Find the dimensions of a rectangle divided into three equal rectangles of maximum area that has total perimeter (including the middle divider) of 120 feet.

The dimensions of the rectangle with the maximum area are 15 feet by 30 feet

Step-by-step explanation:

Optimization

There is a rectangle of dimensions x and y as seen in the figure below.

The side of length y is divided into three equal parts to make three equal rectangles.

The area of the greater rectangle is:

A = xy

It has to be maximized given the condition that the total perimeter including the middle dividers is 120 feet.

The outer perimeter of the rectangle is 2x+2y. There are two additional lines with a length of x feet each. Thus, the total perimeter is:

P = 2x + 2y + 2x = 4x + 2y

It has to be equal to 120 feet:

4x + 2y = 120

Dividing by 2:

2x + y = 60

Solving for y:

y = 60 - 2x

Substituting into the area:

Taking the first derivative:

A'=60 - 4x

Equating to 0:

60 - 4x = 0

Solving for x:

x = 60/4 = 15

Thus x = 15 feet

Since y = 60 - 2x = 60 - 30 = 30

Thus y = 30 feet

The dimensions of the rectangle with the maximum area are 15 feet by 30 feet.

10.4 inches

step-by-step explanation:

2x2x2.6

answer: on graphs, the open and closed circles, or vertical asymptotes drawn as dashed lines us identify discontinuities.

as before, graphs and tables allow us to estimate at best.

when working with formulas, getting zero in the denominator indicates a point of discontinuity.

when working with piecewise-defined functions, check for discontinuities at the transition points where one piece ends and the next begins.

step-by-step explanation: