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
My name is Ann [436]
2 years ago
9

A pigpen is to be enclosed using 640 m of fencing along three of its sides, the fourth side being a barn. Determine the dimensio

ns of the pen that will maximize the area (100 PTS + BRAINLIEST)
Mathematics
1 answer:
Basile [38]2 years ago
3 0

Answer:

W_{max}=480m\\ L_{max}=160m

Step-by-step explanation:

Since we know we only have 640 feet of fence available, we know that L + W + L = 640, \implies 2L + W = 640. This allows us to represent the width, W, in terms of L: W = 640 – 2L

Remember, the area of a rectangle is equal to the product of its width and length, therefore,

A_{\rm pigpen}=L(640-2L)\implies 640L-2L^2

Notice that, quadratic has been vertically reflected, since the coefficient on the squared term is negative, so the graph will open downwards, and the vertex will be a maximum value for the area.

recall,

  • x_{max}=-b/2a
  • f(x)_{max}=f(x_{max})

Since our function is A(L)=640L-2L², we get

  • a=-2
  • b=640

plug in the value of a and b into the first formula:

L_{max}=-(640)/2(-2)\implies 160

A(L)_{max}=640(160)-2(160)^2\implies 76800

hence,the dimensions of the pen that will maximize the area are<u> </u><u>L=</u><u>1</u><u>6</u><u>0</u><u>m</u><u> </u>and<u> </u><u>W=</u><u>7</u><u>6</u><u>8</u><u>0</u><u>0</u><u>/</u><u>1</u><u>6</u><u>0</u><u>=</u><u>4</u><u>8</u><u>0</u><u>m</u>

and we're done!

You might be interested in
Using the trend line y = 8x + 8, for the data shown, complete the residual table.
Anit [1.1K]

Answer:

-1,0,2,-2,0 in that order

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Nine times a number divided by 2 equals 54.
bazaltina [42]

x = the unknown number

\frac{9x}{2} =54

nine <u>times</u>(multiplication) a number(x) divided(division) by 2 equals(=) 54,

so 9x is divided by 2

4 0
3 years ago
Evaluate.
zalisa [80]

Answer:

52

Step-by-step explanation:

14+13= 27+2=29+23=52

7 0
3 years ago
Read 2 more answers
I need help on this. &amp; I'll give brainlyest to anyone who can solve it for me. Thank's!!!!
Olegator [25]

Answer:

I can helpyou with that but im not sure with it

6 0
2 years ago
Show your work on the number line 3-1 3/4?​
Nina [5.8K]
Please provide more information for a anwser
3 0
3 years ago
Other questions:
  • A car traveling at a steady speed. It travels 1 1/2 miles in 2 1/4 minutes. How far will it travel in 44 minutes? In 1 hour?
    11·2 answers
  • Find the perimeter of the rectangle with the following vertices. (−6, −2), (0, −10), (5, 2), (−1, 10) 23 52 46 40
    8·1 answer
  • Solve for h: 10h + 2 = 32​
    9·2 answers
  • What is the value of k?
    15·1 answer
  • (Will give brainliest to correct answer)
    7·1 answer
  • Explain your answer, please.
    11·2 answers
  • What best describes the number 5? write prime, composite, neither prime nor composite, or both.
    15·2 answers
  • Simplify 2/4 please and thank you
    5·1 answer
  • How do you solve for 4-9i/-6i
    10·1 answer
  • The line AB is shown on the grid.
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!