First, let's write it neatly:
. I would try to get an answer for the left (before the equals sign), and the right (after the equals sign). If they are the same, then the equation is true, otherwise it's false.
Answer- vertical;congruent
Answer:
Base Side Length =1.59m
Height = 3.16 m
Step-by-step explanation:
Volume of the box =
Let the base dimensions = x and y
Let the height of the box =h
<em>However, for any optimal configuration, Width = Length as varying the length and width to be other than equal reduces the volume for the same total(w+l)</em>
Volume, V=xyh=8
Since x=y
Surface Area of the box
The material for the top and bottom costs twice as much as the material for the sides.
Let the cost of the sides =$1 per square meter
Cost of the material for the sides = 4xh
Cost of the material for the top and bottom =
Therefore:
Total Cost,
Substitution of into C
To minimize C(x), we find its derivative and solve for the critical points.
To verify if it is a minimum, we use the second derivative test
Since C''(x) is greater than zero, it is a minimum point.
Recall:
Therefore, the dimensions that minimizes the cost are:
Base Side Lengths of 1.59m; and
Height of 3.16 m
Use the chain rule.
E.g. d/dx [sin(x)^3] = 3cos(x)sin(x)^2