CPhill

Since this is a parallelogram and KM = LN, this must be a rectangle (at least) with each corner angle = 90 degrees

And consecutive angles in a parallelogram are supplemental - they add to 180 degrees

Therefore, <KLM and <LMN  = 180

 {I think you must mean that <LMN = 90 = 9x.....therefore x = 10}

So we have

2xy + 9x = 180

2(10)y + 90 = 180

20y = 90      

y = 90/20 = 9/2 = 4.5

The first natural number greater than 150 that is divisible by is 153

And the natural number that is closest to - and less than - 300 that is divisible by 9 is 297

So, the answer you're seeking is given by ..... [(297 - 153) / 9]  +  1` =  17

Any three can be in the first position...any three in the second and any three in the last

So

3 x 3 x 3   = 27

This also implies that for any number of n different letters...nⁿ "words" can be formed in this manner...

There are 6 odd numbers in each row x 11 rows = 66

Hit the "2nd" key.....you will see the inverse functions.....asin, acos, etc.

10^(log (20)/240)=

(log (20)/240)= 0.0054209583152666

So  ...   10^{0.0054209583152666} = about 1.013

The measure in degrees can be found by using the inverse tangent

We have

tan^-1(-5/2)  =  about - 68.198°.....but this is - 68.198° in the 4th quadrant = about 291.8°

Here's a pic......

The arcsec u just means an angle, Θ, whose secant = u.... or just .... u /1

Thus, since the secant ratio is r / x....this means that r = u   and x = 1

And y = √[r^2 - x^2]  = √[u^2 - 1^2] = √[u^2 - 1]

And the cotangent of such an angle is just x / y  =  1 / √[u^2 - 1]    and "rationalizing" the denominator, we have

cot (arcsec u) = cot Θ  = √[u^2 - 1] / [u^2 - 1]

Here's a Venn diagram showing the numbers in each "cat"egory.....Mmmmm....maybe it should be each "dog"etory, huh??