I need some help please

The missing values that make this statement true are as

x² + 9x + 14,  x² - 3x - 10

x² - 2x - 15,   x² + 10x + 21

What is the quadratic equation?

A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and x is the variable. The term "quadratic" comes from the Latin word "quadratus," which means "square."

First, let Xa, Xb, Xc, Xd = each factor

Xd = each factor which shows In the graph

Then, we can know that

Xa, Xb are the roots of x² + ___x + 14

Xb, Xd are the roots of x²= 3x - __

Xc, Xd are the roots of x² - __x - 15

Xa, Xc are the roots of x² + 10x + __

Xa * Xb = 14           Xd = 15/10 +Xa

Xb+ Xd = 3            14/Xa + 15/10 +Xa = 3

Xc* Xd = - 15          140 + 29Xa/Xa(10+Xa)

Xa + Xc = -10x        140 + 29Xa = 30Xₐ + 3Xₐ²

Xb = 14/Xa             3Xₐ² + Xₐ² - 140 = 0

14/Xa + Xd = 3       Xa1 = -7   Xa2 = 20/3

Xd = -15/-3             Xb1 = -2   Xb2 = 21/10

Xc = -10 -X1            Xc1 = -3    Xc2 = -30/3

Xc1 = -3     Xc2 = -30/3

Xd1 = 5         Xd2=9/10

There are two kinds of answers.

1) x² + 9x + 1x           Xa1 + Xb1 = -9

x² - 3x + 10           Xb1 * Xd1 = -10

x² - 2x - 15           Xc1 + Xd1 = 2

x² + 10x + 21           Xa1 * Xc1 = 21

2)

x² - (263/30)x + 14           Xa2 * Xb2 = 263/30

x² - 3x - (-189/100)           Xb2 * Xd2 = 189/100

x² - (413/30)x - 15           Xc2 + Xd2 = 413/30

x² + 10x + (1000/9)           Xa2 * Xc2 = 1000/9

Hence, the missing values that make this statement true are as

x² + 9x + 14,  x² - 3x - 10

x² - 2x - 15,   x² + 10x + 21

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Answer:

B.......................

Reflections, rotations, and translations are all transformations that change the position and/or orientation of a geometric figure.

In mathematics, reflection is a transformation that flips a figure over a line called the line of reflection. This line acts like a mirror, reflecting the original figure onto the opposite side of the line.

Reflections, rotations, and translations are all transformations that change the position and/or orientation of a geometric figure.

Reflections (also known as flips) change the orientation of a figure by flipping it across a line of reflection, which acts like a mirror.

Rotations change the orientation of a figure by rotating it around a fixed point. The figure stays the same shape and size, but its position and orientation in space changes.

Translations (also known as slides) change the position of a figure by sliding it along a straight line without changing its orientation or shape.

All of these transformations are important in geometry and other fields, such as physics and computer graphics, and can be used to describe the motion and properties of geometric objects.

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Step-by-step explanation:

given quadratic equation is

simplification,

by using,

[tex]y^\frac{1}{2} -6y^\frac{1}{4} +8=0

\\ y^\frac{1}{2} -6y^\frac{1}{4} = - 8 \\

[/tex]

[tex]square[/tex]

[tex] \\ {(y^\frac{1}{2} -6y^\frac{1}{4})}^{2} = {(- 8)}^{2}[/tex]

[tex]y + 36 {y}^{ \frac{1}{2}} \: [/tex]

Answer: 5kg

Step-by-step explanation:

If Ms. Walker has 15 kilograms of clay that she wants to distribute evenly among 3 students, all you need to do is divide 15 by 3. Doing so, we get:

15 kg / 3 = 5 kg

Therefore, each student will receive 5 kilograms of clay.

The mass of clay that each student will get is 5kg.

Here, the given questions ask for a solution that deals with the concept of  the basic principle of division. hence implementing the principle we can see that,

The given total amount of clay by Ms. walker is 15 kilograms(kg).

Furthermore, this total amount of clay needs to be divided equally between the  3 students.

Then, let the mass of clay given to each student equally be denoted by M in  the equation to find out the solution can be written as

M = Total amount of clay ÷ Total number of students

Then,

M = 15 ÷ 3

M = 5 kg

Therefore, The mass of clay that each student will get is 5kg.

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Answer:

Step-by-step explanation:

To calculate the amount of money Nathaniel needs to deposit today to fund this gift for his descendants, we can use the present value formula for a perpetuity:

Present Value = Annual Payment / Discount Rate

In this case, the annual payment is R380 000 and the discount rate (expected rate of return) is 6.45% in decimals, or 0.0645 as a fraction. So we can plug these values into the formula:

Present Value = R380 000 / 0.0645

This gives us a present value of approximately R5,899,225.68. Therefore, Nathaniel would need to deposit R5,899,225.68 today into the trust fund to provide R380 000 a year forever for his descendants, assuming a 6.45% expected rate of return.

Answer:1 and 2

Step-by-step explanation:

so, they asked 50 students and then that was later broke down to smaller groups.

10,15,25

so, for every 10 students will be one. 1 vote= 10 students.

also, the dinosaur had the greatest number of votes so that explains answer 2.

We will use sine function, and length of the opposite side is [tex]\frac{25\sqrt{3}}{2}$[/tex] feet.

To solve for the opposite side of the right triangle, we would use the sine function. In a right triangle, the sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse.

In this problem, we are given that one angle of the right triangle is 60 degrees and the hypotenuse is 25 feet. Let's label the opposite side as x and the adjacent side as y. Then we can use the sine function:

[tex]$\sin 60^\circ = \frac{x}{25}$[/tex]

Simplifying the left side, we have:

[tex]$\frac{\sqrt{3}}{2} = \frac{x}{25}$[/tex]

Multiplying both sides by 25, we get:

[tex]$x = \frac{25\sqrt{3}}{2}$[/tex]

Therefore, the length of the opposite side is [tex]\frac{25\sqrt{3}}{2}$[/tex] feet.

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Answer:

Matt's typing speed increased by 18.75%.

Step-by-step explanation:

To find the percent increase, we can use the following formula:

percent increase = (new value - old value) / old value x 100%

Using this formula, we can calculate the percent increase in Matt's typing speed as follows:

percent increase = (38 - 32) / 32 x 100%

percent increase = 6 / 32 x 100%

percent increase = 0.1875 x 100%

percent increase = 18.75%

The total distance that the water tanker has covered in March of 2022 is given as follows:

1860 kilometers.

Velocity is given by the change in the distance divided by the change in the time, hence the following equation is built to model the relationship between these three variables:

v = d/t.

The parameters for this problem are given as follows:

Hence the total distance is then obtained as follows:

d = v x t

d = 60 x 31

d = 1860 kilometers.

The complete question is:

"Assuming that the water tanker travels an average of 60 kilometers a day, calculate the total distance that the water tanker has covered in March 2022​".

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Answer:

It depends on the context of the problem and the interpretation of the ratio represented by the point (7, 8).

If we interpret the point (7, 8) as representing the ratio 7:8, then Adela's claim is incorrect. Adding the same number to both coordinates of the point would change the value of the ratio. For example, adding 1 to both coordinates would give the point (8, 9), which represents the ratio 8:9, which is not equivalent to 7:8.

However, if we interpret the point (7, 8) as representing a different type of ratio, such as the ratio of the distances from the point to two fixed points or the ratio of the areas of two shapes, then it may be possible to find an equivalent ratio by adding the same number to both coordinates of the point. In this case, Adela's claim could be correct.

Without more information about the context and interpretation of the ratio represented by the point (7, 8), it is difficult to determine the correctness of Adela's claim.

