All Answers 358098 Answers

You have posted this here

Posted what twice.

Thanks EinsteinJr,

I have watched those videos and they are interesting but they start out with premises that they do not even attempt to prove.  Not on those clips anyway.

Why do you accept that 1-1+1-1+....... = 0.5    ?      (Edited)

I think that you have posted this twice MathsGod1.

You know I get annoyed when people do that.    

Thanks Chris,

This can be easily done by any good yr 9 student.

$$\\\boxed{(a+b)^2=a^2+2ab+b^2}\\\\
so\\\\
(3x+(2y+1))^2\\
=(3x)^2+2*3x*(2y+1)+(2y+1)^2\\
=etc\\\\
$The only term with xy is going to be $ \\
2*3x*2y=12xy\\
$so the coefficient of xy is 12$$$

I didn't; I didn't gave the mass of 2L of water, nor the molar mass of water; I have just written down the formulas used to calculate this.

In order to calculate the amount of matter, you first have to determinate the mass m of 2L of water, using the first formula given, then you have to determinate the molar mass M of the water, and finally use the second formula to find the value of n.

You might think that all that calculation are wrong; but they AREN'T.

s=total numbers of steps

v= velocity of the escalator  (steps/seconds)

make two different equation with the info given in the text. "Mr anonumous" climbs 20 step by his own, the escalator helps him with v*60 steps. "Mrs anonymous" climbs 16 steps by her own, the escalator helps her with
v * 72 steps.

(1)  s=20+60v

(2)  s=16+72v

(1)------> v=(s-20)/60

now use the "new"(1) and put that one into equation number 2.

s=16+72*(s-20)/60     72/60=6/5 therefore multiplie everything with 5

5s=80+6(s-20)----> 5s=80+6s-120

5s-6s=80-120

s=40

"Mr anonymous"have to climb 40 steps instead of 20 if the escalator breaks down.

Note that, because the diameter is given with units of cm, Headingnorth's result has units of cm²

A=(pi*d^2)/4

                             pi~3,14,  d=diameter  r=radius=d/2

A=(pi*r^2)  

$${\frac{\left({\mathtt{\pi}}{\mathtt{\,\times\,}}{{\mathtt{52}}}^{{\mathtt{2}}}\right)}{{\mathtt{4}}}} = {\mathtt{2\,123.716\: \!633\: \!826\: \!700\: \!229\: \!2}}$$ 

$${\mathtt{\pi}}{\mathtt{\,\times\,}}{{\mathtt{26}}}^{{\mathtt{2}}} = {\mathtt{2\,123.716\: \!633\: \!826\: \!700\: \!229\: \!2}}$$

You've essentially given the solution in your question EinsteinJr!  All you have to do is crunch the numbers (or am I missing something?).

.

Very neat shortcut civonamzuk!  I like elegant solutions but I didn't spot this one.

(Actually, it didn't take me very long to produce my results.  I wrote a very short computer program to do it, and let the computer do the work!).

.

$$\mathrm{ERROR}$$

Suree I'd love too help here!

The question involves 16 benches and 9 bushes 

benches (4x4) so a huge square

And imagine tinier squares inside  made up of 4 benches and in the centre of those benches there will be a huge bush and if i do it for all of the 4 benches there'd be 9 bushes.

 I used Imgur to show you 

EinsteinJr and Daedalus

WHAT ARE YOU TWO DOING  ?????

The sum of every positive integer is infinity.

Thanks DarkBlaze  :)

MG you made a mistake   

You could get 6. (36/6 = 6) 

We do not count the remaing 1/12th of a board as it is not a whole board. Another example of this is if pencils are $2 each and you have $3 you cannot purchase 1.5 pencils. 

It appears that CPhill joined the forum on 13th March and he was apppointed moderator on 11th May.

Two months.  The forum was new born then - barely more than a feotus.  Things happen faster when we are very young :)

Here is the wrap on the day of Chris's knighthood.

There may be other acceptable answers here, but......I think it's possible that she is 66....

The grandson is 1 when she is 61  ......61 times his age

When he is 2, she is 62.......31 times his age

When he is 3, she is 63..... 21 times his age

When he is 4, she is 64.....16 times his age

When he is 5, she is 65..... 13 times his age

When he is 6, she is 66,.....11 times his age

And that's  six birthdays  !!!    {It's also called....."guess and check'.....LOL!! }

after you factor you equation, you got (x+y)(x-y)=y(x-y),then you divided the both sides of the equation by x-y. note that given x=1 and  y=1 so x-y=0.

From both sides of the equation by dividing or multiplying the same number (divisor can not be zero), the resulting equation is still valid.$$\Rightarrow$$ if a=b(c not equal to 0),then $${\frac{{\mathtt{a}}}{{\mathtt{c}}}} = {\frac{{\mathtt{b}}}{{\mathtt{c}}}}$$

So it not vaild to divide 0 from both sides of an equation.

addition explantion from wiki -In ordinary arithmetic, the expression has no meaning, as there is no number which, multiplied by 0, gives a (assuming a≠0), and so division by zero is undefined.

"The thing i messaged you doesn't work..."

What doesnt work MG ?

what you have done looks really good to me :)

Soon you will be teaching me - I am being serious,  if you keep learning this quickly I will be asking you to research and then show me how to do things in LaTex 

I really need helpers on this forum.  NinjaDevo is the only non-moderator who has really helped.

I am very grateful to him for everything that he did.

I am hoping that one day you will be able and willing to help here too :)

Hi again MG

One very important command in LaTex that i have not shown you yet is array,

here is a little example

$$\begin {array}{rll}\\
4+5+9-7&=&y-19\\
11&=&y-19\\
30&=&y\\
y&=&30\\
\end{array}$$

See how everything is lined up  

This is the code.   The ampersand & is the symbol for the lining up.

{rll}  means that first part is pushed right onto the ampersand.

the = sign (or what ever is next) is pushed left on against the &

and the last bit is pushed left onto the second &  

You can do a great many things with the array function - Heureka makes EXCELLENT use of it !!

\begin {array}{rll}             EDITED

4+5+9-7&=&y-19\\

11&=&y-19\\

30&=&y\\

y&=&30\\

\end{array}

Hi MathsGod1,

In response to your private message.  

I had to search for the bullet point on the internet.  I just googled LaTex, fat dot.