What is the slope of the line?

The equation \(4x^2u^n + (1-x^2)u = 0\) has two solutions. One solution is given by \(u_1 = x^{1/2}\left(1 + \frac{x^2}{16} + \frac{x^4}{1024} + \dots\right)\). The other solution is not provided in the given question.

To find the solutions, we can rewrite the equation as \(u^n = -\frac{1-x^2}{4x^2}u\). Taking the square root of both sides gives us \(u = \pm\left(-\frac{1-x^2}{4x^2}\right)^{1/n}\). Now, let's focus on finding the positive solution.

Expanding the expression inside the square root using the binomial series, we have:

\[\left(-\frac{1-x^2}{4x^2}\right)^{1/n} = -\frac{1}{4^{1/n}x^{2/n}}\left(1 + \frac{(1-x^2)}{4x^2}\right)^{1/n}\]

Since \(|x| < 1\) (as \(x\) is a fraction), we can use the binomial series expansion for \((1+y)^{1/n}\), where \(|y| < 1\):

\[(1+y)^{1/n} = 1 + \frac{1}{n}y + \frac{1-n}{2n^2}y^2 + \dots\]

Substituting \(y = \frac{1-x^2}{4x^2}\), we get:

\[\left(-\frac{1-x^2}{4x^2}\right)^{1/n} = -\frac{1}{4^{1/n}x^{2/n}}\left(1 + \frac{1}{n}\cdot\frac{1-x^2}{4x^2} + \frac{1-n}{2n^2}\cdot\left(\frac{1-x^2}{4x^2}\right)^2 + \dots\right)\]

Simplifying and rearranging terms, we find the positive solution as:

\[u_1 = x^{1/2}\left(1 + \frac{x^2}{16} + \frac{x^4}{1024} + \dots\right)\]

The second solution is not provided in the given question, but it can be obtained by considering the negative sign in front of the square root.

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Answer:

The answer is -9

Step-by-step explanation:

Answer:

-9

Step-by-step explanation:

40-52+3

=> -12+3

=> -9

Answer:

The first one is 6√10

The second one is −48√3

The last one is 28√2

Step-by-step explanation:

Answer:

lol sorry for answer what's that

One error-detection method that can compensate for burst errors is the cyclic redundancy check (CRC).

This method involves adding extra bits to the data being transmitted, which can detect and correct errors in the data. and has error detection. CRC is particularly effective in detecting and correcting burst errors, which occur when a group of consecutive bits are corrupted in a data transmission.

An error-detection method that can compensate for burst errors is the "Reed-Solomon code". Reed-Solomon codes are block-based error correcting codes that can detect and correct multiple errors in data transmissions, making them highly effective in handling burst errors. These codes compensate for burst errors by using redundant information added to the original data, allowing the receiver to accurately reconstruct the original data even in the presence of errors.

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Answer:

82 yd²

area of rectangle:

Length * Width

area of 2nd rectangle

area of triangle

total:

Answer:

9 attendees

Step-by-step explanation:

1+4=5

46/5=9 R1 the slash is dividing it hope it help's

Answer:

9 attendees

Hope I helped

Independent variables are the factors that are manipulated or controlled by the researcher in a study. In the context of investigating the impact of a school nutrition program on grade performance of high school students, the independent variable would be the school nutrition program itself.

The researcher would design and implement the program, and this variable would be under their control.

Dependent variables, on the other hand, are the outcomes or variables that are measured in a study and are expected to change as a result of the independent variable. In this case, the dependent variable would be the grade performance of the students. The researcher would collect data on the grades of the students before and after the implementation of the nutrition program, and this would be the variable that is expected to be influenced by the independent variable.

In summary, the independent variable in this research design is the school nutrition program, while the dependent variable is the grade performance of the students. The researcher would manipulate the independent variable (implement the nutrition program) and then measure the dependent variable (student grades) to determine if there is an impact of the program on grade performance.

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The cold will it get if it' 50c outside and the temperature will drop 70c in next 3 hour is -20 c.

Given:

If it' 50 c outside and the temperature will drop 70 c in next 3 hour.

Temperature (cold) = present temperature - temperature in next 3 hour.

= 50 - 70

= -20 c.

Therefore the cold will it get if it' 50c outside and the temperature will drop 70c in next 3 hour is -20 c.

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The Probability Density Function (PDF) for a uniform distribution ranging between 3 and 5 is 0.5. Answer is option C.

In a uniform distribution, the probability of a random variable taking any value between the two endpoints of the interval is constant. The probability density function (PDF) of a uniform distribution is a constant value over the range of possible values, and is 0 outside that range. In this case, the PDF for the uniform distribution ranging between 3 and 5 is 0.5, which means that the probability of the random variable taking any value between 3 and 5 is the same, and is equal to 0.5.

The PDF being a constant value of 0.5 implies that the distribution is symmetric, with equal probability of the random variable taking any value between the two endpoints. Thus, option C is answer.

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After approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

The value of shares t years after their floatation on the stock market, is modelled by V = 10e0.09t

The initial value of shares = V when t = 0. So, putting t = 0 in V = 10e0.09t,

we get

V = 10e0.09 × 0= 10e0 = 10 × 1 = 10 million dollars.

The values after 5 years, 10 years and 12 years, respectively are:

For t = 5, V = 10e0.09 × 5 ≈ 19.65 million dollarsFor t = 10, V = 10e0.09 × 10 ≈ 38.43 million dollarsFor t = 12, V = 10e0.09 × 12 ≈ 47.43 million dollars

The total revenue (TR) in t years' time is modelled as TR = 10e−0.19t (in million dollars)

The current revenue is the total revenue when t = 0.

So, putting t = 0 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 0= 10e0= 10 million dollars

Revenue in 5 years' time is TR when t = 5.

So, putting t = 5 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 5≈ 4.35 million dollars

To find when the revenue of this firm is going to drop to $1 million, we need to solve the equation TR = 1.

Substituting TR = 1 in TR = 10e−0.19t, we get1 = 10e−0.19t⟹ e−0.19t= 0.1

Taking natural logarithm on both sides, we get−0.19t = ln 0.1 = −2.303

Therefore, t = 2.303 ÷ 0.19 ≈ 12.13 years.

So, after approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

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Step-by-step explanation:

Here are the graphs of the two functions:

y

|

|

|

| (1) (2)

| | |

------x------x-------

| | |

| (3) (4)

|

|

Function 1: y = -2x^2

The graph is a downward-facing parabola.

The vertex is located at (0, 0).

The y-intercept is 0.

The function is symmetric about the y-axis.

Function 2: y = -2x^2 + 4

The graph is also a downward-facing parabola.

The vertex is located at (0, 4).

The y-intercept is 4.

The function is symmetric about the y-axis.

Comparing and contrasting the two graphs:

Both functions are downward-facing parabolas.

Function 2 is a vertical shift of Function 1, as it has been shifted 4 units upwards.

The vertex of Function 2 is higher than the vertex of Function 1.

The y-intercept of Function 2 is higher than the y-intercept of Function 1.

The shape and symmetry of the two graphs are the same.

The correct answer is option E which is Cos ( 70 ) = \(\dfrac{LN}{8}\).

The complete question is attached with the answer below:-

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

As we can see from the figure that ∠L = 70 and ∠M = 20 We can see that the length LN will be calculated as:-

Cos 70 = Base / Hypotenuse

So for an angle of 70, the base is LN and the hypotenuse is equal to 8 units.

Cos 70 = LN = 8

Therefore the correct answer is option E which is Cos ( 70 ) = \(\dfrac{LN}{8}\).

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Answer:

A & E

Step-by-step explanation:

Jus took it on edge

Answer:

Step-by-step explanation:

jjj

Answer:

(x + 1)² = 4(y + 10)

Step-by-step explanation:

Equation of parabola:

(x - h)² = 4a(y - k)

with vertex(h, k) and focus (h, k + a)

vertex(h, k) = (-1, -10)

⇒h = -1 and k = -10

focus (h, k + a) = (-1, -9)

⇒ k + a = -9

⇒ -10 + a = -9

⇒ a = 10 - 9

⇒ a = 1

Equation of parabola:

(x - h)² = 4a(y - k):

(x - (-1))² = 4(1)(y - (-1))

= (x + 1)² = 4(y + 10)

Answer:

15 centimeters(cm)

Step-by-step explanation:

:)

Answer:

15

Step-by-step explanation:

\(\sf{}\)

♛┈⛧┈┈•༶♛┈⛧┈┈•༶

✌️

Answer:

-108

Step-by-step explanation:

-8 - ( -10 )²

= -8 - 100

= -108

The solution to the system of equations is:

x = 2

y = -1

To solve the system of equations using an inverse matrix, we need to set up the augmented matrix and find the inverse matrix of the coefficient matrix. Let's go through the steps:

Step 1: Write the augmented matrix:

[4 1 | 10]

[2 1 | 6]

Step 2: Find the inverse matrix of the coefficient matrix [4 1; 2 1]:

To find the inverse matrix, we can use the formula:

A^(-1) = (1/det(A)) * adj(A),

where det(A) represents the determinant of matrix A, and adj(A) represents the adjugate of matrix A.

Let's calculate the determinant and adjugate of the coefficient matrix:

det([4 1; 2 1]) = (4 * 1) - (2 * 1) = 4 - 2 = 2

adj([4 1; 2 1]) = [1 -1;

-2 4]

Now, calculate the inverse matrix by dividing the adjugate matrix by the determinant:

[1/2 * 1 -1 |

1/2 * -2  4] = [1/2 -1 |

-1    2]

Therefore, the inverse matrix is:

[1/2 -1]

[-1    2]

Step 3: Multiply the inverse matrix by the augmented matrix:

[1/2 -1] * [4 1 | 10] = [x y]

[-1   2 |  6]

Performing the multiplication:

[(1/2 * 4) + (-1 * 2)   (1/2 * 1) + (-1 * 1) | (1/2 * 10) + (-1 * 6)]

= [2 -1 | 5]

So, the solution to the system of equations is:

x = 2

y = -1

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The expression where the greatest common factor (GCF) is factored completely is \(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)

The expression completely factored in is

\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)

Please refer below for the remaining answers.

We have,

Part A:

To rewrite the expression 2x³y + 18xy - 10x²y - 90y so that the greatest common factor (GCF) is factored completely, we can factor out the common terms.

GCF: 2y

\(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)

Part B:

To completely factor the expression, we can further factor the quadratic term.

\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)

Now,

Part A:

To determine the length of each side of the square given the area expression (9x² + 24x + 16), we need to factor it completely.

The area expression (9x² + 24x + 16) can be factored as (3x + 4)(3x + 4) or (3x + 4)².

Therefore, the length of each side of the square is 3x + 4.

Part B:

To determine the dimensions of the rectangle given the area expression (16x² - 25y²), we need to factor it completely.

The area expression (16x² - 25y²) is a difference of squares and can be factored as (4x - 5y)(4x + 5y).

Therefore, the dimensions of the rectangle are (4x - 5y) and (4x + 5y).

Now,

f(x) = 2x² - 5x + 3

Part A:

To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.

2x² - 5x + 3 = 0

The quadratic equation can be factored as (2x - 1)(x - 3) = 0.

Setting each factor equal to zero:

2x - 1 = 0 --> x = 1/2

x - 3 = 0 --> x = 3

Therefore, the x-intercepts of the graph of f(x) are x = 1/2 and x = 3.

Part B:

To determine if the vertex of the graph of f(x) is maximum or minimum, we can examine the coefficient of the x^2 term.

The coefficient of the x² term in f(x) is positive (2x²), indicating that the parabola opens upward and the vertex is a minimum.

To find the coordinates of the vertex, we can use the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation.

For f(x),

a = 2 and b = -5.

x = -(-5) / (2 x 2) = 5/4

To find the corresponding y-coordinate, we substitute this x-value back into the equation f(x):

f(5/4) = 25/8 - 25/4 + 3 = 25/8 - 50/8 + 24/8 = -1/8

Therefore, the vertex of the graph of f(x) is at the coordinates (5/4, -1/8), and it is a minimum point.

Part C:

To graph f(x), we can start by plotting the x-intercepts, which we found to be x = 1/2 and x = 3.

These points represent where the graph intersects the x-axis.

Next,

We can plot the vertex at (5/4, -1/8), which represents the minimum point of the graph.

Since the coefficient of the x² term is positive, the parabola opens upward.

We can use the vertex and the symmetry of the parabola to draw the rest of the graph.

The parabola will be symmetric with respect to the line x = 5/4.

