A dairy farmer plans to enclose a rectangular pasture adjacent to a river. To provide enough grass for the herd, the pasture must contain 18 square meters. No fencing is required along the river. What dimensions will use the least amount of fencing?

Answers

Answer 1

Answer:

390 m (perpendicular to river) x 780 m (parallel to river)

Step-by-step explanation:

Let y be the length of the side parallel to the river, and let x be the length of the sides perpendicular to the river.

The total area and length of fence required are given by:

Rewriting the length of fence as a function of only x:

The value of x for which the derivate of L(x) is zero is the length of x that uses the least amount of fencing:

If x = 390 m, then:

The dimensions that will use the least amount of fencing are 390 m x 780 m


Related Questions

Calculate the perimeter of the semi-circle below. Use 3.14 to approximate π.



12 cm

Answers

37.902

Step-by-step explanation:

3.14x12+12

A square is drawn below. What is value of x

Answers

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

The opposite sides of a square are parallel, therefore the given angles are equal by ( Alternate interior Angle pair )

[tex]\qquad \sf  \dashrightarrow \:4x + 5 = 2x + 25[/tex]

[tex]\qquad \sf  \dashrightarrow \:4x - 2x = 25 - 5[/tex]

[tex]\qquad \sf  \dashrightarrow \:2x = 20[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 10[/tex]

Hence, correct choice is B

➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖

What fraction is equivalent to six tenths and has a denominator of 100?

Answers

Answer:

3/5

Step-by-step explanation:

3/5=6/10

3/5=60/100

the volume of this is cone 923.16 cm what is the radius of this cone

Answers

Hey there!

[tex] \rightarrow \sf{ r = \sqrt{3 \frac{v}{\pi \ h} }} \: \rm{or} \: \sf{v = \frac{1}{3} \pi \: {r}^{2} \times h}[/tex]

[tex] \rightarrow \sf{923.16 = \frac{1}{3} (3.14) {r}^{2} \times h}[/tex]

[tex] \rightarrow \sf{\: 1.046667 {hr}^{2} =923.16}[/tex]

[tex] \rightarrow \sf{ \frac{1.046667 {hr}^{2} }{1.046667} = \frac{923.16}{1.046667} }[/tex]

[tex] \rightarrow \: \sf{ {r}^{2} = \frac{923.16}{1.046667h}}[/tex]

[tex] \rightarrow \: \sf{ r = \sqrt{ \frac{923.16}{1.046667h}}}[/tex]

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Using the GCF factor the given expression 4m - 20
4(m - 5)
2(2m - 10)
4m - 20)
2(2m - 20)

Answers

Hey there!

Finding something that’s equivalent to: 4m - 20


Option A.
4(m - 5)

= 4(m) + 4(-5)

= 4m - 20

Possibly Option A. is your answer.

Option B.
2(2m - 10)

= 2(2m) + 2(-10)

= 4m - 20

Possibly Option B. could be your answer


Option C.
4(m - 20)

= 4(m) + 4(-20)

= 4m - 80

Optipn C. isn’t your answer


Option D.
2(2m - 20)

= 2(2m) + 2(-20)

= 4m - 40

Option D. also isn’t your answer just like Option C.

FACTORS OF: 4m - 20

4: 1,2,4, & m

20: 1,2,4,5,10,& 20


LIKE TERMS: 1,2,4


GCF: 4


Good luck on your assignment & enjoy your day!


~Amphitrite1040:)

which number is equivalent to 5√8 x 3√4

A. 15√2

B. 60√2

C. 30√3

D. 60√3​

Answers

Answer:

B

Step-by-step explanation:

5×sqrt(8)×3×sqrt(4) = 15×sqrt(8)×sqrt(4) = 15×sqrt(8)×2 =

= 30×sqrt(8) = 30×sqrt(4×2) =

= 30×2×sqrt(2) = 60×sqrt(2)

Can you guys work it out

Answers

Answer:

x ≤ 45

Step-by-step explanation:

x + 35 ≤ 80

  - 35    -35

x ≤ 45

I hope this helps!

Hello!

Let's solve this inequality.

x+35≤80

Subtract 35 from both sides:

x≤80-35

x≤45

It means "less than or equal to"

So all numbers less than or equal to will make this inequality true.

Hope everything is clear.

Let me know if you have any questions!

Always remember: Knowledge is power!

Andrew drinks 1.9 litres of water each day for three years. By rounding the amount of water an the number of days to one significant figure find the approximate amount of water he drinks during the three years. [One year = 365 or 366 days]

Answers

Answer:

2081days or 2086days

Step-by-step explanation:

1.9(365)=693.5

1.9(366)=695.4

693.5(3)=2080.5

695.4(3)=2086.2

How large a sample must a pollster take in order to estimate with 95% confidence and to within 3 percentage points, the proportion of voters who are in favor of a certain measure

Answers

Answer:   1068

========================================================

Work Shown:

[tex]n = \hat{p}*(1-\hat{p})\left(\frac{z}{E}\right)^2\\\\n \approx 0.5*(1-0.5)\left(\frac{1.96}{0.03}\right)^2\\\\n \approx 1067.111\\\\n \approx \boldsymbol{1068}\\\\[/tex]

Notes:

At 95% confidence, the z critical value is roughly z = 1.96 which is determined using a Z table.E = 0.03 to represent the 3% error. We're not told the value of [tex]\hat{p}[/tex], so we assume the most conservative estimate of 0.5Always round up to the nearest integer. The value 1067.111 is closer to 1067, but we round up to 1068 to clear the hurdle needed.

Help help help help help

Answers

Answer:

A' = (- 3, 0)

Step-by-step explanation:

[tex]A' = (x + 3, \: y - 2) \\ \\ \implies \: A' = ( - 6+ 3, \: 2 - 2) \\ \\ \implies \: A' = ( - 3, \: 0) [/tex]

Answer:

A' = (-3, 0)

Step-by-step explanation:

Pre-Image coordinate:

A (-6, 2)

Translation: (x, y) --> (x + 3, y - 2)

(-6 + 3, 2 - 2)

(-3 0)

Image coordinate:

A' = (-3, 0)

hope this helps!! p.s. i really need brainliest :)

the product of two consecutive odd number is 143 find those two odd numbers show ll workings

Answers

Answer:

11,13

11×13=143

Step-by-step explanation:

please mark me as brainlest

Consider the expression 1.1(1.3)x+4Which of the following is an equivalent expression?

Answers

Answer:

the equivalent expression is 1.1(1.3)^4 ×(1.3)^x

Answer:

d

Step-by-step explanation:

i took the test

The graph displays a linear function.

Answers

Answer:

[tex]y = -\frac{2}{3}x +0[/tex]  OR [tex]y = -\frac{2}{3}x[/tex]

Step-by-step explanation:

First, find the slope (m) using two points (0,0) and (-6, 4)

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{4-0}{-6-0} \\\\m=\frac{4}{-6}\\\\m=\frac{2}{-3}\\\\m=-\frac{2}{3}[/tex]

[tex]y=mx+b[/tex]

[tex]y = -\frac{2}{3}x +b[/tex]

Now, we find b using (-6, 4)

[tex]y = -\frac{2}{3}x +b[/tex]

[tex]4 = -\frac{2}{3}(-6) +b\\\\4 = \frac{12}{3} +b\\\\4 = 4 +b\\\\-4 -4\\\\0=b[/tex]

[tex]y = -\frac{2}{3}x +0[/tex]  OR [tex]y = -\frac{2}{3}x[/tex]

Hope this helps!

(2x+3)+(5x17)+90=180

Answers

Answer:

x=10

Step-by-step explanation:

Answer:

x is 10 degrees

Step-by-step explanation:

180-90=90

(2x+3)+(5x+17) = 90

7x+20=90

7x=70

x=10

Help help help help help hel

Answers

Answer:

12

Step-by-step explanation:

P = 8

Q = 16

The value of PQ = 16 - 8 = 8

Since M is the midpoint of PQ,

PM = MQ

PM + MQ = PQ

PM + PM = PQ

2 PM = 8

PM = 8 / 2

PM = 4

The value of M

= 8 + 4

= 12

Answer:

M = 12

Step-by-step explanation:

If you want to find the midpoint between the numbers 8 and 16, follow the simple steps below.

First, add the two numbers: 8 + 16 = 24

Secondly, divide the total by 2: 24/2 = 12

The midpoint between 8 and 16 is 12.

hope this helps!! p.s. i really need brainliest :)

What's the value of X in the figure


145 (degrees) X (2x + 15)

Answers

Answer:

x=65°

Step-by-step explanation:

2x + 15= 145

2x+15-15=145-15  (Subtract)

2x=130 (Simplify)

2x/2=130/2 (Divide)

x=65 ← (Answer)

^^

。☆✼★━━━━━ ( ~ ) ━━━━━━━★✼☆。

help The area of a square

Answers

Answer:

[tex]2551\dfrac{1}{2}[/tex]

Step-by-step explanation:

[tex]\bf l = 20\dfrac{\sf 1}{4} \ in = \dfrac{81}{4} \ in[/tex]

[tex]\bf w = 10\dfrac{1}{2} = \dfrac{21}{2} \ in\\\\\\h = 12 \ in[/tex]

Volume of rectangular prism = l*w*h

                                                 [tex]= \dfrac{81}{4}*\dfrac{21}{2}*12\\\\\\= 81 *\dfrac{21}{2}*3\\\\\\= \dfrac{5103}{2}\\\\\\= 2551 \dfrac{1}{2} \ cubic \ inches[/tex]

Answer:

[tex]\sf 2551\frac12 \ cubic \ inches[/tex]

Step-by-step explanation:

volume of a cuboid = width × length × height

Given:

[tex]\sf width=10\frac12 \ in[/tex][tex]\sf length=20\frac14 \ in[/tex][tex]\sf height=12 \ in[/tex]

Substituting given values into the formula for volume:

[tex]\sf \implies volume=10\frac12 \times 20\frac14 \times 12[/tex]

                  [tex]\sf =\dfrac{21}{2} \times \dfrac{81}{4} \times \dfrac{12}{1}[/tex]

                  [tex]\sf =\dfrac{21 \times 81 \times 12}{2 \times 4 \times 1}[/tex]

                  [tex]\sf =\dfrac{20412}{8}[/tex]

                  [tex]\sf =2551\frac12 \ in^3[/tex]

Order the numbers from least to greatest. −34, 0.5, 23,−73, 1.2 The order of the numbers from least to greatest

Answers

Answer:

-73, -34, 0.5, 1.2, 23

Step-by-step explanation:

Hope this helps:)....if not sorry for wasting your time and may God bless you:)

-73, -34, 0.5, 1.2, 23

Can someone help me out? I can't understand this shape. (Explanation also please). I'll mark brainliest

Answers

The surface area of the rectangular prism is 46m²

How to find surface area of a rectangular prism?

length = 4mwidth = 2.5mheight = 2m

Surface area of a rectangular prism = 2(width×length + height×length + height×width)

SA = 2(wl + hl + hw)

= 2(2.5×4 + 2×4 + 2×2.5)

= 2(10 + 8 + 5)

= 2(23)

= 46m²

Therefore, the surface area of a rectangular prism is 46m²

Learn more about surface area:

https://brainly.com/question/16519513

Is the data Jamaya collected a random sample if the population is books from her entire household? Why or why not? *Remember that Jamaya picked 15 books from her book shelf in her bedroom.

Answers

Using sampling concepts, it is found that it is not a random sample, as it considers only the books in her bedroom, hence books from other people in the household are likely to not be considered.

What is sampling?

It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which has to involve all groups in the population.

In this problem, a random sample should involve the books of all people in the household, not only Jamaya's. Hence, it is not a random sample, as it considers only the books in her bedroom, hence books from other people in the household are likely to not be considered.

More can be learned about sampling concepts at https://brainly.com/question/25122507

Can yall help me with the answers?

Answers

Answer:

Number 3 is B

Step-by-step explanation:

B is number 3

Answer:

Lakaka 1 by Lakaka 1 vx wfs

Two students each write a function, C(n), that they think can be used to find the number of circles needed to make the nth figure in the pattern shown.

Use the drop-down menus to explain why each function does or does not represent the number of circles needed to make the nth figure in the pattern.

Answers

The function that can be find used to find the number of circles needed to make the nth figure in the sequence is (C + 1) + 4.

How to calculate the sequence?

The sequence can be illustrated through the function (C + 1) + 4 where C is the previous number. For the third picture, the number of circles will be:

= (C + 1) + 4

= 5 + 4

= 9

The fourth term will be:

= 9 + 4

= 13

Therefore, each figure uses 4 circles more than the previous one.

Learn more about sequence on:

https://brainly.com/question/6561461

Answer:

Step-by-step explanation: This function can be used to find the number of circles needed to make the nth figure in the pattern.

Each figure uses 4 more circle(s) than the previous figure because an additional circle is added to the top, bottom, left, and right sides.

the other half i got incorrect.

Can someone please help me

Answers

(x-2)(2x+1)
On the x-axis y=0
x-2 = 0 or 2x + 1 = 0
x= 2 or 2x = -1
x= 2 or x = -1/2
Therefore the intercepts are
(2,0) and (-1/2 , 0)

Answer : 2nd Option

A cat weighs​8 1/4​pounds.

How many ounces does the cat weigh?

Answers

The answer is C 132oz

Answer:

132 ounces

Step-by-step explanation:

1 pound = 16 ounces

8 1/4 x 16 = 132

Help mee plsssssssss

Answers

Answer:

-3

Step-by-step explanation:

you can tell because 12-3=9 and 9 is the output. it's the same for the others. 15-3=12 and 20-3=17

What is the horizontal distance from the origin to the point (1,4)

Answers

Answer:

given ,

a point , let's say , A( 1 , 4 ) on the cartesion plane.

to find - the horizontal distance of the point from the origin.

[tex]\underline\bold{using \: Distance \: formula \:} \\ \\ d(AO) = \sqrt{( x_{2} - x_{1}) {}^{2} +( y_{2} - y_{1}) {}^{2} } \\ \\ d(AO) = \sqrt{(1 - 0) {}^{2} + (4 - 0) {}^{2} } \\ \\ d(AO) = \sqrt{1 + 4} \\ \\ d(AO) = \sqrt{5} units [/tex]

hope helpful :D

This trapezoid represents the base of a right prism that has a surface area of 1280 square feet. The sum of the lengths of the legs of the trapezoid is 52 feet. What is the height of the prism? Enter your answer in the box.

Answers

Answer:

El area del trapecio mresponde a la relación

                      A = 1/2(B + b)*h

                          B = base mayor

                           b = bas menor

                           h = altura

En el caso en esrudio

                                              250 = 1/2(B + 20)*10

                                     2*250/10 = B + 20

                                                50 = B + 20

                                        50 - 20 = B

                                                  B = 30

                                                                BASE MAYOR = 30 PIES

PLEASE HELP WILL MARK BRAINLIEST THANK YOU

Answers

Here is the answer: x=4

A coin is flipped 8 times. Find the probability of the event:
exactly 6 heads
A.0.4375
B.0.75
C.0.0039
D.0.109

Answers

b. 0.75 because if you flip it 8 times and get heads 6 times, the probability would be 6/8 and that would simplify to 3/4 (0.75).

Answer:

D. 0.109

Step-by-step explanation:

Just did the test, its not B

I need help with this question 80 pts

Answers

Answer:

65

Step-by-step explanation:

angle 2 is equal to angle 4, so that means angle 4 is also 130⁰.

130=2y

130/2=2y/2

65=y

Answer:

y = 65°

Step-by-step explanation:

Vertical Angle Theorem:  When two straight lines intersect, the opposite vertical angles are always equal (congruent) to each other.

⇒ m∠2 = m∠4

⇒ 130° = 2y

⇒ y = 130° ÷ 2

⇒ y = 65°

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