A farmer wants to build a rectangular pen which will be bounded on one side by a river and on the other three sides by a single-strand electric fence. If the farmer has 40 meters of wire to use, what is the largest area that the farmer can enclose?

Answers

Answer 1

Answer:

A) Dimensions;

Length = 20 m and width = 10 m

B) A_max = 200 m²

Step-by-step explanation:

Let x and y represent width and length respectively.

He has 40 metres to use and he wants to enclose 3 sides.

Thus;

2x + y = 40 - - - - (eq 1)

Area of a rectangle = length x width

Thus;

A = xy - - - (eq 2)

From equation 1;

Y = 40 - 2x

Plugging this for y in eq 2;

A = x(40 - 2x)

A = 40x - 2x²

The parabola opens downwards and so the x-value of the maximum point is;

x = -b/2a

Thus;

x = -40/2(-2)

x = 10 m

Put 10 for x in eq 1 to get;

2(10) + y = 40

20 + y = 40

y = 40 - 20

y = 20m

Thus, maximum area is;

A_max = 10 × 20

A_max = 200 m²

Answer 2

The area of the pen is the product of its dimensions

The largest area the farmer can enclose is 200 square meters

The perimeter of the pen is given as:

[tex]\mathbf{P = 40}[/tex]

Because one side of the fence is covered by a river, the perimeter would be:

[tex]\mathbf{2x + y = 40}[/tex]

Make y the subject

[tex]\mathbf{y = 40 - 2x}[/tex]

The area of the pen is:

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

Substitute [tex]\mathbf{y = 40 - 2x}[/tex]

[tex]\mathbf{A = x(40 - 2x)}[/tex]

Expand

[tex]\mathbf{A = 40x - 2x^2}[/tex]

Differentiate

[tex]\mathbf{A' = 40 - 4x}[/tex]

Set to 0

[tex]\mathbf{ 40 - 4x = 0}[/tex]

Rewrite as:

[tex]\mathbf{ 4x = 40}[/tex]

Divide through by 4

[tex]\mathbf{x = 10}[/tex]

Substitute 10 for x in [tex]\mathbf{A = x(40 - 2x)}[/tex]

[tex]\mathbf{A = 10 \times (40 - 2(10))}[/tex]

[tex]\mathbf{A = 200}[/tex]

Hence, the largest area the farmer can enclose is 200 square meters

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Related Questions

the equations of four lines are given. Identify which lines are perpendicular

Answers

Answer:

lines 2 and 4 are perpendicular

Step-by-step explanation:

if the slopes of two lines are opposed reciprocals, they are perpendicular. in this case the slope of line 2 is -1/2 and the slope of line 4 is 2 after you solve for y=mx+b form

 I need help the answers that are there are
SSS
SAS
ASA
AAS
HL and
Not enough information

Answers

Answer:

7 is asa. The two trianges share two angles and one side.

8 is sas THe two triangels share two sides and one angle.

[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the Congruency,

8 question answer is RHS,

since both are right angles triangles and have a common hypotenuse.

RHS criterion for Q-8.

Rory bought 4 cartons of milk, each having 2 gallons. He paid a total of $28.80 to buy the milk. How much did a gallon of milk cost to Rory?

Answers

Answer:

$3.60

Step-by-step explanation:

First divide the total cost by how many cartons of milk there are multiplied by how many gallons there are in a carton. So it would look like 28.80/4*2 which is 3.6

The cost of the milk per gallon will be $3.6 per gallon of milk.

What are ratio and proportion?

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

Rory purchased four cartons of milk, each containing two gallons. He spent a total of $28.80 on milk.

The number of gallons of milk is given as,

⇒ 4 x 2

⇒ 8 gallons of milk

Then the cost of the milk per gallon will be

⇒ $28.80 / 8

⇒ $3.6 per gallon of milk

The cost of the milk per gallon will be $3.6 per gallon of milk.

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please help i’ve been stuck on this answer for a while now :(

Answers

Answer:

yeh i see

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Its 3 because Theres 3 blue ballans in 10 red

triangle ABC has vertices at A(1,-3),B(3,0), and C(5,-3). what is the distance from vertex B to the midpoint of AC

Answers

Answer:

The distance from vertex B to the midpoint of AC is 3.

