An open-top box with a square base is to be constructed from 120 square centimeters of material. What dimensions will produce a box with the largest possible volume

Maximum length and breadth of the box is 6.32 cm and the height of the box is 3.16 cm

Step-by-step explanation:

Surface area of box

Volume of box is

Differentiating with respect to

Equating with zero

Double derivative of the volume

So, the volume is maximum at

So, the maximum length and breadth of the box is 6.32 cm and the height of the box is 3.16 cm.

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

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