A 1125ft3 open top rectangular tank with a square base x ft on a side and y ft deep is to be built with its top flush with the ground to catch runoff water. The costs associated with the tank involve not only the material from which the tank is made but also an excavation charge proportional to the product xy. a. If the cost is

c=5(x2+4xy)+10xy

what values of x and y will minimize it?

b. Give a possible scenario for the cost function in part (a)

there is no universally accepted definition of art. although commonly used to describe something of beauty, or a skill which produces an aesthetic result, there is no clear line in principle between (say) a unique piece of handmade sculpture, and a mass-produced but visually attractive item. we might say that art requires thought - some kind of creative impulse - but this raises more questions: for example, how much thought is required? if someone flings paint at a canvas, hoping by this action to create a work of art, does the result automatically constitute art?