CPhill

Uh....7 hours ???

The numbers 2, 5 and 6 all need to be multiplied by one more power to form a perfect square of products.

Thus....  2 x 5 x 6 = 60

√[2^9 * 3^14  * 5^15 * 6^3 * 60] = √[2^10 * 3^14  * 5^16 * 6^4] = 984150000000

Very nice, geno.......I was gonna' look at this one.....but when I saw all those parentheses.....uh, no.......now, after seeing your answer, I realize it's not as bad as all that.....

The probability will be  .09 x .09  = .0081  = .81 %

sin^4@-cos^4@ = sin^2@-cos^2@    ....I'll use "x" instead of "@"......so we have

sin^4x - cos^4x       factor  this

(sin^2x - cos^2x) (sin^2x + cos^2x)       

But note.....  (sin^2x + cos^2x) = 1

So

(sin^2x - cos^2x) (1) =

(sin^2x - cos^2x)    and this equals the right hand side

The y coordinate for any x intercept is 0.......since, if the graph intercepts the x axis, y must be 0 at that point....

Let's look at this again.......

70^2 = 4900

4900 / 120 = 490 / 12 = 40.8333 

D  .....  t >= r+2

You're correct, Tiddle.....I forgot about that detail......mine would be "thrown out of the club".......your answer still reigns supreme  !!!!