A rectangular dog pen is constructed using a barn wall as one side and 80 meters of fencing for the other three sides. Find the dimensions of the pen that give the greatest area.(example to write an answer: 20m×15m).

Answers

Answer 1

Let the dimensions of the pen be L for the length and W for the width. The area of the pen is L*W.

We are given that the width of the pen is 80 meters and that the length of the pen is greater than the width. Therefore, the length of the pen must be greater than 80 meters.

Since the area of the pen is L*W, the area will be greatest when L is as large as possible and W is as large as possible. Therefore, we can set L equal to 80 and W equal to 80 to find the dimensions of the pen that give the greatest area:

L = 80

W = 80

The dimensions of the pen that give the greatest area are 80 meters by 80 meters. Therefore, the answer is 80m x 80m.

Answer 2

The dimensions of the pen are 20 m × 40 m and the area will be 600 m².

What is the area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely encompass the surface of a compact figure. The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.

As per the given data in the question,

Let the length of the rectangle is x and,

Let the width of the rectangle is y.

So, the equation will be,

2x + y = 80 (1)

y = 80 - 2x (2)

Use the formula of the area of a rectangle,

A = x × y

Substitute y = 80 - 2x in the above formula,

A = x × (80 - 2x)

= 80x - 2(x)²

= -2x² + 80x

dA/dx = -2x² + 80x

A' = -4x + 80

-4x = -80

x = 80/4

x = 20 m

Substitute x = 20 in equation (2)

y = 80 - 2(20)

y = 40 m

So, the area should be,

A = 20 × 40

A = 600 m².

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Related Questions

2) √51 is closest to which whole
number?

Answers

After cοmpleting the task, we can state that The whοle number clοsest tο expressiοn 7.141 is 7. Therefοre, √51 is clοsest tο the whοle number 7.

What is whοle number?

The whοle numbers are the part οf the number system which includes all the pοsitive integers frοm 0 tο infinity. These numbers exist in the number line. Hence, they are all real numbers. We can say, all the whοle numbers are real numbers, but nοt all the real numbers are whοle numbers.

Thus, we can define whοle numbers as the set οf natural numbers and 0. Integers are the set οf whοle numbers and negative οf natural numbers. Hence, integers include bοth pοsitive and negative numbers including 0. Real numbers are the set οf all these types οf numbers, i.e., natural numbers, whοle numbers, integers and fractiοns.

√51 is apprοximately equal tο 7.141. The whοle number clοsest tο 7.141 is 7.

Therefοre, √51 is clοsest tο the whοle number 7.

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I am one of Jehovah's Witnesses reply if you are to

Answers

Nope but I respect what you are

Answer:

I am

Step-by-step explanation:

In each rule , copy the chart and fill in the missing parts

Answers

Answer:

7. 14

15. 30

28. 56

32. 64

18 36

x 2x

1/2y. y

2x. 4x

x+3 2x+9

Step-by-step explanation:

each out is double the in

determine the rate of change from the two points (3,4)(5,8)

Answers

Answer: 2

Step-by-step explanation:

8 - 4 = 4

5 - 3 = 2

4/2 = 2

Answer:

Step-by-step explanation:

the rate of change or slope from the given two points is rise over run.

(3, 4) (5, 8)

slope = (y2 - y1) / (x2 - x1)

= (8 - 4) / (5 - 3)

= 4 / 2

= 2

Find the volume of the cylinder. Use 3.14 for π.
Round your answers to the nearest tenth.

Answers

The volume is 621.72

Answer:

V≈565.4

Step-by-step explanation:

V=πr2h=π·32·20≈565.48668

Varia is studying abroad in Europe. She is required pay $3,500 (in US dollars) per year to the university; however, she must pay in euros. How many euros can Varia expect to pay per month to the university?

Answers

Answer: 247.92 euros

Step-by-step explanation:

Given, Varia is required pay $3,500 (in US dollars) per year to the university.

If she must pay in euros , then we convert $3,500 into euros.

Current rate : 1 US dollar = 0.85 euro

Then, $3,500 = ( 0.85 x 3500) euros

= 2975 euros

She can expect 2975 euros to pay per year.

Also, $2975\div 12\approx247.92$ [ 1 years = 12 months]

Hence, She can expect 247.92 euros to pay per month to the university.

A mover places a cylindrical container on a dolly, as shown. Calculate the angle of elevation, U,
from the base of the dolly to the ground.
A. 52.0°
B. 38.0°
C. 38.6°
D. 51.4°

Answers

Check the picture below.

