All Answers 358087 Answers

Well maybe one day I can come and you can show me around.  

And you can come to sydney and I will show you around too.  :)))

ohh Monday , then good luck for your week and also good night too!lol!

Sorry 315, besides the fact that it is late and my brain is shutting down.  My poor eyes really cannot read that. LOL

Yes I am Rosala, it is Monday.   

Mmm, let me see if I can remember this stuff.

sigma=6

so 81 is more than 3 standard deviations below the mean.

so p(X>=81)>99.7%

If you need more precision you can work out the z score 

Z=(81-100)/6=-3.1666666

then look up a z score table to find the associated area.  The tables are slighly diff and I don't know which version you are using.   I used this one.

Melody , 1 am ....that sounds like your already living on the other day hun?

I'm a little tired, it is nearly 1am, but otherwise I am doing very well thank you.  

Yes looks good.

Personally I would say Hence rather than yes but it shouldn't really matter.     

Also, you answer is correct but the original question gave the interval  [0,1]

so personally I would have repeated exactly what they asked for but again it is trivial.

ok now it makes a lot more sense.  although you missed out the words "the gradient of"

f(X)= $${\frac{{\mathtt{ax}}}{\left({\sqrt{{\mathtt{x}}}}{\mathtt{\,-\,}}{\mathtt{x}}\right)}}$$

 you have  the gradient of the tangent at the point x=4 is 1/4

The gradient of the tangent of any function is given by the first derivative.

So  what you are really being told is that   f '(4)=1/4

You have to find f ' (x)   (using the product or the quotient rule)

then solve for a using f '(4)=1/4

Can you work out the derivative yourself ?   Or can you at least give it a go?

So is my answer correct?  

ok , now its very clear thank you 

I am doing my homework!what about you?

See on Alan's graph.

All the intervals where the blue graphs are will be alright.

Yes Melody it would be really good if they did!i , in particular am really interested in History , nevermind , of which culture it is!i would be really interested in knowing about other people's heritage!

You know Melody , this is a really speical city , Delhi , becoz it has a long history behind it!and that history indeed is really amazing and amusing!

No,

sin 0 = 0

ln(0) is undefined

same goes with x=pi

So

ONE of the intervals is (0,pi)

But to get all of them i will redirect you to my first answer 

f(X)= $${\frac{{\mathtt{ax}}}{\left({\sqrt{{\mathtt{x}}}}{\mathtt{\,-\,}}{\mathtt{x}}\right)}}$$
 you have the tangent at the point x=4 is 1/4

Matrices are used for many things.

Mainly I think that they are used to simultaneously solve sets of equations with any number of variables.

This is probably a very limit view.

Here are some more ideas.

amazing 

thank you melody 

so the interval is [ 0 , pi ]  right ? 

Is this half of a question?  I'm confused.

Mi tangent at point X = 4 is  1/4     What does this mean?????

ALSO

Do you mean

$$\frac{ax}{\sqrt{x}}-x$$

Where is your working radio?  Remember the aim is to teach people.

An incomplete answer can be excellent.

An answer without the working would not usually help much.

By the way.  

You have given lots of great answers.  Thanks for helping.  

If this is true radio you need to tell anon how you know this.  

