CPhill

Thanks, bertie, I like your way better.......

Anonymous, here's what bertie is saying:

Note that, since theta is the same same angle in both triangles, the tangent of this angle must be equal in both triangles!!

So we have

tan(Θ) =  2/3 = 5/x

Therefore, 2x = 15   and x = 7.5.......bertie's method eliminates the need to find theta altogether !!!

Hie, Morgan Tud......!!!  M'Lady looketh none too pleased with thy bold reply......!!! She hath already condemned Sisyphus to boulder pushing.......for perpetuity.....

..........delete..........

I'll second what Melody said....nice graphic, too!!!........"points" from me......Welcome aboard!!!

Well..bertie, as you can tell, probability isn't my strong suit.....I am happy when my answer actually agrees with anyone's .....but, when I actually agree with myself, it's truly odd !!!    LOL!!!

We need a permutation for this one.

(5 P 2) = 20

If we had just wanted to count all the possible sets that could be formed by choosing 2 people from any 5, the answer would have been 10. But, the permutation considers order within sets.

Thus, the set {person 1 , person 2} is considered a different set from {person 2 , person 1}.

It's where e^(3x) = 70

Take the natural log of both sides

 Ln e^(3x) =  Ln 70     And by  a property of logs, the left side just becomes 3x...so we have..

3x = Ln 70                  Divide both sides by 3

x =  Ln70 / 3    ≈ 1.416

Let's take it term by term

4x* 2x^2  =  4*2*x*x^2  =  8x^3

4x *(-7x) =  4*(-7)*x*x = -28x^2

4x*3 = 4*3*x = 12x

Put it all together...

8x^3 - 28X^2 + 12x

And that's it ... !!!

natasza...I've made a change to one of these answers ....No. 5....I saw what it wanted....I realized that my answer to the y° part was incorrect and I also saw that it wanted an answer  for "x°"...look at it again!!

IMHO = In My Humble Opinion

NO!!...I'm not blaming you.....it's just hard to determine some of the labellings...not your fault !!!

Let's find "theta" in the first triangle....we know an opposite side and an adjacent side.....the thing that relates these is the tangent...so we have

tan(Θ) = 2/3    .... now......we need to take the inverse tangent to find this angle....so we have...

tan^-1(2/3) = about 33.7 degrees

So...in the second triangle, we have

tan(33.7) = 5/x     or, rearranging slightly...   x = 5/ tan(33.7)  = about 7.497 or just 7.5

And there you go......