Melody

Do not ask the same question , in full, twice.  

You can do a repost but just put a link in it referring back to your orriginal post.

Ask people to answer on the original.

Have you attempted this yourself?

There are 2010 chocolate bars.  Is it ok to give your friend just one?  How many would you have then?

Yopu have to have AT LEAST twice as many,  So it you divide them into 3 piles and you take 2 piles and he takes 1 pile,You will havee twice as many as him.

2010/3 = 670

So if he has 670 how many will your friend get?

You can think about these questions and finish the problem youself. 

Please make a new post with your answer and some  working. 

Here it is:

I answered this question, or one very similar maybe 2 weeks ago. If you look under my posts you will most likely find it.

I assume that is meant to be a Isosceles triangle? ??

1*3*3 *3= 27

Why are you appologising for the Latex, why didn't you just edit it out?

Thanks guest answerer :)

I did this by hand and got the same answer.

N is a four-digit positive integer. Dividing N by 9 , the remainder is 5. Dividing N by 7, the remainder is 2. Dividing N by 5, the remainder is 4. What is the smallest possible value of N?

N=9A+5    N=7B+2       N=5C-1

Solve diophantine equations.

9A+5=7B+2

A whole stack of work got me down to   A=-12+7T   B=-15+9T

Which both gave me  

N=-103+63T

So now I have    N=-103+63T    and N=5C-1

Solve diophantine equations.

 -103+63T    = 5C-1

A whole stack more work got me to

T=204+5X     and C=2550+63X

Which both gave me  the general solution  N=12749+315X

I'm only interested in 4 digit solutions so

\(1000 \le N <10000\\ 1000\le12749+315X<100000\\ -11749\le315X<-2449\\ -37.3

When X=-37 N=1094     When X=-8  N=9914

-8--37+1=30

There are 30 four digit solutions, the smallest is  1094 and the largest is  9914

-------------------

looking at what I have done, I should have simplified the general term first.

N=12749+315X

12749/315=approx 40.5

12749-40*315=149

Nicer general term

N=149+315Y

It is easeier to check that this is correct too.

If anyone wants a more detailed solution then just ask.

If we write \(\sqrt2 + \sqrt3 + \frac{1}{(2\sqrt2+ 3\sqrt3)}\) in the form \(\frac{(a\sqrt2 + b\sqrt3)}{c}\) such that a, b, and c are positive integers and c is as small as possible, then what is a + b + c?

\(\sqrt2 + \sqrt3 + \frac{1}{(2\sqrt2+ 3\sqrt3)}\\ =\sqrt2 + \sqrt3 + \frac{1}{(2\sqrt2+ 3\sqrt3)}*\frac{(2\sqrt2- 3\sqrt3)}{(2\sqrt2- 3\sqrt3)}\\ =\sqrt2 + \sqrt3 + \frac{(2\sqrt2- 3\sqrt3)}{(8- 27)}\\\)

You can finish it.

Ja das hilft    

Measurements are in cm.

\(\pi r^2 h = 1000\\ r=\sqrt{\frac{1000}{\pi h}}\\or\\ h=\frac{1000}{\pi r^2}\\ \text{where h and r are positive real numbers}\)

For the sack of graphing I will let   y= height and  x= radius\\

\(y=\frac{1000}{\pi r^2}\)