 2^(2x)
and use logs
Bob
Wolfram agrees.
Bob
Yes.
Bob
Yes; do it twice so the denominator = 2
Bob
The inconsistency shows I've performed an illegal act so that suggests I cannot cancel as that's really division by zero. That leads to the possibility that x=0. Then check it fits. Anything^0 =1 so LHS = RHS = 0. It works.
Bob
Have to. I'd start by using logs
Bob
If 1 is the zero row and 1 1 the first row and 1 2 1 the second row then the formula is
where n is the row number and r the (r+1) th element.
So put n=20 and r = 6
Bob
If you ask me nicely on Wednesday I'll show you the proof (by induction).
You know that list I told you to keep. Well it's easy to just check. Or start with the squares and add 8.
Bob
Normally I'd say yes but if you do the x cancel out and you're left with an inconsistency.
Just checking Wolfram Alpha
Back again. As suspected WA gives x=0 as the only real solution.
Bob
When you encounter repeat indices like this the rule is work from the top down.
So 3^(3^27)=3^(3×3×3×....3)
That's one BIG number.
Bob
There are no patterns nor formulas for this, so I think you just have to list and count.
Keep the list: it'll be useful later.
Bob
Bus A times are 11.00 11.10 11.20 11.30 etc
Bus B times are 11.00 11.12 11.24 11. 36 etc
Bus C times are 11.00 11.14 11.28 11.42 etc
Bob