2. Suppose that you have 2000 yards of fencing with
to build two adjacent rectangular corrals.
a) Find the dimensions so that the total enclosed area is
as large as possible.
b) Find the maximum area.

Answer:

72

Step By Step Explanation:

The circumference of the circle 48.4 inches.

The circumference of a circle is the perimeter of the circle. Therefore, let's find the circumference of the circle as follows:

length of arc = ∅ / 360 × 2πr

where

Therefore, let's find the radius

length of arc = 35 / 360 × 2 × 3.14 × r

4.6 = 219.8 / 360 r

4.6 = 0.61055555555 r

divide both sides by 0.61

r = 4.6 / 0.6

r = 7.7 inches

Therefore,

circumference = 2 × 3.14 × 7.7

circumference = 48.356

circumference = 48.4 inches

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Answer:

complementary angles

Step-by-step explanation:

Complementary angles add to 90 degrees

Supplementary angles add to 180 degrees

A right angle is 90 degrees so they are complementary angles

The rectangle has a length of 8 units along the top and bottom sides, and a height of 6 units along the vertical sides.

A rectangle is a four-sided flat shape with four right angles (90 degree angles) between the sides. It is a type of quadrilateral, which means a shape with four sides.

To find the length of the sides of the rectangle, we can use the distance formula:

d = √((x2 - x1)²+ (y2 - y1)²)

Using the coordinates (-4,4) and (4,4) for the two endpoints of the top side of the rectangle, we get:

d = √((4 - (-4))² + (4 - 4)²) = 8

Since the top side has length 8 and there are two top and two bottom sides of equal length, the perimeter is:

20 = 28 + 2L

where L is the length of one of the vertical sides. Solving for L, we get:

L = (20 - 2*8)/2 = 2

Therefore, the length of the vertical sides of the rectangle is 2 units.

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The length of rectangle is 8 units on the x-axis, and the width of rectangle is 4 units along the y-axis.

The whole distance encircling a rectangle's edge is known as its perimeter. It is the total of the measurements of the rectangle's four sides.

The formula for calculating the perimeter P of a rectangle with length L and width W is as follows:

P = 2L + 2W

According to question:

To find the length of the sides of the rectangle, we can use the distance formula:

\(d = \sqrt{((x_{2} - x_{1} )^2+ (y_{2} - y_{1})^2)}\)

Using the coordinates (-4, 4) and (4, 4)

\(d = \sqrt{((4 - (-4) )^2+ (4 - 4)^2)}\) = 8 units

L (length) = 8 Units

So, the length of the horizontal sides (x-axis) of the rectangle is 8 units.

then, the top side has length 8 and there are top and bottom sides are equal length, the perimeter is: P = (8+8) + 2W

20 = 16 + 2W

where, L is the length of one of the vertical sides. Solving for L, we get:

W = (20 - 16)/2 = 2

So, the length of the vertical sides (y-axis) of the rectangle is 2 units.

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it is going to be 10'000

Step-by-step explanation:

Answer:

the answer is d

Step-by-step explanation:

the shape of it as well

The probability that both players show rock in the first round is 1/9 or 0.1111 (rounded to four decimal places).

In rock, paper, scissors there are three possible outcomes for each player: rock, paper, or scissors. Assuming both players choose randomly and independently of each other, each player has a 1/3 chance of showing rock in the first round.

To find the probability that both players show rock in the first round, we can use the multiplication rule of probability for independent events. The multiplication rule states that the probability of the intersection of two independent events is the product of their probabilities.

Therefore, the probability that both players show rock in the first round can be calculated as follows:

P(both show rock) = P(player 1 shows rock) x P(player 2 shows rock) P(both show rock) = 1/3 x 1/3 P(both show rock) = 1/9

So the probability that both players show rock in the first round is 1/9 or approximately 0.111.

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The slope of ascent of the flight is 0.04

From the question, we have the following parameters that can be used in our computation:

The above parameters can be represented as

(x, y) = (4.3, 4200) and (167.5, 36,700)

The slope is then calculated as

Slope = (y₂ - y₁)/(x₂ - x₁)

Where x and y are defined above

So, we have

Slope = (36700 - 4200)/(167.5 - 4.3)

Evaluate

Slope = 199.14 feet per mile

Recall that 5280 feet = 1 mile.

So, we have

Slope = 199.14 feet/5280 feet

Evaluate

Slope = 0.04

Hence, the required slope is 0.04

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Answer:

20° and 70°

Step-by-step explanation:

complimentary angle sum to 90°

let x be the compliment then the angle is 3x + 10 , so

x + 3x + 10 = 90 , that is

4x + 10 = 90 ( subtract 10 from both sides )

4x = 80 ( divide both sides by 4 )

x = 20

3x + 10 = 3(20) + 10 = 60 + 10 = 70

the 2 angle measures are 20° and 70°

Given:

The data are,

To find:

Sample variance and the Sample Standard Deviation

Explanation:

Using the formula,

Answer: A) 2 and a half B) 5 pints

Step-by-step explanation:

in 1 cup there are 16 table spoons.

a) 4tbsp (2 servings) times 10 (to reach 20 servings) =40 tbsp

40/16 =2.5

ANSWER A= 2 and a half cups of lemon juice.

in 1 pint there are 2 cups.

b)

1 cup = 1/2 a pint,

1/2 pint (2 servings) times 10 (to reach 20 servings) = 5 pints

ANSWER B= 5 pints of olive oil

Answer: exponential growth function

Step-by-step explanation:

The slope of the graph is equal to 1 for all x between x= 0 and x=3.

Starting at x=3 the function value y increases as x increases.

The slope of the graph is equal to 3 for x between x=3 and x=5

For x between x=0 and x=4, the function value of y is ≤ 0.

For x between x=4 and x=8 the function of value y is ≥ 0.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope (m) = (0 - 3)/(3 - 0)

Slope (m) = -3/3

Slope (m) = -1.

For x between x=3 and x=5, the slope is given by;

Slope (m) = (3 + 3)/(5 - 3)

Slope (m) = 6/2

Slope (m) = 3.

By critically observing the graph of this function, we can logically deduce that the function value of y is less than or equal to 0 for x between x=0 and x=4 and greater than or equal to 0 for x between x=4 and x=8.

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The solutions to these system of equations are given as follows:

1. x = 1, y = 7.

2. x = 0.5, y = 2.

3. x = 6, y = -2.

4. x = 3, y = 3.

A system of equations is a set of equations involving multiple variables that are related, and then operations are made to solve these equations and identify the numeric value of each variable in the context of a problem.

For item 1, it is already stated that the solution for x is x = 1, hence the solution for y is obtained as follows:

y = 2(1) + 5 = 7.

For item 2, we are given two equations for y, hence the solution for x is obtained as follows:

2x + 1 = 6x - 1

4x = 2

x = 2/4

x = 0.5.

Hence the solution for y is:

y = 2(0.5) + 1 = 1 + 1 = 2.

For item 3, from the second equation, we have that:

y = 4 - x.

Then the solution for x will be of:

2(x - 7) = 4 - x

2x - 14 = 4 - x

3x = 18

x = 18/3

x = 6.

The solution for y is:

y = 4 - 6 = -2.

For item 4, from the first equation, we have that:

y = 3x - 6.

Then, replacing on the second equation, the solution for x is obtained as follows:

x + 3(3x - 6) = 12

x + 9x - 18 = 12

10x = 30

x = 3.

Then the solution for y is:

y = 3x - 6 = 3(3) - 6 = 9 - 6 = 3.

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Answer:

60 miles

Step-by-step explanation:

Since 1 inch on the map equals 20 miles, you just have to multiply 3 by 20.

3x20=60

Answer:

\(Area =192\pi\)

Step-by-step explanation:

Given

\(\theta = 120^o\)

\(r =24\)

Required

The area of the shaded sector

This is calculated as:

\(Area =\frac{\theta}{360} * \pi r^2\)

This gives

\(Area =\frac{!20}{360} * \pi *24^2\)

\(Area =\frac{1}{3} * \pi *576\)

\(Area =\pi *192\)

\(Area =192\pi\)

The only automorphism of a well-ordered set is the identity.

To prove this statement, we need to show that any automorphism of a well-ordered set must be the identity function. An automorphism is a bijective function that preserves the order structure of the set.

Assume we have a well-ordered set (W, ≤), where W is the set and ≤ is the order relation.

Let f: W → W be an automorphism of the set.

We aim to prove that f is the identity function, i.e., f(x) = x for all x ∈ W.

Suppose, for contradiction, that there exists an element a ∈ W such that f(a) ≠ a.

Since f is a bijective function, there must exist some b ∈ W such that f(b) = a.

Since (W, ≤) is well-ordered, there is a least element c in the set {x ∈ W : f(x) ≠ x}.

Let d = f(c). Since f is an automorphism, f(c) ≠ c, and thus d ≠ c.

