CPhill

https://web2.0calc.com/questions/probability_27845

        1                               1                           1

_____________  +  _____________ + _______________

sqrt 36 +sqrt 39       sqrt 39 + sqrt 40      sqrt 40 + sqrt 45

Multiplying numerartors/denominators by the conjugate of the  denominators, we can write

 sqrt 36 - sqrt 39         sqrt 39  -sqrt 40       sqrt 40 -sqrt 45

_______________  +  ______________ +  ______________

     36 - 39                        39 - 40                     40 - 45

sqrt 39 - sqrt 36           sqrt 40 - sqrt 39           sqrt 45 - sqrt 40

_____________  +   _______________ +   ______________

          3                              1                                   5

(-2/3)sqrt 39 - 2  + (4/5)sqrt 40  + (1/5)sqrt 45

(-2/3)sqrt 39 -  2 + (4/5)* 2 sqrt 10  + (1/5) 3sqrt 5

(-2/3)sqrt 39  - 2  + (8/5)sqrt 10 + (3/5)sqrt 5

3(2c + 1) = 28*(3c) - 9 + 45(3c) - 18

6c + 3 =  84c + 135c - 27

30  =  213c

c =  30 / 213 =  10  / 71

https://web2.0calc.com/questions/frustum_2

https://web2.0calc.com/questions/plane-and-sphere#r1

sin theta =  [sqrt (4^2 -1^2) ] /  4  =  sqrt (15) / 4

tanx + sec x =  0

sin x / cos x  +  1 / cos x =   0

sin x / cos x =   -1  / cos x           square both sides

sin^2 x / cos^2x  = 1 / cos^2 x

[ 1 - cos ^2 x ]  / cos ^2 x  = 1/ cos^2 x

1/ cos ^2 x  -  1  = 1/ cos^2 x

-1  =  0         →  no solution

https://web2.0calc.com/questions/bisector

(3 + 2 + 2 ) !  = 7 !  = 5040 ways

https://web2.0calc.com/questions/triangles_144