(1 point) An open box will be made by cutting a square from each corner of a 10 ft by 16 ft piece of cardboard and then folding up the sides. What size square should be cut from each corner in order to produce a box of maximum volume

2 feet

Step-by-step explanation:

We are given that

Length of piece,l=10ft

Width of piece,b=16ft

Let x be the side of square

Length of box=10-2x

Width of  box=16-2x

Height of box=x

Volume of box=lbh

Differentiate w.r.t x

Because when substitute the value x=20/3

Then, the width of box is negative which is not possible.

Substitute x=2

Hence, the volume is maximum at x=2

Side of square=2 feet

Hence, square of side 2 feet should be cut from each corner in order to produce a box of maximum volume.

the correct answer is option c.   3

step-by-step explanation:

points to remember

equation of the line with coordinates (x₁, y₁) and (x₂, y₂) is given by,

slope m = (y₂ - y₁)/(x₂ - x₁)

from the figure we can see a line with two coordinates given

to find the slope of given line

here   (x₁, y₁)   = (-1, -1 ) and (x₂, y₂) = (1, 5)

slope m = (y₂ - y₁)/(x₂ - x₁)

  = (5 - -1)/(1 - -1)

  = (5 + 1)/(1 + 1)

  = 6/2 = 3

therefore the correct answer is option c.   3