a farmer plans to fence a rectangular pasture adjacent to a river. the pasture contains 125,000 square meters in order to provide enough grass for the herd. what dimensions will require the least amount of fencing if no fencing is needed along the river?

Answers

Answer 1

The required dimensions are 500 meters and 250 meter for the fencing to be minimum.

Uses for maxima and minima:

If a rectangle has dimensions x and y, then its area is equal to x and y, and its perimeter is equal to 2(x + y). The edge of a figure has anything to do with fencing. Use the idea of maxima and minima by combining all the variables into a single variable.

According to the given data:

Let the dimensions of the rectangular pasture be x and y.

Equate the area of the rectangle to 125,000 and solve for y.

Where:

xy = 125000

y = 125000/x

If one side of the rectangle is left out, figure out how much fencing or perimeter is needed.

P = 2(x + y) - x

= x + 2y.

Set y = 125000/x into obtained perimeter.

P = x + 2(125000/x).

= x + (2,50,000/x)

Differentiate P with respect to x.

dP/dx = 1 - (2,50,000/x²)

Equate the obtained derivative to 0 and solve for x (can not be negative).

1 - (2,50,000/x²) = 0

(2,50,000/x²) = 1

x² = 2,50,000

x = 500

Calculate the second derivative of P and set x = 500.

d²P/dx² = 1 - (2,50,000/x³)

= (2,50,000/x³)>0

Calculate y by setting x=500 into y = 125000/x .

y =  125000/x

y =  125000/500

y = 250

The required dimensions are 500 meters and 250 meter for the fencing to be minimum.

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Related Questions

What’s 9x38328292672

Answers

Answer:

344954634048

Step-by-step explanation:

Theres something called a caculator

Answer:

344954634048

Step-by-step explanation:

can i get brainliest

I need this answer as soon as possible

I need this answer as soon as possible

Answers

The perimeter is the distance all the way around. So it's the sum of the lengths of all 4 sides.

From the picture, you can clearly see the lengths of all 4 sides.

Writum down and adum up !


please answer
4. Suppose that for 3MA Forecast, my Mean Absolute Deviation (MAD) is \( 3.0 \) and my Average Error (AE) is \( -2.0 \). Does my forecast fail the bias test? a. Yes b. No

Answers

The answer is: a. Yes, the forecast fails the bias test.

To determine whether the forecast fails the bias test, we need to compare the Average Error (AE) with zero.

If the AE is significantly different from zero, it indicates the presence of bias in the forecast. If the AE is close to zero, it suggests that the forecast is unbiased.

In this case, the Average Error (AE) is -2.0, which means that, on average, the forecast is 2.0 units lower than the actual values. Since the AE is not zero, we can conclude that there is a bias in the forecast.

Therefore, the answer is:

a. Yes, the forecast fails the bias test.

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two times a number plus three equals one half of the number plus 30. What is the number?

Answers

Answer:

17 x 2 = 34

34 = 30 + 4

4 is and -0

Step-by-step explanation:

make-believe starny_xx :0

rounded to the nearest thousandth the number 0.00006132 is___​

Answers

Answer:

to the right of the decimal is tenths > hundredths > thousandths so since at the thousands place the following number is 0 you round down so the answer is 0

Step-by-step explanation:

(b) Part B
How many solutions does the following the system of equations have?

(b) Part BHow many solutions does the following the system of equations have?

Answers

Answer:

Its C.

Step-by-step explanation

:Took the test

5!, called 5 _______ is the product of all positive integers from _______ down through _______. by definition, 0!_______.

Answers

Answer:

120

Step-by-step explanation:

5!, called 5 factorial is the product of all positive intergers from 5 down though 1. by definition, 0! is 0.

Factorials are basically the number times itself-1 the 2 the 3 until it times it by itself-(itself-1). n!=n*(n-1)*n(n-2).....*n-(n-1).

For example 2!=2*1=2 and 6!=6*5*4*3*2*1=720

keep in mind that I am not an expert so the blanks I filled in might be wrong and the explanation might have errors

5!, called "5 factorial," is the product of all positive integers from 5 down through 1. By definition, 0! is equal to 1.

