How do I solve for X?

To describe a linear program for finding the largest axis-aligned square that lies entirely inside a polygon (p), we can define the decision variables, objective function, and constraints as follows:

Decision Variables:

Let x be the side length of the square.

Objective Function:

Maximize x. The objective is to find the largest possible side length for the square.

Constraints:

Square Within Polygon Constraint:

For each vertex (xᵢ, yᵢ) of the polygon p, we can define the following set of inequalities:

xᵢ ≤ x, for all vertices of the polygon.

These inequalities ensure that the square lies entirely within the polygon.

Square Symmetry Constraint:

To ensure that the square is axis-aligned, we can impose symmetry constraints. For example, if the coordinates of the center of the square are (c_x, c_y), then we can add the following constraints:

c_x ± (x/2) = constant, for fixed values of c_x.

c_y ± (x/2) = constant, for fixed values of c_y.

These constraints ensure that the sides of the square are parallel to the x and y axes.

Non-Negative Constraint:

x ≥ 0, to ensure a non-negative side length for the square.

By formulating and solving this linear program, we can find the optimal value for x, which represents the largest axis-aligned square that lies entirely within the given polygon p.

Learn more about function here:

https://brainly.com/question/30721594

#SPJ11

The measure of the first angle is x + 18, and the measure of the second angle is 2x. To find the measure of both angles, we can set up an equation based on the fact that the two angles form a linear pair.

A linear pair consists of two adjacent angles that form a straight line, totaling 180 degrees. In this case, the measure of the first angle is given as x + 18, and the measure of the second angle is given as 2x. To find the values of x and the measures of both angles, we can set up the equation (x + 18) + (2x) = 180, representing the sum of the two angles. Simplifying the equation, we have 3x + 18 = 180. Subtracting 18 from both sides, we get 3x = 162. Dividing by 3, we find x = 54. Substituting the value of x back into the expressions for the angles, the measure of the first angle is 54 + 18 = 72 degrees, and the measure of the second angle is 2 * 54 = 108 degrees. Therefore, the first angle measures 72 degrees, and the second angle measures 108 degrees.

Learn more about angles here:

https://brainly.com/question/31996286

#SPJ11

Answer:

Step-by-step explanation:

Answer:

$2.40

Step-by-step explanation:

Soooo if 5 stuffed animals = $12, then you would divide 12 by 5 and your answer would be 2.4

Answer:

x = 4, y = –5

Step-by-step explanation:

2x = 18 --------(1)

x-5y = 29. -------(2)

x = 5y + 29 -----(3)

just substitute for x in equation 1

2( 5y + 29) = 18

10y + 58 = 18

10y = 18 – 58

10y = –50

y = –5

since y = –5 we will just substitute for y in equation (2)

x = 5(–5) + 29

x = –25 + 29

x = + 4

Let's check if our answer is correct

x – 5y = 29

4 – 5(–5) = 29

4 + 25 = 29

29 = 29

LHS = RHS

please rate as brainliest

The integral of \(x^3/\sqrt(x^2+4)\) using trigonometric substitution is: \(8 * (1/3)tan^2\theta(1 + tan^2\theta)^(3/2) + C\), where θ is determined by x = 2tanθ, and C represents the constant of integration

What is integration?

Integration is a fundamental concept in calculus that involves finding the integral of a function.

To integrate the function \(\int(x^3/\sqrt(x^2+4))\) dx using a trigonometric substitution, we can use the substitution x = 2tanθ. Let's go through the steps:

Substitute x = 2tanθ. This implies \(dx = 2sec^2\theta d\theta.\)

Rewrite the integral in terms of θ:

\(\int((8tan^3\theta)/(\sqrt(4tan^2\theta+4))) * 2sec^2\theta d\theta.\)

Simplify the expression inside the square root:

\(\int((8tan^3\theta)/(2sec\theta)) * 2sec^2\theta d\theta.\\\\\int(8tan^3\theta) * sec\theta d\theta.\)

Simplify further:

\(16\int tan^3\theta sec\theta d\theta.\)

Apply the trigonometric identity: \(sec^2\theta = 1 + tan^2\theta\). Rearranging, we get: \(sec\theta = \sqrt(1 + tan^2\theta).\)

Substitute \(sec\theta = \sqrt(1 + tan^2\theta)\) in the integral:

\(16\int tan^3\theta * \sqrt(1 + tan^2\theta) d\theta.\)

Let u = tanθ, which implies \(du = sec^2\theta d\theta\). We can rewrite the integral in terms of u:

\(16\int u^3 * \sqrt(1 + u^2) du.\)

Now we have a rational power of u. We can use the substitution \(v = 1 + u^2\) to simplify it:

\(v = 1 + u^2\), which implies dv = 2u du.

Rewrite the integral using v:

\(16\int (u^3 * \sqrt v) * (1/2u) dv.\\\\8\int (u^2\sqrt v) dv.\)

Simplify and integrate:

\(8\int (u^2\sqrt v) dv = 8\int(u^2 * v^{(1/2)}) dv = 8\int u^2v^{(1/2)} dv.\)

Integrate \(u^2v^{(1/2)\) with respect to v:

\(8 * (1/3)u^2v^{(3/2)} + C.\)

Replace v with \(1 + u^2\):

\(8 * (1/3)u^2(1 + u^2)^{(3/2)} + C.\)

Substitute u = tanθ back into the expression:

\(8 * (1/3)tan^2\theta(1 + tan^2\theta)^{(3/2)} + C.\)

So, the integral of \(x^3/\sqrt(x^2+4)\) using trigonometric substitution is:

\(8 * (1/3)tan^2\theta(1 + tan^2\theta)^{(3/2)} + C,\)

where θ is determined by x = 2tanθ, and C represents the constant of integration

To learn more about integration visit:

https://brainly.com/question/30094386

#SPJ4

The ways in which companies can attract and retain employees are given below.

The term human resources (HR) refers to the department responsible for managing employee-related resources.

It's an essential partner in an organization's success.

Given is that to answer some ways in which companies can attract and retain employees.

The ways in which companies can attract and retain employees are -

Therefore, the ways in which companies can attract and retain employees are given above.

To solve more questions on employee benefits, visit the link below-

https://brainly.com/question/12143528

#SPJ1

Using quantifiers; a) ∀ student ∈ this class, ∃ exactly 2 mathematics classes ∈ this school that the student has taken and b) ∃ person, ∀ country ∈ the world (country ≠ Libya), the person has visited that country.

a) "Every student in this class has taken exactly two mathematics classes at this school."

In this statement, we have two main quantifiers:

Universal quantifier (∀): This quantifier denotes that we are making a statement about every individual student in the class. It indicates that the following condition applies to each and every student.

Existential quantifier (∃): This quantifier indicates the existence of something. In this case, it asserts that there exists exactly two mathematics classes at this school that each student has taken.

So, when we combine these quantifiers and their respective conditions, we get the statement: "For every student in this class, there exists exactly two mathematics classes at this school that the student has taken."

b) "Someone has visited every country in the world except Libya."

In this statement, we also have two main quantifiers:

Existential quantifier (∃): This quantifier signifies the existence of a person who satisfies a particular condition. It asserts that there is at least one person.

Universal quantifier (∀): This quantifier denotes that we are making a statement about every individual country in the world (excluding Libya). It indicates that the following condition applies to each and every country.

So, when we combine these quantifiers and their respective conditions, we get the statement: "There exists at least one person who has visited every country in the world (excluding Libya)."

In summary, quantifiers are used to express the scope of a statement and to indicate whether it applies to every element or if there is at least one element that satisfies the given condition.

Therefore, Using quantifiers; a) ∀ student ∈ this class, ∃ exactly 2 mathematics classes ∈ this school that the student has taken and b) ∃ person, ∀ country ∈ the world (country ≠ Libya), the person has visited that country.

To know more about quantifiers check the below link:

https://brainly.com/question/13146953

#SPJ4

a. The exact area of the circle is 16π square inches.

b. The approximate area of the circle is 50.24 square inches.

(a) The exact area of a circle can be calculated using the formula:

Area = π * radius^2

Given that the radius is 4 inches, we can substitute it into the formula:

Area = π * (4)^2

= π * 16

= 16π square inches

Therefore, the exact area of the circle is 16π square inches.

(b) To approximate the area of the circle using the ALEKS calculator, we can use the value of π provided by the calculator and round the answer to the nearest hundredth.

Approximate area = π * (radius)^2

≈ 3.14 * (4)^2

≈ 3.14 * 16

≈ 50.24 square inches

Rounded to the nearest hundredth, the approximate area of the circle is 50.24 square inches.

Learn more about radius at https://brainly.com/question/29165128

#SPJ11

Answer:under

Step-by-step explanation:

so if you do 54times 2 it is 108so then you do 16 times 108 and you get 1728

Answer:

flight is under the limit

Step-by-step explanation:

1 suitcase=16kg

2 suitcases=16kgx2=32kg

1 passenger has 32kg

54x32=1728kg

54 passengers have 1728kg

1728kg is less than 2250kg which means flight is under the limit

Answer:

A) 75 levels

B) Level 35

Step-by-step explanation:

A) 37 - (10 - 3) = 37 - 7 = 30

\(\frac{2}{5}\) = \(\frac{30}{x}\)

2x = 150

x = 75

B) Gym = 37 + 3 = 40

12\(\frac{1}{2}\)% = 12.5% = 0.125

40 x  0.125 = 5

40 - 5 = 35

The coordinates of the vertex are (-2, 2). The equation of the axis of symmetry is x = -2. The parabola opens downward.

We are given a graph. The graph represents a function. The function is quadratic in nature. We need to find the coordinates of the vertex. It is a downward parabola. The vertex of the parabola is its maximum.

The x-coordinate of the vertex of the parabola is -2. The corresponding y-coordinate of the vertex of the parabola is 2. Hence, the coordinates of the vertex are (-2, 2).

The graph shown is of a downward parabola. The axis of symmetry passes through the vertex and is parallel to the y-axis. The equation of the axis of symmetry is x = -2.

To learn more about vertex, visit :

https://brainly.com/question/29030495

#SPJ1

Answer:

67-63x

Step-by-step explanation:

Figure L is a translation of Figure J.

Option B is the correct answer.

We have,

Translation refers to the movement of an object in a certain direction without changing its shape, size, or orientation.

In other words,

The object is shifted or moved from one location to another in a straight line while maintaining its properties such as length, angles, and size.

Now,

Translation will give the same shape and size.

So,

Figure J has the same shape and size as Figure L.

Thus,

Figure L is a translation of Figure J.

Learn more about translation here:

https://brainly.com/question/12463306

#SPJ1

The expected return for Umbrella Company is .40.

Expected Return for Umbrella Company is calculated by the following formula;`ER = p1r1 + p2r2`

Where `ER` is the expected return, `p` is the probability and `r` is the return for each state.

Therefore, the expected return for Umbrella Company can be calculated as follows:

\($$ER = (.60 \times .20) + (.40 \times .70)$$$$

ER = .12 + .28$$$$

ER = .40$$\)

To know more about probability visit:

https://brainly.com/question/31828911

#SPJ11

An equivalent expression is an expression that is equal in value to a given expression. For example, consider the following expression: 4x + 2y

An equivalent expression is an expression that represents the same value as a given expression, regardless of the specific values of any variables that appear in the expression. Equivalent expressions can be obtained by applying the rules of algebra, such as the associative, commutative, and distributive properties.

This expression is equivalent to the following expressions:

2(2x + y)

2y + 4x

(4 + 2)x + 2y

All of these expressions are equivalent because they all represent the same value, regardless of the specific values of x and y. They can all be simplified to the same expression by applying the rules of the algebra.

To learn more about the equivalent expression, visit:

brainly.com/question/28170201

#SPJ4

The correct answer is option D) 22,25,33,35,37,40,45.

To create a box plot, we need to find the minimum value, the maximum value, the median, and the quartiles of the data set.

Now, let's check which of the given data sets matches the information provided in the box plot:

A) 22,29,34,36,39,45: This data set does not have a minimum value of 20 or a maximum value of 45, so it cannot be represented by the given box plot.

B) 20,30,35,40,45: This data set has the correct minimum and maximum values, but it does not have a median of 32.5 or an IQR of 10, so it cannot be represented by the given box plot.

C) 22,25,35,35,35,35,36,44,45: This data set has the correct minimum and maximum values and a median of 32.5, but it does not have an IQR of 10. The Q₁ and Q₃ values are also different from the given box plot, so it cannot be represented by the given box plot.

