The back of george's property is a creek. george would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a pasture. if there is 140 feet of fencing available, what is the maximum possible area of the pasture?

The maximum possible area of the pasture = 2450 square feet

Step-by-step explanation:

Let the length of the creek be 'L'

and, the width of the rectangular area be 'B'

Data provided:

The rectangular area is enclosed using the creek as one side and fencing for the other three sides

Thus, 2B + L = 140 feet      

or

L = 140 - 2B              .........(1)

Now,

Area of the rectangular land, A = L × B

using (1)

A = ( 140 - 2B) × B

or

A = 140B - 2B²

Now to maximize the area, differentiating the area with respect to width 'B'

we have

 = 140 - 2 × 2 × B ...........(2)

for point of maxima or minima ,  = 0

thus,

140 - 2 × 2 × B = 0

or

4B = 140

or

B = 35 feet

differentiating  (2) with respect to B, for verifying the maxima or minima

 = 0 - 2 × 2 = -4

since, is negative,

therefore,

B = 35 feet is point of maxima

from (1)

L = 140 - 2B

or

L = 140 - 2 × 35

or

L = 140 - 70 = 70 feet

Hence,

The maximum possible area of the pasture = L × B

= 70 × 35

= 2450 square feet

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2

. + λrh() e 1 1 2 4 4 4 4 4 3 4 4 4 4 4 + th−1(− s(x)2 dx ω + λrh−1() e 2 1 2 4 4

step-by-step explanation: