CPhill

Here's my  best attempt :

0   =    w         ( L^2x^2     -   x^4      -  7L^4  )

         ____        ______        ___         _____

         EI6L           2                 4             60

Multiply both sides by   EI6L / w     and the lead term "disappears"

0  =   L^2 x^2     -   x^4     -  7L^4

        ______         ____      _____

             2                4            60

Multiply through by  - 60

15x^4  -  30L^2x^2  +  7L^4   =   0

15x^4  -  30L^2x^2     =  -  7L^4         factor  out 15

15 ( x^4 - 2L^2x^2)  = - 7L^4            divide both sides  by 15

x^4  - 2L^2x^2   =     - 7L^4 / 15

Take  1/2  of 2L^2  = L^2

Square this  = L^4

Add to both sides

x^4 - 2L^2 x^2  + L^4  =   -7L^4 / 15   + L^4   

Factor the left side   and simplify

( x^2  - L^2)^2  =   8L^4 / 15

Take both roots  and simplify

x^2  - L^2  =   ±√ [ (8L^4 / 15) ]

x^2 - L^2  =  ±2L^2√ [ 2/15 ]

Add L^2  to both sides

x^2  =  L^2  ± 2L^2√ [ 2/15 ]

Take both roots again

x =  ±√ ( L^2 ± 2L^2√ [ 2/15 ]  )  =    ± L√ ( 1 ± 2√ [ 2/15 ]  ) 

I"d say  " Personal Interview "

Good job,  creepercraft   !!!!!

C ( 12,5)  *  C(9.3) * C(6, 4)   = 997920 ways

I think you mean "vertex" form

y  =  x^2 + 5x +  36

Take 1/2 of 5  = 5/2...square this  = 25/4.....add it and subtract it on the right

y =  x^2 + 5x  + 25/4  + 36  - 25/4     factor  and simplify

y = ( x + 5/2)^2  + [ 144 - 25] / 4

y = ( x + 5/2)^2  + 119/4   ⇒   vertex form

The vertex  is  (-5/2, 119/4)

Let the vertex of the angle lie at  (0,0)

Note that  we move 6  units to the right and 4  units up to get to the point  ( 6 ,4)  that is the top right vertex of the triangle

So...we have the points  (0,0)  and ( 6,4)

And  slope  =  [  subtract the y  coordinates of each point in some order ]

                       __________________________________________________

                        [ subtract the   x coordinates of each point in the same order ]

So we have

[  4 - 0 ]               4               2          rise

_______   =       ___   =      __   =   ____

[ 6 - 0  ]                6              3          run

f(x)  = (x + 6)^2  for x  ≥ 6

For  f(x)......write y

y = ( x + 6)^2      take the square root of both sides

√y =  x + 6     subtract 6 from both sides and "swap"  x and y

√x  - 6   =   y      for y, write g(x)

So

g(x)  =  √x - 6   

Since  the first point on the original graph  is  (-6,0)

The first point on this graph  is  (0,-6)

So    x ≥ 0

As you have it written....no  solution

Think about this....whatever √ x  is on one side it is the same thing on the other side

But  adding 5 to this value on one side will always be  3 more than adding 2 to it on the other side

So.... the left side > right side for any  x value  ≥ 0

The inverse reverses the original coordinates...so.....

(1, -1)     (0, 0)  and (4,2)  are on the inverse graph

Let's see if I remember this....

A function has to pass the "horizontal line" test to be a strict inverse....that is......any horizontal line drawn can only cut the function one time....

So...the two functions on the left will be strictly invertible, but not those on the right