The length of a rectangle is 2 cm less than 6 times the width. find the possibilities for the width of the rectangle such that the area is not more than 840 cm2

To solve this problem, let us first assign the variables. Let us say that:

l = length of rectangle

w= width of rectangle

The given problem gives us the relation that:

l = 6 w – 2                            ---> 1

We know that the formula for area of rectangle is given as:

A = l w                                   ---> 2

Substituting equation 1 into 2:

A = (6 w – 2) w

A = 6 w^2 – 2 w

The area must not be greater 840 cm^2, therefore:

840 cm^2 = 6 w^2 – 2 w

w^2 – (1/3) w = 140

By completing the square:

w^2 – (1/3) w + (1/36) = 140 + (1/36)

(w – 1/6)^2 = 5041/36

w – 1/6 = ± 11.83

w = -11.66, 12

Therefore the maximum value that the width can take is 12 cm. Therefore the possibilities of width such that the area does not exceed 840 cm^2 is from 1 to 12 cm.

1 cm to 12 cm

a

step-by-step explanation:

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