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.

step-by-step explanation:

i found the life tables for the year 2012. 

life table of males at age 30. probability of dying between ages x and x+1

total population:  

29–30 . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . 0.001061

males:  

29–30 . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . 0.001399

non hispanic white population

29–30 . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . 0.001116

non hispanic white males

29–30 . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . 0.001503

jacob, non hispanic white male. 30 years old.

probability that jacob lives to be 30 years old. 

since the given probabilities are probabilities of dying, i think we simply subtract it from 1 to get the probability of living. we will use the probability of non hispanic white male.

                                          probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497

answer: #1 ads up by 8 and i don't know #2