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1) Number of grains on the 64th square=2^(64-1)

2) Number of grains on the entire chess board=(2^64)-1

a man

oky doky a friend i am a  chicken

Australian kids are off until the first week of February :))

In general, the half life, L,  and the constant k are related by k = -ln(2)/L, so k = -ln(2)/5700 per year = 1.216*10^-4, as Guest has determined in the previous reply.

I assume i and j are unit vectors in the x- and y-directions respectively and that a dot product is required for v.w.

If so, then i.i = i, j.j = j and i.j = j.i = 0  so:

(3i + 5j)(-2i + 2/3j) =   -6i.i + 2i.j - 10j.i +10/3j.j   =  -6i + 10/3j

If v*w is meant to be a cross product (vxw) then the third, z, dimension is involved and 

ixi = jxj = kxk = 0

ixj = -jxi = k

jxk = -kxj = i

kxi = -ixk = j

This is undefined.

29.9

There are some Great Birthday Greetings here, Sir CPhill. Hayley gave the best one: “Don't drink too muuchh! you might want to remember you'r birthday!”  Hayley even slopped up the spelling to emphasize her point. Truly great!

 You might remember what happened last year – oh wait, you probably don’t – I’ll remind you: Melody “whited out” my main greeting to you, but alas your mod-god powers allowed you to see it. So, in keeping with tradition, another greeting, this time slightly encrypted with ones and zeros for your enjoyment.

01001000 01100001 01110000 01110000 01111001 00100000 01000110 01110101 01100011 01101011 01101001 01101110 01100111 00100000 01000010 01101001 01110010 01110100 01101000 01100100 01100001 01111001 00100001 00100000 01010011 01101001 01110010 00100000 01000011 01010000 01101000 01101001 01101100 01101100 00100000 00111010 00101001

Alas, none of the zeros are Roman – you’ll have to continue your quest.    . . .

I'm on that right now :/

Maybe I'm typing it wrong. I'll try it again. :)

Thank you for you're help and patience! :)

Try graphing it on "Desmos graphing calculator" and see what you get.

When I graph it, there are two "U"s.. 

Maybe my scientific caluculator is messed up?

Hayley: Yor are a bright girl, at least in Math. I have seen you solve difficult simultaneous equations before, so I know you can do this one with ease. So, by just looking at it, y should be=2.

Go online and use this mixed fractions calculator:

http://www.calculatorsoup.com/calculators/math/mixednumbers.php