$\sin( \theta )=\cfrac{\stackrel{opposite}{0.5}}{\underset{hypotenuse}{0.64}} \implies \sin^{-1}(~~\sin( \theta )~~) =\sin^{-1}\left( \cfrac{0.5}{0.64} \right) \\\\\\ \theta =\sin^{-1}\left( \cfrac{0.5}{0.64} \right)\implies \theta \approx 51.4^o$

Make sure your calculator is in Degree mode.

Find the surface area of the pyramid.

Answers

24huhvfghuuijnvcdry. Hubby

Factorise fully 6x+8

Answers

Answer: To factorize the expression 6x + 8 fully, we can first look for the greatest common factor (GCF) of the two terms. In this case, the GCF is 2.

Step 1: Factor out the GCF:

2(3x + 4)

Now, we have the expression 3x + 4 inside parentheses. This expression cannot be further factorized since there are no common factors other than 1.

Therefore, the fully factorized form of 6x + 8 is:

2(3x + 4)

Step-by-step explanation:)

The factored expression is:

↬ 2(3x + 4)

Step-by-step explanation:

To factor the expression, look at its GCF (greatest common factor).

Clearly the GCF of both terms is 2. So what we do next is we divide both terms by 2 :

6x ÷ 2 + 8 ÷ 2

The result is :

3x + 4

And now the 2 goes outside the parenthesis:

2(3x + 4)

Hence, the answer is 2(3x + 4).

What is the value of 364?

Answers

Step-by-step explanation:

could you make the question full please

4x ^ 2 + 300 = 1, 596 help solve for the x please show work I will mark brainliest

Answers

Answer:

x=18 OR x=-18

Step-by-step explanation:

$4x^2=1296\\x^2=324\\x=+-sqrt(234)\\x=18 OR x=-18$

HELP!!

Next, you will make a scatterplot. Name a point that will be on your scatter plot and describe what it represents.

Answers

A point on the scatter plot is defined as (19, 3), which means that an input of 19 is mapped to an output of 3.

What is the scatter plot?

The scatter plot is built inserting all the points of the table in a graph, which are in the following input-output format:

(Input, Output).

One point on the scatter plot for this problem has the coordinates given as follows:

(19, 3).

Hence the meaning is that an input of 19 is mapped to an output of 3.

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write 1000 as a product using 10 as a factor

Answers

Answer:

Step-by-step explanation:

Answer:

The answer is right here for you!

Here it is:10x100

Surface area of a rectangular prism?

Dimensions
Length: 3
Width: 4
Height: 5

Answers

Answer:

Step-by-step explanation:

Surface area of a rectangular prism = 2(lw + wh + lh)

where l = lenght, w = width and h = height

here we are given that the rectangular prism has a lenght of 3, a width of 4 and a height of 5.

So we have SA = 2(lw + wh + lh)

==> plug in l = 3, w = 4 and h = 5

SA = 2((3)(4) + (4)(5) + (3)(5))

==> find products of numbers that are next to each other seperated by parenthesis

SA = 2(12 + 20 + 15)

==> find sum of values in parenthesis

SA = 2(47)

==> multiply 2 and 47

SA = 94

Answer:

Surface area = 94

Step-by-step explanation:

║Formula for {Area of a Rectangular Prism} ║:

2(lw + wh + lh)

Which can also express as:

2(Lw) + 2(Wh) + 2(Lh)

While,

L = Length

W = Width

H = Height

║ Given ║ :

Length: 3

Width: 4

Height: 5

║Solve ║:

2( 3 × 4) + 2(4 × 5) + 2(3 × 5)

(6 × 4 )+ (8 × 5) +( 6 × 5)

24 + 40 + 30

64 + 30

Hence, the surface area of a rectangular prism is:

Kavinsky

Arrange the steps in order to simplify the expression

Answers

Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5. Combining like terms

6. getting rid of parentheses

Convert to use rational exponents: $\sqrt[3]{2}\sqrt[5]{2}$

Answers

The answer is 16 two

She decides to change the length of the top of the trapezoid-shaped garden from 32 ft to 24 ft. Which expression finds the change in the scale factor?
StartFraction 4 inches over 24 feet EndFraction
StartFraction 32 feet over 4 inches EndFraction
StartFraction 24 feet over 32 feet EndFraction
StartFraction 32 feet over 24 feet EndFraction

Answers

Answer:well i think it’s c

Step-by-step explanation:

I took the test

Answer:

c .

Step-by-step explanation:

On a number line, point C is at 8, and the midpoint E of CD is at -3.
Point D is at
on the number line.

