Remember that Matrix division is undefined and they use the inverse instead. As such I know of the formula

]]>]]>

Numbers have the value that is defined for them. For counting numbers it is straight forward, but as you delve into the number system it becomes harder to decide on a value.

Most mathematicians work with the definition zero to the power zero equals 1. This maintains consistency across several theorems and gives completeness.

Bob

]]>]]>

The average person has 100000 hairs on their head. Woodbridge, New Jersey has 100001 people in it according to my last door to door count. By the pigeonhole principle that means that there are 2 people in Woodbridge that have the same number of hairs on their head.

]]>8 properties of probability

Classical probability

Basic rules of probability

Thank you!

]]>When you have an exam to work towards you get a syllabus which tells you the topics to study. I like the idea that you just want to learn for the fun of it and I'll happily help where I can. But what is your topic list? I suggest you go here:

http://www.mathsisfun.com/geometry/index.html

and then come to the forum when you need help.

Best wishes.

Bob

]]>362. The area of fencing a circular field at the rate of $24 per meter is $5280. The field is to be ploughed at the rate of $0.50 per square meter. Find the cost of ploughing the field.

Now if you put several zeros on the right of some non zero number, e.g. 9, then it becomes a bigger quantity, e.g. 9,000.

If everyone had a good memory, you could have a counting number system in which every number had it's own symbol. Counting might look something like this:

0,1,2,3,4,5,6,7,8,9,£,$,&,*,?,............. Of course it isn't very practical as you quickly run short of symbols. And if someone has made up every symbol up to a certain large value, what happens if someone wants to add 1 to it? Are they allowed to make up yet another symbol for the answer? And what happens if someone else has also done this but not used the same one?

Don't get me wrong. I'm not advocating such a way of counting. But it does help to demonstrate just how handy the decimal system is. You only need 10 symbols and you can make any number by using 'place value'. 9000 didn't come from 9 with a few zeros added. It's more than that. The 9 now indicates 9 thousand instead of 9 units. And how do I know that it's in the thousand column? Because the zeros are showing no hundreds, no tens and no units. Without them we don't know what place value the 9 has. But here there are a lot of zeros that you don't need. I've underlined the ones that are essential for place value purposes.: 000.0009000

I'm not sure how this affects your theory but I think you need to factor it in.

You might find this interesting:

https://en.wikipedia.org/wiki/Set-theor … al_numbers

Bob

]]>You can use 1 for the constraints. I am getting a maxima of 1 at (0,0,0).

]]>I am sorry, I thought you only wanted a hint.

If you use the Pythagorean theorem you will get:

Take the square root of both sides.

]]>