a school has 400 feet of fencing to build a set of 3 athletic fields as shown below. What dimensions should they use to build the largest possible athletic complex. Include appropriate units with your answer.

A School Has 400 Feet Of Fencing To Build A Set Of 3 Athletic Fields As Shown Below. What Dimensions

Answers

Answer 1

The area of a shape is the amount of space it occupies.

The dimensions to build the largest possible athletic complex is 100 by 50 feet

Assume the length of the fence is y.

So, we have:

[tex]\mathbf{Area = xy}[/tex]

[tex]\mathbf{Perimeter = 2y + 4x}[/tex]

Substitute 400 for perimeter

[tex]\mathbf{2y + 4x = 400}[/tex]

Divide through by 2

[tex]\mathbf{y + 2x = 200}[/tex]

Make y the subject

[tex]\mathbf{y = 200 -2x}[/tex]

Substitute [tex]\mathbf{y = 200 -2x}[/tex] in [tex]\mathbf{Area = xy}[/tex]

[tex]\mathbf{Area =x(200 - 2x)}[/tex]

[tex]\mathbf{Area =200x - 2x^2}[/tex]

Differentiate

[tex]\mathbf{A' =200 - 4x}[/tex]

Set to 0

[tex]\mathbf{200 - 4x = 0}[/tex]

Collect like terms

[tex]\mathbf{4x = 200}[/tex]

Divide both sides by 4

[tex]\mathbf{x = 50}[/tex]

Recall that: [tex]\mathbf{y = 200 -2x}[/tex]

So, we have:

[tex]\mathbf{y = 200 - 2 \times 50}[/tex]

[tex]\mathbf{y = 200 - 100}[/tex]

[tex]\mathbf{y = 100}[/tex]

Hence, the dimensions to build the largest possible athletic complex is 100 by 50 feet

Read more about areas and perimeters at:

https://brainly.com/question/11957651


Related Questions

Which expression has a value located to the right of 1 on the number line?
A - 1-7
B. 1 - 7
C. -7 - 1
D. 7 + 1​

Answers

Answer:

The correct answer is D

Step-by-step explanation:

because a, b, and c all equal a negative which goes on the left side of 1 but d is the only one that equals a positive number which goes on the right side of

Correct me if I'm wrong

Please give thanks

Find the quotient or 4/5 and 6/7 give ur answer as a fraction in simplest form

Answers

Answer:

14/15

Step-by-step explanation:

Let me know if i got it right if not I'm sorry :(

The required quotient would be 14/ 15 which is a fraction.

What is the Quotient?

A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.

We have been given that two numbers are 4/5 and 6/7

To determine the quotient or 4/5 and 6/7

⇒ 4/5 ÷  6/7

⇒ 4/5 / 6/7

Reciprocal the term of denominator,

⇒ 4/5 × 7/6

Apply the multiplication operation,

⇒ 28 / 30

Reduce the above fraction to the simplest form

⇒ 14/ 15

Therefore, the required quotient would be 14/ 15 which is a fraction.

Learn more about the quotient here:

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the differentiation of x^4 + y^4=0 is..?​

Answers

Answer:

I am doinnnnnmngggg gggg

given cosec theta = 7/2 find sin theta​

Answers

Answer:

Sin0=7/25

Step-by-step explanation:

the difference of two number is 6 if the greater one is 17 find the smallest number​

Answers

Answer:

11

Step-by-step explanation:

17-6=11

big brain

Answer:

11

Step-by-step explanation:

17-11=6 the smallest number is 11

Helppppppppppppppppppppppppppppppppppp

Answers

Answer:

The answer would be 7 I hope this helps! : )

Answer:

it's 2

Step-by-step explanation:

if we solve 3×2×1/3

then we will get 2 .

use the given zero to find all the zeros of the function.

g(x)= 3x^3+11x^2+11x-5
zero: -2+i

Answers

Answer:

11x + 5

Step-by-step explanation:

1.(154)10=(?)2
helpme! to solve it plz.​

Answers

Answer:

I think its (10000110)2

Part A 4.59 is 3.4% of what number ?
Part B 98% of 66 is what number ?
Part c what number is 36% of 142 ?

