CPhill

.5 x .03  .....just forget the decimals and multiply 5 x 3  .... so we have

5 x 3 = 15

Now.... this is really...

15.

But, we moved the decimal point one place to the right in multiplying the ".5" and two places to the right in multiplying the ".03"....so that's a total of three places to the right....so....we must "correct" this in the answer of "15" by moving the decimal point back to the left three places....so we have...

.015  ..  and that's it...!!!

(x/y) - (y/x) + (3/xy)  ..  I assume you want to simplify this???.....assuming that the "y" in the last term is in the denominator, we have

[ x^2 - y^2 ] / xy + 3/(xy) =

[ x^2 - y^2 + 3 ] / (xy)

Using the Pythagorean Theorem, we have

15^2 +(3x)^2  = (3x + 3)^2    expand

225 + 9x^2 = 9x^2 + 18x + 9   rearrange and simplify

18x - 216 = 0

18x = 216

x = 12

It's probably better to give to much info than too little......"labeling" your answers is always a good thing....

Since sine and cosine are co-functions, cos x = sin(90-x)

Therefore, cos x = 1/3

And using the cosine inverse, we have

cos^-1 (1/3)  = about 70.53°

And the sin (90 - 70.53) = 1//3   !!!!

You can evaluate this using the on-site calculator.

Very nice, Tetration.

Thanks, heureka.

"Brute Force" and "Ignorance"  are two of my favorite math techniques....in fact, I would feel lost without them....!!!

Thanks, Alan...for those answers....

Very nice, heureka......can you show us how you arrived at your solution???