David wants to build a rectangular fencing with the 5 identical parts for his animals. he has 780 feet of fencing to make it. what dimensions of each part will maximize the total enclosed area?

Step-by-step explanation:

So we're looking at a rectangle split into 5 smaller rectangles.  If the height of each rectangle is y and the width of each rectangle is x, then the amount of fencing is:

P = 6y + 10x

And the area of the large rectangle is:

A = 5xy

We know that P = 780:

780 = 6y + 10x

10x = 780 - 6y

5x = 390 - 3y

If we substitute this into our area equation:

A = (390 - 3y) y

A = -3y² + 390y

This is a vertical parabola pointing down, so we know the maximum is at the vertex, which is at -b/(2a).  Or, we can use calculus to take the derivative and set to 0.

dA/dy = -6y + 390

0 = -6y + 390

y = 65

Solving for x:

5x = 390 - 3y

5x = 390 - 3(65)

5x = 195

x = 39

So each part will have a width of 39 feet and a height of 65 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