Apiece of cardboard is 1 meter by 1/21/2 meter. a square is to be cut from each corner and the sides folded up to make an open-top box. what are the dimensions of the box with maximum possible volume?

The maximum dimensions of the box:

Length of the box  = 0.788676 m

Breadth of the box  = 0.288676 m

Step-by-step explanation:

Original piece of cardboard is a square with sides of length s.

Length of the card board = l = 1 m

Breadth of cardboard = b = 1/2 m = 0.5 m

Squares with sides of length x are cut out of each corner of a rectangular cardboard to form a box.

Now, length of the box = L = 1 - 2x

And breadth of the box = B = 0.5 - 2x

Height of the box ,H = x

Volume of the box ,V= L × B × H

x = 0.394338  , 0.105662

When , , (maxima)

The maximum dimensions of the box:

Length of the box = L = 1 - 2x = 1 - 2(0.105662) m = 0.788676 m

Breadth of the box = B = 0.5 - 2x = 0.5 - 2(0.105662) m = 0.288676 m

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: