CPhill

Apparently.....the "smart" cookies are beating the fossils, tonight !!!

You're makin' me look bad, GL !!!

Good answer !!

Very nicely done, GL...I was gonna' use trig, but your way is definitely more elegant.....

3 pts. and a thumb from me!!!

HaHa!!....you got me on that one......!!!

We can use the sine to find this....

sin(45) = opp/6     where 'opp" = altitude

6sin(45) = opp = 6/√2  or 6√2/2 or 3√2

Hey, zegroes....who you calling "olds??"

I'll echo zegroes' thoughts....good to see you back on here.......I was about to check the obituaries....you know....just in case......(just kidding)

3 points and a thumb for that answer....

zegroes is correct.....4132 miles..........since there are numbers involved, we'll consider it a math question and give zegroes a Field Goal (3 points)

We can us the tangent to find  the length of a side. So we have

tan(60) = (2/√3) / (s/2)   where s   = side length

√3 = 4/ (√3s)

3s = 4

s = 4/3

Let's take it from what you have, Quazars......

We have

1000 = 100000(.8)ⁿ

Divide both sides by 100000

1/100 = (.8)ⁿ

Take the log of both sides

log(1/100) = log (.8)ⁿ

And by a property of logs, we can bring the "n" out front

log(1/100) =n log(.8)

Divide both sides by log (.8)

log(1/100) / log(.8)  = n = about 21 wars are required

A factorial is just the product of the first n positive integers. For instance, 4! is the product of 1*2*3*4 = 24.

Usually the terms are multiplied in reverse order.....so 4! is usually writen as 4*3*2*1. (I'm not sure that there is any particular justification for doing this, but maybe someone else knows why....)

Let me throw one more thing in....by definition, 0! = 1

Does that help, DS???