A farmer plans to fence a rectangular garden next to a river. There will be no fence along the river side. Draw a picture of this situation. The pasture will contain 405,000 square meters. Find the dimensions of the garden that will require the least amount of fencing.

Answers

Answer 1

Answer:

x  =  450 m

y =  900 m

P (min)  = 1800 m

Step-by-step explanation:

Let´s call   "x"  and  "y" de sides of the rectangular garden, y is the side parallel to the river ( that is it will be fenced only one )

Then:

2*x + y = P        ( perimeter of the area)

And   x * y  = 405000 m²

y = 405000/ x

And P as a function of x is:

P(x) = 2*x +  405000/x

Tacking derivatives relative to x on both sides of the equation.

P´(x)  = 2  - 405000/x²

P´(x) =  0      2*x²  - 405000 = 0

x²  = 202500

x = 450 m

And y =  405000 / 450

y = 900 m

And

P(min) = 2*450 + 900

P(min) = 1800 m

We know P is minimm at x =450 snce the second derivative of P

P´´(x) = 405000*2*x / x⁴   is always positive

A Farmer Plans To Fence A Rectangular Garden Next To A River. There Will Be No Fence Along The River

Related Questions

Look at this graph:

What is the slope?

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answers

1/3, Slope is Rise over Run. Rises 10 runs 30, which makes it 10/30 or 1/3.
Ok so I took two points, one in the t axis and one random one that didn’t have a decimal. (0,70) (40,80)

M=y2-y1/x2-x1

M= 70-80/0-40

M= -10/-40 or 1/4

Use rise/run and that would be the slope.

Which set of mixed numbers has a difference less than 1?

Answers

It’s going to be A
the other answers gave a difference more than 1
Answer
A
Explanation
Others have a difference more than 1

Which of the following represents A U B?

(There's a venn diagram with a box around it

-in the box outside the diagram- 5, 11, 1, and 7
- in the circle labelled "A"- 3 and 9
-in the circle labelled "B"- 2, 4, 8, and 10
-in the middle portion where the circles overlap- 6 and 12)

Answer Choices
{6, 12}
{2, 3, 4, 6, 8, 9, 10, 12}
{1, 5, 7, 11}
{2, 3, 4, 8, 9, 10}​

Answers

Answer:

Step-by-step explanation:

Mofor bought 12 Avocados for $18. How many avocados can Stefan buy if he has $6

Answers

Answer:

4

Step-by-step explanation

Stefan can buy 4 apple with $6 because the apples are $1.50 each

use repeated subtraction to divide 93÷10​

Answers

Answer:

9r3

Step-by-step explanation:

93-10=83-10=73-10=63-10=53-10=43-10=33-10=23-10=13-10=3

so 93÷10=9 remainder of 3

Factor completely 3x^2+ 2x -1.
O (3x + 1)(x - 1)
O (3x + 1)(x + 1)
O (3x - 1)(x + 1)
O (3x - 1)(x - 1)

Answers

Answer:

option C

Step-by-step explanation:

[tex]3x^2+2x-1\\\\=(3x+a)(x+b)\\\\(3b+a)=2\\\\ab=-1[/tex]

and here we think of b=1 and a=-1

so we have

[tex](3x-1)(x+1)[/tex]

Choose the rule to describe the transformation:

D(-3, -4), C(-3, -1), B(0, -4)

to

D '(3, -4), C '(3, -1), B '(0, -4)



a. reflection across the y-axis

b. reflection across y = -x

c. translation: (x,y)LaTeX: \longrightarrow⟶(x + 4, y)

d. reflection across y = x

Answers

Answer:

a. reflection across the y-axis

What is the total cost or sale price to the nearest cent?
$65 Jacket; 35% Discount

Answers

22.75 will be the total sale price to the nearest cent. If this answers was helpful for you please mark as best thank you.

the area of square Garden is 625 metre square find its length its perimeter and find the cost of fencing it with 5 round at Rs 25 per metre​

Answers

Answer:

Length=25m

Parameter=100m

5 round cost RS 12500

Step-by-step explanation:

The area of a square

=x²

According to the question the equation is

x²=625

x=√625

x=25

The parameter is

25×4

100 meter

So

1 meter costs 25

100 " " 25×100

2500

1 round = 100 meter

So

5 round cost 2500×5

12500

Find the value of 3(5. 10 + 2).

Answers

Answer:

the value is

Step-by-step explanation:

=3(5.10+2)

=3(7.1)

=21.3

Answer:

3(5. 10+2)

Step-by-step explanation:

3(5.12)

3(60)

180

Hamburger-R-Us offers 8 toppings on its made to order burgers. you can order plain or any combination of toppings. How many types of burgers are possible?​

Answers

Step-by-step explanation:

For every topping, you can either "take-it or leave-it" for your burger. This means there are 2 options for every topping.

Hence number of possible burgers = 2⁸ = 256.

Describe the error in the simplification below.

2^4x2^5 = (2 • 2)4+5
= 49

Answers

Answer:

You need to multiply the exponents, then you can multiply the two factors.

Correct answer of the equation:

2^4 x 2^5, multiply exponents

16 x 32, multiply

= 512

A ball is drawn from a bag of 26 red and 12 yellow balls. The process is repeated 50 times, replacing each ball that is drawn. Which of the following statements about the distributions of counts and proportions is true?A. The count of drawing a yellow ball is not a binomial distribution.B. The count of drawing a red ball is a binomial distribution.C. The distribution of the count of drawing a red ball cannot be approximated with a normal distribution D. The distribution of the count of drawing a yellow ball from a sample size of 10 can be approacimated with a normal distribution.

Answers

Answer:

B. The count of drawing a red ball is a binomial distribution.

Step-by-step explanation:

The count of drawing a red ball can be gotten by binomial distribution because:

the chance of success; p = 26/50 and chance of no failure; q = 24/50

For example, If we want to find probability of getting 5 red balls out of 20 selections, we will use the binomial probability distribution formula;

P(X = 5) = C(20, 5) × p^(5) × q^(20 - 5)

This same procedure also applies if we want to get the probability of getting a number of yellow balls out of a number of selections from the bag.

Looking at the options, the best option that explains how it's binomial probability that works is option B

Answer:b

Step-by-step explanation:

If Sin theta=3/4,find the value of cos theta

Answers

Answer:

[tex]Cos \ \theta = \frac{\sqrt{7} }{4}[/tex]

Step-by-step explanation:

Given;

Sin θ = 3/4

To calculated Cos θ;

make a sketch of right-angled triangle with following sides;

opposite side = 3

hypotenuse side = 4

then, the adjacent  side will be calculated from Pythagoras theorem;

let the adjacent side = b

b² = 4² - 3²

b² = 16 - 9

b² = 7

b = √7

Therefore, Cos θ is now calculated as;

Cos θ = adjacent / hypotenuse

Cos θ = √7/4

[tex]Cos \ \theta = \frac{\sqrt{7} }{4}[/tex]

Therefore, [tex]Cos \ \theta = \frac{\sqrt{7} }{4}[/tex]

Let V(t) represent the values of a bank account, in thousands dollars, t years after the account is opened at the bank. Determine whether each statement below is true

Answers

Complete question is;

Let V(t) represent the value of a bank account, in thousands of dollars, t years after the account is opened at the bank. Determine whether each statement below is true. Select True or False for each statement.

V(0) = 2 means that the value of the bank account when it is opened is $2000

V(5) = 2.2 means that 2.2 years after the bank account is opened, its value is $5000

V(10) – V(5) = 0.4 means that the bank account grows by $400 between 5 and 10 years after its opening

Answer:

Statement 1: True

Statement 2: False

Statement 3: False

Step-by-step explanation:

We are told that the function V(t) represents the value of a bank account, in thousands of dollars, t years after the account is opened at the bank.

This means that if V(10) = 50, it means that the bank account is valued after 10 years is $50,000

From this little explanation, it's clear that only statement 1 is correct.

please help me i dont understand this ​

Answers

Answer:

Step-by-step explanation:

the range is the out put of the function.. what can y be.. in other words

so it's all real numbers...  :)

(a) Complete the table of values for y = 6 - 4x.

Please help ❤️

Answers

Answer:

[tex]\boxed{\begin{tabular}{|c|c|c|c|c|c|}\cline{1-6} \bf x & -1 & 0&1&2&3\\\cline{1-6} \bf y & 10& 6& 2&(-2)&-6 \\\cline{1-6}\end{tabular}}[/tex]

Step-by-step explanation:

Given equation to us is :-

[tex]\implies y = 6 - 4x [/tex]

So , here we can put different values of x in order to get different values of y .

Initial table given to us is ,

[tex]\begin{tabular}{|c|c|c|c|c|c|}\cline{1-6} \bf x & -1 & 0&1&2&3\\\cline{1-6} \bf y & & & 2&&-6 \\\cline{1-6}\end{tabular}[/tex]

Put x = (-1) :-

[tex]\implies y = 6 - 4x \\\\\implies y = 6 -4(-1) \\\\\implies y = 6 + 4 \\\\\red{\bf\implies y = 10} [/tex]

Put x = 0 :-

[tex]\implies y = 6 - 4x \\\\\implies y = 6-4(0) \\\\\implies y = 6 - 0 \\\\\pink{\bf\implies y = 6 }[/tex]

Put x = 2 :-

[tex]\implies y = 6-4x \\\\\implies y = 6 - 4(2) \\\\\implies y = 6 - 8 \\\\\blue{\bf\implies y = (-2)} [/tex]

Hence the final table would be :-

[tex]\begin{tabular}{|c|c|c|c|c|c|}\cline{1-6} \bf x & -1 & 0&1&2&3\\\cline{1-6} \bf y & 10& 6& 2&(-2)&-6 \\\cline{1-6}\end{tabular}[/tex]

What is the value of n in the equation below? a^n/a^3=a^9
3
6
12
27

Answers

The answer is definitely 6


O A. (-2, 1)
O B. (-2,-1)
O c. (-1,-2)
O D. (1.-2)

Answers

Answer:

the answer is C -1-2 to the equation

Joanna is building 2 square planter boxes in her garden . Each box is 2 yard wide . What is the total perimeter of the boxes ?

Answers

Answer:

16 yards

Step-by-step explanation:

Square: all sides are equalSquare: 4 sides totalPerimeter of square: 2 + 2 + 2 + 22 + 2 + 2 + 2 = 8 yardsPerimeter of second box: 2 + 2 + 2 + 2 = 8 yardsPerimeters in total: 8 + 8 = 16 yards

I hope this helps!

Baseball hat for
$22.90 at 5% sales tax

Answers

Answer:I got $21.76

Step-by-step explanation:

;-;

How can I find the area for a semi circle that is 11 inches tall, 4.8 inches wide and 3.7 feet long (if I’m not making to much sense, I have a reference photo here)

Answers

Answer:

195.36

Step-by-step explanation:

11 x 4.8 =52.8

52.8 x 3.7 = 195.36

A=195.36

please awnser asap asap

Answers

Answer:

d) 280

Step-by-step explanation:

40320/3=6720

8720/24=280

280 is the answer you are looking for

The daily output at a plant manufacturing chairs is

approximated by the function

f(L,K) = 453KL 3/5 chairs

where L is the size of the labor force measured in hundreds

of worker-hours and K is the daily capital investment in

thousands of dollars. If the plant manager has a daily budget

of $13,000 and the average wage of an employee is $9.00

per hour, what combination of worker-hours (to the nearest

hundred) and capital expenditures (to the nearest thousand)

will yield maximum daily production?

Answers

Complete Question

The daily output at a plant manufacturing chairs is  approximated by the function

[tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex] chairs

where L is the size of the labor force measured in hundreds

of worker-hours and K is the daily capital investment in  thousands of dollars. If the plant manager has a daily budget  of $13,000 and the average wage of an employee is $9.00  per hour, what combination of worker-hours (to the nearest  hundred) and capital expenditures (to the nearest thousand)  will yield maximum daily production?

a)200 worker-hours and $9000 in capital expenditure

b)1100 worker-hours and $3000 in capital expenditure

c)500 worker-hours and $8000 in capital expenditure

d)900 worker-hours and $5000 in capital expenditure

e)600 worker-hours and $6000 in capital expenditure

f)300 worker-hours and $10,000 in capital expenditure

Answer:

d)900 worker-hours and $5000 in capital expenditure

Step-by-step explanation:

From the question we are told that

Daily output at a plant manufacturing chairs is  approximated by the function  [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex]

Daily budget  of $13,000

Average wage of an employee is $9.00  per hour

a) Generally the function  [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex]  can be use to for (a)

Mathematically solving with L=200 K=9000

[tex]f(L=200,K=9000) = (45\sqrt[3]{9000})200^3^/^5[/tex]

[tex]f(L=200,K=9000) = 45*20.8*24[/tex]

[tex]f(L=200,K=9000) = 22464[/tex]

b)Generally the function  [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex]  can be use to for (b)

Mathematically solving with L=1100 K=3000

[tex]f(L=1100,K=3000) = (45\sqrt[3]{3000})1100^3^/^5[/tex]

[tex]f(L=1100,K=3000) = 45*14.4*66.8[/tex]

[tex]f(L=1100,K=3000) = 43286.4[/tex]

c)Generally the function  [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex]  can be use to find (c)

Mathematically solving with L=500 K=8000

[tex]f(L=500,K=8000) = (45*\sqrt[3]{8000})*500^3^/^5[/tex]

[tex]f(L=500,K=8000) = 45*20*41.63[/tex]

[tex]f(L=500,K=8000) =37467[/tex]

d)Generally the function  [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex]  can be use to find (d)

Mathematically solving with L=900 K=5000

[tex]f(L=900,K=5000) = (45*\sqrt[3]{5000})*900^3^/^5[/tex]

[tex]f(L=900,K=5000) = 45*17.09*59.2[/tex]

[tex]f(L=900,K=5000) =45577.88[/tex]

e)Generally the function  [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex]  can be use to find (e)

Mathematically solving with L=600 K=6000

[tex]f(L=600,K=6000) = (45\sqrt[3]{6000})600^3^/^5[/tex]

[tex]f(L=600,K=6000) = 45*18.17*46.4[/tex]

[tex]f(L=600,K=6000) =37974[/tex]

f)Generally the function  [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex]  can be use to find (e)

Mathematically solving with L=600 K=6000

[tex]f(L=300,K=10,000) = (45*\sqrt[3]{10,000})*300^3^/^5[/tex]

[tex]f(L=300,K=10,000) = 45*21.5*30.6[/tex]

[tex]f(L=300,K=10,000) = 29704.2[/tex]

Therefore the function f shows maximum at L=900 K=5000

Giving the correct answer to be

d)900 worker-hours and $5000 in capital expenditure

Luna's bill for lunch at a restaurant was $11. She left a 20% tip. What was the amount of the tip?

Answers

Answer:

$2.20

Step-by-step explanation:

If you want to leave a 20% tip, multiply the cost by 0.20 to get the tip amount or multiply the cost by 1.20 to get the total including tip.

A hexagon ABCDEF is shown.
С-115
D
B
145
Angle CDE is twice the size of angle DEF.
Work out the size of angle CDE.
You must show all your working.
E
160°
+
F

Answers

Answer:

140

Step-by-step explanation:

115+165+140+90=510

180*4=720 (sum of interior angles of hexagon)

115+165+140+90+x+2x=720

why 2x because i kept ANGLE DEF as x and ANGLE CDE is twice so 2x

510+2x+x=720

3x=210

x=210/3

x=70

ANGLE DEF IS 70

so  because ANGLE CDE IS TWICE ANGLE DEF thus 70*2=140

ANGLE CDE =140

The angle CDE is 140°.

What is a hexagon?

A hexagon can be defined as a closed two-dimensional polygon with six sides. Hexagon has 6 vertices and 6 angles.

According to the given problem,

We know,

Sum of the interior angles of a polygon is,

Sum = 180° (n - 2) where n is the number of sides,

Here n = 6 , then

Sum = 180° × 4 = 720°

Let ∠ DEF be x  

Therefore ∠ CDE = 2x,

Sum the interior angles,

⇒ 160 + 90 + 145 + 115 + 2x + x = 720

⇒ 510 + 3x = 720 ( subtracting 510 from both sides )

⇒ 3x = 210 ( dividing both sides by 3 )

⇒ x = 70

∠ CDE = 2x

           = 2 × 70

           = 140°

Hence, we can conclude, in the hexagon, the angle CDE is 140°.

Learn more about hexagon here:

https://brainly.com/question/2001860

#SPJ2

Which is the distance between the points M ( -21, -7)and N ( -5, -7)

Answers

Answer:

16

Step-by-step explanation:

becasue from -21 to -5 it's 16 units (-21 - -5= 16).

If f(x) = (4784), what is 13)?

Answers

Answer:

f(x)=4784

f(13)= 0 because there is x value on the right hand side

Is it true that m || n?
Your response should be at least 3 complete sentences. Be sure to include information about the slopes of the line and calculations. NO PLAGIARISM!!

Answers

Answer:

False

Step-by-step explanation:

Lines m and n are not parallel

See attached that shows vertical segment of 6 units, its longer than the distance between the lines on the right and its shorter on the left

Parallel lines should have same distance at any point between them

What is the surface area of an orange with a 3inch radius

Answers

Orange = sphere

S.A of sphere

= 4πr²

= 4 × π × r × r

[tex] = 4 \times \pi\times 3 \times 3[/tex]

[tex] = 36\pi[/tex]

Answer:

Step-by-step explanation:

the surface area of a sphere ( orange)

SA=4*3.14*r^2

radius=3

SA=4*3.14*3*3=113.04

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