Asquare piece of tin has 12 inches on a side. an open box is formed by cutting out equal square pieces at the corners and bending upward the projecting portion which remain. find the maximum volume that can be obtained.

Explanation:

Given a square Piece whose side is 12 inches

Now square pieces are cut from each corner to make it a open box

Suppose x is the length of square piece at each corner

then

base square has a length of

Dimension of new box is

Volume

For maximum volume differentiate with respect to x we get

we get x=6 and 4 but at x=6 volume becomes zero therefore x=4 is valid

answer;

d. are made mostly of liquid

explanation;

-the general   composition and structure planets includes; they have a thick gas and liquid layer covering a small,solid core. mostly the gases are hydrogen and helium atmosphere and layers of liquid hydrogen. for instance neptune and uranus are examples of the outer planets, they have a core covered by ice and ammonia.

-neptune's atmosphere is hydrogen and helium with a bit of methane so there is no oxygen to breath and the interior is made up of frozen water and ammonia with a rock and iron core. thus, there is no liquid water or solid surface to survive.