Step-by-step explanation:

y = x^2 / z      now triple x and z

y = (3x)^2 / 3z = 9x^2 / 3z = 3 * x^2 / z  <==== this is 3 times the original

    y is tripled

The type of transformation represented in the figure is the translation transformation i.e. (c) none of these

Given the triangles ABC and A'B'C'

The transformation between the triangles is translation

The translation transformation is a type of transformation that moves an object without changing its size, shape, or orientation.

This transformation involves sliding an object in a particular direction by a certain distance, either horizontally or vertically.

In this case, the direction is horizontally and vertically

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Because the x2 term's coefficient is positive, the function will rise without  equation bound as x approaches infinity or negative infinity. As a result, no horizontal asymptote exists.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9".

The y-intercept of the equation y = (0,0) is the point on the line where it meets the y-axis and corresponds to the value of y when x equals 0. As a result, the equation y = 0's y-intercept is (0,0).

An equation's domain is the set of all possible values of x for which the equation is defined.

a) Because there are no constraints on the potential values of x, the domain of the equation y = x2 - 4x is all real integers.

b) The domain of the equation y = 1/(x-4) includes all real numbers except x = 4, which is undefined since division by zero is undefined.

c) Because the term within the square root must be non-negative, the domain of the equation y = sqrt(x-3)(x-4) is x >= 3.

As x approaches a specific value, the graph of the function approaches but never reaches vertical asymptotes. As the denominator of a rational function hits 0, they arise.

Because y = (x-3)(x-4) is not a rational function, it lacks vertical asymptotes.

A function's horizontal asymptote is a horizontal line that it approaches when x approaches infinity or negative infinity.

The dominant term in the formula as x gets extremely large or very tiny is x2, thus we can rewrite the equation as [tex]y = x2 - 7x + 12[/tex]  .

Therefore, Because the x2 term's coefficient is positive, the function will rise without bound as x approaches infinity or negative infinity. As a result, no horizontal asymptote exists.

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The angles and lines that match the angles and lines in the diagram consisting of two lines and their common transversal to the correct description  are;

Alternate Interior Angles; 2. ∠4 and ∠8

Consecutive Exterior  Angles; 5. ∠1 and ∠6

Alternate Exterior Angles; 3. ∠1 and ∠5

Transversal; line l

Consecutive Interior Angles; 4. ∠3 and ∠4

Corresponding Angles; 1. ∠1 and ∠7

A transversal is a line that intersects two or more other lines.

The description of the relationship between the angles in the question are;

Alternate Interior Angles

Alternate interior angles are a pair of angles formed when a transversal intersects two lines. They are located between the two lines on opposite side of the transversal.

Consecutive Exterior Angles

Consecutive Exterior Angles are a pair of angles formed when a transversal intersects two lines. They are located outside the two lines on the same side of the transversal

Alternate Exterior Angles

Alternate exterior angles are a pair of angles formed when a transversal intersects two lines. They are located outside the two lines on the opposite sides of the transversal.

Consecutive Interior Angles

Consecutive Interior Angles, also known as Same-Side Interior Angles are a pair of angles formed when a transversal intersects two parallel lines. They are located between the two parallel lines on the same side of the transversal.

Corresponding Angles

Corresponding angles are a pair of angles formed when a transversal intersects two lines. They are located on the same relative positions with respect to the transversal and the two lines.

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In the equation y = 10 - 0.1x, the coefficient 0.1 represents the slope of the line.

it represents the rate of change of y with respect to x, which is the amount by which y changes for every unit increase in x.

In this case, the slope is negative (-0.1), which means that as the number of minutes on hold (x) increases by 1 unit, the level of satisfaction (y) decreases by 0.1 units.

In other words, the longer a customer spends on hold, the lower their level of satisfaction is likely to be. The slope is a key parameter in the equation and provides valuable information about the relationship between the two variables.

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Answer: 566.55 US dollars

Step-by-step explanation: i think, please give 5 stars

The graph is increasing from 0 minutes to 40 minutes, decreasing from 40 minutes to 80 minutes, and constant from 80 minutes to 200 minutes.

