You are giving 24 linear feet of fencing all 3 feet tall you wish to make the largest rectangular enclosure possible to maximize space what should the dimensions of the enclosure be

The largest area enclosed is  A = xy = 6 feet 6 feet = 36

Step-by-step explanation:

i) The perimeter of the area is 2(x + y) =24  ∴ x + y = 12    ∴ y = 12 - x

ii) The area of rectangle enclosed A  = xy    ⇒ A  = x ( 12 - x) = 12x -

iii) differentiating both sides of the equation in ii) we get

   ⇒  x = 6 feet

iv) Differentiating both sides of equation in iii) we get     =  -2

   Therefore the area enclosed is maximum as the double derivative is negative

v) therefore for largest area enclosed   x  = 6 feet and  y = 12 - 6 = 6 feet

vi) therefore the largest area enclosed is

 A = xy = 6 feet 6 feet = 36

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)

2, 2, 2 or -4, 20, 29

step-by-step explanation:

there is two ways you can do it.