A rectangular field is built next to a house and is enclosed by 400 m of fencing for the 3 remaining sides. Determine the dimensions of the field to maximize the area to nearest tenth of a metre.

Answers

Answer 1

Answer:

The dimensions of the field to maximise the area are 100 metres (width) and 200 metres (height).

Step-by-step explanation:

The formulas for the area ([tex]A[/tex]), measured in square metres, and the perimeter ([tex]p[/tex]), measured in metres, of the rectangle are, respectively:

[tex]A = x\cdot y[/tex] (1)

[tex]p = 2\cdot x +y[/tex] (2)

Where:

[tex]x[/tex] - Width, measured in metres.

[tex]y[/tex] - Height, measured in metres.

Note: We assume that height of the rectangle is parallel to the wall of the house.

By (2):

[tex]y = p - 2\cdot x[/tex]

In (1):

[tex]A = x\cdot (p-2\cdot x)[/tex]

[tex]A = p\cdot x - 2\cdot x^{2}[/tex] (3)

Then, we obtain its first and second derivatives by Differential Calculus:

[tex]A' = p - 4\cdot x[/tex] (4)

[tex]A'' = -4[/tex] (5)

By equalising (4) to zero, we find the following critical value for [tex]x[/tex]:

[tex]x = \frac{p}{4}[/tex]

And besides the Second Derivative Test, this solution is associated to an absolute maximum. Given that [tex]p = 400\,m[/tex], then the maximum area enclosed by fencing is:

[tex]x = 100\,m[/tex]

[tex]A = 20000\,m^{2}[/tex]

And the height of the triangle is:

[tex]y = 200\,m[/tex]

The dimensions of the field to maximise the area are 100 metres (width) and 200 metres (height).

Related Questions

(50Pts) When using the vertical method to multiply polynomials, your like terms must be lined up in ____________.

descending order
ascending order
columns
rows

Answers

I think you line them up in columns

Answer:

C. Columns

Step-by-step explanation:

It's correct, I took the test and got it right.

A refrigerator has a marked price of $5000. Mr. Jones bought it on hire purchase for $7500. What is the extra cost Mr. Jones paid as a percentage of the cash price? *

A) 66.6%
B) 33.3%
C) 50%
D) 75%

Answers

The answer is C. 50% because 50% of 5,000 is 2,500 and 2,500+5,000= 7,500

50% because the 50% of 5000 is 2500 and 5000+2500=7500

Which is the following functions is graphed below?

Answers

Answer:

A.y=|x|+7

Step-by-step explanation:

your answer is A !!!!

A gym charges an initial fee plus $25 per month. John paid $200 for six months. Assume the relationship is linear.

a.What is the rate of change and what does it mean in context to the situation?
b. What is the initial value and what does it mean and context to the situation?

i will give brainliest!!!!!

Answers

Step-by-step explanation:

a. The rate of change is $33.33 per month

200/6 = approximately $33.33 per month

This means that in addition to the initial fee, Josh has to pay $33.33 per month for the gym membership.

b. The initial value is $25. This is a constant value and a one time fee to open and attain a gym membership.

Which of the following is an irrational number?
A. Vo
B. 73
C. 1.36
D. -0.19

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

root three is irrational

Which planet in the chart is most likely Earth? Yeah
Does somone no the answer

Answers

Answer:

Kepler-452b has a probable mass five times that of Earth, and its surface gravity is nearly twice as Earth's, though calculations of mass for exoplanets are only rough estimates. If it is a terrestrial planet, it is most likely a super-Earth with many active volcanoes due to its higher mass and density.Step-by-step explanation:

help me please..........

Answers

Answer:

oof thats hard

Step-by-step explanation:

Measure Math | Welcome, HAILEE KNOTT
What is another way to write 15 divided by 2?
15
O 15+2
O 15 x 2

Answers

Answer: [tex]15\times\frac{1}{2}[/tex]

Explanation:

Multiplying by 1/2 is the same as dividing by 2.

For example, if you have 10 slices of cake and 2 friends, then each friend gets 10/2 = 5 slices. We could also say [tex]10\times \frac{1}{2} = 5[/tex]

The fraction 1/2 converts to the decimal form 0.5, which means [tex]10 \times \frac{1}{2} = 10*0.5[/tex]

Can someone explain this to me please will give brainliest
Bill's new porch is rectangular, with an area of 50 square feet. If the length of the porch is two times the width, what is the perimeter of the porch?
A.30
B.40
C.50
D.60

Answers

the answer is A. for this, you have to set up a system of equations. the first one will be the area equation. since you know area=length x width, your equation will be LxW=50. the next equation is L=2W, since the length is two times the width. then, plug in 2W for the L in the other equation and you get 2W^2=50. divide by 2 and get W^2=25. square root both sides and you get W=5. plug back into the other equation to find L=10. Then, add the sides of the rectangle for the perimeter. 10+5+10+5=30.

Can someone please help me

Answers

Answer:

a) y = 1.6x .

b) 197.8 .

Step-by-step explanation:

a) y ( Weight lbs. ), x ( Week ), Constant rate ( 1.6 ) .

b) 1.6 x 16 = 25.6 .

Hope this helps !