Answers

A= (4.59 x 100)/ 3.4= 135
B= (66 x 98)/100= 64.68
C= (142 x 36)/100= 51.12

Bvtcctctctc CJ bububuv

Answers

Answer:

A) [tex]y+7=-3(x-4)[/tex]

Step-by-step explanation:

Hi there!

The given equations are written in point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where m is the slope of the line and [tex](x_1,y_1)[/tex] is a point that falls on the line

Notice how the line is travelling infinitely down as x increases. This means that the slope is negative.

Therefore, the equation of the line is either A or B.

Now, let's look at A:

[tex]y+7=-3(x-4)[/tex]

This equation suggests that the point (4,-7) falls on the line, which it does.

Therefore, the equation of the graph is [tex]y+7=-3(x-4)[/tex].

I hope this helps!

Answer: A.) y + 7 = - 3 ( x - 4 )

Step-by-step explanation:

i didnt know i was a graph lolz im just playin have a nice day kind person and sorry for answering late!!!!!!

A line passes through the points (0,5) and (3,6). What is its equation in slope-intercept
form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answers

Answer:

Slope intercept form:

y = 1/3x + 5

6
LA
3
2
1
-6
-5
-4
-3
-2
- 1
1
2
3
4
- 1
N-
-2
What is the slope of line segment AB?
A
NIN
B)
3
4
o
4
3
D
IN

Answers

Answer:)

Step-by-step explanation:

When do we use 180 or 360 to solve interior or exterior angles

Answers

Answer:

when it is alternate

Step-by-step explanation:

Answer:

here

Step-by-step explanation:

when it iş alternate

solve pls brainliest

Answers

1- 192
2-36

1- 168(original altitude)
+360(because the question says the hill is ______ 360 feet higher than checkpoint 2)
192


2- 168(checkpoint 2)
-132( checkpoint 4)
______
036

Write a compound inequality for the graph shown below
Use x for your variable

Answers

I can’t type symbols so I’ll just write it out.

-1 is less that or equal to x is greater than 1

I have more question then this one

Answers

Answer:

option b

Step-by-step explanation:

have a great day

Someone please help me with this.

Answers

Answer:

Step-by-step explanation:

I know this is rather sneaky, but on a multiple choice question on a quiz, you need all the help you can get.  I'm not saying this is a quiz, by the way. It doesn't say that it is anywhere.

Look carefully at the first three statements. Is there an angle mentioned at all? There isn't, is there? That being the case (and since nothing is marked as a right angle), the only possible answer is SSS which D.

Answer:

D

Step-by-step explanation:

There are not any angles shown, and the triangle is not a right triangle, so it is SSS

PLS HELP ME I NEED IT

Answers

Step-by-step explanation:

the area = [tex](\frac{1}{2}) (18)(4)\\[/tex] = [tex]36ft^{2}[/tex]

please give me a brainliest answer

Isis is 8 years younger than
her sister. The sum of
their ages is 44 years
How old is Isis and
how old is
her sister,

Answers

Answer:

Isis 18 and her sister 26

Step-by-step explanation:

Isis is 8 years younger than

her sister. The sum of

their ages is 44 years

How old is Isis and

how old is

her sister,

(44 - 8) : 2 = 18

18 + 8 = 26

------------------------

check

23 + 18 = 44

the answer is good

Please show steps please

Answers

Answer:

x - 2, remainder -4

or

x - 2 + (-4)/(x + 6)

Step-by-step explanation:

                           x - 2

                      --------------------------------

           x + 6   |  x^2 + 4x - 16

                 -       x^2 + 6x

                -----------------------

                                -2x - 16

                         -      -2x - 12

                        ------------------

                                          -4

Answer:

x - 2, remainder -4

or

x - 2 - 4/(x + 6)

Answer:

x - 2

Step-by-step explanation:

I uploaded a photo!

A large pool has a faucet to allow water to enter the pool and a drain to allow water to leave the pool.

Each minute, the faucet allows 1215 gallons of water to enter the pool, and the drain allows 1523 gallons to leave the pool.

What is the change in the amount of water in the pool after 112 minutes?


Enter your answer as a simplified mixed number by filling in the boxes. FRACTION PROBLEM

Answers

Answer:

-34496 gallons = 34496 gallons less

Step-by-step explanation:

In 112 minutes, 1215(112) = 136080 gallons of water is added by the faucet

In 112 minutes, 1523(112) = 170576 gallons of water are drained from the pool.

