Melody

WOW Chris, this is great.  We now have Sir La-TeX working with us.

I know he works for bananas too!!

Just as well we have no greenbacks or Aussie plastic to pay him with!

We could probably throw in a few peanuts though.  I know chimps are partial to peanuts.

Welcome to the team Sir La-TeX  

Well I guess you are not Australian.  If you were I guess you would be asleep.

That is good for me.             ....albinos do not like silver bullets much.       

You haven't given him any silver bullets have you Chris?  ...

Is your sister an albino?

Perhaps wer have similar taste in music too.

https://www.youtube.com/watch?v=SPtqRjirC6o

Maybe she will like it.

Hi curious admirer,

Well it is 4:39am in Sydney right now.  This is a good time for me.

 If I allow direct sunlight to touch my skin I will burst into flames.  So this is a safe time :))

Do you mean

Find the second derivative of  3sec(pi/5)   ??

That is easy.  It is 0.  That is becasue there is no variable.   3sec(pi/5) is just a constant so the derivative is 0.

Hi Rosala,

I am glad you are back :))

That is a really nice post too :)

{3/2x^2-1/3x)^ 6

\(\left(\frac{3x^2}{2}-\frac{x}{3}\right)^ 6\)

Here is a nintroduction to binomial expansions  :)

https://www.khanacademy.org/math/algebra2/polynomial-functions/binomial-theorem/v/binomial-theorem

Thanks Nauseated.

MN is parallel to PQ

Consider triangle MNO and triangle QPO

< MOP = < QOM          Vertiacally opposite angles are congruent.

<MNO = < QPO          Alternate angles on parallel lines are congruent

<NMO = < PQO          Alternate angles on parallel lines are congruent

Therefore triangle MNO and triangle QPO   (3 equal angles.)

Therefore 

\(\frac{0M}{ON}=\frac{OQ}{OP}\\ \frac{9}{ON}=\frac{6}{OP}\\ \frac{9}{6}=\frac{ON}{OP}\\ \frac{3}{2}=\frac{ON}{OP}\\ But \;NP=24\\ \mbox{We need to divide 24 in the ratio 3:2}\\ 3/5*24 = 14.4\\ 2/5*24 = 9.6\\ So\\ ON=14.4\;units\;\;\; and\;\;\; OP=9.6\;units\)

Mellie, if you do not understand you need to ask questions  :)