The rate of global warming is increasing. Every year, average global temperatures continue to rise, leading to more extreme weather events and disruptions to the environment. This has been caused by human activities, such as burning fossil fuels, which release carbon dioxide and other greenhouse gases into the atmosphere. These gases trap heat, leading to a rise in temperatures.

The domain of the relation is the set of all time values, ranging from 0 minutes to 200 minutes. The range of the relation is the set of all depth values, ranging from 0 feet to 8 feet.

The graph represents a function because for every value of time, there is exactly one corresponding value of depth.

The graph shows the depth of water in a horse trough over a certain amount of time. The graph starts at 0 feet and increases to a maximum of 8 feet over the first 40 minutes. After 40 minutes, the depth of the water starts to decrease until it reaches a minimum of 2 feet at 80 minutes. After 80 minutes, the depth of the water remains constant at 2 feet until the end of the graph at 200 minutes.

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The domain is all real numbers, The range is all real numbers and There is one y-intercept is true from the given option in context of all linear functions. option B. The domain is all real numbers, C. The range is all real numbers , and E. There is one y-intercept is right choice.

All linear functions have a domain that includes all real numbers, a range that includes all real numbers, and exactly

one y-intercept.

The rate of change of a linear function is non-zero only if the function is not constant (i.e. its slope is not zero).

However, there are linear functions that have a slope of zero, such as the function f(x) = 2, which is a horizontal line.

This means that statement A is not true of all linear functions.

Furthermore, there are linear functions that have no x-intercept (if the line is parallel to the x-axis) or that have more

than one x-intercept (if the line intersects the x-axis more than once).

Therefore, statement D is also not true of all linear functions.

The correct answers to this question are B. The domain is all real numbers, C. The range is all real numbers , and E. There is one y-intercept.

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Answer:

4/8 in lowest terms is 1/2.

Step-by-step explanation:

Answer: 1/2

4/8 is equivalent to 1/2

There are 1,350 desks in 45 classrooms that each have 6 rows of 5 desks.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Each classroom has 6 rows of 5 desks.

So the total number of desks in one classroom.

= 6 rows x 5 desks per row

= 30 desks

To find the total number of desks in 45 classrooms, we can multiply the number of desks in one classroom by the number of classrooms.

= 30 desks per classroom x 45 classrooms

= 1,350 desks

Therefore,

There are 1,350 desks in 45 classrooms that each have 6 rows of 5 desks.

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By using chi-squared test, we can conclude that there is evidence of an association between breed and milk yield at the 5% significance level.

What is chi-squared test?

To perform a chi-squared test for independence between breed and milk yield, we need to set up the hypotheses:

Null hypothesis: There is no association between breed and milk yield.

Alternative hypothesis: There is an association between breed and milk yield.

We will use a significance level of 0.05.

To calculate the expected counts for each cell, we will use the formula: (row total x column total) / grand total.

The observed counts and expected counts are:

The grand total is 100.

The degrees of freedom for the test are (number of rows - 1) x (number of columns - 1) = (2 - 1) x (3 - 1) = 2.

Using a chi-squared distribution table or calculator, we find the critical value for a chi-squared test with 2 degrees of freedom and a 0.05 significance level to be 5.99.

To calculate the test statistic, we use the formula:

chi-squared = [tex]sum((observed\ count - expected\ count)^2 / expected\ count)[/tex]

The calculated value of chi-squared is:

[tex]chi-squared = ((32-25.76)^2 / 25.76) + ((20-19.04)^2 / 19.04) + ((16-13.20)^2 / 13.20) + ((10-16.24)^2 / 16.24) + ((18-18.96)^2 / 18.96) + ((4-4.80)^2 / 4.80) = 10.92[/tex]

The degrees of freedom for the test are 2, and the critical value is 5.99.

Since the calculated value of chi-squared (10.92) is greater than the critical value (5.99), we reject the null hypothesis.