We can also plot additional points by substituting other x-values into the equation f(x) = 2x² - 5x + 3.

By connecting the plotted points, we can draw the graph of f(x).

The steps to graph f(x) involve plotting the x-intercepts, the vertex, and additional points, and then connecting them to form the parabolic curve.

The answer in part A (x-intercepts) and part B (vertex) are crucial in determining these key points on the graph.

Thus,

The expression where the greatest common factor (GCF) is factored completely is \(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)

The expression completely factored in is

\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)

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Answer:

$2,660

Step-by-step explanation:

9.5% of 1300 is 123.5

So to figure out what the rent would cost in 11 years, we just have to multiply 123.5 by 11.

123.5 × 11 = 1358.5

We can then add that number to 1300.

1358.5 + 1300 = $2658.5

Then we round.

Your final answer would be:

$2,660

Answer:

$3221.70 per month.

Step-by-step explanation:

After 1 year the monthly rate is 1300 * 1.095

= $1423.50 - that is during the second year.

The third  years  rent will be  1423.50 * 1.095  (  = 1300 * 1.095^2 - and so on every year.

During the  11th  year it will be 1300 * 1.095^10

= $3221.70 per moth.

=

Answer:

Use mathematical skills to acquire the correct answer of 7.

Step-by-step explanation:

Hee hee hee haw.

Answer:

7 is the answer

Step-by-step explanation:

3x + 8 = 29

or, 3x + 8 - 8 = 29 - 8

or, 3x = 21

or, 3x/3 = 21/3

or, x = 7

Answer:

25

Step-by-step explanation:

10+7+8=25 this is because her cat weighs 8 pounds and her dog weighs 10 pounds more so that's 18 lb. after words it says Cameron's dog weighs 7 pounds less than bills so you do 18+7 and that equals 25

Answer:

x = -6

Step-by-step explanation: I hope I helped! :)

Answer:

5.64 cm

Step-by-step explanation:

Required:How much more rain fell in Dubaku's town than in Elliot's town?

8 centimeters of rain fell in Dubaku's hometown

2.36 centimeters of rain fell in Elliot's hometown

We are asked to find how much more rain fell in Dubaku's town than in Elliot's town so it is calculated as the difference between the rain in both of there towns and is given by:

Difference in rain= 8-2.36

Difference in rain= 5.64 cm.

Therefore, 5.64 cm of more rain fell in Dubaku's town than in Elliot's town.

Answer:

5.64

Step-by-step explanation:

Answer:

Below in bold,

Step-by-step explanation:

a. There's is only one card that fits this description so

Probability = 1/52.

b. There are 2 black Kings so

Probability = 2/52 = 1/26.

c. There are 2 of these - 7 of diamonds and 7 of hearts

so

Probability = 2/52 = 1/26.

d.  There 13 diamonds and 13 hearts so

Probability = 26/52 = 1/2.

e.  There  26 black cards

Probability = 26/52 = 1/2.

Answer:

7 inches

Step-by-step explanation:

56 divide by 8

Hope this helps.

The shape of distribution for a polygon of the average annual rainfall in Los Angeles over the past 110 years would be normal.

In Statistics, the shape of distribution of a data set can be determined by examining the frequency distribution, which explicitly shows the number of score or numerical data associated with each member of a population.

Over the past 110 years, we can logically deduce that the shape of distribution for a polygon of the average annual rainfall in Los Angeles would be normal because very few number of years had extremely low rainfall, high rainfall and many years with average rainfalls.

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Answer/Step-by-step explanation:

\(\begin{gathered}\boxed{\begin{array}{c|c}\boxed{\bf Form} &\boxed{\bf Equation} \\ \sf Slope\: intercept\:form &\sf y=mx+b \\ \sf Intercept\:form &\sf \dfrac{x}{a}+\dfrac{y}{b}=1\\ \sf Normal\:form &\sf xcos\omega+ysin\omega=p \\ \sf Two\: point\:form &\sf y-y_1=\left(\dfrac{y_2-y_1}{x_2-x_1}\right)(x-x_1)\\ \sf Point\:slope\:form &\sf y-y_1=m(x-x_1) \\ \sf Standard\:form &\sf Ax+By+C=0 \end{array}}\end{gathered}\)

[RevyBreeze]

Answer:

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Step-by-step explanation: