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
pashok25 [27]
3 years ago
15

A farmer has 520 feet of fencing to construct a rectangular pen up against the straight side of a barn, using the barn for one s

ide of the pen. The length of the barn is 310 feet. Determine the dimensions of the rectangle of maximum area that can be enclosed under these conditions. (Hint: Be mindful of the domain of the function you are maximizing.)
Mathematics
1 answer:
Setler [38]3 years ago
5 0

Answer:

310\text{ feet and }210\text{ feet}

Step-by-step explanation:

GIVEN: A farmer has 520 \text{ feet} of fencing to construct a rectangular pen up against the straight side of a barn, using the barn for one side of the pen. The length of the barn is 310 \text{ feet}.

TO FIND: Determine the dimensions of the rectangle of maximum area that can be enclosed under these conditions.

SOLUTION:

Let the length of rectangle be x and y

perimeter of rectangular pen =2(x+y)=520\text{ feet}

                                                x+y=260

                                               y=260-x

area of rectangular pen =\text{length}\times\text{width}

                                       =xy

putting value of y

=x(260-x)

=260x-x^2

to maximize \frac{d \text{(area)}}{dx}=0

260-2x=0

x=130\text{ feet}

y=390\text{ feet}

but the dimensions must be lesser or equal to than that of barn.

therefore maximum length rectangular pen =310\text{ feet}

                              width of rectangular pen =210\text{ feet}

Maximum area of rectangular pen =310\times210=65100\text{ feet}^2

Hence maximum area of rectangular pen is 65100\text{ feet}^2 and dimensions are 310\text{ feet and }210\text{ feet}

You might be interested in
Please answer 1-8 godbless​
Alexandra [31]

Answer:

1. A

2. D

3. B

4. B

5-6. B

7. D

8. D

5 0
3 years ago
0.12 times 0.08 divided by 2.40​
blagie [28]

Answer:

Step-by-step explanation:

515615151

5 0
3 years ago
Read 2 more answers
The dot plot shows the height, in feet, of a group of trees being studied. How many trees are being studied
TEA [102]
If you are reffering to this dot plot, it would be 13 trees being studied.

4 0
3 years ago
Help me graph<br><br> y=3-|x-1|
nexus9112 [7]

Answer:

In the photo below.

6 0
3 years ago
Part C: Give an example of a situation in which a percentage is greater than 100%. (2 points)
insens350 [35]

Answer:

If your weekly allowance is 5, then for Christmas week your allowance was 15, then your allowance went up by: 5 =3 - 1 = 2 x 100 =200%.

6 0
3 years ago
Other questions:
  • 40 POINTS is (4,7) a solution of equations? Explain your answer 2x+4y=36 3x-4y=-6
    9·2 answers
  • 5% of what number is 12
    14·2 answers
  • Identify all sets to which the number 3/2 belongs
    11·1 answer
  • Who is correct Derek or Delilah
    14·2 answers
  • Find the RANGE for the data set: 8, 4, 6, 6, 8, 2, 6,5
    12·2 answers
  • A function and its inverse are shown on the same graph. Which statement describes the relationship between the function and its
    9·1 answer
  • -4(y-2)=12 help please​
    8·2 answers
  • Wat is 100÷59 and how yo make more detrails
    10·1 answer
  • I Neeedd it quickk pleasee anyonee helpp
    14·2 answers
  • Question 3 options: A school is preparing a trip for 400 students. The company who is providing the transportation has 10 buses
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!