1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
bekas [8.4K]
3 years ago
11

A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No fencing is needed along the bar

n, and the fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. If the fencing costs $14 per linear foot to install and the farmer is not willing to spend more than $7000, find the dimensions for the plot that would enclose the most area. (Enter the dimensions as a comma separated list.)
Mathematics
1 answer:
Dmitriy789 [7]3 years ago
4 0

Answer:

Width  = 166.7 ft

Length = 250 ft.

Step-by-step explanation:

From the diagram at the ATTACHMENT

Let us denote the the length of the rectangular area as "x" and

the width of the rectangular area as "y"

Since, cost of the fence on the western side is shared with a neighbor, we can say  it is $7 per foot. Otherwise, it is $14 per foot. The northern length is not fenced.

From the question, we know that the  cost is not to exceed $7000, therefore we can expressed it as

7y + 14x + 14y = 7000

14x + 21y = 7000

Divide through by 14, we have

(x + 1.5) = 500  ------------- eqn (*)            

But the area of the fenced

= A = (x×y)      -------------- eqn  (**)                    

Substitute (*) into (**) we have

A = (500 - 1.5y)*y

= 500y - 1.5y²

In other to maximize the Area, we can find the differential of A

A'(y) = 500 - 3y

At A'(y) = 0.

500-3y= 0

3y=500

y= 166.67 ft

From eqn(*)

(x+ 1.5) = 500

x = 500 - 1.5y

500-1.5(166.67)

= 250ft

Therefore, the dimensions for the plot that would enclose the most area are

Width  of 166.67 ft and Length = 250 ft.

You might be interested in
Write down the formula to calculate the area of an isosceles triangle whose equal sides are 'a' unit and base is 'b'unit.​
Elena-2011 [213]

Step-by-step explanation:

I hope this will help you..........

7 0
2 years ago
Which number is NOT in the solution set of the inequality x > 10?
Serjik [45]

Answer:

5

Step-by-step explanation:

5 0
2 years ago
ASAP
Semenov [28]

Answer:

6 is the answer's answer answer

8 0
3 years ago
Convert to a percent 4.44 3/5
worty [1.4K]

Answer:

\large\boxed{4.44=444\%,\ \dfrac{3}{5}=60\%}

Step-by-step explanation:

p\%=\dfrac{p}{100}\to p=p\cdot100\%\\\\\text{multiply a number by}\ 100\%\\\\4.44=4.44\cdot100\%=444\%\\\\\dfrac{3}{5}=\dfrac{3}{5}\cdot100\%=\dfrac{300}{5}\%=60\%

5 0
3 years ago
Simplify the expression (k^2)^4
Andrews [41]
It would be K^{8}
7 0
2 years ago
Read 2 more answers
Other questions:
  • Find the value of two numbers if their sum is 23 and their difference is 3.
    9·1 answer
  • Order of operations:<br><br> 2 • {390 – [5 • (10 – 4 ÷ 2)] + 15} • 2
    7·2 answers
  • A toy company has determined that the revenue generated by a particular toy is modeled by the following equation: 13x - 0.025x²
    8·2 answers
  • Can someone tell me how to do this problem? (Steps)
    5·1 answer
  • Do you have a recipe that requires 1/3 cup of sugar, but you only want to make a fourth of the recipe how much sugar do you need
    12·1 answer
  • Ali saved Rs. 36. .
    13·2 answers
  • HURRY PLEASE! i need this asap
    12·1 answer
  • Tomas is a commercial real estate agent who earns a yearly salary of $82,500 and a 2.
    6·1 answer
  • Cora and Hannah measured how high their pet frogs could jump. Cora's jumped x inches,
    12·1 answer
  • Meryl needs to add enough water to 11 gallons of an 18% detergent solution to make a 12% detergent solution. Which
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!