CPhill

Melody makes a

Out of a

LOL!!!!!!!!!   [ Don't worry .......We still love you, Melody.....!!!!! ]

I also believe that EP is correct......I think that the focus and vertex  are generally accepted to be distinct points......

U     2

Thanks Gibson.....here's another "trick".....note     (a /b)^-m/n   =  (b /a)^m/n     ....therefore........

(8/125)^-2/3   =

(125 / 8 )^2/3   =

[(125 / 8)^1/3 ] ²  =

[ 5 / 2 ] ²  =

25 / 4

Going from this point in Melody's answer....

P(z)  = z^4 - z^3 + z^2+ 2

We know that 1 + i  is a root....therefore (1 - i)  must also be a root.....thus, the resulting polynomial is

[z -  ( 1 + i ) ]  [ z - (1 - i ) ]  =

 z^2    -z(1 + i) -z(1-i)  + 2  =

z^2  - 2z + 2

Now.....using some polynomial long division, we can determine the other factor

                         z^2  + z  + 1

z^2 - 2z + 2  [   z^4     - z^3  + z^2            + 2   ]

                        z^4     - 2z^3 + 2z^2

                       ________________________

                                    z^3  - z^2            +    2

                                    z^3 -2z^2   + 2z

                                    -------------------------------

                                            z^2  - 2z    +  2

                                           z^2   -2z     + 2

                                          _____________

And the two factors are  ( z^2 - 2z + 2 ) (  z^2  + z  + 1 )

I just realized that I committed a cardinal sin on this one....I cannot divide by sin A....since A  = 0°

Here's a correct approach :

sin A  = tan A

sin A  = sin A / cos A

sin A - sin A/ cos A   = 0     factor out sin A

sin A [ 1 - 1/cos A]  = 0

sin A  [ 1 - sec A ]  = 0

So either   sin A  = 0     in which case A = 0°   or   sec A  = 1......which further confirms that A = 0°  .....and cos A  = cos 0°  = 1

log₉₍x+8)+log₃₍x+6) = 2 

Uisng the change of base formula, we have

log ( x + 8) / log 9   +  log (x + 6) / log 3   = 2      multiply both sides by  log 9 * log 3

log 3 *log ( x + 8) +log 9* log ( x + 6)   =  2 * log9 * log3   by the exponent law, we  can write

log (x + 8)^log3 + log(x + 6)^log9  =  2*log9 * log 3   and further, we can write

log[ (x + 8)^log3 * (x + 6)^log9] = 2*log9 * log 3    this would be difficult to solve by normal means

WolframAlpha gives the solution as ≈ -2.24754

OK.......  

It's not.....!!!

0.000548 - 20 = -19.999452

Let the side = S

And the area of a square = S^2  ...so...

S^2 = 1764      take the square root of each side

S= √1764  =  42 ft