All Answers 358090 Answers

Yeah but I couldn't finish my whole slice. It seems a waste to waste infinate cake. Anyone else want it?

Thanks Alan,

That makes me feel better, it definitely is not simple!

Perhaps it was meant to be a perfect square so that it would fall into place easily.

BUT what was the  x+1/x = -1/2     for ?

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Make sure you get some of my cake Alan, there is plenty.  Here is your peice :)

Enjoy   

F12 brings up some controls for the browser you are using (you can usually change the colour and font, for example).  If you make any changes it won't affect anybody else on the forum.

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D**n it that's what I meant 

I am going to put it in the wrap - it is a good enquiry Zac :)

this is a neat little simultaneous equation question :))

Let the number be 10a+b  so it will look like ab

a+b=5      (1)

10a+b+27=10b+a

9a+27=9b

a+3=b      

a-b=-3      (2)

(1)+(2) 

2a=2

a=1

b=1+3=4

So the original number is 14

checking:

14+27=41  that is good

1+4=5   that is good too   :)

Thanks 

I wouldn't want to bring down the whole forum

A frog, The incredible hulk, a grasshopper.

asec is the same as inverse sec

asec(3/2) = acos(2/3)     

on the web 2 calc you can enter it as asec without changing it anyway

$${asec}{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)} = {\mathtt{48.189\: \!685\: \!104\: \!221^{\circ}}}$$

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)} = {\mathtt{48.189\: \!685\: \!104\: \!221^{\circ}}}$$

Hi Zac,

Yes it is HTML  (Hyper text mark up language) 

That is code that is used for the forum.  I think it is used just about everywhere on the internet.  

I know very little about it but you can bring it up for any web page. 

I don't think you could actually change anything but if you learn a little bit of code you coud use it to help you learn more.  That is my theory anyway. :)

Maybe anon is right.  If you don't understand it maybe you shouldn't touch it but there is no harm in looking 

Maybe someone else can give you a more informed answer :/

Did you get some of my cake Zac and Heureka.  There is plenty to go around :)

You are on a calculator website and the web2 calc is a great calc.

There are others about if you prefer - just google 'calculator'    

It is not the cube root Zac, it is the 4th root.

$$2^{1/4}=\sqrt[4]{2}$$    

$${{\mathtt{2}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{4}}}}\right)} = {\mathtt{1.189\: \!207\: \!115\: \!002\: \!721\: \!1}}$$

It is an irrational number so this is an approximation :)

You may.   $${\mathtt{2.22}}{\mathtt{\,\small\textbf+\,}}{\mathtt{7}} = {\frac{{\mathtt{461}}}{{\mathtt{50}}}} = {\mathtt{9.22}}$$                              

Only joking you are not allowed to need some help on asec.

Oh I didn't quite give the whole story.

you can think of positive numbers as hot numbers and negaive numbers as cold numbers.

If you take away heat it gets colder so    - + = -

If you add cold into the room it gets colder    + - = -

If you add heat it gets hotter    + + = +

If you take cold away it also gets hotter     - - = +

These are only for when the signs are so close together that you can put a circle around them with nothing else in the way.

Here is some more on this topic if you are interested :)

Thanks Badinage :)

When plusing and minusing directed numbers always think about the number line.

If you are working in an exercise book you ccan think about 0 being in the crease of your book and the positives will be on the right and the negatives will be on the left.

Like this:

say I want to find -2-6

I put my pen on the -2.  I am subtracting so I go left towards the negative end.

Now i have to go left 6 places.  That will land you on -8

Here are my thoughts:

The values of the function are complex in the approximate range 0.17<X<5.83.

Outside this range they are real.

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Thanks Bertie,

Thanks anon for asking this great question :))

I took about another 10 steps to get to the end but that is quite neat.

(I used yours as a guide.)

Thank you

Oh Bertie,

I saved some of my birthday cake for you.  I shall get it from the fridge

Chris and the regular foum users cooked it for me and it is delicious.

Also it is not as fattening as it looks and I can have an infinite number of big slices from the one cake.

It defies the laws of physics, matter is not conserved, it is endlessly reproduced.  

Enjoy :)

PLEASE CAN WE GET SOME HELP HERE    

$$\\f(x/((x^2)+x+1)=(x^2)/((x^4)+(x^2)+1) \\\\
f\left(\frac{x}{(x^2)+x+1}\right)=\frac{(x^2)}{(x^4)+(x^2)+1}\qquad find\;f(2)\\\\\\$$

Now I divided

 $$\\(x^4+x^2+1) \;\;by\;\;(x^2+x+1) \;\;and\;\;got\;\;(x^2-x+1)\\\\
so\\\\
(x^2+x+1)\times (x^2-x+1)=(x^4+x^2+1)\\\\
so\\\\
\frac{x}{(x^2+x+1)}\times \frac{x}{(x^2-x+1)}=\frac{x^2}{(x^4+x^2+1)}\\\\
so\\\\
$Now I am confused again$\\\\$$

I haven't thought about this bit   x+(1/x) = -1/2      I wonder what that is for ?

Rewrite as  10t² - t - 65 = 0 

This can be factored  (2t + 5)(5t - 13) = 0

so  t = -5/2  and  t = 13/5 are the two solutions

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$$2^{1/4}=$$ the 4th root of 2 $$\approx$$ 1.189

(I fixed it)

973.1707317073170732 is smaller than 1000.

Don't let all the decimal places fool you. Is 973 less than 1000? By how much?

Also, any number with 3 or less digits before the decimal place is less than 1000.