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A rancher has 200 feet of fencing to enclose two adjacent corrals

Arturiano [62]

Answer:

a) Each corral should be 33⅓ ft long and 25 ft wide

b) The total enclosed area is 1666⅔ ft²

Step-by-step explanation:

I assume that the corrals have identical dimensions and are to be fenced as in the diagram below

Let x = one dimension of a corral

and y = the other dimension

(a) Dimensions to maximize the area

The total length of fencing used is:

4x + 3y = 200

4x = 200 – 3y

x = 50 - ¾y

The area of one corral is A = xy, so the area of the two corrals is

A = 2xy

Substitute the value of x

A = 2(50 - ¾y)y

A = 100 y – (³/₂)y²

This is the equation for a downward-pointing parabola:

A = (-³/₂)y² + 100y

a = -³/₂; b = 100; c = 0

The vertex (maximum) occurs at

y = -b/(2a) = 100 ÷ (2×³/₂) = 100 ÷ 3 = 33⅓ ft

4x + 3y = 100

Substitute the value of y

4x + 3(33⅓) = 200

4x + 100 = 200

4x = 100

x = 25 ft

Each corral should measure 33⅓ ft long and 25 ft wide.

Step 2. Calculate the total enclosed area

The enclosed area is 50 ft long and 33⅓ ft wide.

A = lw = 50 × 100/3 = 5000/3 = 1666⅔ ft²

6 0

3 years ago

Use long division to find a repeated decimal equivalency for the fraction. Upload all of your work as part of your final answer.

Kay [80]

You would divide 8 by 9, because the is inside the bracket division sign.
Hope this helps!

3 0

3 years ago

Read 2 more answers

In a state where license plates contain six digits, what is the probability that the license number of a randomly selected car h

andre [41]

Answer:

Step-by-step explanation:

Given : In a state where license plates contain six digits.

Probability of that a number is 9 = $\dfrac{1}{10}$ [Since total digits = 10]

We assume that each digit of the license number is randomly selected .

Since each digit in the license plate is independent from the other and there is only two possible outcomes for given case (either 9 or not), so we can use Binomial.

Binomial probability formula: $P(X=x)=^nC_xp^x(1-p)^{n-x}$

, where n= total trials , p = probability for each success.

Let x be the number of 9s in the license plate number.

$X\sim Bin(n=6, p=\dfrac{1}{10}})$

Then, the probability that the license number of a randomly selected car has exactly two 9's will be :

$P(X=2)=^6C_2(\dfrac{1}{10})^2(1-\dfrac{1}{10})^{6-2}\\\\=\dfrac{6!}{2!(6-2)!}(\dfrac{1}{100})(\dfrac{9}{10})^4=0.098415$

Hence, the required probability = 0.098415

5 0

3 years ago

One counting number is 4 times great as a counting number.The product of the two number is 36.What is the sum of the two number

VARVARA [1.3K]

Answer:

The sum of the two numbers is 15

Step-by-step explanation:

Let the counting numbers be x and y.

Then we can write the following equations

x=4y.......1 (one is four times greater )

x(y)=36.....2 (the product of the two)

Putting equation 1 into equation 2, we get

4y(y)=36

${4y}^{2} = 36$

Dividing through by 4,we get

${y}^{2} = \frac{36}{4}$

${y}^{2} = 9$

Taking square root of both side, we obtain

y=3

Putting the value of y into equation , we get

x=4(3)=12

Hence the numbers are 3 and 12

Therefore the sum of the two numbers is 3+12=15

3 0

3 years ago

Determine the slope of the line that has the following coordinates: (-3,6) (4,-2)

AveGali [126]

-8/7 is the correct answer.

6 0

3 years ago

What is the value of x? Enter your answer in the box.