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.
Answers
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
HELP HELP
Referring to the Fig. in Question #19, given FGHI≅WXYZ,
find m∠Y
Answers
Answer:
m∠Y= 120
Step-by-step explanation:
Given,
FGHI≅WXYZ
m∠H=m∠Y [ Corresponding parts of congruent figures]
m∠Y= 120
If 2+√3/2-√3= a+b√3 Find a and b
Answers
Answer:
a = 7, b = 4Step-by-step explanation:
Simplify the left side:
(2 + √3)/(2 - √3) = (2 + √3)(2 + √3)/(2 + √3)(2 - √3) =(4 + 4√3 + 3)/(4 - 3) =7 + 4√3Compare with the right side:
a = 7, b = 4 The scale drawing at right shows the first slope of a house, the actual dimensions of the garage are 20 feet by 25 feet. All angels are right angels.
A. how many feet does each inch represent? That is, what is the scale?
B. What are the length and width of the living room on the scale and drawing( in inches)?
C. What are the actual length and width of the living room( in feet)?
D. if the family wants to lay carpet in the living room and carpeting cost $1.25 per square foot, how much will carpet cost
Answers
Answer:
See belowStep-by-step explanation:
A)
According to dimensions of the garage, the scale is:
1 in : 20 ft, as the width of the garage is 20 ft and on paper is 1 inB)
Living room
Dimensions on paper:
2 in x 1 1/4 inC)
Actual dimensions:
2*20 ft = 40 ft and1 1/4 * 20 ft = 25 ftD)
The area of the living room:
A = lw = 25*40 = 1000 ft²Cost of carpet:
1000*$1.25 = $1250Length
20(2)=40ftWidth
1.25(20)25ftArea
25(40)1000ft²Total cost
1000(1.25)$1250help #2 #4 #6 #8 #10 #12
Answers
Assume that adults have IQ scores that are normally distributed with a mean of ?=100 and a standard deviation ?=20. Find the probability that a randomly selected adult has an IQ less than 140.
Answers
Answer:
The probability that a randomly selected adult has an IQ less than 140 is 0.9772
Step-by-step explanation:
Given:
Standard deviation: σ=20
Mean: μ=100
P(X<140)=?
Calculate:
normalcdf(lower,higher,μ,σ) = normalcdf(0,140,100,20) = 0.9772496509 ≈ 0.9772 ≈ 97.72%
81 x
3y + 72x
2y
2 + 16xy
3
Answers
Answer:
Step 1 :Equation at the end of step 1
((81•(x4))-((72•(x2))•(y2)))+24y4
Step 2 :
Equation at the end of step 2 :
((81 • (x4)) - ((23•32x2) • y2)) + 24y4
Step 3 :
Equation at the end of step 3 :
(34x4 - (23•32x2y2)) + 24y4
Step 4 :Trying to factor a multi variable polynomial
4.1 Factoring 81x4 - 72x2y2 + 16y4
Try to factor this multi-variable trinomial using trial and error
Found a factorization : (9x2 - 4y2)•(9x2 - 4y2)
Detecting a perfect square :
4.2 81x4 -72x2y2 +16y4 is a perfect square
It factors into (9x2-4y2)•(9x2-4y2)
which is another way of writing (9x2-4y2)2
How to recognize a perfect square trinomial:
• It has three terms
• Two of its terms are perfect squares themselves
• The remaining term is twice the product of the square roots of the other two terms
Trying to factor as a Difference of Squares:
4.3 Factoring: 9x2-4y2
Put the exponent aside, try to factor 9x2-4y2
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 9 is the square of 3
Check : 4 is the square of 2
Check : x2 is the square of x1
Check : y2 is the square of y1
Factorization is : (3x + 2y) • (3x - 2y)
Raise to the exponent which was put aside
Factorization becomes : (3x + 2y)2 • (3x - 2y)2
Final result :
(3x + 2y)2 • (3x - 2y)2
Step-by-step explanation:
Answer:
81x+16y
should be the correct one
6 (31 + 163 72)6 +2=
Answers
6 x 16403 = 98418
98418 x 6 = 590508
590508 + 2 = 590510
x-10<-26
help lololololol
Answers
Hope this will help you!! <3
Answer:
Step-by-step explanation:
1) -90 ≥ 18x
Divide both sides by 18
-90/18 ≥ 18x/18
-5 ≥ x
2)x/3 > -8
Multiply by 3,
3*(x/3) > -8*3
x> -24
3)x - 10 < -26
Add 10 to both sides
x < -26 +10
x < -16
4) 19 -x ≥ 21
Subtract 19 from both sides,
-x ≥ 21 - 19
-x ≥ 2
Divide both sides by (-1)
x < -2
Some banks now use continuous compounding of an amount invested. In this case, the equation that models the value of an initial investment of P dollars in t years at an annual
interest rate of r is given by A = Pelt. Using this equation, find the value in 5 years of an investment of $2000 that earns 7% annual interest. (Round your answer to the nearest cent.)
Answers
Answer:
In this case, the equation that models the value of an initial investment of P dollars in t years at an annual interest rate of r is given by A = Pert.
Step-by-step explanation:
Can someone please help me with this question
Answers
Answer:
40 degrees
Step-by-step explanation:
i'm use......
Help as soon as possible please if the answer is correct I’ll give brainliest
Answers
Answer:
The slope is 4, while the y intercept is 2
...starting with 2 cards and adding 4 cards each week
Step-by-step explanation:
The slope is always the coefficient (the number in front) of x.
The y intercept is the number on its own.
Hope this helps!
What is the solution to the equation 3 − 5 + 10 = 36
Answers
Answer:
False (no solution)
Step-by-step explanation:
What is the solution to the equation 3 − 5 + 10 = 36?
3 − 5 + 10 = 36
8 = 36
it's false
1. given w(x)=4x
a. graph r(x)=4 x w(x). then complete the table of corresponding points on r (x). How do you graph this?
Answers
Answer:
Step-by-step explanation:
a). When graph w(x) is transformed to r(x) = 4 × w(x), graph of w(x) is vertically stretched by a scale factor of 4.
Table for the corresponding points will be,
x w(x) r(x)
0 0 0×4 = 0
15 60 60×4 = 240
30 120 120×4 = 480
45 180 180×4 = 720
b). As discussed in part (a), graph of w(x) will be vertically stretched by a scale factor of 4 to produce the graph of r(x).
c). Since, w(x) = 4x
and r(x) = 4[w(x)]
r(x) = 4(4x) = 16x
r(x) = 16x
The midpoint of AB is M (4,2). If the coordinates of A are ( 6,-4) what are the coordinates of B?
Answers
Answer:
(2,8)
Step-by-step explanation:
m (4,2)
(6,-4)
(2,8)
A worker gets paid overtime at the rate of normal time plus one third. One week he works 40 hours of normal time and 6 hours overtime. If his hourly rate is $15 how much did he earn for that week?
Answers
Answer:
$ 720
Step-by-step explanation:
Normal time $ 15
Overtime: 15 x 1/3 = $5 + $15 = $20
(40 x 15) + (6 x 20) = 600 + 120
Mrs. Trip landed at Boston Logan airport and exchanged 700 Euro for $875 at a currency exchange store. Then she realized that she would need more cash and exchanged 400 Euro more. How many dollars did she receive for the second transaction?
Answers
Answer:
$500
Step-by-step explanation:
find the ratio
875/700=5/4
apply the ratio
5/4*400=500
How much is does 8×10 equal to?
Answers
Have a great day! :)
Answer:
80
Step-by-step explanation:
8x10= 80
PLEASE HELP ITS MATH THANK YOUUUU
Answers
9 inches = 14 yard
Formula: divide the value in inches by 36 because 1 yard equals 36 inches. So, 9 inches = 936 = 14 or 0.25 yard.
