Jacques is an engineer. he has been given the job of designing an aluminum container having a square base and rectangular sides to hold screws and nails. it also must be open at the top. the container must use at most 750 cm2 cm 2 of aluminum, and it must hold as much as possible (i. e., have the greatest possible volume). what dimensions should the container have?

We let x be the length of the edge of the base of the rectangular prism and h be the height. The total surface area that needs to be covered is calculated through the equation,
                                A = x² + 4xh = 750
Calculating the value of h from the equation will give us,
                                      x = (750 - x²) / 4x
The volume is equal to,
                                 V  = x²h
Substituting the expression for h, differentiating the equation and equating it to zero (concept of maxima-minima)
                                 V = x²(750 - x²)/4x
                                 V = 750x/4 - x³/4
                                dV = 750/4 - 3x²/4 = 0 
                                        x = 15.81 cm
Thus, the dimensions of the container should be 15.81 cm x 15.81 cm x 7.9 cm. 

Hello!

the answer is:

the answer is:

why?

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!