If 1,200 cm2 of material is available to make a box with a square base and an open top, find the maximum volume of the box in cubic centimeters. answer to the nearest cubic centimeter without commas. for example, if the answer is 2,000 write 2000.

An open-top box uses a minimum of material when the shape of it is half a cube. Two such boxes would form a cube with area 2400 cm², so side area of 2400/6 = 400 cm², and edge dimensions of √(400 cm²) = 20 cm.

The volume of the half-cube is then (1/2)·(20 cm)³ = 4000 cm³.

Let x represent the edge-length of the square base of the box. Then the height of the side is v/x², and the total area of the open-top box is

... 1200 = x² +4x(v/(x²))

Multiplying by x  and subtracting the left side of the equation gives

... x³ -1200x +4v = 0

Differentiating, we have

... 3x² -1200 +4v' = 0

At the maximum volume, v' = 0, so this becomes

... 3x² -1200 = 0

... x² = 400

... x = 20 . . . . . . . . as argued above.

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?