Factorial is a mathematical operation denoted by an exclamation mark (!). It represents the product of all positive integers from a given number down to 1. In the case of 5!, it is calculated as 5 × 4 × 3 × 2 × 1, resulting in the value of 120.

The exclamation mark notation allows us to represent the factorial of a number concisely. For example, 5! represents the factorial of 5. It is important to note that 0! is defined to be equal to 1. This is a special case in factorial calculations. While it may seem counterintuitive, it is defined this way to maintain consistency and enable certain mathematical calculations and formulas.

Therefore, 5! is the product of all positive integers from 5 down through 1, equaling 120, and 0! is defined to be 1.

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Find the value of x.​

Find the value of x.

Answers

Step-by-step explanation:

\( log_{x}(16) = 2 \\ 16 = {4}^{2} \\ x = 4\)

how many gallons of a 16%-salt solution must be mixed with 4 gallons of a 25%-salt solution to obtain a 20%-salt solution?

Answers

The gallons of 16%salt solution required to obtained 20% of salt solution is equal to 5 gallons.

Let us consider 'x' be the salt solution of 16%

And 'y' be the salt solution with 25%

Total gallons of salt used is equal to 4 gallons

Required salt solution = 20%

Equation formed as per given information :

16% of x + 25% of 4 = 20% of ( 4 + x )

⇒ ( 16 / 100 ) × x + ( 25 / 100 ) × 4 = ( 20 / 100 ) × ( 4 + x )

⇒ 0.16x + 1 = 0.8 + 0.20x  

⇒ 0.20x - 0.16x  =  1 - 0.8

⇒ 0.04x = 0.2

⇒ x  = 0.2 / 0.04

⇒ x =  20 / 4

⇒ x = 5 gallons

Therefore, 5 gallons of salt solution is required to obtained 20% of salt solution.

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Given z₁ = 4 cos(cos(π/4)+isin(π/4)) and z₂=2(cos(2π/3)+isin(2π/3)), i, find z₁z₂ ii, find z₁/z₂

Answers

z_1 and z_2 are complex number;

i) z₁z₂ = 8(cos(7π/12) + isin(7π/12))

ii) z₁/z₂ = 2(cos(π/12) + isin(π/12))

To calculate z₁z₂ and z₁/z₂, we need to perform the complex number operations on z₁ and z₂. Let's break down the calculations step by step:

i) To find z₁z₂, we multiply the magnitudes and add the angles:

z₁z₂ = 4cos(cos(π/4) + isin(π/4)) * 2cos(2π/3) + isin(2π/3))

= 8cos((cos(π/4) + 2π/3) + isin((π/4) + 2π/3))

= 8cos(7π/12) + isin(7π/12)

ii) To find z₁/z₂, we divide the magnitudes and subtract the angles:

z₁/z₂ = (4cos(cos(π/4) + isin(π/4))) / (2cos(2π/3) + isin(2π/3))

= (4cos((cos(π/4) - 2π/3) + isin((π/4) - 2π/3))) / 2

= 2cos(π/12) + isin(π/12)

i) z₁z₂ = 8(cos(7π/12) + isin(7π/12))

ii) z₁/z₂ = 2(cos(π/12) + isin(π/12))

Please note that the given calculations are based on the provided complex numbers and their angles.

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what is the factored form of 3x^2+9x=0

Answers

Answer:

3x(x + 3) = 0

Step-by-step explanation:

3x² + 9x = 0 ← factor out common factor of 3x from each term on the left

3x(x + 3) = 0 ← factored form

Which expression can be used to find the surface area of the following triangular prism?
5
5
2.
11
8.

Which expression can be used to find the surface area of the following triangular prism?552.118.

Answers

Answer:

214.

Step-by-step explanation:

To get Surface area take

(cross section area) × 2 +(perimeter of crossection area × length)

the cross section area is a triangle

so area of a triangle =1/2 base times height

1/2×8×2=8

let's get perimeter of cross section

the cross section is still at triangle so let's find its perimeter.

5+5+8=18

18×length of which is 11

18×11=198

and 188 + 16=214. that's the answer

maybe you can get a expression from the work that I've just done cuz I can't see the answers clearly in the picture you have taken.if you don't mind just send the picture back then I'll get the answer.

state the trigonometric substitution you would use to find the indefinite integral. do not integrate.
∫ (81+x^2)^−5 dx
X(θ) = ______

Answers

To find the trigonometric substitution for ∫ (81+x^2)^−5 dx, we can use x = 9tanθ.
This substitution is useful because it allows us to rewrite the expression in terms of trigonometric functions, which we can then integrate using trigonometric identities.
Therefore, X(θ) = 9tanθ.


To find the indefinite integral of the given function using trigonometric substitution, you'll need to choose an appropriate substitution. For the integral ∫ (81+x^2)^−5 dx, we can use the substitution:

x(θ) = 9 * tan(θ)

This is because we can relate x^2 to a trigonometric identity. After substituting, you would proceed with integration, but since you asked to not integrate, I'll stop here. So the trigonometric substitution for this problem is:

x(θ) = 9 * tan(θ)

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A measure of goodness of fit for the estimated regression equation is the.

Answers

A measure of goodness of fit for the estimated regression equation is the residual standard error (RSE)

It is a measure of goodness of fit for the estimated regression equation. It measures the average amount that the response variable (y) deviates from the estimated regression line, in the units of the response variable.

The RSE is calculated as the square root of the sum of squared residuals divided by the degrees of freedom. A smaller RSE indicates a better fit of the regression line to the data.

It represents the proportion of the variation in the dependent variable that is explained by the independent variable(s) in the model. The value of R-squared ranges from 0 to 1, with higher values indicating a better fit of the model to the data.

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Mary is determining the maximum quantity given the seasonality is constant. If the coefficients are 117t and −22.9906t
2
in a quadratic model, what is the maximum quantity that can be reached? 12.52 B 3 0.098 5.09

Answers

The maximum quantity that can be reached in a quadratic model can be determined by finding the vertex of the quadratic function. In this case, with coefficients of 117t and -22.9906t^2, the maximum quantity can be calculated.

To find the maximum quantity in a quadratic model, we need to locate the vertex of the quadratic function. The vertex is the point where the quadratic curve reaches its maximum or minimum value. In a quadratic equation of the form ax^2 + bx + c, the x-coordinate of the vertex can be found using the formula x = -b / (2a). In this case, the coefficients of the quadratic model are 117t and -22.9906t^2. Since there is no constant term, we can disregard it in this calculation. By substituting the values into the formula, we find that the x-coordinate of the vertex is -117 / (2 * -22.9906) = 2.5415.

To determine the maximum quantity, we need to substitute this value back into the quadratic equation. However, since the problem statement does not provide the complete quadratic equation or the context for the variable t, we cannot calculate the exact maximum quantity. Therefore, the specific value of the maximum quantity cannot be determined without additional information.

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Ryan's friends have organized a treasure hunt. He is using the map below to find the clues. The position of the last clue, which
leads to the treasure, is located at point (-2,4).
6
+
2
2
-2
He figures that the treasure is 3 units either to the east or south of the location of the last clue. Which of these could be the
location of the treasure?
OA. point (1, 4) or point (-2, 1)
OB. point (-5, 4) or point (-2, 1)
OC. point (1, 1) or point (-5,7)
OD. point (1, 4) or point (-2,7)

Ryan's friends have organized a treasure hunt. He is using the map below to find the clues. The position

Answers

Using translation concepts, it is found that the location of the treasure could be given by these following points:

A. point (1, 4) or point (-2, 1)

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

We consider that he is at point (-2,4), hence:

A shift east 3 units leads to point (1,4).A shift south 3 units leads to point (-2,1).

Hence option A is correct.

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A cloest contains 4 hangers with pants, 3 hangers with shirts and 2 hangers with coats. If you randomly asign an order of the hangers, what is the possibility of having all 4 hangers with pants next to eachother?

A) 3/368
B) 1/21
C) 3/315
D) 24/12096

Answers

Answer:

c answer

Step-by-step explanation:

if you calcolate you will get the answer 3/215

among those who answered the question (n students), what is the percentage of your classmates in favor of increasing tuition fees by 50 dollars to implement new security measures and ensure isla vista is safer during weekends? hereafter, let p denote that number.

Answers

To find the percentage of your classmates in favor of increasing tuition fees by $50 to implement new security measures, you need to know the number of classmates in favor (p) and the total number of students who answered the question (n).

The formula to calculate the percentage is: (p/n) * 100.
To calculate the percentage, divide the number of classmates in favor (p) by the total number of students who answered the question (n). Multiply the result by 100 to get the percentage. To calculate the percentage of your classmates in favor of increasing tuition fees by $50, you need to know the number of classmates in favor (p) and the total number of students who answered the question (n). Once you have these values, you can use the formula (p/n) * 100 to find the percentage. For example, if 20 out of 50 students are in favor of the fee increase, the percentage would be (20/50) * 100 = 40%. This means that 40% of the students who answered the question are in favor of the fee increase.

To find the percentage of your classmates in favor of increasing tuition fees by $50, divide the number of classmates in favor by the total number of students who answered the question and multiply by 100. This will give you the percentage.

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the sample proportion is always included in the confidence interval for population proportions. is this surprising?

Answers

It is not surprising that the sample proportion is always included in the confidence interval, as the sample proportion is considered as the estimate of the confidence interval.

Given a confidence interval what are the point estimate of the population mean and the margin of error?

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

The margin of error is the difference between the two bounds, divided by 2.

The point estimate is the sample proportion for a confidence interval of proportions, hence it is not surprising that the sample proportion is always included in the confidence interval for population proportions.

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under what circumstances is the point-biserial correlation used?

Answers

Answer: when one of the variables is dichotomous; when you need to measure the relationship between a continuous variable and a dichotomous variable.

Step-by-step explanation:

The graph shows the path of a diver's
jump from a diving board. Circle all
that apply:
A.The diver reaches maximum height at one se
B.The diving board is 25 meters high.
C.The diver hits the water at 3.5 seconds.
D.The diver's height is always decreasing
E.The vertex is the minimum of (1, 30).

The graph shows the path of a diver'sjump from a diving board. Circle allthat apply:A.The diver reaches

Answers

I think it’s A I don’t know

Someone help meee?
This is soo hard

Someone help meee?This is soo hard

Answers

Answer:

100

Step-by-step explanation:

angles CHF and EHI are congruent angles because CD is a straight line.

Therefore EHI must be 20 degrees.

angles DIG and EIH are congruent angles because CD is a straight line.

Therefore EIH must be 60 degrees.

Now that you know two of the three angles in the triangle HEI,

Total degrees in a triangle - EIH - EHI = HEI

180 - 60 - 20 = 100

the sum of a number and -2 is -9 . what is the number

Answers

Answer:

x=-7

Step-by-step explanation:

Translate into an equation.

“A number” + -2 = -9

Assign “a number” to be “x”

X+-2=-9

Add 2 on both sides to even it out and get x

X-2+2=-9+2

X=-7

The number is -7. :)

Answer:

-7

Step-by-step explanation:

Let's put this into an equation with x being the unknown number. Then use the reversed order of operations to find the value of x.

x + -2 = -9

   + 2   + 2

x = -7

Pls mark Brainliest with the crown

Writer the equal ratios 6:8,24:32,3/4:1

Answers

Answer:

12:16

48:64

3:4

12:16

48:64

3:4

Are your answers

Rachel works for a clothing store. She is paid $150 every week plus a 10% commission on any clothes that she sells.

Answers

Answer:

$165

Step-by-step explanation:

Rachel works for a clothing store. She is paid $150 every week plus a 10% commission on any clothes that she sells.

Let's find the total amount she is being paid per week

Amount paid originally = $150

Percentage Commission = 10%

Commission = 10% of 150

Commission = 0.1×150

Commission = $15

Total amount paid = originally amount + Commission

Total amount paid = $150+$15

Total amount paid =$165

Hence the amount paid to Rachel okus Commission is $165

sherry had $7/8$ of a cup of sugar in her kitchen, and then she used $1/2$ of a cup of sugar to make sweet tea. she used what fraction of her sugar to make sweet tea?

Answers

Sherry used 3/8 of her sugar to make sweet tea, which is the fraction obtained by subtracting 1/2 from 7/8.

The fraction of sugar that Sherry used to make sweet tea, we need to subtract the amount of sugar she used from the total amount of sugar she had.

Sherry had $7/8$ of a cup of sugar in her kitchen, and she used $1/2$ of a cup of sugar to make sweet tea.

To find the remaining amount of sugar, we subtract $1/2$ from $7/8$:

$7/8 - 1/2$

To subtract fractions, we need a common denominator. In this case, the common denominator is 8. We can rewrite $1/2$ as $4/8$:

$7/8 - 4/8$

Now we can subtract the numerators:

$3/8$

Therefore, Sherry used $3/8$ of her sugar to make sweet tea.

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What is the area of this trapezoid?

What is the area of this trapezoid?

Answers

To find the area of a trapezoid take half it’s height times the sum of it’s bases. Half of 6 = 3
3 x 16 = 48

In parallelogram RODY, angle R = (7x + 22) and angle O = ( 9x – 2 ) . What is the measure of angle R?

Answers

6Hello there. To solve this question, we'll have to remember some properties about parallelograms.

Given the parallelogram RODY, and the measure of the angles as functions of a variable x:

\(\begin{gathered} m\angle R=(7x+22)^{\circ} \\ m\angle O=(9x-2)^{\circ} \end{gathered}\)

We have to determine the measure of the angle R.

For this, we'll have to remember the following property about parallelograms:

The sides with one and two lines have the same measure, respectively.

Now imagine the following angles:

And that we move this triangle to the other side, that is:

With this, you notice that the angles might be supplementary, or mathematically it is the same as:

\(\alpha+\beta=180^{\circ}\)

We also know that the angle at R might be:

When we moved the triangle, we now have that:

\(m\angle R-(90^{\circ}-\alpha)=m\angle R-90^{\circ}+\alpha=90^{\circ}\Rightarrow m\angle R=180^{\circ}-\alpha=\beta\)

So the measure of the angle at O will be:

\(m\angle O=\alpha\)

In the end, we reached the equation we need to solve:

\(m\angle R+m\angle O=180^{\circ}\)

Plugging the measures in function of x, we get

\((7x+22)^{\circ}+(9x-2)^{\circ}=180^{\circ}\)

Add the values

\(16x+20^{\circ}=180^{\circ}\)

Subtract 20º on both sides of the equation

\(16x=160^{\circ}\)

Divide both sides of the equation by a factor of 16

\(x=10^{\circ}\)

Now, to find the measure of the angle R, simply plug the value of x:

\(m\angle R=(7\cdot10+22)^{\circ}=(70+22)^{\circ}=92^{\circ}\)

This is the answer we were looking for.

is:

With this, you notice that the angles might be supplementary, or mathematically it is the same as:

In parallelogram RODY, angle R = (7x + 22) and angle O = ( 9x 2 ) . What is the measure of angle R?
In parallelogram RODY, angle R = (7x + 22) and angle O = ( 9x 2 ) . What is the measure of angle R?
In parallelogram RODY, angle R = (7x + 22) and angle O = ( 9x 2 ) . What is the measure of angle R?

What is the Y-intercept of the following quadratic graph?
(1 Point)

What is the Y-intercept of the following quadratic graph?(1 Point)

Answers

Answer: 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

The red graph intersects the y-axis at (0, 1).  This is the "y-intercept."

Bill bought a shirt for $35.80 plus he paid an additional 7% in sales tax. What was the sales tax? * 10 points

Answers

Answer:

2.51

Step-by-step explanation:

The tax would cost 2.51 and in total would cost 38.31.

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