Answer:
4 yards
Step-by-step explanation:
Use a ratio and then cross multiply
120 yd x yd
--------- = ---------
270 in 9 in
270x = 1080
x= 1080 / 270
x = 4 yd
Construct five examples of simple sentences.
Answers
Answer:
Open the jar carefully.
Read the directions.
Don't cry.
Use common sense.
Make the best of things.
Catch up!
She doesn't study German on Monday.
Does she live in Paris?
He doesn't teach math.
Cats hate water.
Every child likes an ice cream.
Step-by-step explanation:
How much greater is the surface area of the rectangular prism than the surface area of the cube?
A. 36 cm2
B. 33 cm2
C. 18 cm2
D. 45 cm2
Answers
Answer: 18 cm2
Step-by-step explanation: the surface area of the cube is 54 cm2 and the rectangular prism is 72 cm2 so 72 - 54 = 18
Anyone know this? ..........
Answers
Answer:
Yes, Each value in the domain goes to only one value in the range.
Step-by-step explanation:
Since each x goes to a different y value, the relation is a function
Each value in the domain goes to only one value in the range.
Will give brainliest answer
Answers
random text so that it would let me send.
Mrs. Miller deposited a check for $245.83 and a check for $418.72. She went to a non-company ATM and withdrew $80. She was charged a fee of $2.50. What is her current balance if she started with $50 in her account?
Play media comment.
Group of answer choices
–$692.05
$632.05
$634.55
$639.55
Answers
Answer: Your answer should be B
Step-by-step explanation: Give brainliest if it works!
I am using remainders
Answers
Answer:
Step-by-step explanation:
Is there an image or question?
Find the missing side
Answers
Answer:
A. 8
The missing side is 8
Does this look correct again?
Answers
Answer:
Correct
Step-by-step explanation:
This is correct because if you divide fourteen by one fourth the answer would be fifty-six teddy bears.
Combine the like terms to create an equivalent expression:
−
2
k
−
(
−
5
)
+
1
Answers
Answer:
-2k + 6
Step-by-step explanation:
We start out with the expression -2k - (-5) + 1. We should first distribute the negative outside of (-5), which gets us to 5: -2k + 5 + 1. Now, we can combine like terms with 5 and 1 to get 6, giving us a final answer of -2k + 6. We can't simplify any further since there aren't any like terms.
If you have any questions or need clarification on anything, let me know!
Aman bought a computer for 24000 and its accessories pack worth for 1750. He sold it all for *26780. Find his gain and gain per cent.
Answers
Answer:
4%
Step-by-step explanation:
Gain percentage = 1030/25750 x 100 = 4%
Answer:
$1,030, 4%
Step-by-step explanation:
Aman spent $25,750 on a computer and accessory packs (totally worth it). He sold it for $26,780. So let's say Aman is at 0 before he bought this. He spent $25,750, so we subtract that from 0 to get -25,750. Then he sells it all for $26,780 (again totally worth it for the person buying). So we add 26,780 to the total.
-25,750 + 26,780 = 1,030
So Aman made a profit of $1,030 (now he can buy a REASONABLY priced MacBook Air or something)
So to find the percentage that he gained, we divide 1,030 by his original spending price, namely 25,750
1,030/25,750 = 0.04
Convert that to percentage form, you get 4%
Also, it's questions like this that make me question whether the people who write these questions into the textbooks should be talked to lol.
A meter is a unit of length approximately equal to 39.37 inches. If someone is 77 meters tall, what is his or her approximate height in inches?
Answers
Answer:
It is 3031.49 Inches.
Step-by-step explanation:
77 times 39.37
= 3031.49
Estimate and solve 3,836 ÷ 63
Answers
Answer:
estimating it's 548/9
Step-by-step explanation: