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
Find a degree 3 polynomial having zeros -5, 1 and 5 and the coefficient of x^3 equal 1
mote1985 [20]

Answer:

x^3 -x^2 -25x +25

Step-by-step explanation:

\text{The roots are,}~ \alpha  = -5,~ \beta = 1 ~ \text{and}~ \gamma = 5\\\\\text{The polynomial is,}\\\\~~~x^3 - (\alpha + \beta + \gamma)x^2+(\alpha \beta + \beta \gamma+ \gamma \alpha)x - \alpha\beta \gamma\\\\=x^3 - (-5+1+5)x^2 +(-5 \cdot 1 + 1 \cdot 5 + 5 \cdot -5)x - (-5)(1)(5)\\\\=x^3 -(0+1)x^2 + (-5+5-25)x +25\\\\=x^3 -x^2 -25x +25

7 0
2 years ago
#3) Eddie's salary is $1,100 per month. Find his annual salary.
Nana76 [90]

Answer:

Hourly: $6.60

Annually: $13,200.00

7 0
3 years ago
Read 2 more answers
I know the answer is A....but why?
katrin2010 [14]

Answer:a

Step-by-step explanation:

throughout the table it is presented that the answer, A, is correct becuase within the percentages is is obvious that a is correct.

6 0
4 years ago
Read 2 more answers
How do you solve this problem? With work!!
Evgesh-ka [11]
You would put 9 times v because you are multiplying it to the 9 and you do not know what v is then you would divide it by 3 and get your answer so for example if you should have gotten 9 times v = 72 then 72 divided by 3 = 24 and 24 divided by 3 = 8

7 0
3 years ago
Read 2 more answers
What is the sum of the first five terms of a geometric series with a1=15 and r=1/3
Solnce55 [7]

Answer:

15, 5, 5/3, 5/9, 5/27

Step-by-step explanation:

Recall, that the general form of a geometric series is

a, ar, ar², ar³, .........

where a is the first term and r is the ratio

It is given that the first time is 15, hence a = 15

also given that ratio is 1/3

hence the first 5 terms are:

15, (15)(1/3), (15)(1/3)^2, (15)(1/3)^3, (15)(1/3)^4

simplifying each term gives

15, 5, 5/3, 5/9, 5/27

6 0
3 years ago
Read 2 more answers
Other questions:
  • How are graphs used to represent patterns??
    9·2 answers
  • What number should be placed in the box to help complete the division calculation?
    12·1 answer
  • A jacket is on sale for 70% of the original price. If the discount saves $45, what was the original price of the jacket? What is
    14·2 answers
  • What kind of angles are ADB and BDC
    11·1 answer
  • Keith is a salesperson.he sold a beach umbrella for 98$ and earned 10% commissions. How much commission did Keith get
    8·2 answers
  • Fill in the missing exponents in each box &amp; show reasoning (5^?)^3=5^1
    13·2 answers
  • PLEASE HELP EXTRA POINTS / WRONG ANSWERS WILL BE REPORTED
    14·1 answer
  • 25. What is the equation of a line that has a slope of 3 and passes through the point (1, 2)?
    15·1 answer
  • Amy types at an average speed of 38 words per minute. She has already typed 1,450 words of her final paper, which will be more t
    10·1 answer
  • Give the domain and range of each relation
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!