Since (W, ≤) is well-ordered, there is a least element e in the set {x ∈ W : f(x) = d}.

Consider the element f(e). Since f is a bijective function, there must exist some f^{-1}(f(e)) = e' ∈ W such that f(e') = f(e) = d.

By the definition of automorphism, f(f^{-1}(y)) = y for all y ∈ W. Applying this property to e', we have f(f^{-1}(f(e'))) = f(e') = d.

However, f^{-1}(f(e')) = e' ≠ c, and thus f(e') ≠ d. This contradicts the fact that e is the least element in the set {x ∈ W : f(x) = d}.

Therefore, our assumption that there exists an element a such that f(a) ≠ a is false.

Since we assumed f(a) ≠ a for arbitrary a ∈ W, it follows that f(x) = x for all x ∈ W.

Hence, the only automorphism of a well-ordered set is the identity function.

Therefore, we have proven that the only automorphism of a well-ordered set is the identity function.

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Answer:

Step-by-step explanation:

el

Steve is correct. Steve can find the difference in temperature between 7 AM and 12 PM on Wednesday by adding the distances from 0.

By using a number line, Steve can find the difference in temperature between 7 AM and 12 PM on Wednesday by adding the distances from 0. One temperature is negative and the other is positive, but by adding their distances, he can find the difference. Kelly's method of subtracting -5.1 from the temperature at 12 PM on Wednesday is not necessarily incorrect, but it does not give the exact difference in temperature between the two times. Therefore, using Steve's method, the change in temperature would be the sum of the distance from 0 to the temperature at 7 AM (which is 2.5) and the distance from 0 to the temperature at 12 PM (which is also 2.5), resulting in a difference of 5 degrees.

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Answer:

x = 6

Step-by-step explanation:

x + 2(4x-6) = 42

x + 8x - 12 = 42

9x = 42 + 12

9x = 54

9/9 x = 54/9

x = 6

The inverse of f(x) = x^(7/9) using exponential notation is f(x) = x^(9/7)

An inverse function in mathematics is a function that "undoes" another function.

In other words, if f(x) yields y, then y entered into the inverse of f yields the output x.

An invertible function is one that has an inverse, and the inverse is represented by the symbol f⁻¹.

The given function is of the form

f(x) = x^(7/9), this is equivalent to ⁹√x⁷

say f(x) = y, then

f(x) = y = x^(7/9)

y = x^(7/9)

solving for the inverse, of y = x^(7/9)

y = x^(7/9)

y^(9/7) = x

interchanging the letters

y = x^(9/7)

hence the inverse function is solved to be f⁻¹(x) = x^(9/7)

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Notice that:

Therefore, to compute the following terms we have to alternate between subtracting 5 and adding 3.

Then, the next number in the list is:

Answer: -4.

Answer:

f(-3) = 9

Step-by-step explanation:

Step 1: Define

f(-3) = x = -3

f(x) = x²

Step 2: Substitute and Evaluate

f(-3) = (-3)²

f(-3) = 9

The value of Sin(90) is equal to 1.

In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.

Given here: Sin(90) and to find the value using the unit circle

Rotate ‘r’ anticlockwise to form a 90° angle with the positive x-axis.

The sin of 90 degrees equals the y-coordinate(1) of the point of intersection (0, 1) of unit circle and r.

The value of sin 90 degrees can be calculated by constructing an angle of 90° with the x-axis, and then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of sin 90° is equal to the y-coordinate (1). ∴ sin 90° = 1.

Hence, Sin (90) is equal to 1.

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Answer:

the answer is D

Step-by-step explanation:

leshawna should've won season 1 PERIODT

6.51 × \(10^{-2}\) oz grain of spice weighs more than the particle of unobtainium.

Given that, the weight of a particle of unobtainium is \(2.66\times10^{-6}\) oz and the weight of a grain of spice is \(9.17\times10^{-4}\) oz.

We need to find how much more grain of spice weighs than the particle of unobtainium.

To determine the power or exponent of 10, let us understand how many places we need to move the decimal point after the single-digit number.

Now,  \(9.17\times10^{-4}\) - \(2.66\times10^{-6}\)

=9.17-2.66 × \((10^{-4}-10^{-6})\)

=6.51 × \(10^{-2}\)

Therefore, 6.51 × \(10^{-2}\) oz grain of spice weighs more than the particle of unobtainium.

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Answer:

C i-statistic,ii) statistics III) statistics iv) statistics v) statistics