All Answers 358233 Answers

Thanks Heureka, that looks impressive  

That is not much of a comment Rosala.  :)

anyway - hello :)

(x-(i-1))*(x-(i+1))

$$\small{\text{
$
(x-(i-1))*(x-(i+1)) =[(x-i)+1] [(x-i)-1]= (x-i)^2-1
$
}}\\
\small{\text{
$
=x^2-2xi+i^2-1 \quad | \quad i^2=-1$
}}\\
\small{\text{
$
=x^2-2xi-2 = (x^2-2) - 2xi $
}}$$

Yah and the site is even fast on Firefox just dont set it as your default, cause you may wanna use Google Chrome for regular searching and stuff if your used to it.

Here's a rather simplified "proof"

3!  = 4! / 4

2! =  3!/ 3

1!  = 2! / 2

So

0!  = 1! / 1  = 1

ln ( 10.75 + 6.98i )

$$\small{\text{
$z=10.75+6.98\ i \quad \ln{(z)} = ?$
}}\\
\small{
Solution:
\boxed{ln{(z)} = \ln{(|z|)} + i*(arg(z)+2\pi k ) }
}
\\\\
\small{\text{
I. $ |z| = \sqrt{10.75^2+6.98^2} = 12.8172891050 $
}}\\
\small{\text{
II. $ \phi\ensurement{^{\circ}} = \tan^{-1}{(\frac{6.98}{10.75} )} = 32.9957575073\ensurement{^{\circ}} $
}}\\
\small{\text{
III. $ arg(z) = \phi \ensurement{^{\circ}} *
\frac{ \pi }{ 180\ensurement{^{\circ}} }+2\pi k = 0.57588460769 + 2\pi k$
}}\\\\
\small{\text{
$
\ln{(z)} = \ln{(12.8172891050 )}+i*(0.57588460769+2\pi k)
$
}}\\
\small{\text{
$
\boxed{ \ln{(10.75+6.08\ i)} = 2.55079497086+(0.57588460769+2\pi k) \ i } \quad k=0,1,2\dots
$
}}$$

(x-(i-1))*(x-(i+1))

$$\\(x-(i-1))*(x-(i+1))\\
=x^2-x(i+1)-x(i-1)+(i^2-1)\\
=x^2-xi-x-xi+x+(-1-1)\\
=x^2-2xi-2\\
=x^2-2-2xi$$

It's night time and oh I see Jerry leaping out of his hole, ohh melody you can dine the " left overs " with jerry Hun???

Thanks Melody,

I appreciate all the help offered and the facts that we are at many different time zones and there are many other questions to be answered.

I'm not quite OCD (I hope) but I'm not using the title Tenacious just because it's a nice word, though it does sound better than stubborn old fool, which might be judged to be more accurate sometimes?

As I have no tutor or sylabus to follow, I just scour the net for math tests/worksheets etc. When anything crops up that I can't do or understand I start digging into it until I can do it and understand it. As each subject in maths relies on many other math subjects it's keeping me quite busy, it's a pretty broad subject.

As I found this problem in a worksheet I pressumed it was relevant/important though tests/worksheets can be a bit artificial sometimes as the questions haven't neccessarily come from real problems/situations.

If I am getting a bit OCD on the HCF of fractions (if they are not really that likely/important) then please tell me and I will move onto the next (of many) subjects within maths.

Thanks

It is 1:54 am

I am typing that it is 1:54 am    

I don't know - sorry  

@@ End of Day Wrap     Thurs  15/1/15     Sydney, Australia      Time 12:55am    (Really Fri)   ♪ ♫

Hello everyone,

Lots of fabulous answers today from Heureka, CPhill, Rampager1998, diamond, all-them-marvel-feels, Alan, Rosala, Cairo, Geno3141, Mathew120 and yllen.  A great big thank you to each of you.  I hope I didn't forget anyone. 

I stumbled  upon some really interesting maths clips today.  You might like to take a look.  

Fri 15/1/15

I constantly see people change mixed numeral into improper fractions for addition and subtraction and it is just not necessary.  Tetration, you have done a nice, very well presented answer here and I thank you but I would really like you and others to take a proper look at my answer.   It is always good to examine new techniques.  I get excited when I see and learn better methods to solve or teach an old problem.

He probably ate it all.  

Chris, did you leave any for me?     

Thanks Heureka,

Sorry I did not notice that we were talking only of right triangles.  

In my defence there is no 'right' in the question it is only in the title.   

ALSO note:

The height that is being found here is the perpendicular distance from the hypotenuse to the right angle vertex.

Thanks Heureka for going back and collecting these ones.

There are more unanswered questions from today as well.

I guess this will be the norm as the forum gets better known.

We can only do our best.  Thanks very much for all your wonderful contributions.     

It's no more mine.......ask CPhill if he can part with it!!!😋😎😉

Please can other mathematicians comment on this one.

Tenacious is in a knot over it so serious comment would be appreciated.   

Thank you

Sorry Tenacious,

I have only just seen your question.

If your question gets overlooked then I suggest you follow these instructions to highlight this fact.

Here you go.

Hi Rosala and Chris

That breakfast looks pretty good.  Can I have some too?

-887-(-522.5)=- 887 - -522.5= - 887 + 522.5 = -(887-522.5)  etc