Abox with a square base and open top is to have a volume of 72000 cubic inches. the material for the base costs 4 cents per square inch, while the material for the sides costs 6 cents per square inch. find the dimensions which minimize the cost of material.

Volume of box=a²h=72000, where a is the side of the base and h the height. h=72000/a²
Area of base=a².
Area of sides=4ah. Total=a²+4ah.
Total cost=4a²+24ah=4a²+24×72000/a=4a²+1728000/a.
Differentiate wrt a: 8a-1728000/a². When 8a=1728000/a², there is a minimum.
So 8a³=1728000, a³=216000, a=60.
Therefore h=72000/3600=20.
The dimensions are: base side=60 in, height=20 inches.

i = 2 / - 5

step-by-step explanation:

evaluation of ( 2 - 4 ) ( p + q ) when p = 2 and q = 5 i, by putting values of p and q,                                                                    

0 = ( 2 - 4 ) ( p + q )0 = ( 2 - 4 ) ( 2 + 5 i ),   by multiplying these0 = ( 4 + 10 i - 8 - 20 i )0 = 4 - 8 + 10 i - 20 i0 = - 4 -10 i   0 = 2 ( - 2 - 5 i )0 / 2 = - 2 - 5 i- 2 - 5 i = 0- 5 i = 2i = 2 / - 5