SOLUTION: Hello. Please, if someone could give me an explanation on how to solve this problem, I'd really appreciate. Suppose that you are given an open top box with the square base. Let

Algebra ->  Functions -> SOLUTION: Hello. Please, if someone could give me an explanation on how to solve this problem, I'd really appreciate. Suppose that you are given an open top box with the square base. Let      Log On


   

Question 1024986: Hello. Please, if someone could give me an explanation on how to solve this problem, I'd really appreciate.
Suppose that you are given an open top box with the square base. Let x be the length of the side of the base and let the volume of the box be V=1. Express the surface area of the box in terms of two power functions of x.
Thank you very much.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Base surface but not a top surface. You have volume of 1 unit of whatever this volume unit may be, as V=1.

The dimension for height may be any variable you choose. Try assigning y for the height.
V=x%2Ax%2Ay
x%5E2%2Ay=1
y=1%2Fx%5E2---------still two unknown variables, x and y.

The question to answer is, what is the expression for the surface area?
Four of the surfaces each are xy, and the base area is x%5E2.
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The surface area for this box is 4xy%2Bx%5E2. You already know something about y, so you can substitute for y:
4x%281%2Fx%5E2%29%2Bx%5E2
4%2Fx%2Bx%5E2
but since you are asked for all power functions of x, express this area as highlight%284%2Ax%5E-1%2Bx%5E2%29.