Melody

I have just looked at you post record.

It seems that so far you have never responded to an answer.

Perhaps this is why it took you five days to get an answer here.

You are expected to respond to your answerers.

I worked this out algebraically

Let the little squares be x*x   and the  big ones are   y*y   so the long ones are   x*y

Ths sum of the areas is 

 \(10x^2+9xy+2y^2\\ \)

I want two numbers that multiply to 10*2=20 and add to  9   Those numbers are  4 and 5

\(10x^2+9xy+2y^2\\ =10x^2+5xy+4xy+2y^2\\ =5x(2x+y)+2y(2x+y)\\ =(5x+2y)(2x+y)\\\)

So one side is    5x+2y   long and the other is   2x+y   long

Now it is quite easy.  If you have problems then assign a number to x and to y.   

I chose 1 and 7 but any numbers that have only 1 as a factor will do.

People ususally find it easier to deal with real numbers instead of with pronumerals

ok, that explains the confusion.  :)

You have not asked a question Manuel.     

Looks like it has been translated a couple of times.  Who knows what the original was...

Not BilderBoi     and     not me either

The inominative interest rate rate is  8% p.a   or   0.08% pa

\(\frac{0.08}{12} = 0.00\dot 6\)       per month

No that is not why our results differ.    Your r is the same as mine, you, or rather your calculator, has just rounded off r. 

BUT it would not make THAT mcuh difference.  

You have to use 2 formulas for Karlee.

First the Future value of an annuity due (120 months), and then the compound interest formula  (12*39 months)

Hi proyaop,

The general term is

\(\displaystyle {\binom{9}{n}(\sqrt x)^{9-n}(\frac{5}{x})^n}\\~\\ =\displaystyle {\binom{9}{n}(x)^{\frac{9-n}{2}}(\frac{5}{x^n})}\\~\\ =\displaystyle {\binom{9}{n}*5(x)^{\frac{9-n-2n}{2}}}\\~\\ =\displaystyle {\binom{9}{n}*5(x)^{\frac{9-3n}{2}}}\\~\\\)

You want the constant term so     

\(\frac{9-3x}{2}=0\\ 9-3x=0\\ 9=3x\\ x=3\)

So the contatn term is

\(=\displaystyle {\binom{9}{n}*5(x)^{\frac{9-3n}{2}}}\\~\\ =\displaystyle {\binom{9}{3}*5(x)^{\frac{9-3*3}{2}}}\\~\\ =\binom{9}{3}*5\\~\\ =84*5\\~\\ =420\)

You do need to check my working for careless mistakes of course. 

LaTex:

\displaystyle {\binom{9}{n}(\sqrt x)^{9-n}(\frac{5}{x})^n}\\~\\
=\displaystyle {\binom{9}{n}(x)^{\frac{9-n}{2}}(\frac{5}{x^n})}\\~\\
=\displaystyle {\binom{9}{n}*5(x)^{\frac{9-n-2n}{2}}}\\~\\
=\displaystyle {\binom{9}{n}*5(x)^{\frac{9-3n}{2}}}\\~\\

here is the graphical solution

k less than 0                      0 solutions

k=0                                   4 solutions

k is between 0 and 1         8 solutions

k=1                                     7 solutions

k is between 1 and 3          4 solutions

k=3                                  6 solutions

kis bigger than 3               8 solutions