Answers

Answer: C

Step-by-step explanation:

Point D is at -14 on the number line.

How to determine the midpoint of a line segment?

In Mathematics, the midpoint of a line segment with two end points can be calculated by adding each end point on a line segment together and then divide by two (2).

Since E is the midpoint of line segment CD, we can logically deduce the following relationship:

Line segment CD = Line segment C + Line segment D

Midpoint E = (point C + point D)/2

By substituting the given points into the equation above, we have the following:

-3 = (8 + D)/2

-6 = 8 + D

D = -6 - 8

D = -14

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what is the measure of FAB?

Answers

Answer: 117

Step-by-step explanation: Angle FAB is just 360 degrees minus all the other angles except 30. If you view the green/shaded area as a circle, there are 360 degrees, and FAB is a section of it. So 360-70-71-48-54=117. I hope this helps!

Answer:

117

add all and subtract from 360

Angle A is 87

meaning that to find angle FAB you need to add 30 and 87

And answer is 117

3 · {(300 - 70 ÷ 5) - [3 · 23 - (8 - 2 · 3)]}

Answers

Answer:

(657)

Step-by-step explanation:

Simplify the following:

3 (300 - 70/5 - (3×23 - (8 - 2×3)))

The gcd of -70 and 5 is 5, so (-70)/5 = (5 (-14))/(5×1) = 5/5×-14 = -14:

3 (300 + -14 - (3×23 - (8 - 2×3)))

-2×3 = -6:

3 (300 - 14 - (3×23 - (-6 + 8)))

8 - 6 = 2:

3 (300 - 14 - (3×23 - 2))

3×23 = 69:

3 (300 - 14 - (69 - 2))

| 6 | 9

- | | 2

| 6 | 7:

3 (300 - 14 - 67)

300 - 14 - 67 = 300 - (14 + 67):

3 ((300 - (14 + 67)))

| 1 |

| 6 | 7

+ | 1 | 4

| 8 | 1:

3 (300 - 81)

| | 9 |

| 2 | | 10

| | |

- | | 8 | 1

| 2 | 1 | 9:

3 (219)

3 (219) = (3×219):

(3×219)

3×219 = 657:

Answer: (657)

Which is more, 7 kilometers or 7,001 meters?

Answers

Answer:

7,001 meters is more than 7 kilometers. 1 kilometer is equal to 1000 meters, so 7 kilometers is equal to 7 x 1000 = 7000 meters. Therefore, 7,001 meters is greater than 7000 meters, or 7 kilometers.

Step-by-step explanation:

Which number is between -1 and 1?

Answers

Answer:

Step-by-step explanation:

6. Determine the system of equations based on the following relationships and then solve
for the two integers.
a. Fourteen more than twice the first integer gives the second integer
b. The second integer increased by one is the square of the first integer

Answer: (-3,8) and (5,24)

Answers

The two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).

To solve the system of equations, let's assign variables to the two integers. Let the first integer be represented by 'x' and the second integer by 'y'.

According to the given information:

a. Fourteen more than twice the first integer gives the second integer:

This can be expressed as: 2x + 14 = y

b. The second integer increased by one is the square of the first integer:

This can be expressed as: y + 1 = x^2

Now, we have a system of equations:

1) 2x + 14 = y

2) y + 1 = x^2

To solve this system, we can substitute the value of 'y' from equation 1) into equation 2):

2x + 14 + 1 = x^2

2x + 15 = x^2

Rearranging the equation, we have:

$x^2 - 2x - 15 = 0$

Factoring the quadratic equation, we get:

(x - 5)(x + 3) = 0

Setting each factor equal to zero:

x - 5 = 0 --> x = 5

x + 3 = 0 --> x = -3

Substituting the values of 'x' back into equation 1), we can find the corresponding values of 'y':

For x = 5:

2(5) + 14 = y

10 + 14 = y

y = 24

For x = -3:

2(-3) + 14 = y

-6 + 14 = y

y = 8

Therefore, the two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).

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Complete the following statement.
+(-7) = 3
I need help

Answers

Answer:

Step-by-step explanation:

Well is you do 10+(-7), the signs would change to 10-7, therefor it equals 3

Answer:

it's 10.

