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
Natalija [7]
2 years ago
11

Find the dimensions of the rectangular corral producing the greatest enclosed area given 320 feet of fencing. (Assume that the l

ength is greater than or equal to the width.)
Mathematics
1 answer:
jenyasd209 [6]2 years ago
4 0

Answer:

The dimensions of the rectangular corral producing the greatest enclosed area  is a square of 80 ft x 80 ft

Step-by-step explanation:

Let

x -----> the length of the rectangular corral in feet

y -----> the width of the rectangular corral in feet

we know that

The area of the rectangular corral is equal to

A=xy -----> equation A

The perimeter of the rectangular corral is equal to

P=2(x+y)

P=320\ ft

so

320=2(x+y)

Simplify

160=(x+y)

y=160-x -----> equation B

substitute equation B in equation A

A=x(160-x)

A=-x^2+160x

This is a vertical parabola open downward

The vertex is a maximum

The x-coordinate of the vertex represent the length for the maximum area

The y-coordinate of the vertex represent the maximum area

Convert the quadratic equation in vertex form

A=-x^2+160x

Factor -1

A=-(x^2-160x)

Complete the square

A=-(x^2-160x+80^2)+80^2

A=-(x^2-160x+80^2)+6,400

Rewrite as perfect squares

A=-(x-80)^2+6,400

The vertex is the point (80,6,400)

so

x=80\ ft

The maximum area is 6,400 ft^2

<em>Find the value of y</em>

y=160-x  ----> y=160-80=80\ ft

therefore

The dimensions of the rectangular corral producing the greatest enclosed area  is a square of 80 ft x 80 ft

You might be interested in
What is the Slope of a line that passes through the points (-3,5) and (1,7) ?
Naya [18.7K]
Find the change in the y coordinates

7-5=2

Find the change in the x coordinates 

1--3 or 1+3= 4

Divide the changes in the y and x coordinates

2/4= 1/2

The slope is 1/2. Hope this helps!
6 0
3 years ago
Read 2 more answers
A public school in your city has 1710 girls among the 2970 students. What is the ratio of boys to girls in school
Minchanka [31]

Answer:

The simplest answer would just be 14:19

However the unsimplified answer is 1260:1710

3 0
3 years ago
a school musical soild 353 tickets. $5 for adults and $3.50 for students. the school made $1500 how many adult tickets were sold
IrinaVladis [17]

Answer:

177 Students

176 Adults

Step-by-step explanation:

Adult - (A) $5

Student - (S) $3.50

Equation 1: A+S = 353 tickets

Equation 2: 5A + 3.50S = $1500

Sub equation 1 into 2:

5A + 3.50(353 - A) = 1500

Multiply: 5A + 1235.50 -3.50A =1500

Subtract 1235.50 and -3.50A from both sides: 1.50A = 264.50 and then divide:

264.50/1.50 = 176 Adults

Sub into equation 1:

176 +S = 353

Solve: 353 - 176 = 177 Students

Check: 5(176) + 3.50(177) = $1500

1499.5 rounded = 1500 = 1500 ✔

I hope this helped!

3 0
3 years ago
3x = 6<br><br> Help me p l e a s e
GuDViN [60]

Answer:

x=2

Step-by-step explanation:

have a nice day

3 0
3 years ago
Abigail shows up at a restaurant that has 30 tables 12 of them are booth and 18 of them are tables with chairs what is the proba
elixir [45]
30 divided by 12 will give you the percentage 40% , or c
8 0
3 years ago
Read 2 more answers
Other questions:
  • 60 boys at a summer camp were asked to complete a survey about their favorite outdoor activity. 18 boys chose biking and 29 boys
    11·1 answer
  • Write the Explicit Rule for the arithmetic sequence:<br>Qp = Q1 +(n-1)d<br>8, 5, 2, -1, ...​
    9·1 answer
  • If 8x=-4(x+3) then x equals
    15·1 answer
  • How do I solve this?
    15·2 answers
  • This table shows a proportional relationship between the number of cups of sugar and flour used for a recipe.
    13·1 answer
  • 40 free throws and was successful on 25% of them.How many successful free throws did she make?
    14·1 answer
  • Graphing Exponential Function in Exercise ,sketch the graph of the function.See example 3 and 4.
    12·1 answer
  • Using the equation 4x^3-6x^2-144x+8, find the function values f(-3) and f(-4) at the interval {-4,5}
    7·1 answer
  • In a group of 20 there are 7 boys what is the ratio of girls to boys?​
    11·1 answer
  • The question is attached
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!