Therefore, we can conclude that there is evidence of an association between breed and milk yield at the 5% significance level.

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Answer:

  -15

Step-by-step explanation:

You want the average rate of change of g(x) = 3x² +3 on the interval [-9, 4].

The average rate of change is defined as ...

  AROC(g) = (g(b) -g(a))/(b -a)

We can evaluate this directly, or we can simplify it a bit first.

 AROC = ((3b² +3) -(3a² +3))/(b -a)

  = (3b² -3a²)/(b -a)

  = 3(b -a)(b +a)/(b -a)

  = 3(b +a)

The AROC on the interval [a, b] = [-9, 4] is then ...

  AROC = 3(4 +(-9)) = 3(-5)

  AROC = -15

__

Additional comment

In the attachment, a graphing calculator is used to evaluate the rate of change directly from the definition. It gives the same value, as expected.

Answer:

Step-by-step explanation:

The surface area of a sphere is given by the formula:

S = 4πr^2

where S is the surface area and r is the radius of the sphere.

We are given that the surface area of the sphere is 60 square feet. Using the formula above, we can solve for the radius:

60 = 4πr^2

Dividing both sides by 4π, we get:

15/π = r^2

Taking the square root of both sides, we get:

r = sqrt(15/π)

Using 3.14 as an approximation for π, we can evaluate this expression:

r ≈ sqrt(15/3.14)

r ≈ 2.20

Therefore, the best approximation for the radius of the sphere is 2.20 feet.

Answer:

Radius is 2.18

Step-by-step explanation:

;)

Answer:

1x

Step-by-step explanation:

Firstly lets expand the brackets for the equation

(x - 7 )2 = 36

If we multiply what's in the brackets by 2 we get this:

2x - 14 = 36

Add 14 to both sides:

2x = 50

Divide both sides by 2:

x = 25

Answer = 1x (Only possible solution

Answer:

The two solutions to the given equation are x = 13 and x = 1.

Step-by-step explanation:

To solve the given equation (x - 7)² = 36, begin by square rooting both sides:

[tex]\implies \sqrt{(x-7)^2}=\sqrt{36}[/tex]

[tex]\implies x-7=\pm6[/tex]

Now add 7 to both sides of the equation:

[tex]\implies x-7+7=\pm6+7[/tex]

[tex]\implies x=7\pm6[/tex]

Therefore, the two solutions are:

[tex]\implies x=7+6=13[/tex]

[tex]\implies x=7-6=1[/tex]

Answer:

Step-by-step explanation:

To find the LCM of the given expressions, we need to factor each expression completely and then find the product of the highest powers of all the factors.

ax² - (a² + ab)x + a²b can be factored as:

ax² - (a² + ab)x + a²b = a(x - b)(x - a)

bx² - (b² + bc)x + b²c can be factored as:

bx² - (b² + bc)x + b²c = b(x - c)(x - b)

cx² - (c² + ac)x + c²a can be factored as:

cx² - (c² + ac)x + c²a = c(x - a)(x - c)

Now, the LCM is the product of the highest powers of all the factors.

The highest power of a is a², the highest power of b is b², and the highest power of c is c². So, the LCM is:

LCM = a²b²c²(x - a)(x - b)(x - c)

Therefore, the LCM of ax² - (a² + ab)x + a²b, bx² - (b² + bc)x + b²c and cx² - (c² + ac)x + c²a is a²b²c²(x - a)(x - b)(x - c).

The slope for the given point through which it passes through the graph is [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex] = infinity .

What about slope?

The slope of a line is a measure of its steepness. It is defined as the ratio of the vertical change (rise) between two points on the line to the horizontal change (run) between the same two points. In other words, it is the rate at which the line rises or falls as we move along it in the horizontal direction.

Define graph:

In mathematics, a graph is a visual representation of a set of data or mathematical relationships between variables. Graphs can be used to display and analyze data in a variety of formats, including line graphs, bar graphs, scatter plots, and pie charts.

