Math Is Fun Forum

Actually, cancel that.  I just took an intelligent guess and got the right answer.

But I'm keeping it to myself 'cos it makes me feel superior.  :)

Bob

hi bobbym

How are you today?  Looks like I've lost this poster.  I'm not going to attempt this one until I know the problem is as posted because it looks horrid, don't you think.

Bob

You may find it useful to learn some Latex in order to make your posts look mathematical.

You start with square bracket math  the the code then finish with square bracket /math

Without the square bracket bit here's what I did for the above.

\frac{(19^{98}+ 342\times 19^{97} )}{19^{99}}=?

The top post in the help me section will teach you how to do it.

Bob

hi Agnishom

Did you mean

Looks like you can factorise 19^97 and cancel.

Bob 

Hi Dave,

Good to hear from you.  I'm fine.  In the throws of decorating the lounge ... and relatives, 2 + 3 kids,  want to come and stay.

Where to put everything? Now if I could scale things a bit (selectively of course)

Hhhhmmmm. 

Bob

hi pi_muncher

You want the answer so soon?  I expected at least a few days of thinking ......

Ok. There was a hint in an earlier post so here it is again.

http://en.wikipedia.org/wiki/Euler_characteristic

Oh yes and here's a hint that is useful for many problems, mathematical and real life:

If you cannot find a solution to a problem;  question your assumptions.

Bob

Hi

Further thoughts on this homework sheet.

I believe it is a requirement of the curriculum that children learn the properties of shapes and the correct names for shapes.

It sounds like this sheet is designed to get children looking at the properties of the shapes on the sheet; identifying those that a set of shapes have in common; and then finding a good 'name', 'description', or 'title' for those shapes.

There is no one correct answer.

Look at my example below.  Any of the following is an answer.

Polygons. 
Quadrilaterals.
Straight sided, closed shapes.
Four sided shapes with at least one pair of parallels.

So if the child puts a suitable title, she has satisfied the homework.

But, to show off how well she has met the curriculum objectives, some answers are better than others.

I wouldn't give high marks for "I called them Henry because that was what they looked like to me." although I'd probably laugh and make a mental note that here is a very clever child.

I would try to avoid using the same Title twice and, if I could see several possibilities I'd try to put them all:
eg. 'Polygons which are quadrilaterals with a pair of parallel sides.'

In fact, the best outcome from the homework has already been satisfied.  Parents are taking an interest in their child's school work and showing they think it's important.

It could also be argued that showing that even parents don't always know the answers is beneficial.

Plus, they have discovered Maths Is Fun and that's got to be a good thing! 

See http://www.mathsisfun.com/geometry/polygons.html and similar pages for hints.

Bob

hi dolgopolov

What age are your kids?

I'd start with nets for tetrahedron, cube, octahedron, dodecahedron and icosahedron and get them to make them and discover their properties.

See http://en.wikipedia.org/wiki/Euler_characteristic

Then start an investigation:  (i) Draw a plane shape or network  (ii) count nodes, arcs and regions (iii) summarise results in a table (iv) ask "What do you notice?"

You might look up http://en.wikipedia.org/wiki/Schlegel_diagram as well.

Bob

Obviously, my abstract algebra isn't up to it;  but his is;  it's his specialism; so it seemed appropriate.  And I loved that little touch at the end .... just finish this off   .... he does that to me    .... and three days later .... I think I need another hint please.

He once solved one of those string and rod with holes in puzzles that I'd been struggling with by watching me and just doing it straight off once I stopped moving it about and let him have it!

Not that I'm suggesting I'm Sherlock or anything, that would be vain, but he is definitely my Mycroft.

Bob

Oh drat! 

They are good explanations.  Any chance of viewing them on someone's computer?

Bob

hi again,

The link above that one is good too for how to find a det.

B

hi All_Is_Number

Any rule that you make that 'connects' values in the domain to values in the range is a relation.

These become functions when they are 'well defined';  ie. from a start point in the domain you have one path only leading to the range, so you know where you're going.

An inverse is something that takes you back from the co-domain to the domain.

Notice I didn't use the word range this time; I deliberately said co-domain.  There's a difference.

If the domain is all positive integers and the co-domain is all positive integers and the function is square, then the range is only part of the co-domain because for example you cannot get to 17 in the co-domain by squaring an integer.

If I try to create an inverse function on the co-domain, I cannot make it 'well defined' because there's no √17 in the domain.

But if I change the co-domain to, say, the square numbers, then the function square root becomes 'well defined'. 
(because I've made the co-domain = the range)

So whether an inverse function is possible doesn't just depend on the function; it also depends on the domain and co-domain you choose.  By setting a limit as I did in my example, I can turn a relation into a function or not.  That's why I took care to specify my sets in the earlier post.

Does that help to clear this up?

Bob