Melody

\(|x^2 - 30x - 1| + |x^2 - 30x + 1| = 30\)

This is how I would takle it.

Let     \(T = x^2-30x\)

Then sove for T     where    

\(|Z - 1| + |Z + 1| = 30\)

consider the expressions in the abolut signs

You have 3 cases to consider

Z<1

-1<= Z <= 1

Z>1

try solving for Z for each of thoses cases

Once you have your Z solutions you can solve for x

Hi Tiggsy,

Thanks that was fun.

I won't give away the whole answer but the     e+g = 11132

This question has been asked a lot ot times recently.

there are probably a number of different answers given.

I let the children be     A1    A2    B1    B2    C1    C2

If there were no restrictions there would be 6! ways to seat them

How many ways can they NOT be seated.

We cannot have all the pairs under each other so  that would be

6 places to put A1    then 1 place to put A2

4 places to put B1   then 1 place to put  B2

2 places to put  C1  then 1 place to put C2

6*4*2 = 48

We cannot have one pair vertically alligned with the others not so

Say the As are vertially alligned but not B or C

6 places to put A1, 1 place to put A2

4 places to put B1, 2 places to put B2

2 places to put C1 and 1 place to put C2

6*1*4*2*2*1 = 96 ways

BUT ic could have been A or B or C that are vertically aligns so we have to multiply by 3

96*3=288

So I think the answer is   

6! - (48+288) = 6! - 336 = 720 - 336  =  384  ways

Its money so you can stop after the first nine :))

Thanks Alan    

Thanks guest answerer,

a=13

You are certainly right that |r|<1

\(S_{\infty}=\frac{a}{1-r}\\~\\ S_{\infty}=\frac{13}{1-r}\\~\\\)

Now for this question  \(S_{\infty}\)    must be an integer so I will let it be N

r must be between -1 and 1   which means that  1-r  is between 0 and 2

so N is between (not including)  13/2   and  infinity

So the smallest is infinitesimally bigger than 6.5   

Which means ths smallest integer value is 7

\(S_{\infty}=\frac{13}{1-r}\\~\\ N=\frac{13}{1-r}\\~\\ 7=\frac{13}{1-r}\\~\\ 7(1-r)=13\\~\\ -7r=6\\~\\ r=\frac{-6}{7} \)

Has anyone seen that notation before?    I haven't.

Maybe it just means to the power of ???

C(9) = 27

27^m=1

m=0

The only counting you need to do is

1) all sides are the same,        2         

2) two sides are the same        2

=4   

I'll head you in the right direction.

Its easier if you think in cents

275+725=1000

Let a,b and c represent the 3 digits

abc+bac=1000

Now just do it as an addition puzzle and you will bet all the possible numbers this can work with.

This  was asked and answered a few days ago. Probably by you or someone in our class.

Try looking for the earlier post.