Ajewelry box with a square base is to be built with copper plated sides, nickel plated bottom and top, and a volume of 40cm^3. if nickel plating costs $2 per cm^2 and copper plating costs $1 per cm^2, find the dimensions of the box to minimize the cost of the materials. write out the process of solving this question in plain english

Length and width = 2.71 cm and height = 5.43 cm

Step-by-step explanation:

Let the length of the jewelry box = x

Let the width = x          [box is square, so length and width are same]

Let the height = y

Given volume = 40 cm³

Therefore, V = x²y

x²y = 40  

y =

Cost of Nickle plating on top and bottom = $2 per cm²

Cost of copper plating on sides = $1 per cm²

Cost = 2(Areas of top and bottom) + 1(Areas of sides)

       = 2(x² + x²) + 1(xy + xy + xy + xy)

       = 4x² + 4xy

       = 4x² = 4x

f(x)   = 4x² +  

f'(x)  = 8x -  

f"(x)  =

f'(x)  = 0

x³ = 20

x = ∛20

x  = 2.71 cm

x²y = 40  

∛400y = 40

y =

  =

y  = 5.4288 ≈ 5.43 cm

Length and width = 2.71 cm and height = 5.43 cm

step-by-step explanation: the declaration of the rights of man and of the citizen (french: déclaration des droits de l'homme et du citoyen de 1789), set by france's national constituent assembly in 1789, is a human civil rights document from the french revolution.[1]

the declaration was drafted by the abbé sieyès and the marquis de lafayette, in consultation with thomas jefferson.[2] influenced by the doctrine of "natural right", the rights of man are held to be universal: valid at all times and in every place, pertaining to human nature itself. it became the basis for a nation of free individuals protected equally by the law. it is included in the beginning of the constitutions of both the fourth french republic (1946) and fifth republic (1958) and is still current. inspired by the enlightenment philosophers, the declaration was a core statement of the values of the french revolution and had a major impact on the development of freedom and democracy in europe and worldwide.[3]

the 1789 declaration, together with the 1215 magna carta, the 1689 english bill of rights (1689), the 1776 united states declaration of independence, and the 1789 united states bill of rights, inspired in large part the 1948 united nations universal declaration of human rights