Melody

1) Average rate of change is change in f(x) value divided by change in x values.   

This is the gradient of the line joining the end points.

Please no one answer further on question 1

Who cares  ?  

When you ask too many questions you draw negative attention to yourself.

A very nice answer and a very nice acknowledgment response.   

Thanks guys  ( In Australia guys includes males as well as females )

THANKS TERTRE    

Tertre, I have written a more full answer.   (I started before you but finished after)

I could not get it from your hint.  EDIT : (Maybe I could, I have not thought about your hint very much yet)

Even what I have done is only one scenario.  I have not shown that it will always be the case.

I have not been able to get my head around the general case myself.    

Anyway, I will leave mine hidden for a bit and see if the guest comes back and interacts with you.   :)

40 boys and 28 girls stand in a circle, hand in hand, all facing inward.

Exactly 18 boys give their right hand to a girl. How many boys give their left hand to a girl?

If you had the   King at one 'end' of the the table with the Queen on his right    KQ                  

then you have all the maids to the right of the queen (there are 10 of them)      FFFFFFFFFF                      

then you have the married couples  with the wife always on the right. (17 of them )    MF MF MF MF MF MF MF MF MF MF MF MF MF MF MF MF MF

then you have all the bachellors with the king to the right of the last one    (   22 of them)   M .....    M  

Which boys have girls on their left ?

Not the king

All 17 of the couples do

One of the bachelors does  (lucky him)

So that is 18.

It probably always works out to 18.        

That is a really tricky question.  I wonder if there really is just one answer???

thanks :)

Gravity has to do with objects being attracted to each other.  

Remember, the story goes about Newton thinking about gravity when the apple fell on his head.

Take a glimpse at this page:

Ok here it is without knowing the formula at all.

I think my hand sketching needs practice though  LOL

I'll try and show you how to graph it by hand.  I will be back in a little while :)