$${{\mathtt{x}}}^{{\mathtt{3}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{72}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\frac{{\mathtt{19}}{\mathtt{\,\times\,}}\left({\frac{{\sqrt{{\mathtt{3}}}}{\mathtt{\,\times\,}}{i}}{{\mathtt{2}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right)}{\left({\mathtt{9}}{\mathtt{\,\times\,}}{\left({\frac{{\sqrt{{\mathtt{10\,342}}}}}{{\mathtt{3}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{919}}}{{\mathtt{27}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\left({\frac{{\sqrt{{\mathtt{10\,342}}}}}{{\mathtt{3}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{919}}}{{\mathtt{27}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\times\,}}\left({\mathtt{\,-\,}}{\frac{{\sqrt{{\mathtt{3}}}}{\mathtt{\,\times\,}}{i}}{{\mathtt{2}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right){\mathtt{\,-\,}}{\frac{{\mathtt{2}}}{{\mathtt{3}}}}\\
{\mathtt{x}} = {\left({\frac{{\sqrt{{\mathtt{10\,342}}}}}{{\mathtt{3}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{919}}}{{\mathtt{27}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\times\,}}\left({\frac{{\sqrt{{\mathtt{3}}}}{\mathtt{\,\times\,}}{i}}{{\mathtt{2}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right){\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{19}}{\mathtt{\,\times\,}}\left({\mathtt{\,-\,}}{\frac{{\sqrt{{\mathtt{3}}}}{\mathtt{\,\times\,}}{i}}{{\mathtt{2}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right)}{\left({\mathtt{9}}{\mathtt{\,\times\,}}{\left({\frac{{\sqrt{{\mathtt{10\,342}}}}}{{\mathtt{3}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{919}}}{{\mathtt{27}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}\right)}}{\mathtt{\,-\,}}{\frac{{\mathtt{2}}}{{\mathtt{3}}}}\\
{\mathtt{x}} = {\left({\frac{{\sqrt{{\mathtt{10\,342}}}}}{{\mathtt{3}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{919}}}{{\mathtt{27}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{19}}}{\left({\mathtt{9}}{\mathtt{\,\times\,}}{\left({\frac{{\sqrt{{\mathtt{10\,342}}}}}{{\mathtt{3}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{919}}}{{\mathtt{27}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}\right)}}{\mathtt{\,-\,}}{\frac{{\mathtt{2}}}{{\mathtt{3}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\mathtt{2.965\: \!540\: \!944\: \!547\: \!592\: \!7}}{\mathtt{\,-\,}}{\mathtt{3.085\: \!633\: \!727\: \!967\: \!809\: \!5}}{i}\\
{\mathtt{x}} = {\mathtt{\,-\,}}{\mathtt{2.965\: \!540\: \!944\: \!547\: \!592\: \!7}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3.085\: \!633\: \!727\: \!967\: \!809\: \!5}}{i}\\
{\mathtt{x}} = {\mathtt{3.931\: \!081\: \!889\: \!095\: \!185\: \!4}}\\
\end{array} \right\}$$

Just doing this on the web2 calc, there does appear to be one real  but it is not an integer.That is 

(x-3.931...) is a factor  3.931 is an approximation

Here is another approximation of the factorisation.  It is the same.

Please use the site calc on the home page.  

3/4-1/3(1/2y-2)=3(y-1/4)

$$\\\frac{3}{4}-\frac{1}{3}(\frac{1}{2}y-2)=3(y-\frac{1}{4})\\\\
\frac{3}{4}-\frac{1}{3}(\frac{y}{2}-2)=3(y-\frac{1}{4})\\\\
\frac{3}{4}-\frac{y}{6}+\frac{2}{3}=3y-\frac{3}{4}\\\\
$Now it will be easier if there were no fractions$\\
$The lowest common multiple of 4,6 and 3 is 12$\\\\
$So multiply both sides by 12 to get rid of all the fractions$\\
12(\frac{3}{4}-\frac{y}{6}+\frac{2}{3})=12(3y-\frac{3}{4})\\\\
\frac{12*3}{4}-\frac{12y}{6}+\frac{12*2}{3}=12*3y-\frac{12*3}{4}\\\\
9-2y+8=36y-9\\\\
17=38y-9\\\\
26=38y\\\\$$

$$\\y=\frac{26}{38}\\\\
y=\frac{13}{19}\\\\$$

It means

 $$\sqrt{a}$$

The value depends on what a is

For instance, if a=16 then

$$\sqrt{16}=4\\\\
$because $ 4*4=16$$

You can factor out  2^2013 and you will get

$$2^{2013}(2^1-1)\\\\
=2^{2013}$$