Math Is Fun Forum

hi popsyclover

I think there is more than one answer. 

I drew 5 boxes and put 16 in the middle.

Then I filled in with 4 numbers above and below 16.

Then I juggled the numbers until the other conditions were met.

Here's an answer:

12,  13.1,  16,  16.9,  17

You could change the numbers by making 13.1 bigger and 16.9 smaller by the same amount.

For key stage 2 I would expect whole numbers so I'll look some more.

Bob

Still thinking ............................

Back when I've got something 

Bob

Hi gr8girl101

Can you do 'short division' ?  Or any division at all.  Maybe tell me one you can do first so I can pitch in at the right level for you.

Long division isn't so bad once you see what's going on.

Post back soon.

Bob

hi Agnishom

You might notice that

is in there and then use the 'difference of two squares'.

Or this diagram might help

Bob

hi

Exactly what Reuel has in his first post.

I've just seen your edit.  Our answers are the same.  You have C = -26.43428  I think.  I had C positive.

Bob

hi

Plug in t = 1, N = 15  an d also  t = 5, N = 20 to give

and

Take the C term across to the LHS and the numbers to RHS

Divide one by the other to eliminate C

So

Then you can get C from either and hence finish the question.

Bob

hi MathsIsFun

Would a shortened form of "Advanced / University " do the trick ?

A user won't know if there is a page on the topic they want anyway until they try it, but it helps to narrow the search.

In the US and in the UK, "Advanced" seems to give the right impression about the level of the topic.

Bob

hi chineseballer06

Sorry, I thought you had part 1 sorted.

See diagram below.  The small triangle ADE and the larger one ABF, are similar. 

Height ABF = h       base ABF = b

Height ADE = h-d    base ADE = b x  (h-d)/h      this being the scale factor for the (fractional) enlargement.

So the probability (being the ratio of the areas) will be

This simplifies to the answer you have.

Bob

hi Reule,

Me too.  I think the last words should be "find I at time t".

Next bit under review while I consult a scientist.

Aarhh I think I get it.  Apologies to any physicists reading this.  The inductor offers reistance to the currect of electricity flowing through it.  At the start t = 0 so I = 0.  No change of current.  As time passes the inductor stores energy. (Think of it as being like rolling a rock up a hill.  When you stop rolling you still have to hold the rock against tumbling down again.)  As t tends to infinity (like I'm slowing down my rate of assent) all that is needed is to overcome the resistor and that (by ohms law) leads to a current of 2 amps.  But it must be maintained or the inductor lets go its stored energy.  So your equation describes this perfectly.  Hurrah for mathematicians!

Bob

hi Haiying Liao

It's a great trick, isn't it?

It is a property of the nine times table (up to 10 x 9) that the tens and units digits add up to 9 and that if these digits add up to 9, then the number is in the table.

So putting down one finger creates two numbers (left of finger; right of finger) that have the property and so are in the table.

Furthermore n x 9 has a tens digit of (n-1) so the finger down gives the correct value in the table.

It remains to prove the property.

Post back if you want me to show you that.

Bob

hi aqa

You are very welcome,

Bob

hi chineseballer06

See diagram below.

The circle has BC as diameter.

When D is on the circle angle BDC = 90.

Inside the circle, it is obtuse and beyond the circle it is acute.

Hope that helps.

Or post again for more help.

Bob