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
Every year, for the annual school bake sale,
Leno4ka [110]

Answer: Annie will have to make 228 cookies

explanation:

let y represent the total number cookies   that Annie will make.

<h3>y= 342*(2/3)</h3><h3>y=228</h3><h3 /><h3 />

5 0
3 years ago
Math 7 Grade 7
OleMash [197]
The conclusion is valid
it is a systematic random sample
and the second one is a line graph (I think)
8 0
3 years ago
Read 2 more answers
Question 8 (2 points)<br> 15 is 25% of<br> Brank 1:<br> HELPPP MEEE
Ilya [14]

Answer:

15 is 25% of 60

Step-by-step explanation:

15 x 4 = 60

25% x 4 = 100%

3 0
2 years ago
Read 2 more answers
How many leaves on a tree diagram are needed to represent all possible combinations tossing a coin and rolling a dice
dolphi86 [110]
The total number of outcomes of rolling a die      = 6
The total number of outcomes of  tossing a coin = 2

The total number of possible outcomes of executing both experiments is 6*2=12, which is also the number of leaves (end of the branch of a tree) on a tree diagram.
4 0
3 years ago
Read 2 more answers
The ratio of the profit, material cost and production labour of an article is 5:7:13.
IRINA_888 [86]

Answer:

The cost of producing the article is -3500 (Negative cost)

Step-by-step explanation:

The given parameters are

The ratio of the profit to material cost to production labor = 5:7:13

The amount of the material cost = 840 + Labor cost

Let the total cost = X

Therefore, we have;

The fraction of the total cost that is material cost = 7/(5 + 7 + 13) = 7/25

Therefore, the material cost = 7/25 × X

The fraction of the total cost that is labor cost = 13/(5 + 7 + 13) = 13/25

Therefore, the labor cost = 13/25 × X

However, the amount of the material cost = 840 + Labor cost, which gives;

7/25 × X = 13/25 × X + 840

7/25 × X - 13/25 × X = 840

-6/25 × X= 840

X = 840/(-6/25) = 840×(-25/6) = -3500

The cost of producing the article = -3500.

8 0
3 years ago
Other questions:
  • The probability of the intersection of two events is known as a ________ probability.
    15·1 answer
  • Dayson is covering a package in the shape of a rectangular prism with wrapping paper. The package is 50 centimeters by 20 centim
    9·1 answer
  • ABCO is the image of ABCD What transformation(s) would result in this image?
    11·1 answer
  • Plzzz answer question number 2 I will give you 100 points
    14·2 answers
  • Which of these best describes the Pythagorean theorem?
    15·1 answer
  • It takes 3 3/4 spoons of chocolate syrup to make 2 1/2 gallons of chocolate milk. How many spoons of syrup would it take to make
    10·1 answer
  • I need help with these questions
    11·1 answer
  • Help please if you know the answer
    6·1 answer
  • Which of these does NOT describe an equivalent ratio or rate? A) 10:35 and 8:28 B) 4:10 and 10:25 C) 40km/h and 0.06 km/min D) 1
    14·1 answer
  • The length and width of a rectangle are consecutive integers. The perimeter of the
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!