Melody

A regular octagon will tesselate.

Some of the others probably do too

BUT not all octagons would tesselate.

Remember an octagon is ANY 8 sided polygon!

hi Blaster0

***How did you get -2 from log6,25/log0,4***

To be perfectly honest I just put the whole thing straight into a calculator and it spat out -2

However, since I am on a roll here I will explain why it is so!

$$\frac{log6.25}{log0.4}=log_{0.4}6.25$$     I did this by applying the change of base law the opposite way around to usual.

Let

$$x=log_{0.4}6.25$$

Rearranging this we get

$$6.25=0.4^x\\

2.5^2=0.4^x\\

\left(\frac{5}{2}\right)^2=\left(\frac{2}{5}\right)^x\\

\left(\frac{2}{5}\right)^{-2}=\left(\frac{2}{5}\right)^x\\

x\:=\:-2$$

 Hey Blaster0,  

When you are happy with your answer can we have a thank you and some thumbs up please. 

Speaking for myself I put a lot of effort into these answers!  

(Don't mind me I am just trying to train people to be polite.  I figure that the more people who do it then the more normal it becomes and hopefully the 'idea' will catch on.  )

Melody     And no chris you can not have your glasses back - I like them!

The maths books would not exist if the maths did not exist therefore it can be argued that maths is deadly!

I was referring to this statement of yours

***that was a real math question wow didnt know***

Yes, he might do zegroes.

I have referenced it at the end of this thread

Hi Chris, your answer is correct right down to the last statement.  Then you have drawn an incorrect conclusion.

In NSW, Australia, the dept of Education demand that the second derivative used to determine the nature of the stat point.  In this case there could even be a good reason.

I let T=x+4z=x+144x^-1

What sould be noted is that T=x+144x^-1 has a discontinuity at x=0  

This is why your 'obvious' conclusion is incorrect. (Look at the graph)

$$\frac{dT}{dx}=1-144x^{-2}\\\\
\frac{d^2T}{dx^2}=288x^{-3}\\\\$$

When x>0, T''>0 therefore any stat pt will be a minimum

When x<0, T''

Therefore there is a local minimum at x=12 and z=3 but this is not an absolute minimum(not sure about the wording)

All negative x values will make x+4z smaller.  There is no absolute minimum value.

BIDMAS does apply Zegroes BUT this is NOT an equation because it does not have an Equal sign.

$$48\div 2*(9+3)\\
=24*(12)\\
=288$$

hey Zegroes,

How about using the Math(Input=Result) to put the whole thing.

You could even try to explain why.

People can't learn anything if you only give the answer!

this should be the last one for the night - It is 1:30 am

$$0.4^{((6-5x)/(2+5x))}<6.25\\\\
log0.4^{((6-5x)/(2+5x))} \frac{6-5x}{2+5x}log0.4 \frac{6-5x}{2+5x}>\frac{log6.25}{log0.4}\\\\
\frac{6-5x}{2+5x}>\frac{log6.25}{log0.4}\\\\
\frac{6-5x}{2+5x}>-2\\\\
(2+5x)^2\frac{6-5x}{2+5x}>-2(2+5x)^2\\\\
(2+5x)(6-5x)>-2(25x^2+20x+4)\\\\
12-10x+30x-25x^2>-50x^2-40x-8\\\\$$

$$25x^2+60x+20>0\\\\
5x^2+12x+4>0\\\\
5x^2+10x+2x+4>0\\\\
5x(x+2)+2(x+2)>0\\\\
(5x+2)(x+2)>0\\\\
\mbox{concave up parabola roots are -2 and -2/5}\\\\
x<-2 \mbox{ OR }x>\frac{-2}{5}$$

Okay I decided to check this by plotting the original question.  And to my delight it appears to be correct!