Step-by-step explanation:

10+(-7) =3

10-7=3

A. (1,1,) , (2,2) , (3,3)

B. (1,6),(2, 12) , (3, 18)

C. (1,6), (2,7), (3,8)

D. (6 ,6), (12, 12) (18,18)

Answers

Step-by-step explanation:

HahhagavBBgBNHafVabBgababaggvab

Find the length of the missing side. Round to the nearest whole number. Hypotenuse of 25 long leg of 24

Answers

Answer:

Step-by-step explanation:

Use pythagorean thereom:

24^2+x^2=25^2

x^2=49

x=7

So, the missing side is 7.

Answer:7

Step-by-step explanation:

hypotenuse =25

The long leg =24

Let the missing side be B

B=√(25^2-24^2)

B=√(25x25-24x24)

B=√(625-576)

B=√(49)

B=7

Which sequence shows the numbers in order from least to greatest?
A. -2.14<3.16227766017<2.8
B. 2.8<3.16227766017<2.14
C. 2.14<3.16227766017 <2.8
D. 2.14<2.8<3.16227766017

Answers

The sequence that shows the numbers in order from least to greatest is D. 2.14 < 2.8 < 3.16227766017.

The sequence that shows the numbers in order from least to greatest is D. 2.14 < 2.8 < 3.16227766017.What is the meaning of the inequality symbols?The inequality symbols are mathematical symbols that are used to compare two values.

They indicate the relationship between two values that are not equal to each other. Here are the inequality symbols:

< (less than)≤ (less than or equal to)> (greater than)≥ (greater than or equal to)What is the meaning of the sequence?

A sequence is a set of numbers arranged in a particular order. The order of the numbers in a sequence can be from smallest to largest or largest to smallest.

The sequence D. 2.14 < 2.8 < 3.16227766017 is arranged from smallest to largest because the first number in the sequence, 2.14, is the smallest, and the last number in the sequence, 3.16227766017, is the largest.

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It takes 9 builders 54 days to complete a house.

How long would it take 6 builders to complete the same house?

Answers

Answer:

81 days

Step-by-step explanation:

Formula to solve this type of equation $t=\frac{k}{p}$

t is time

k is a constant

p is people

We must substitute the values into the equation

$54=\frac{k}{9}$

$k=486$

Now we must substitute it to find the time

$t=\frac{486}{6}$

you get 81

It would take $6$ builders $36$ days to complete the same house.

Who are builders?

Builders are those person whose job is to build or repair houses and other buildings.

We have,

$9$ builders take $54$ days to complete a house.

So,

$1$ builder will take $(\frac{54}{9})$ days to complete a house,

In the same way,

$6$ builder will take $(\frac{54}{9}*6)$ days to complete a house,

i.e.

$6$ builder $=(\frac{54}{9}*6)= 36$ days.

Hence, we can say that it would take $6$ builders $36$ days to complete the same house.

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the poultry farmer decided to make his own chicken scratch by combining alfalfa and corn in rail car quantities.A rail car of corn costs $400 and a rail car of alfalfa costs $200. The farmer's chickens have a minimum daily requirement of vitamin K (500 milligrams) and iron (400 milligrams), but it doesn't matter whether those elements come from corn, alfalfa, or some other grain. A unit of corn contains 150 milligrams of vitamin K and 75 milligrams of iron. A unit of alfalfa contains 250 milligrams of vitamin K and 50 milligrams of iron.Formulate the linear programming model for this situation.

Answers

Answer:

- Min Z = $400C + $200A

Step-by-step explanation:

The linear programming model deals with the minimization or maximization of a linear function of several variables and inequalities. This method assists the industries in minimizing costs and maximizing production.

In the given situation,

The Linear programming model would be:

Min Z = $400C + $200 A

which is based on:

150 mg of vitamin K in corn C + 250 mg of vitamin K in AlfaAlfa ≥ 500

75 mg of iron in Corn + 50 mg of iron in AlfaAlfa ≥ 400

∵ C, A ≥ 0

Thus, the equation would be,

Min Z = $400C + $200 A

Which statement about the distance between 6 and 0 and the distance between the opposite of 6 and 0 is true?
A. The distance is the same.
B. The opposite of 6 is farther from 0 than 6.
C. The number 6 is farther from 0 than the opposite of 6.
D. You cannot compare the distances because one is negative, and the other is positive.

Answers

Answer:

Step-by-step explanation:

Use the absolute value to find the difference between the points

6 and 0

distance = | 6 - 0 | = | 6 | = 6 , or

distance = | 0 - 6 | = | - 6 | = 6

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

the opposite of 6 is - 6

- 6 and 0

distance = | - 6 - 0 | = | - 6 | = 6 , or

distance = | 0 - 6 | = | - 6 | = 6

Thus the distance is the same → A

Answer: a

Step-by-step explanation:

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