A campground owner plans to enclose a rectangular field adjacent to a river. the owner wants the field to contain 180,000 square meters. no fencing is required along the river. what dimensions will use the least amount of fencing?

Answers

Answer 1

Calling x and y the two sizes of the rectangular field, the problem consists in finding the minimum values of x and y that give an area of [tex]A=180000 m^2[/tex].
The area is the product between the two sizes:
[tex]A=xy[/tex] (1)
While the perimeter is twice the sum of the two sizes:
[tex]p=2(x+y)[/tex] (2)

From (1) we can write
[tex]y= \frac{A}{x} [/tex]
and we can substitute it into (2):
[tex]p=2(x+ \frac{A}{x})=2x+2 \frac{A}{x} [/tex]

To find the minimum value of the perimeter, we have to calculate its derivative and put it equal to zero:
[tex]p'(x)=0[/tex]
The derivative of the perimeter is
[tex]p'(x) = 2 -2 \frac{A}{x^2}= \frac{2x^2-2A}{x^2} [/tex]
If we require p'(x)=0, we find
[tex]x^2=A[/tex]
[tex]x= \sqrt{A} = \sqrt{180000 m^2}=424.26 m [/tex]
And the other side is
[tex]y= \frac{A}{x}= \frac{180000 m^2}{424.26 m} =424.26 m[/tex]

This means that the dimensions that require the minimum amoutn of fencing are (424.26 m, 424.26 m), so it corresponds to a square field.

Related Questions

Two campers leave their campsite at point A to go on a hike. Camper one heads east for 2 miles, then heads north 1 mile to point B. Camper two heads north for 4 miles, then east for 3 miles to point C. Referencing the triangle formed by A, B, and C, m
A.
27°
B.
36°
C.
45°
D.
53°

Answers

Answer:

its not C. It's A. 27

I just did it with my math teacher

98 POINTS PLEASE HELP
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Determine the standard form of the equation for the circle

With center (h,k)=(-5,1/2) and radius r=1

A) (x-5)^2 + (y + 1/2)^2 = 1

B) (x-5) + (y - 1/2) = 1

C) (x+5)^2 + (y - 1/2)^2 = 1

D) (x+5)^5 + (y- 1/2)^2 = 105/2

Answers

The standard form of a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex]. We will fill in our h, k and r accordingly. [tex](x-(-5))^2+(y- \frac{1}{2})^2=1^2 [/tex] which simplifies down to [tex](x+5)^2+(y- \frac{1}{2})^2=1 [/tex] choice C. There you go!

Hello!

I believe the answer is C) (x+5)^2 + (y - 1/2)^2 = 1.

I hope it helps!

15 min left! Anyone know this geometry question?

Answers

Option B is your answer. Those two angles are alternate interior angles.

What is the value of r?

Answers

good day ^-^ ///////////////

Answer:R = 4

Step-by-step explanation:

0.6704 repeating as a fraction?

Answers

Suppose [tex]x=0.67046704\ldots[/tex].

Then [tex]10^4x=6704.67046704\ldots[/tex], and we have

[tex]10^4x-x=9999x=6704[/tex]

which means

[tex]x=\dfrac{6704}{9999}[/tex]

What are angle a and the 60-degree angle to one another?

Answers

The answer to this is vertical angles i just got finished taking it

A test was marked out of 80. A boy scored 60% of the marks on the test. How many marks did he score?

Answers

He score 48 marks.

This can be found by simply multiplying 80 by 60% (0.6). This will give you your rinal answer of 48.

I hope this helps!

A pet store has two tanks of tropical fish. The first tank contains 7 blue fish and 3 yellow fish and the second tank contains 10 blue fish and 8 yellow fish. If Keisha randomly purchases a fish from each tank, what is the probability that both fish will be blue? A. 1/70 B. 17/180 C. 7/18 D. 17/28

Answers

In the first tank we have 7 blue fish and 3 yellow fish, so total number of fishes in tank 1 = 10

The probability of picking a blue fish in tank 1 = number of blue fishes/ total number of fishes = 7/10

The second tank has 10 blue fish and 8 yellow fish, so the total number of fishes in tank 2 = 18

The probability of picking a blue fish in tank 2 = number of blue fishes/ total number of fishes = 10/18

The probability that both fish will be blue = 7/10 * 10/18 = 70/180 = 7/18 (Option C)

Leah pays $40 a month for cable TV, plus $4 for each movie she orders on pay-per-view. Which equation gives Leah’s total monthly cable bill as a function of the number of pay-per-view movies m that she orders?

Answers

m = movies
b = bill

b = 4m + 40

I hope this helps

An equation which gives Leah’s total monthly cable bill is b=4m+40.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Leah pays $40 a month for cable TV, plus $4 for each movie she orders on pay-per-view.

Let the number of pay-per-view movies she orders be m and the total monthly cable bill be b.

Now, b=4m+40

Therefore, an equation which gives Leah’s total monthly cable bill is b=4m+40.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ5

Suppose that a small town has seven burger shops whose respective shares of the local hamburger market are (as percent- ages of all hamburgers sold): 23 percent, 22 percent, 18 percent, 12 percent, 11 percent, 8 percent, and 6 percent. what is the four-firm concentration ratio of the hamburger industry in this town

Answers

SADNADDDDDDDDDDDDDSLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLDNNNNNNNNNNNNNNNNNNNNNNNNNNNNEL

If Jane has 3 3/4 dozen boxes of envelopes, and she ordered 11 1/2 dozen more, how many dozen boxes will she have in all?

Answers

Final answer:

Jane has a total of 61/4 dozen boxes of envelopes after adding the original 3 3/4 dozen with the additional 11 1/2 dozen she ordered.

Explanation:

If Jane has 3 3/4 dozen boxes of envelopes, and she orders 11 1/2 dozen more, we must add these two amounts together to find out how many dozen boxes she will have in all. First, we convert 3 3/4 to an improper fraction: 3 x 4 + 3 = 12 + 3 = 15, so 3 3/4 dozen becomes 15/4 dozen. Similarly, we convert 11 1/2 to an improper fraction: 11 x 2 + 1 = 22 + 1 = 23, so 11 1/2 dozen becomes 23/2 dozen.

Next, we add the two amounts of dozens of boxes together:

(15/4) dozen + (23/2) dozen

To add these fractions, we need a common denominator, which is 4, so we convert 23/2 to 46/4.

(15/4) dozen + (46/4) dozen = (61/4) dozen

So, in total, Jane will have (61/4) dozen boxes of envelopes.

a ice cream shop offers 5 different flavors of ice cream and 12 different toppings how many choices are possible for a single serving of ice cream with one topping

a. 18
b. 22
c. 46
d. 60
PLZ HELP

Answers

60 because 5 times 12 equals 60

Answer:

D)60

Step-by-step explanation:

All you do is multiply 5 by 12.

5x12=60

Question 2 (Matching Worth 4 points)

Match the sequence (term) with the correct type of sequence (definition).

Match Term Definition

128, 32, 8, 2, … A) Geometric, common ratio is 0.25

1, 3, 9, 27, … B) Geometric, common ratio is 3

5, 10, 15, 20, … C) Arithmetic, common difference is −3

20, 17, 14, 11, … D) Arithmetic, common difference is 5

Answers

Switch c, and d.
Which makes it so that the common difference between 5, 10, 15, 20 is 5.
Then the difference between 20, 17, 14, 11 ... is -3.
Other than that your correct

pls help with this pre-calc question on vectors!!

Answers

The answer is the option C, which is:

C. √29

The explanation of this exercise is:

To solve this problem you must apply the proccedure shown below:

1- You have that:

W (-2,8,-3) and X(1,4,-1)

2- Therefore, you can calculate the magnitude as below:

|WX|=√[(1-(-2)]²+(4-8)²+[(-1-(-3)]²)
|WX|=√29

Find the volume of the square pyramid to the nearest cubic unit. edge 10 ft; height 11 ft 1,467 ft3 1,100 ft3 550 ft3 367 ft3

Answers

we know that
[volume of square pyramid]=(1/3)*b²*h
where
b is the length side of the square base-----> 10 ft
h is the height-----> 11 ft
[volume of square pyramid]=(1/3)*10²*11----> 366.67 ft³-----> 367 ft³

the answer is
367 ft³

Aaron is rolling the fair number cubes. What is the probability both cubes show a 5

Answers

The probability of two dice being the same particular number is 1/6 x 1/6 = 1/36. This is not the same as saying that both dice are the same number. There are six different possible numbers, so that would be 6/36 or 1/6.

Brainly please

Help me with this algebra problem. Thank you :)

Answers

To solve this problem you must apply the proccedure shown below:

1. You must make a system of equations, as below:

2. Let's call:

x: the number of first class tickets bought.
y: the number of coach tickets bought.

3. Then, you have:

x+y=7 (First equation)
970x+370y=3790 (Second equation)

x=7-y

4. By substitution, you have:

970x+370y=3790
970(7-y)+370=3790
y=5

x=7-y
x=7-5
x=2

Therefore, the answer is:

- Number of first class tickets bought=2

- Number of coach tickets bought=5

A sporting goods store sells 2 fishing reels and 5 fishing rods for $195. Later, they sell 4 fishing reels and 3 fishing rods for $131. Find the price of each item.

Answers

Let
Fishing reel = x
Fishing rods = y

Therefore,
2x + 5y = 195 ---- 1
4x + 3y = 131 ---- 2

Solving 1 and 2 above;
Multiply expression 1 by 2 and subtract 2 from the results;
4x + 10y = 390
4x + 3y = 131
-------------------
0x + 7y = 259 => y = 259/7 = 37

Using the value of y in expression 1;
2x + 5(37) = 195
2x + 185 = 195
2x = 10
x = 10/2 = 5

Therefore, the price of fishing reels is $5 and fishing rods is $37.

Richard can read 1/4 of a book in 3/5 of an hour. At this rate, how much can Richard read in one hour

Answers

3/5 hour ⇒ 1/4 of the book

Find 1/5 hour:
1/5 hour ⇒ 1/4 ÷ 3 = 1/4 x 1/3 = 1/12 of the book

Find 5/5 (1 hour):
5/5 hour ⇒ 1/12 x 5 = 5/12 of the book

Answer: 5/12 of the book

Someone please help me?

Answers

(AE + ED) *AE = (CB+ AB) *AB

(4 + ED) * 4 = (4+5) *5

(4 + ED) * 4 = 45

4ED +16 = 45

4ED = 29
ED = 29/4 = 7.25

AD = AE + ED

AD = 4 + 7.25

AD = 11.25

Answer is A

A gazebo is located in the center of a large circular lawn with a diameter of 300 feet. straight paths extend from the gazebo to a sidewalk around the lawn. if two of the paths form a 45 angle, how far would you have to travel around the sidewalk to get from one path to the other? Round your answer to the nearest foot

Answers

1.To solve this problem you must apply the formula for calculate the arc length, which is:
arc length=2πr(central angle/360)
r=300 feet/2
r=150 feet
central angle=45°
2. When you substitute the values, you obtain
arclength=118 feet
The answer is: 118 feet

Answer: 118

Step-by-step explanation:

1.To solve this problem you must apply the formula for calculate the arc length, which is:

arc length=2πr(central angle/360)

r=300 feet/2

r=150 feet

central angle=45°

2. When you substitute the values, you obtain

arclength=118

Evaluate the following in polar and standard forms. Select all answers that apply. [3(cos(27°) isin(27°))]^5

Answers

Using De Moivre's formula

if z = a ( cos x + i sin x ) ⇒⇒⇒ ∴ z^n = a^n ( cos nx + i sin nx)

Part (1)
∴ [ 3 (cos 27° + i sin 27°) ]⁵ = (3⁵) ( cos 5*27° + i sin 5*27°)
= 243 ( cos 135° + i sin 135°) ⇒⇒⇒⇒ Polar form
=================================
Part (2)

The angle 135° in the second quadrant ⇒ sin is (+) and cos is (-)
and its reference angle = 180° - 135° = 45°
sin 45° = cos 45°= 1/√2 = (√2)/2
∴ sin 135° = (√2)/2    and cos 135° = -(√2)/2
∴ 243 ( cos 135° + i sin 135°) = 243 [ -(√2)/2 + i (√2)/2 ]

= - 243(√2)/2 + 243 (√2)/2 i ⇒⇒⇒⇒ standard form
===========================================
The correct answers are options (1) and (3)

option (1) ⇒⇒⇒ 243 ( cos 135° + i sin 135°) ⇒⇒⇒⇒ Polar form
option (3) ⇒⇒⇒ - 243(√2)/2 + 243 (√2)/2 i     ⇒⇒⇒⇒ standard form

A standard number cube is tossed. Find P (3 or odd)

A. 1/2
B. 2/3
C. 1/3
D. 1/6

Answers

Total number of possible outcomes = 6

Total number of outcomes with 3 or odd = 3
They are : 1, 3, 5

P(3 or odd) = 3/6 = 1/2

Answer: 1/2

E = event space = set of outcomes we want to happen
E = set of numbers that are either 3 or odd
E = {1, 3, 5}

S = sample space = set of all possible outcomes
S = set of all the values on the standard number cube (aka dice)
S = {1, 2, 3, 4, 5, 6}

There are 3 items in the event space out of 6 total in the sample space
Using math notation, we can say n(E) = 3 and n(S) = 6. The small n means "number". So writing "n(E)" means "number of items in the event space".

So,
P(3 or odd) = n(E)/n(S)
P(3 or odd) = 3/6
P(3 or odd) = 1/2

The probability as a fraction is 1/2, which is 0.5 in decimal form. This represents a chance of 50%. Note: since 3 is an odd number, saying "P(3 or odd)" is the same as just saying "P(odd)"

Answer: Choice A. 1/2

Anybody know the answer to this question?

Answers

I'm pretty sure it is 17.5

what does –x2 – 6x – 8 look like on a graph
The 2 is a power

Answers

Does this answer your question?

The equation -x^2 - 6x - 8 looks like this when graphed.

I hope this helps!

Please Help! 16 points!

The equation 1.6x − 2.2 = 1.4x can be transformed to form which of the following expressions?

Select one:

a. 3.0x = 2.2

b. 0.2x = −2.2

c. 3.0x = −2.2

d. 0.2x = 2.2

Answers

The answer is D, 0.2x = -2.2

You must simplify the equation using SADMEP, the reverse order of operations in which subtraction is the first step. Your goal is to isolate the variable.

First, subtract 1.6 from each side:

1.6x - 2.2 = 1.4x
-1.6x -1.6x
------ --------

This will get you to 0x - 2.2 = -0.2x, or -2.2 = -0.2x

This is equivalent to 2.2 = 0.2x

So, the equation can be simplified to 0.2x = 2.2

Hope this helps, let me know if you need anything else! :)

Answer:

Step-by-step explanation:

Does anyone know how to find x?

Answers

Hello!

We can solve this using trigonometric functions. We will be referring to the 70 degree angle. We need to solve for the hypotenuse. We have the length of the opposite side and need to find the hypotenuse. Therefore, we use the sine.

sin70=12/x

Since we cannot immediately solve for x, we will simplify this equation. We multiply both sides by x.

x(sin70)=12

Divide both sides by sin70.

x=12/sin70

Now we solve this equation.

12/sin70≈15.51

Therefore, x=15.51 cm.

I hope this helps!

x=15.51cm

70+90+x=180

Using differentiation from first principles, prove that the gradient of the line y=mx + c is m

Answers

[tex] \frac{dy}{dx} = m[/tex]
because when you differentiate, only the constant of the x remains (which is m in this case), and c being another constant independent of x, is 0 when differentiated. hence, since dy/dx is the gradient of the line, m is therefore the gradient

For a propular Broadway musical the theater box office sold 356 tickets at $80 apiece,275 tickets for $60 apiece and 369 tickes $45 apiece. How much money did the box office take in

Answers

The first step to solving this equation would be to how much they made for every apiece. To do this we must multiply the cost of the $80 apiece by how much they sold, as well multiplying the $45 apiece by how many they sold. And also the $60 apiece by the how many they sold.

$80 apiece × 356 tickets = ?

$60 apiece × 275 tickets = ?

$45 apiece × 369 tickets = ?

Now we must solve our equations.

$80 apiece × 356 tickets = $28,480

$60 apiece × 275 tickets = $16,500

$45 apiece × 369 tickets = $16,605

The next step would be to add up all the total costs of each apiece.

$28,480 + $16,500 + $16,605 = $61,585

So our answer is...

The box office took in a total of $61,585

The volumes of two spheres are in a ratio of 1:8. what is the ratio of their radii?

Answers

we know that

volume of a sphere=(4/3)*pi*r³

let
A-----> smaller sphere
B-----> larger sphere

VA=(4/3)*pi*rA³
VB=(4/3)*pi*rB³
VA/VB=1/8--------> (1/8)=[(4/3)*pi*rA³]/[(4/3)*pi*rB³]

(1/8)=[rA³]/[rB³]-----> (1/8)=[rA/rB]³-----> rA/rB=∛(1/8)----> rA/rB=1/2

the answer is
the ratio of their radii is (1/2)

Other Questions

Some people think wind power should be used for all the electricity in the united states. which argument could be used to dispute this idea? The wild type of a species represents the characteristics that prevail among individuals in natural conditions. For dogs, the wild type has a short body, upward-pointing ears, and a curly tail. Even though dachshunds are descended from the wild-type dog, they have long bodies, downward-pointing ears, and a straight tail. Which of these best explains how the shape of the dachshund came into being?Humans bred various dogs over many generations to select for the dachshund's shape.Humans created a gene for the dachshund shape, which they inserted into the DNA of a wild-type dog. Natural selection led to the shape of the dachshund over many generations.The unique shape of the dachshund spontaneously appeared during a single generation. Rand watched fearfully as each camper in front of him effortlessly scaled the rock wall. He had started sweating when Ted, the camp counselor, had said it was rock climbing day, but now that it was almost his turn, the sweat was pouring off him like a waterfall. You can't fall, he chanted to himself, they won't let you fall. But the closer he got to the and his turn, the more his hands began to shake.Which statement best describes describes the conflict in the passage?A. Rand doesn't want to climb the rock wall because he thinks he will look silly.B. Rand doesn't want to climb the rock wall because his hand are too sweaty.C. Rand doesn't want to climb the rock wall because he is afraid.D. Rand doesn't want to climb the rock wall because he is afraid Tad will drop him. I think its C Why is the Bataan Death March called a "death" march? Question 1: The sum of two consecutive even integers is 70. Find the numbers. Question 1 options: 28 and 32 30 and 40 33 and 37 34 and 36Question 2: Cat is 5 less than twice Dog's age. Cat is 11 years old. Find Dog's age.Question 2 options:8765Question 3: The sum of three consecutive numbers is 46. Find the numbers.Question 3 options:19, 20, and 2120, 21, and 2221, 22, and 2322, 23, and 24Question 4: What is the equation for the sum of three consecutive even numbers totaling 198.Question 4 options:n+n+1+n+2=198n+n+2+n+4=1983n=198n+3=198Question 5: What is the equation for the sum of four consecutive numbers totaling 86.Question 5 options:4n=86n+4=86n+n+1+n+2+n+3=86n+n+2+n++4+n+6=86Question 6: The perimeter of a rectangle is 150 cm. The length is 15 cm greater than the width. Find the dimensionsQuestion 6 options:length = 45 and width = 30length = 30 and width =45 length = 75 and width = 60length =60 and width =75 Question 7: A couch cost $825. If the state has a 10% sale's tax. What was the price of the couch before taxes?Question 7 options:785$750735700Question 8: A bicycle and a bicycle helmet cost 240 dollars. How much did each cost, if the bicycle cost 5 times as much as the helmet?Question 8 options:bike = $200 and helmet = $40bike = $160 and helmet = $80bike = $120 and helmet = $60bike = $100 and helmet = $90Please help. How do environmental factors contribute to evolution by natural selection? A car tire has a radius of 15 inches. Suppose the car is traveling at 60 miles per hour (1 mile = 5,280 feet). What is the approximate rate of spin, in revolutions per minute, of the tire? Round the answer to the nearest whole number. According to the essay "A Discourse on the Original and Progress of Satire," how does Dryden say that the fool would most likely react to satire written about him or her? A. He would embrace the truth. B. He would miss the point of it. C. He would find it funny. D. He would only see scorn and mocking. Baking soda is often used in experiments to neutralize vinegar. In the picture above, the beaker on the left contains a solution of vinegar. 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