D) 22,25,33,35,37,40,45: This data set has the correct minimum and maximum values, a median of 32.5, and an IQR of 10. The Q1 and Q3 values also match the given box plot. Therefore, this data set could be represented by the given box plot.

So, the correct answer is option D) 22,25,33,35,37,40,45.

To know more about box plots follow

https://brainly.com/question/9283011

#SPJ1

Option 1 (not paying 100k) has a higher expected value of 108k, while Option 2 (paying 100k) has an expected value of 8k. Therefore, it would be more financially beneficial not to pay the 100k.

Your question is about a painting and whether it is an original or not. If it is an original, it is worth 500k, and if it is not, it is worth 10k. The probability that it is an original is 0.2. You have the option to pay 100k.

Based on the information provided, let's calculate the expected value of each option:

1. Option 1: Do not pay 100k:
  - Probability of it being an original: 0.2
  - Value if it's an original: 500k
  - Value if it's not an original: 10k
  - Expected value: (0.2 * 500k) + (0.8 * 10k) = 100k + 8k = 108k

2. Option 2: Pay 100k:
  - Probability of it being an original: 0.2
  - Value if it's an original: 500k - 100k (paid) = 400k
  - Value if it's not an original: 10k - 100k (paid) = -90k (negative value)
  - Expected value: (0.2 * 400k) + (0.8 * -90k) = 80k - 72k = 8k

Comparing the expected values, Option 1 (not paying 100k) has a higher expected value of 108k, while Option 2 (paying 100k) has an expected value of 8k. Therefore, it would be more financially beneficial not to pay the 100k.

Learn more about original painting https://brainly.com/question/33954884

#SPJ11

Answer:

$1,218

Step-by-step explanation:

In ordwe to figure this out you have to first change the % into a decimal 29% = 0.29

Then you will take his income per month and times it by the decimal

4,200x0.29=1,218

So the most he can spend on a house payment every month is 1,218 dollars

Answer:

B

Step-by-step explanation:

8 weeks, 2 sessions per week =16 sessions

45mins each = 16*45=720 mins = 12 hours

52 /12 =4.33 / hour

B: $4.33/hour is the closest to the charge per hour for the courses. Hence, the correct option is (B)

The total charge for the 8-week course is $52, which means each 45-minute session costs $52 / (2 sessions/week * 8 weeks) = $1.67.

To convert this to an hourly rate, we divide by 45 minutes to get an hourly rate of $1.67 / (45 minutes/hour) = $3.93/hour.

Therefore, the answer closest to this is $4.00/hour, which is not one of the options, but we can see that $3.93/hour is closest to option B: $4.33/hour.

To learn more about total charge, visit

https://brainly.com/question/18102056

#SPJ11

Answer:

52 miles per hour

Step-by-step explanation:

I think you're missing some info, so this is all I can help with right now

Answer:

Option B

Step-by-step explanation:

One of the  basic property of Rhombus is that its diagonal intersect each other in a way that they bisect each other and also make angle of 90 degrees

Angle RMS comprises of angle formed by the bisecting diagonals. Hence angle RMS is of 90 degrees.

Thus, option B is correct

0.42 > 0.4 > 0.19

Hope it helps..Thank you

Answer:

Step-by-step explanation:

The problem as stated asks for the limit as x approaches 2 of (0/x) -2.

As written, the limit is (0/2) -2 = -2.

Explanation: f(x) is a constant, so the numerator is 0. The ratio 0/x -2 is defined as -2 everywhere except x=0. So, the value at x=2 is 0/2 -2 = -2.

__

If you mean (f(2) -f(x))/(x -2), that limit is the limit of 0/(x-2) = 0 as x approaches 2.

Explanation: f(x) is a constant, so the numerator is 0. The ratio 0/(x-2) is zero everywhere except at x=2. The left limit and right limit are both 0 as x approaches 2. Since these limits agree, the limit is said to be 0.

__

If you mean f(x) = ln(x) and you want the limit of (f(2) -f(x))/(x -2), that value will be -1/2.

Explanation: The value of the ratio is 0/0 at x=2, so we can find the limit using L'Hôpital's rule. Differentiating numerator and denominator, we have ...

  lim = (-1/x)/(1)

The value is -1/2 at x=2.

Answer:

See Explanation

Step-by-step explanation:

B. Just saying, this is an estimate, yet it seems more logical.