Step-by-step explanation:

From Linear Algebra we understand that location of the midpoint of AC is determined by the following formula:

[tex]M(x,y) = \frac{1}{2}\cdot A(x,y) + \frac{1}{2}\cdot C(x,y)[/tex] (1)

Where:

[tex]A(x,y)[/tex], [tex]C(x,y)[/tex] - Locations of vertices A and C regarding origin, dimensionless.

[tex]M(x,y)[/tex] - Location of the midpoint regarding origin, dimensionless.

If we know that [tex]A(x,y) = (1,-3)[/tex] and [tex]C(x,y) = (5,-3)[/tex], then the midpoint of AC is:

[tex]M(x,y) = \frac{1}{2}\cdot (1,-3)+\frac{1}{2}\cdot (5,-3)[/tex]

[tex]M(x,y) = \left(\frac{1}{2},-\frac{3}{2} \right)+\left(\frac{5}{2}, -\frac{3}{2} \right)[/tex]

[tex]M(x,y) = (3, -3)[/tex]

Lastly, the distance from vertex B to the midpoint of AC is calculated from the Pythagorean Theorem:

[tex]d = \sqrt{(M_{x}-B_{x})^{2}+(M_{y}-B_{y})^{2}}[/tex] (2)

If we know that [tex]M_{x} = 3[/tex], [tex]M_{y} = -3[/tex], [tex]B_{x} = 3[/tex] and [tex]B_{y} = 0[/tex], then the distance is:

[tex]d = \sqrt{(3-3)^{2}+(-3-0)^{2}}[/tex]

[tex]d = 3[/tex]

The distance from vertex B to the midpoint of AC is 3.

Cara played a card game using a deck of 52 cards after she dealt the same number of cards to 4 players she had 24 cards left over how many cards did each player get

Answers

Answer:

She gave the players 7 cards each

Step-by-step explanation:

Answer:

7 cards each

Step-by-step explanation:

52-24=28

28÷4=7

Is 4/5 more than 2/3

Answers

Answer:

Yes

Step-by-step explanation:

Because if you Mult. the denominator to 15 you get 12/15 and 10/15 Which is less than 12/15

Lucy makes 8 dollars for each hour of work.write an equation to represent her total pay p after working h hours

Answers

Answer:

Answer: H x 8 = P

Explanation: Every hour Lucy gets paid $8 so if she works for 1 hour she gets $8 and for 2 hours of work she gets paid $16. It's just multiplying by 8.

Please help, I'll mark brainliest to first person who answers, I need my response in about 15 minutes.
THanks :)

Answers

Answer:

1. The hare sprinted the farthest.

2.

First place: Antelope: (1.6093 kilometers)

Second place: Cougar (1.2875 kilometers)

Third place: Hare (1.2607 kilometers)

Fourth Place: Ostrich and Coyote (1.15 kilometers)

Fifth Place: Kangaroo (1.073 kilometers)

Step-by-step explanation:

Just convert them all into kilometers.

Mary bought a new Apple Watch for $845.00. She made a down payment of $95 and financed the rest with six monthly payments of $128.75. Find the total installment price.

Answers

Answer:

867.5

Step-by-step explanation:

Solve d+6/2=5 d= Help me because I need help

Answers

Step-by-step explanation:

d+6/2=5

d = 5 - 6/2

d = 10- 6/2

d = 4/2

d = 2

Answer:

d = 4 or d=2

Step-by-step explanation:

Given equation

d+6/2=5

It is not clear so will solve two different equations

(d + 6)/2 = 5d + 6 = 2*5d + 6 = 10d = 10 - 6d = 4

The other option (I think incorrect)

d + 6/2 = 5d + 3 = 5d = 5 - 3d = 2

what is the slope of the line that passes through the points (1,-5) and (3,5)?
a. 5
b. -5
c. 0
d. undefined​

Answers

Answer:

a) 5

Step-by-step explanation:

Put them into slope intercept form AKA y=mx+b: -5=m1+b and 5=m3+b

Subtract the equations to get -10=-2m

Divide both sides by two to get: 5=m

Hope this helps! (^-^)

6x - 5 is greater than -29

Answers

6x-5>-29
6x>-24
x>-4 so x is greater than -4

Answer:

x > -4

Step-by-step explanation:

Write it out: 6x - 5 > -29Add 5 to each side, so it now looks like this: 6x > -24Divide each side by 6 to cancel out the 6 next to x. It should now look like this: x > -4

I hope this helps!