Answer:

215.4

Step-by-step explanation:

first u do 223.4 - 221.8 to find how much we losses a week which is 1.6 then u do 218.6 - 1.6 = 217 (week 5) then 217 - 1.6 = 215.4 (week 6)

work out: 0.03 x 0.6

Answers

0.03 x 0.6

= (3 x 6) / 1000

= 18 / 1000

0.018

Tom drives 200 miles in 4 hours.
He drives the first 32 miles at an average speed of 64 mph
Work out his average speed for the rest of the journey, in mph.
Please help??

Answers

His average speed for the rest of the journey was of 48mph.

if tom is driving 200 miles in 4 hours... and drives the first 32 miles in half an hour... his speed for the rest of the trip would most likely be 48 mph because 3.5 hours are left and 168 miles are left and when you divide that it comes out to 48.

THE COFFICENT OF y in term -y /3 is

Answers

Answer:

-1/3

Step-by-step explanation:

hope it helps thanks

Answer:

-1/3

Step-by-step explanation:

write the product form of 3 a² b ³

Answers

Answer:

a³-b³= (a-b)(a²+ab+ b²)

Step-by-step explanation:

The price of a gallon of unleaded gas was 2.84 yesterday. Today, the price rose to 2.90 . Find the percentage increase. Round your answer to the nearest tenth of a percent.

Answers

Answer:
102.1%
Explanation: 2.90/2.84=1.021x100

HELP ON A TIMER

WHAT IS THE x-intercept of the graph?

Answers

It is 6 just look at the x

HELP ME PLEASE!! I DON’T KNOW WHAT I’M DOING

Answers

41u+6

Sorry I don't really know anything about this subject.

statistics is a numerical value summarizing the sample date

true or false

Answers

True szzzzzzzzzzzzzzzzz

i have i need to use the substitution method to work out what x and y is
5y−2x=10
8x+5y=60

Answers

Answer:

pick the simplest of the 2 equations

Step-by-step explanation:

5y-2x=10

5y = 2x +10

y = 2/5x + 2

now substitute

8x + 5(2/5X +2)=60

8x + 2x + 10 = 60

10x = 50

x = 5

y = 4

X=5
Y=4
Did u want the answer of the method?

What value of y will make the equation true? The square root of 34 times the square root of y = 34

Answers

y=34 but i’m not sure i hope it’s right luv. N E WAYZ , GOOD DAY IN MY MIND SAFE TO TAKE A STEP OUT

Help me plsss

And show identity. Thank you:)

Answers

Answer:

see the formula in book

Step-by-step explanation:

change the first 2 brackets into cos sin like that

then after,change both into another formula

sin theta plus cos theta will come ans

Plz I need help ASAP

Answers

Answer:

Step-by-step explanation:

5.50p=5.50x4=22

I hope this is the answer you're looking for! :)

I just edited it.

Monique bought 3 boxes of cereal at the grocery store. Each box of cereal costs c dollars. Which equation represents the total amount of money, t, Monique spent on cereal?

Answers

Answer:

3c = t

Step-by-step explanation:

3 cereal boxes is 3c and the total is t. so 3c = t

Answer:

3c = t

3 is the amount of boxes, c is the money, therefore, it is 3c=t, which means c times the number of boxes equals t

how many inches are in 3 yards

Answers

Answer:

108

Step-by-step explanation:

36 inches in a yard

12 inches in 1 foot, 3 feet in 1 yard.

12 * 3 = 36, 36 * 3 = 108

108 inches in 3 yards

Hope this helps!

Identify the vertex for the graph of y = -2x2 - 12x +1. (1 point)
O (-3, 19)
0 (-3,55)
(3, -53)
(3, -47)

Answers

Answer:

(-3, 19)

Step-by-step explanation:

help with this question please

Answers

Number of chores is independent, the other is dependent

Independent variable (often denoted by x ) whose variation does not depend on that of another.
Dependent variable (often denoted by y ) whose value depends on that of another.

Independent- c (number of chores)
Dependent- d (number of dollars)

Depending on how many chores you complete will determine how much money you will earn.

If 48% of the students in a certain college are female and there are 2,400 female students, how many students are male?

Answers

Answer:

2,600 male students

Step-by-step explanation:

[tex]\frac{2,400}{0.48} = 5,000[/tex]

There are 5,000 students in total.

Since 2,400 of them are female, the remaining students must be male.

5,000 - 2,400 = 2,600 male students

Hi I need help with this hope someone has the answer.A triangular window is above the door to a café. The length of the base of the window is 12 feet, and the height is 10 feet

What is the area of the window?

Answers

Answer:

the answer is 60

Step-by-step explanation:

12×10=120

120÷2=60

Step-by-step explanation:

Sample Response: The height of the triangle will be twice the height of the rectangle. The area of a triangle is ½ bh and the area of a rectangle is bh. If the bases are the same, then the height of the triangle has to be double that of the rectangle in order to get the same area.

Select the correct answer from each drop-down menu.
Two sides of a right triangle measure 5 inches and 6 inches, and the third side measures V61 inches.
inches.
The length of the third side is about
inches. The perimeter of the triangle is about
Please help

Answers

Answer:

7.8 and 18.8 is your answer

Step-by-step explanation:

give other person brainliest and yes Ik I’m very late ~w~

two times the sum of a number and 18 is at least -21

Answers

Answer:

2x + 18 ≥ 21

x ≥ 2/3

Step-by-step explanation:

Let sum be X

2 times the sum means 2x

the sum of a number and 18 means x + 18

at least -21 means ≥ 21

put them together, and you get, 2x + 18 ≥ 21

If solving for x,

2x + 18 ≥ 21

2x ≥ 3

x ≥ 2/3

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