CPhill

I'm just  playing around with this......I don't know if it's correct....

L * W * H

Volume

Surface Area

1 * 1 * 100  m^3

2 ( 1  + 100 + 100) =  400  m^2

2 * 2 * 25 =  100m^3

2 ( 4 + 50 + 50)  = 208  m^2

2 * 5 * 10   = 100 m^3

2( 20 + 10 + 50)  =  160 m^2

5 * 5 * 4 =  100 m^3

2(25 + 20 + 20)  =  130 m^2

WolframAlpha  shows that the surface area is minimized when each dimension ≈ 4.64159 m

And the surface area ≈ 129.266 m^2 

Which is exactly what Melody got........

But.....since each dimension must be an integer.........

I'm assuming that my last answer must be pretty close, since the surface area  = 130 m^2

That is.....we have  a square base of 5m on each side  and a height of 4 m

We have a right triangle with a hypotenuse =  27 and a leg   = 22

So.....the height is

sqrt  ( 27^2  -  22^2 )  ≈ 15.65 in  =  16  in

"D"  is correct

Look  at the pic :

AB  = DE,  AC = DF  and BC  = EF

So.....by SSS  the triangles are congruent  which implies that matching angles are also congruent

⁵√243   =   3

45% off  means that  the cost of the phone is 55%  of its original price....so

55% *  83   =   .55 * 83  =  $ 45.65

$40  rebate means the cost is  83  - 40  =  $43

The rebate is the better  deal

Good job, hectitctar......at least you got it down to a cubic ....

But you're correct.....it's still hard to solve....!!!!

Note.... There is a "formula" for solving a cubic, but it's pretty messy !!!  

Also......here's a procedure involving some substitutions.....

http://www.sosmath.com/algebra/factor/fac11/fac11.html

Not sure it's worth pursuing for this problem, but if you can work it out.....I'd be willing to chip in a point  (or two).......LOL!!!!!

MBND  is a parallelogram   with a base  = 1/2  and height  = 1

So....its area  =  (1/2) (1)  = 1/2

And....because  of symmetry, the diagonal AC divides the parallelogram into equal areas......so.....the shaded  area  = 1/4 

3 log ( x - 2) =  log (2x) - 3

Don't see a way to solve this algebraically  [but maybe someone else on here knows one ]......

Here is a graphical solution :  https://www.desmos.com/calculator/tbdqhaxixk

The solution is   x ≈  2.163

B is the correct answer

"D"  is correct