Calculate the density of the cube.
240 grams
4 cm
3 cm
5 cm​

Answers

Answer:

3750, 8888.89, 1920

Step-by-step explanation:

p=m/v

p1=240/(0.04^3)= 3750 kg/m^3

p2=240/(0.03^3)= 8888.89 kg/m^3

p3=240/(0.05^3)= 1920 kg/m^3

Answer:

3750, 8888.89, 1920

Hope this helped!

If we have the following equations, y = 2x + 6 and 3y = 3x - 5, which function
has the highest rate of change?

Answers

y=2x+6 has the highest rate of change the other equations rate of change is 5/4

WILL MARK BRAINLIST!!!!!

Gillian made a drawing using a rectangle and 4 congruent 3/4 circles as shown. Which measurement is closest to the area of Gillian's drawing in square inches?

[tex]a. \: \: 44.56 {in}^{2} [/tex]
[tex]b. \: \: 35.14 {in}^{2} [/tex]
[tex]c. \: \: 41.42 {in}^{2} [/tex]
[tex]d. \: \: 38.28 {in}^{2} [/tex]

Answers

Answer:

b???

Step-by-step explanation:

Answer:

I think it is c. 41.42

Step-by-step explanation:

you would have to multiply the length and the width and then add the 1 inch because each wheel is one inch to the 4 to make 5 then you would multipy  8x5 which eqals 40 which is closes to 41.42!

(I am so sorry if im wrong)

A rental car agency charges $240.00 per week plus $0.15 per mile to rent a car. How many miles can you travel in one week for $381.00.

Answers

Answer: In a week you can travel 941 miles

Step-by-step explanation:

$240+0.15m=$381

Subtract $240 on both sides:

$240-$240+0.15m=$381-$240

0.15m=$141

Divide 0.15 on both sides:

0.15m/0.15=141/0.15

m=941 miles

An initial investment of $1000 grows at an interest rate of 4% per year. How long will it take that investment to reach $1,500? Assume that you make no further deposits or withdrawals from the investment account. Round to the nearest tenth of a year.
a. 12.6 years
b. 5.4 years
c. 9.8 years
d. 10.3 years

Answers

Answer:

ITS 10.3 !!!

Step-by-step explanation:

just trust me <3 also

GOD LOVES YOU!

12.6 years will be taken for the amount to reach to $1,500.

What is Simple Interest?

Simple interest is the interest which are accumulating over the principal amount. This interest rate only depends on the principal amount, contrary to the compound interest.

The formula for calculating the final amount in Simple interest is,

A = P(1 + r t)

where A is the final amount, P is the principal amount, r is the interest rate and t is the time period.

Simple interest rate, r = 4% = 4/100 = 0.04

Principal amount, P = $1000

Final amount A = $1500

We have to find the time 't'.

1000 [1 + (0.04 × t)] = 1500

1 + 0.04 t = 1500 / 1000

1 + 0.04 t = 1.5

0.04 t = 1.5 - 1

0.04 t = 0.5

t = 0.5 / 0.04

t = 12.5 ≈ 12.6

Hence it will take 12.6 years to reach $1,500.

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can someone help on #2 , will be followed & marked as brainliest .​

Answers

Answer:

x = 4.33

Step-by-step explanation:

3x - 4 = 17

     -4 = -4

3x = 13

/3  = /3

x  = 4.33

4.33

could not delete my wrong answer sorry :/

I need help the answers that are there are
SSS
SAS
ASA
AAS
HL and
Not enough information

Answers

[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the Congruency,

Question 2.) => since all sides are equal, so SSS is the answer for Q-2

Question 3.) => Two angles and one side, so AAS is the answer for Q-3

*I WIlL MARK U BRAINLYST*
Mark the angles and sides of each pair of triangles to indicate that they are congruent.

