Due to an influx of wild animals, you need to enclose your garden. you have 500 feet of fencing and will enclose the garden on three sides, with your barn providing protection for the fourth size. determine the length of the fence opposite the barn which maximizes the area enclosed.

so  length of the fence  is 250 feet

Explanation:

Given data

fencing (L) = 500 feet

enclose the garden = 3 sides

to find out

length of the fence

solution

we consider barn length x and width y

so we say  x +2y = 500   1

we want to maximize length i.e xy = f

so we say

df/dx = ƛ × dL/dx

y =  ƛ × 1

and

df/dy = ƛ × df/dy

x = ƛ × 2

from equation 1 we can say

2 ƛ + 2 ƛ = 500

so  ƛ = 500/4 = 125

so that x = 2× 125 ,  y = 125

so x = 250 , y = 125

so  length of the fence  is 250 feet

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day

that tool is called an altimeter which measures your altitude which can be used to tell which atmosphere you are currently in, including the stratosphere.

hope this ! : )