According to the given information:

As, we know that the slope =  [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

⇒ In which the point given are (-1,8) and (-1,-4)

By putting the value of the given point we have that

⇒ [tex]\frac{-4-(8)}{-1-(-1)}[/tex] = infinity.

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The blanks of the number pyramid puzzle can be filled with numbers calculated below.

A number pyramid puzzle is a type of mathematical puzzle where a pyramid-shaped grid of numbers is given, with some of the numbers missing.

Check the attached image for labeling. Since each number is the product of the two numbers directly beneath it. We can say:

m = -4 * 0.5 = -2

k = 0.5 * 1/8 = 1/16

x * (-1/8) = 8

x = 8/(-1/8)

x = -64  

y = x * 1/8

y = -64 * 1/8

y = -8

j = m * k

j =  -2 * 1/16 = -1/8

p = -48 * m

p = -48 * (-2) = 96

n = y * 8

n = -8 * 8 = -64

t = p * j

t = 96 * (-1/8) = -12

w = -1/2 * n

w = -1/2 * (-64) = 32

c = t * 1/16

c = -12 * 1/16 = -3/4

u = 1/16 * w

u = 1/16 * 32 = 2

d = c * u

d = -3/4 * 2 = -3/2

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The differentiation of the variable y is equal to  [tex]\frac{1}{2} ( \frac{y^{2}-4x^{3}-4xy^{2} }{2x^{2} y+2y^{3}-xy } )[/tex]  for the differential equation.

Given equation: [tex](x^{2} +y^{2} )^{2} = 2xy^{2}[/tex]

differentiate with respect to x

2 [tex](x^{2} + y^{2})[/tex] [ [tex]2x+2y.\frac{dy}{dx}[/tex] ] =[ (1).[tex]y^{2}[/tex] + [tex]x (2y) + \frac{dy}{dx}[/tex] ]

4 [tex](x^{2} + y^{2})[/tex] [ [tex]x+y \frac{dy}{dx}[/tex] ] = [tex]y^{2}[/tex] + [tex]2xy \frac{dy}{dx}[/tex]

4( [tex]x^{3} + x^{2} y \frac{dy}{dx} + xy^{2} + y^{3} \frac{dy}{dx}[/tex] ) = [tex]y^{2}[/tex] + [tex]2xy \frac{dy}{dx}[/tex]

[tex]4x^{3} +4 x^{2} y \frac{dy}{dx} +4 xy^{2} +4 y^{3} \frac{dy}{dx}[/tex] = [tex]y^{2}[/tex] +  [tex]2xy \frac{dy}{dx}[/tex]

[tex]4x^{2}y \frac{dy}{dx}[/tex] + [tex]4y^{3}[/tex] [tex]\frac{dy}{dx}[/tex] - [tex]2xy\frac{dy}{dx}[/tex] = [tex]y^{2} - 4x^{3} - 4xy^{2}[/tex]

[tex](4x^{2}y + 4y^{3} - 2xy )[/tex]  [tex]\frac{dy}{dx}[/tex] =  [tex]y^{2} - 4x^{3} - 4xy^{2}[/tex]

[tex]\frac{dy}{dx}[/tex]  = [tex]y^{2} - 4x^{3} - 4xy^{2}[/tex] / [tex](4x^{2}y + 4y^{3} - 2xy )[/tex]

[tex]\frac{dy}{dx}[/tex] = [tex]\frac{1}{2} ( \frac{y^{2}-4x^{3}-4xy^{2} }{2x^{2} y+2y^{3}-xy } )[/tex]

Hence solved. The differentiation for the given differential equation is done using the technique of implicit differentiation. The differentiation of the variable y is equal to  [tex]\frac{1}{2} ( \frac{y^{2}-4x^{3}-4xy^{2} }{2x^{2} y+2y^{3}-xy } )[/tex]  for the differential equation.

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