Answers

Answer:

C)

Step-by-step explanation:

Sides:

WX = FE

XY = EY

WY = FY

Angles:

W = F

∠X = ∠E

∠Y = ∠Y

Answer:

a= x-f

b=y-b

Step-by-step explanation:

Calculate the slope of a line that passes through the points (3, -20) and (5, 8).
A. 14
B. 6
C. 26
D. 4

Answers

C, it is six. Welcome

Answer:

A. 14

Step-by-step explanation:

10 points please help

Colton is taking a long bike ride where he rides at a constant speed. The distance he bikes is
proportional to the amount of time he has been biking. After 3.5 hours, he has traveled a distance
of 49 miles. Find the ratio of the distance Colton has traveled to the amount of time he has been
traveling. Express this as a unit rate and use appropriate units.

Answers

Answer:

14/1

14 miles per hour.

Step-by-step explanation:

At a store, the price per pound of heart candies (h) is 30 cents more than three times the price per pound of jelly beans (j). The equation that represents the price of heart candies to the price of
jelly beans, in cents, is

Answers

Answer:

Step-by-step explanation:

h = 3x + 30

The equation representing price of heart candies to price of jelly beans is h = 30 + 3j.

It is given that price per pound of heart candies (h) is equal to 30 cents more than three times the price per pound of jelly beans (j).

We have to find out the equation which represent above statement.

What is algebra ?

Algebra is the branch that deals with various symbols and the arithmetic operations such as multiplication , division , etc.

As per the question ;

Jelly beans are represented by j and heart candies by h.

And given ;

h is equal to 30 cent more than three times of j

i.e.,

h = 30 + 3 × j

or

h = 30 + 3j cents

Thus , the equation representing price of heart candies to price of

jelly beans is h = 30 + 3j.

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PLease help me please

Answers

Xy+24=x22 that is the answer hope it helps

HELP! WILL GIVE BRANLIEST!!

Answers

Answer:

18 options.

Step-by-step explanation:

Review the proof (not in order) of the identity Tangent (StartFraction theta Over 2 EndFraction) = plus-or-minus StartRoot StartFraction 1 minus cosine (theta) Over 1 + cosine (theta) EndFraction EndRoot..
What is the correct sequence of steps?

1-3-2-4-5
1-3-4-2-5
1-4-2-3-5
1-4-3-2-5

Answers

Answer:

b

Step-by-step explanation:

edge 2020

Answer:

the answer is b i just took the test

Step-by-step explanation:

A Gallon of milk cost $2.79 in 2000.In 2015,It cost $3.98

Answers

Answer:its 42.65232974910394

Step-by-step explanation:

WILL MARK BRAINLIST!!

Anthony drew a picture of the front view of a doghouse using two congruent triangles and a rectangle, as shown in the diagram. 3 in. 4 in. 12 in. What is the area of the picture of the doghouse in square inches?​

Answers

Answer:

Step-by-step explanation:

144

The area of the picture of the doghouse will be 66 square inches.

What is the area?

The quantity area demonstrates the amount of a sector on a planar or hemispherical cup. Surface area refers to the area of an open surface or the border of a multi-object, whereas the area of a plane region or plane field refers to the area of a form or planar material.

The figure is the combination of two congruent triangles and one rectangle. Then the area is given as,

A = 2 (Area of triangle) + (Area of rectangle)

A = 2 x 1/2 x 3 x 6 + 4 x 12

A = 18 + 48

A = 66 square inches

The area of the picture of the doghouse will be 66 square inches.

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What is the product?
[5 -2 -6 2] x [2 -1 -1 -7 8]

Answers

Answer:

Step-by-step explanation:

[tex]\left[\begin{array}{ccc}5&-2\\-6&2\end{array}\right] \times\left[\begin{array}{ccc}-1\\-1\end{array}\right] \\=\left[\begin{array}{ccc}5*-1+(-2)*-1\\-6*-1+2*-1\end{array}\right] \\=\left[\begin{array}{ccc}-5+2\\6-2\end{array}\right] \\=\left[\begin{array}{ccc}-3\\4\end{array}\right][/tex]

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