Abox with a square base and no top is to have a volume of 32 cm3. find the least amount of material (surface area) needed to construct such a box.

The least amount of material will be required when the box is half a cube, so its surface area is half that of a cube with volume 64 in³. Such a cube has sides that are 4 in squares, so has an area of 4²×6 = 96 in². Half that is 48 in².

The least amount of material required for an open square box of volume 32 in³ is 48 in².

Let x represent the edge length of the square base. Then the height of the box is 32/x², and its surface area is

... A = x² + 4x(32/x²) = x² +128/x

The derivative of this is

... dA/dx = 2x -128/x²

and it will be 0 where the area is a minimum:

... 0 = 2x -128/x²

... 64 = x³ . . . . . multiply by x²/2 and add 64. Note this is the answer we had above.

... x = ∛64 = 4, and the area is

... A = 4² + 128/4 = 16 + 32 = 48 . . . . in²

median is the value separating the higher half of a data sample, a population or probablity distribution from the lower half.

step-by-step explanation:

say you have 3,8,7,3,1,9,8 order them from lowest to highest

if orderd it would be 1,3,3,7,8,8,9 now you take away from the lowest and the highest until you end up in the middle.

so you would remove the 1 and 9 leaving you with 5 digits remaining

when you've reached the middle that would be your answer so in this case the answer is 7

if there were two numbers left say 7 and 5 you'd and them together so 12 then divide by 2 witch would equal 6 so the answer would be 6

good luck on that project hoped i you at all

the translated point is (5,2)