![nellymbh4227](/avatars/40535.jpg)
nellymbh4227
15.12.2020 •
Mathematics
A farmer plans to fence a rectangular garden next to a river. There will be no fence along the river side. Draw a picture of this situation. The pasture will contain 405,000 square meters. Find the dimensions of the garden that will require the least amount of fencing.
Solved
Show answers
More tips
- S Style and Beauty Is Hot Scissor Haircutting Beneficial or Dangerous?...
- S Style and Beauty How to Get Rid of Under Eye Bruises?...
- F Food and Cooking Is Bacon Good for You?...
- S Style and Beauty Discover the Art of Nail Design: How Do You Paint Your Nails?...
- P Philosophy How to Develop Extrasensory Abilities?...
- O Other Everything You Need to Know About Kudyabliks...
- C Computers and Internet The Twitter Phenomenon: What it is and How to Use it...
- C Computers and Internet How to Choose a Laptop: Expert Guide and Tips...
- C Computers and Internet How to Choose a Monitor?...
- H Horoscopes, Magic, Divination Where Did Tarot Cards Come From?...
Answers on questions: Mathematics
- M Mathematics Solve the rational equation. 5 3x +2 2 X-+10 type your answer......
- M Mathematics I need help ! Solve for x...
- M Mathematics Naomi paints 16.5 square feet of mural at this at a rate of two square feet per hour Clara paints 7.5 square feet of the mural at a rain rate of four square feet...
- M Mathematics An army of ants was migrating. The ants moved 120 grams less than half of their food on their first trip. On their second trip, they managed to move 100 g more...
- M Mathematics You are filling bags with cookies to give to your friends. The list shows the cookies you are putting into the bags. You want identical groups of cookies in each...
- M Mathematics Use the diagram to explain why PQR is isosceles...
- M Mathematics (2,4) slope = 2 djekwkwksk...
- M Mathematics IM BORED YALL SHOULD JOIN MY Z O O M id 445-926-8868 Password ZN4sJz...
- M Mathematics (-a)^3 in expanded form?...
- M Mathematics + = − − = −� how many solutions...
Ответ:
x = 450 m
y = 900 m
P (min) = 1800 m
Step-by-step explanation:
Let´s call "x" and "y" de sides of the rectangular garden, y is the side parallel to the river ( that is it will be fenced only one )
Then:
2*x + y = P ( perimeter of the area)
And x * y = 405000 m²
y = 405000/ x
And P as a function of x is:
P(x) = 2*x + 405000/x
Tacking derivatives relative to x on both sides of the equation.
P´(x) = 2 - 405000/x²
P´(x) = 0 2*x² - 405000 = 0
x² = 202500
x = 450 m
And y = 405000 / 450
y = 900 m
And
P(min) = 2*450 + 900
P(min) = 1800 m
We know P is minimm at x =450 snce the second derivative of P
P´´(x) = 405000*2*x / x⁴ is always positive
Ответ: