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thanks you guys!

I'd go for infinity.  

Aziz,

Thanks for  that great answer, I have given you thumbs up.

I just want to suggest that instead of using right arrows you move to another line, I think it would be easier to read.  You do this in latex with \\   If you want the spacing to be bigger you can use \\\\

This is how I do it because I like my working well spread.  

|10-U|  or  |U-10|

Both of these will have the same value. 

Q1001.  

The following image should help here:

Q will be 88*|e|.

Q2014.

Use the standard equation for force, F, (as in my first post above) with q1 = 4|e| and q2 = 8|e|. The distance, r, is √(3.3² + 6.9²) mm (You might want to change this into metres to make sure your units are consistent).

The angle of interest, θ, is tan^-1(3.3/6.9) (which I get to be 25.56°, not 27.4°), giving the component of force along the x-axis as F*cos(θ).

NB k ≈ 9E+9  not 9E-9.

The particles act on each other with the same magnitude force (opposite directions):- Newton's 3rd law of motion.

sorry there was no special character for the "little" numbers! :(

A printing firm borrows $50,000 to purchase a new printing machine. Under the loan agreement, the firm will make 12 equal monthly repayments with the first repayment made 6 months after the loan amount is transferred to the firms bank account. If the rate of interest charged on the loan is 12% per annum compounded monthly, what amount will be each of the 12 monthly repayments? 

Inital loan = $50000, interest rate = 1% per month = 0.01

The loan accrues interest for 5 months before the repayment period starts.

$$\boxed{Future \;value\; with\; compound\;interest=P(1+i)^n}$$

Effective loan = 50000(1.01)^5 = $52550.50

Now it is a present value of an ordinary annuity problem,

$$\boxed{PV=R\times \frac{1-(1+i)^{-n}}{i}}$$

$$\begin{array}{rll}
PV&=&R\times \frac{1-(1+i)^{-n}}{i}\\\\
52550.50&=&R\times \frac{1-(1.01)^{-12}}{0.01}\\\\
52550.50\times \frac{0.01}{1-(1.01)^{-12}} &=&R \\\\
R&=&\$4669.05 \\\\
\end{array}\\\\
\mbox{Each monthly payment will be \$4669.05}$$

Yes e is in terms of e. I recall now. Still my answer with the same approach was way off. Shocking. 

Here is two more fails. Though I believe my intial answers were close to correct, before trying alternatives values. 

Q1001: A certain atom has 88 protons. Assume that the nucleus is a sphere with radius 7.04 fm and with the charge of the protons uniformly spread through the sphere. At the nucleus surface what are (a) the magnitude and (b) direction (radially inward or outward) of the electric field produced by the protons?

For the above equations I worked out Fe / into 7.04 x by (10^-15)^2 all x by 88. This was wrong, so I / by 88 to get initial Fe per partical which was wrong. 

Q2014: In the figure particle 1 of charge +4e is above a floor by distance d₁ = 3.30 mm and particle 2 of charge +8e is on the floor, at distance d₂ = 6.90 mm horizontally from particle 1. What is the x component of the electrostatic force on particle 2 due to particle 1?

t

Number

Here the solution I found was more complicated perhaps than needed to be. Can you check if it should work? I calulated (tan^-1(o/a)) = 27.40 degrees. Next, Fe = 9E^-9*4*1.6E^-19*8*1.6E^-19. The equation Fecos(27.40) was used to solve the x axis component of force. I think I left our r^2 a few times in here which is 7.64852927E-3. 

{Please elaorate where solving for one partical acting on another is involved and how that is different to using Fe.}

consider a cube that is just big enouugh for one orange.

Let the radius of the orange be 2 units.

The volume of the orange is       $$\frac{4}{3}\pi \times 2^3 = \dfrac{8*4\pi}{3}\;units^3$$

Now in that same box you can fit 8 tangarines.  the radius of each one is 1unit

The volume of the tangarines is       $$8\times \frac{4}{3}\pi \times 1^3 = \dfrac{8*4\pi}{3}\;units^3$$

The volume of the 8 tangarines is exactly the same as the volume of 1 orange so the ratio of the spaces in the boxes must be 1:1

The two boxes have exactly the same amount of empty space.   

infinity^2

You might notice here that 22 + 81 = 103, so I suspect that what is wanted is 103!/(22!*81!) which is nCr(103,22)  (or nCr(103,81), which is the same).  This can be calculated using the website calculator using the ncr function:

$${\left({\frac{{\mathtt{103}}{!}}{{\mathtt{22}}{!}{\mathtt{\,\times\,}}({\mathtt{103}}{\mathtt{\,-\,}}{\mathtt{22}}){!}}}\right)} = {\mathtt{15\,197\,882\,802\,514\,693\,962\,310}}$$

$${\left({\frac{{\mathtt{103}}{!}}{{\mathtt{81}}{!}{\mathtt{\,\times\,}}({\mathtt{103}}{\mathtt{\,-\,}}{\mathtt{81}}){!}}}\right)} = {\mathtt{15\,197\,882\,802\,514\,693\,962\,310}}$$

2 times as many across

2 times as many back

2 times as many up

2x2x2=8

8 times more tangerines. 

800% times as many tangerines as oranges.

Haven't thought about the rest yet.

It's hard to think on a phone.  :)

On mine, the link is doing nothing but appearing like the normal google sign. :(

$${\frac{\left({\mathtt{50\,000}}{\mathtt{\,\times\,}}\left({{\mathtt{1.01}}}^{{\mathtt{6}}}\right)\right)}{{\mathtt{12}}}} = {\mathtt{4\,423.000\: \!627\: \!504\: \!166\: \!666\: \!7}}$$

have look at google!its also hopping with joy!

Oh, I see..well looks like lots of fun! 

yes a dragon!

and as much as i know i think this place is India gate !

Oh, neat!! What's the last picture...looks like a dragon!

yes!and he just denied for a lot of security!i saw it in the news channel when i woke up!

found some more pics!

kites!

Today there might be a lot of activivties taking place out here!

Sounds very festive, rosala!  It must have been extremely fun!

Also, yes, the PM did a wonderful thing meeting children personally without interference...usually so much security would be there for presidents but it just shows how approachable and friendly he can be...

and u know , there was a function as well held celebrating the day in my school!its was awesome!

there were dances , singing , acts and many more!

and yes the children might be very happy to meet the PM as well as the new PM he just went between the children with no security and just shook hands with them!this has happened the first time!

Your right!even thats happening with me too and im sure with everyone else!

I see. Yes, must be lots on social media websites and other places. 

This is not that crucial of a matter, but: Is it just me or do we have to hit enter twice to create a single space...because when I am making a post, I have to create a double space, but it appears as a single space once I see the created post.

umm yeah!i just found this suddenly!

i think many more pics might be there but just that i havent looked up!

I see. Oh, yes, the number 68 this time and nice canon and close-up pics! The close-ups really do let you feel the emotions and wonder!

The children must be proud to do it for their country so that's good although the work may be tough. It reminds me of the opening ceremonies in the Olympics.

I wish i studies in a school of Delhi but i study in Noida and live in Delhi!lol!

but it hink even if i had studies i wouldnt be selected becoz im not that good in marching !lol!

anyways , ive got the pics of this year!heres the link!