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@@ End of Day Wrap - Sunday 18/5/14   Sydney, Australia Time 15:30

Hi everyone,

Considering it is weekend, the forum has been very busy the last 2 days.  Lots of great answers were given by Kitty<3, zegroes, CPhill, Alan, GoldenLeaf and Rom. Thank you all.

There are 2 unanswered questions.  I have put their addresses in a new post.

Here are some interesting posts for the day.  I haven't checked my answers - maybe they are wrong.

Inequality

#YOUTH FOR TEH WIN!!!!!!

Yea whatever - there is no point arguing with an adolescent - you can never win - they know EVERYTHING!  LOL

It's not the first one I ever got "wrong.'

Believe me....!!

--- Francis says, It may not be your first mistake, but it’s your last.

One smart Mule, that Francis is. … Yes Sir! One smart Mule.

Is this a loan or are you investing the $300 and then adding to it?  I don't understand your question.

thank you for your good manners anonymous!

I gave you 3 points but since you are not a member you cannot see them.  So I thought I better tell you too.

Chris and I take turns at getting things wrong. I'm on a roll at the moment but a few days back I was starting to feel like everything I posted was wrong!  

Maybe they are still wrong and the errors just haven't been 'pick up' yet. lol

Integrate x^3+3x^2+15x+4 and factorise the integral

$$\int (x^3+3x^2+15x+4)\:dx\\\\
=\frac{x^4}{4}+\frac{3x^3}{3}+\frac{15x^2}{2}+4x+c\\\\
=\frac{x^4}{4}+x^3+\frac{15x^2}{2}+4x+c\\\\$$

I can't factorise because I don't know what c is.

It's not the first one I ever got "wrong.'

Believe me....!!

I never noticed that, either, zegroes. Thanx for pointing it out!!

I didn't know that was there zegroes - not that i would ever use it!

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!

WHAT CPhill getting a question wrong mind blown......

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!

Now melody i think we can both see the logic in this.especially you since you know your ehem WAY older than me the book killed you not the math if the math killed you numbers would had flew out the book and killed you but it didnt so.....#youth wins!!! 

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

Just one final thing....kitty<3 and I took completely different approaches to this.....

It just proves that there might be more than one way to produce the same solution!!

I was referring to this statement of yours

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

Yes, he might do zegroes.

Thanks, Melody....I wasn't too sure about this one!!! I see my error, now!!

Glad you checked it !!! "Thumbs Up" and a green check from me!!

I have referenced it at the end of this thread

Thumbs up to both of you so much work and problems in there #HULK FINGERS

Oh, it's fine:) Thanks!

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.

Sorry, kitty<3.....didn't know you were posting, too!!

I'll give you the credit with a "Thumbs Up" and a green check!!