CPhill

2.2244*1.01^n  = 2.2244 + 1.01^n

2.2244* 1.01^n  - 1.10^n  = 2.2244

1.01^n(2.2244 - 1)  = 2.2244

1.01^n ( 1.2244) = 2.2244

1.01^n = 2.2244 / 1.2244         take the log of both sides

log 1.01^n  = log [ 2.2244/1.2244]

n*log 1.01  = log [ 2.2244/1.2244]

n = log [ 2.2244/1.2244] / log [1.01]  = about  60.0016519101031466

1024  = 2^10

So

1024 x 1024 x 1024  =    1024^3   =   [2^10]^3  = 2^30  = 1,073,741,824

Happy Birthday, Geno......!!!!!

No......

A prime number is only divisible by itself and 1

0 is definitely not divisible by itself, but it is divisible by every other number except itself.

By convention, we take the principal root which is +5, unless we are solving an equation involving the roots of 25. Then, both roots [positive and negative] are taken.

Thus

sqrt(25)  = 5

But

x^2  = 25

Then, 

x  =  +/- 5

Thanks, Alan......!!!!!

Pretty good.......how about you???

WolframAlpha evaluates it as  :

399313452966 / 1975

BTW.....welcome to the site......!!!!!

I wanted to come back to this one and solve it with substitutions......

(1) b=d+f   →  f = b - d  

(2) e=c+f   →  f = e - c

(3) 12=10c+20e   →   6 = 5c + 10e

(4) 0=10f+20b-10c  →  0 = f + 2b - c

 (5) 0=10d-20e-10f  →   0 = d - 2e - f

Subtract (2) from (1)

b - e  = d - c   (6)

Add  (4) and (5)

0 = 2b - 2e + d - c   →   d - c  = 2e - 2b

Substitute  the previous result into (6) for d - c

b - e = 2e - 2b  →  3b = 3e   →   b = e    and from(6) this implies that  →   d = c

Substitute (2)  and  the fact that b = e   into the rearrangement of (4)

0 = e - c + 2e - c → 2c = 3e  → e = [2/3]c

Substitute the previous result into the rearrangement of   (3)

6 = 5c + 10(2/3)c  →  18 = 15c + 20c  →  18 = 35c  →  c = 18/35  →  d = 18/35

And   e = [2/3]c  = [2/3](18/35)  = 12/35  =  b

And f = b - d    .....so   f =  12/35 - 18/35  = -6/35

Alan's answers are correct......I may have mis-typed something when I put the system into WolframAlpha.....!!!!

[When I put this system back into WolframAlpha, it still says no solutions exist.....odd!! ]

You can enter it just like this in the on-site calculator :

0.9807^10

It will give you the result   0.8229......