So, assuming that the pool is not completely drained in the 112 minute time interval, the change in the amount of water = 136080 - 170576 = -34496 gallons; i.e., the amount of water in the pool is 34496 gallons less.

help please i will give brainliest ^^;;

Answers

Answer:

The slope for number 4 is 5/-4 and for number 6 is 4/1

Step-by-step explanation:

5/-4: slope is rise over run so you have to go up (positive) 5 and you have to go to the left (negative) so its 5/-4

4/1: again it's rise over run so you have to go up (positive)  4 and right one (positive)

Answer:

hello

are you army

who is your bias

Please help thank you

Answers

I’m not sure, what is the unit called

Please help me out. Thanks

Answers

Answer:

y=-2x+5

Step-by-step explanation:

2,1 and 3,-1

gradient

=(3-1)/-1-1

gradient = -2

y=5

y=-2x+5

SOLVE ASAP!!!!! NO LINKS!!!!!!∛²³1 + 4 x -96

Answers

Answer:

All i got was 3√23+4x−96

Step-by-step explanation:

PLEASE HURRY HELP!
Find the product (3a4 + 4)2

Answers

Answer:

(3a4 + 4)2

= (12a+4)2

= 24a+8

AWARDING 100 POINTS

Write blue, red, or orange in each section of the circle graph based on the following data:

There are 32 children. 25% of the children like blue, 16 children like red, and 8 children like orange.

Answers

25% of the children like blue, so 0.25*32 = 8 like blue. This is the same number of people who like orange.

So you'll have "blue" in one quarter slice and "orange" in another quarter slice.

So far, we've counted 8 blue + 8 orange = 16 total. Because there are 32 kids overall, this leaves 32-16 = 16 left. This matches up with the fact that 16 like red. This is half of 32, meaning we'll shade two quarter slices to indicate red. Put another way, you'll have "red" in two slices.

Check out the diagram below. That's one possible configuration (other combos are possible).

Ok so 25% like blue, so if we had to make an equation it would be 0.25 x 32 because that would give us the number of children who like blue. So, when we do that we get 8 which is the same amount of kids who like orange. So, 1/4 of that circle would be blue and another one fourth of the circle would be orange. So now we have to look at the red. It says "16 children like red" and we know that theres a total of 32 kids. So, since 1/2 of the circle was of the kids who like blue and orange, the other half has to show the amount of kids who just like red. Look at screenshot below to help.

gloria rode her bicycle 11.75 miles in the morning and 2.3 miles in the afternoon how many miles did gloria ride altogether.

Answers

Answer:

13.05

Step-by-step explanation:

1

11.75

+ 2.3

13.05

Answer:

14.05 miles

Step-by-step explanation:

To find the total amount of miles, we have to add 11.75 and 2.3, or 2.30. First, we add our hundredths:

0.05 + 0.00 = 0.05

Then, we add our tenths:

0.7 + 0.3 = 1

Then, we add our ones:

1 + 2 = 3

Finally, we add our tens:

10 + 0 = 10

Now, let's add all those numbers together. 10 + 3 + 1 + 0.05 = 14.05.

Two movies, an action movie and a drama, were released on the same day. The producers of the action movie claimed that their movie would be better received by audiences than the drama. To test the producers' claim, CinemaScore randomly selected 100 people and showed them both movies. Then the viewers were asked whether they liked or disliked each movie. The results are shown in the table. ​

Answers

Answer:

C is the correct answer.

If you need an explanation tell me.

More people like the action movies.

What is comparison of two numbers?

Comparison of two numbers, means to examine the differences between numbers, quantities or values to decide if it is greater than, smaller than or equal to another quantity.

According to the given question

We have a data in which

Number of people who liked action movie = 78

Number of people who liked action movie = 60

Number of people who disliked the action movie = 22

And, number of people who disliked the drama movie = 40

From the given data we conclude, that action movie is liked by more people as compared to drama movie because 78 > 60.

Hence, the action movie is better received by the audience than the drama.

Learn more about comparison of two numbers here:

https://brainly.com/question/5220791

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I need help with this math problem

Answers

Answer:

F(x)=(x+6)^2

Step-by-step explanation:

Hope this helps!

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