A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Four hundred and eighty feet of fencing is used.
Find the dimensions of the playground that maximize the total enclosed area. What is the maximum area?
The smaller dimension is ? feet

Answers

Answer 1

Answer: h = 120 ft;    w = 80 ft

A = 9600 ft^2

Step-by-step explanation: Let h and w be the dimensions of the playground. The area is given by:

A = h*w   (eq1)

The total amount of fence used is:

L = 2*h + 2*w + w    (eq2)    (an extra distance w beacuse of the division)

Solving for w:

w = L - 2/3*h = 480 - 2/3*h   (eq3)  Replacing this into the area eq:

We derive this and equal zero to find its maximum:

  Solving for h:

h = 120 ft.  Replacing this into eq3:

w = 80ft

Therefore the maximum area is:

A = 9600 ft^2


Related Questions

1. Identify each part of the exponent: (-4)3
Base =
Exponent =

Answers

-45 x -43 = ~34
ThTs my answer I hope it’s correct

A park shaped like a rectangle. The diagram shows the how the park is split into a sports field and a playground. Let x represent the length in meters of the sports field. Write an expression to represent the area of the park as the sum of the areas of the sports field and the playground.

Answers

Answer:

20r + 310

Step-by-step explanation

For the first part.

The required expression is 20x + 310 which represents the area of the park as the sum of the areas of the sports field and the playground.

What is the expression?

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Let x represent the length in meters of the sports field.

Here, the area of the sports field = 20 × x = 20x units

And, the area of the playground = 15.5 × 20 = 310 units

Now, the required expression to represent the area of the park will be :

⇒ area of the sports field + area of the playground

⇒ 20x + 310

Thus, the required expression is 20x + 310.

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29-3x=5x+5


Can you work it out

Answers

Answer:

x=3

Step-by-step explanation:

29 - 3x = 5x + 5

Subtract 5 from both sides:

24 - 3x = 5x

Add 3x to both sides:

24 = 8x

Divide both sides by 8:

X = 3

combine like terms 2x - 3 - 2y - 4x + 2y + 5​

Answers

Answer:

-2x + 2

Step-by-step explanation:

2x - 3 - 2y - 4x + 2y + 5

2x - 4x + 2y - 2y + 5 - 3

-2x + 2

Jan tossed a coin 50 times and got a head 20 times. What is the
experimental probability? What is the theoretical probability?

Answers

Answer:

The standard answer for this is 50%.  

Step-by-step explanation:

  However, this is based on the implicit assumption that the coin is fair.

 

If there are reasonable grounds to doubt that the coin is fair, the theoretical probability must be based on observed statistics.   In this scenario, the probability is 60%.  

Below are two parallel lines with a third line intersecting them.

Answers

Answer:

x = 132

Step-by-step explanation:

180 - 48 = 132

On a coordinate plane, the x-axis is labeled Number of Days and the y-axis is labeled Number of Computers. A line goes through points (3, 36), (4, 48), (5, 60). The graph shows a proportional relationship between the number of computers produced at a factory per day. In three days, 36 computers are produced; 48 computers are produced in 4 days; and 60 computers are produced in 5 days. Find the unit rate of computers per day using the graph. Unit rate: computers per day

Answers

Answer:

12 is the answer ppl  hope  it helps you all

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

i got it right on edg

7(3x -4) = 49



can you help me

Answers

Answer:

3 2/3

Step-by-step explanation:

7(3x-4)=49

21x-28=49

21x=77

x=3 2/3

4x - 4 - 8y + 8 - 5x + 1 =

Answers

Answer:

-x - 8y + 5

Step-by-step explanation:

Add the numbers

4x - 4 - 8y + 8 - 5x + 1 =

4x + 5 - 8y - 5y

Combine like terms

4x + 5 - 8y - 5y

-x + 5 - 8y

Rearrange terms

-x + 5 - 8y

-x - 8y + 5

The solution of expression is,

⇒ - x - 8y + 5

We have to given that,

An expression is,

⇒ 4x - 4 - 8y + 8 - 5x + 1

Now, We can simplify by combining like terms as,

⇒ 4x - 4 - 8y + 8 - 5x + 1

⇒ 4x - 5x - 8y - 4 + 8 + 1

⇒ - x - 8y + 5

Therefore, The solution of expression is,

⇒ - x - 8y + 5

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what is one thousandth less than 0.061

Answers

Answer:

one thousandth is greater than 0.061

Step-by-step explanation:

arange the number line in the following spending order 20,-40,5-1,10​

Answers

-40 4 10 20 I think this is the answer I’m not sure

Veronica take 1/3 of an hour to write 1/4 of a page of calligrahpy how long will it take Veronica to write one page

Answers

Answer:

b because it takes 1 hour to complete 3/4 of a page so 3/3 = 1 hour 1 1/3 =1 and a third of an hour

Step-by-step explanation:


A bag contains 5 RED beads, 3 BLUE beads, and 4 GREEN beads. If a single bead is picked at random, what is the probability

Answers

Answer:

total number of beads :-

5+3+4=12

probability is :-

number of times a specific outcome has occurred

total number of possible outcomes

red beads - 5/12

blue beads - 3/12

green beads - 4/12

the above given fractions are the probabilities of each color bead.

Step-by-step explanation:

hope this helps, if yes please can u give me a brainly?

i would really apreciate it...

have a great day ahead :)

If m∠ACD = 136° and m∠B = 42°, Find m∠A.

Answers

Answer:

Step-by-step explanation:

Hello

I see you are very confused by this problem. However, there is an easy way to solve this one.

It has been proved that the sum of all angles in a rectangle is always 180°. Here is a way to prove it:

x y

_______A_________

/\

/ \

/ \

/ \

___/_______ \__

B C

we have two parellel lines xy and BC. It is true that:

xAy = 180°

xAB + BAC + CAy = xAy = 180

xAB = ABC

CAy= ACB

=> ........

I'll let you finish with your great intellect ^_^

HOPE YOU LEARN WITH JOY AND GOOD GRADE

What is the value of square root 30 is between witch two integers
A-4and5
B-5and6
C-6and7
D-7and8

Answers

Answer:

b

Step-by-step explanation:

because

Steph bought a used bicycle restored it and then marked it up by 1/4 of the price she paid later she sold it for the marked-up price of $80 how much in dollar did steph pay for the bicycle ?

Answers

Answer: would be $64

Answer:

Steph payed $64 for the bicycle

Step-by-step explanation:

80/5=16

16×4=64

hopefully this helps :)

Some algae contains up to 50% oil by weight. How much oil is in a 7.3-ounce sample of this type of algae?

This would help if you could solve anyone.

Answers

Answer: 3.65

Step-by-step explanation:

This question is asking basically what is 50% or 1/2 of 7.3.

Let's expand the number 7.3

Then, we end up getting 7.30.

We have to find 1/2 of 7.30.

[tex]\frac{1}{2}[/tex] of 7.30 = [tex]3.65[/tex]

Hope this helps you!

Tara is graphing the equation 4x + 2y = 10. Which of these shows the correct equation in slope-intercept form, slope, and y-intercept? Question 2 options: y = –2x + 5 slope = –2 y-intercept = 5 y = 4x + 5 slope = 4 y-intercept = 5 y = 2x + 4 slope = 2 y-intercept = 4 y = –4x + 5 slope = –4 y-intercept = 5

Answers

the answer should be : y=-2x+5

I need help please Will mark brainliest. Thank you so much.

Answers

The answer is, 168.....(extra characters)

AB×6=BBB (playing with numbers.)

Answers

Answer:

A = 7

B = 4

Step-by-step explanation:

If u wanna know how i got this answer plz look at the comments below since it will delete my answer U-U

9 ⋅ (-.5) what is the answer

Answers

Answer:

-45

Step-by-step explanation:

9x5=45, and since there is a negative, you put it before 45.

Hope I helped!

Please mark Brainliest!!!


At a local baseball game, the concession stand has two different meal choices. You can get 7 hotdogs and 5
drinks for $41.00 or you can get 4 hotdogs and 8 drinks for $44.00. If the price of hotdogs and drinks is the
same for each meal, find how much it costs for an individual hotdog and how much it costs for an individual
drink.
per hotdog:

per drink:

Answers

Answer:

Each hotdog is $3 and each drink is $4.

Step-by-step explanation:

Let h be the number of hotdogs and d the number of drinks,

7h + 5d = 41

4h + 8d = 44

Let's eliminate h.  Multiply the first by 4 and the second by 7.

28h + 20d = 164

28h + 56d = 308

Subtrat the first from the second.

36d = 144

d = 4

Substitute back into one of the equations.

7h + 5(4) = 41

7h + 20 = 41

7h = 21

h = 3

Stu
The point on the parabola y = 3 - x2 that is closest to the point (3,3) is
(Type an ordered pair. Round to two decimal places as needed.)​

Answers

Step-by-step explanation:

i!ieirurieiewjsisks

Anyone help with this

Answers

Answer:

Anyone help with this

x = 3t / b

Please answer the screenshot I attached below

Answers

Answer:

i think the answer is

[tex] \frac{1}{ {x}^{ \frac{4}{3} }} [/tex]

Help me with this please it says how can you isolate the term f/3 in f/3 + 22 = 17

Answers

Answer:

Given:

[tex]\sf {\dfrac {f}{3}}+22=17 [/tex]

To find:-

[tex]\sf {\dfrac {f}{3}}[/tex]

Solution:-First write the equation

[tex]{:}\dashrightarrow[/tex][tex]\sf {\dfrac {f}{3}}+22=17 [/tex]

Now take 22 to the other side by which the "+"sign will turn "-".

[tex]{:}\dashrightarrow[/tex][tex]\sf {\dfrac {f}{3}}=17-22 [/tex]

Simplify

[tex]{:}\dashrightarrow[/tex][tex]\sf {\dfrac {f}{3}}=-5 [/tex]

[tex]\therefore[/tex][tex]{\underline{\boxed{\bf {\dfrac {f}{3}}=(-5)}}}[/tex]

Answer: Subtract 22 from both sides.

Step-by-step explanation:

f/3 +22 = 17

f/3 +22 -22 = 17 -22  Subtracting the same value from both sides keeps the equation equal.  

Then simplify. The +22 and -22= 0 They "cancel"   17-22 = -5

f/3 = -17  f/3 is now isolated-- by itself-- in the equation.

If you had to solve for f, the next step would be to multiply both sides by  3.

Monthly, Juan's net earnings are $6,000, and expenses are $5,000. If Juan saves the difference, how much will Juan have saved after 6 years

Answers

Answer:

$72,000

Step-by-step explanation:

6000-5000=1000

1000x6 =6000

6000x12=72,000

A theater has 384 seats. Each row has 16 seats. The area model represents this situation.What is the value of x in the area model? Enter your answer in the box.​

Answers

Answer:

X = 4 because 20 times 16 is 320 than if you add 4 to the 20 you will get 24. 24 times 16 is 384. BOom thats your answer and i know because i just answered it.

Step-by-step explanation:

425 divided by 14 please i need to know fast

Answers

Answer:

30.3571429

Step-by-step explanation:

30.3
Explanation: calculator

can i get help here ?

Answers

It will be 10z-30
Because you are collecting like terms with -5z and +5z and it will give you 10z and 30 will be by it’s self because it has nothing to add or subtract with .
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