Question 1187070
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Packaging is one important feature in producing quality products. A box designer needs to produce a package 
for a product in the shapes of the pyramid with a square base having a total volume of 200 cubic inches. 
The height of the package must be 4 inches less than the length of the base. Find the dimension of the product
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<pre>
The "volume" equation is

    {{{(1/3)*x^2*(x-4)}}} = 200   cubic inches,

or

    {{{x^2*(x-4)}}} = 600.



One solution can be easily guessed:  x = 10.


Indeed,  {{{10^2*(10-4)}}} = {{{10^2*6}}} = 600.


Next, notice that the function {{{x^2*(x-4)}}}  monotonically increases in its domain x > 4.


It means that x = 10  is the UNIQUE solution to the "volume" equation, and THERE IS NO other real solution.


<U>ANSWER</U>.  Under given conditions, the unique set of the dimensions of the pyramid is  10 inches for the square base 
         and  6 inches for the height.
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Solved.