If

y=∑n=0[infinity]cnxny=∑n=0[infinity]cnxn

is a solution of the differential equation

y′′+(3x−1)y′−1y=0,y″+(3x−1)y′−1y=0,

then its coefficients cncn are related by the equation

cn+2=cn+2= cn+1cn+1 + cncn .

Answer:

1.) it is the same way as subtracting a fraction be cause a pizza is cut into 8 so it will be 1/8th of each slice if some one ate a slice of pizza

Step-by-step explanation:

The series n=0 to infinity [tex]2^{n}[/tex] [tex]3^{n}[/tex] /n! is (e) convergent by ratio test and its sum is e⁶.

The given series can be written as:

S = Σ(n=0 to ∞) (2ⁿ * 3ⁿ) / n!

In order to determine if the series is convergent, let's apply the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1, then the series converges. Mathematically, this can be expressed as:

lim(n→∞) |(a(n+1) / an)| < 1

Taking the ratio of a(n+1) to an is 6 / (n+1)

Now, let's take the limit as n approaches infinity:

lim(n→∞) |(6 / (n+1))| = 0

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The set of ordered pairs that represents a function from A to B is {(1, -1), (3, 2), (4, 0), (2, 1)}. A function from A to B is a relation that assigns a unique element from B to each element in A.

In order for a set of ordered pairs to represent a function, each element in A must have exactly one corresponding element in B.

Let's analyze each set of ordered pairs:

1. {(1, -1), (3, 2), (2, -2), (4, 0), (2, 1)}: This set is not a function because the element 2 in A is assigned two different elements (-2 and 1) in B. Each element in A should have a unique corresponding element in B.

2. {(1, 2), (4, 0), (2, 1)}: This set is a function because each element in A is assigned a unique element in B.

3. {(1, 1), (2, -2), (3, 0), (4, 2)}: This set is a function because each element in A is assigned a unique element in B.

4. {(1, 0), (2, 0), (3, 0), (4, 0)}: This set is a function because each elementin A is assigned a unique element (0) in B.

Based on the analysis, the set of ordered pairs that represents a function from A to B is {(1, -1), (3, 2), (4, 0), (2, 1)}.

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Answer:

Log Linear Model : log y = a + bx. Slope 'b' represent % change in ice cream sale, due to unit change in temperature.

Step-by-step explanation:

Assuming a log linear regression model, with dependent variable 'y' ie Ice cream sale & independent variable 'x' ie temperature sale.

In form of regression, log y = a + bx  {a = intercept}. Here, slope b represents response of one unit change (Increase) in temperature leading to b% change (ie rise) in ice cream consumption. Slope coefficient 'b' is likely to be positive, as temperature & ice cream sale are likely to be directly related, higher temperature (hot weather) imply high ice cream sale, & vice versa less sales for lower temperature (cool weather)

The simplification based on Laurent series of the function (22-9)(2+3) centered at z = −3

[((1/4)(3)⁴ + (2/3)(3)³ + (9/2)(3)² - 27(3))] - [((1/4)(-3)⁴ + (2/3)(-3)³ + (9/2)(-3)² - 27(-3))]

The given problem involves finding the Laurent series of a function centered at z = -3 and evaluating the integral of another function over a specific interval. The Laurent series simplifies to a constant term of 65.

(a) To find the Laurent series of the function (22-9)(2+3) centered at z = −3, we can expand the function in powers of (z + 3):

(22-9)(2+3) = (13)(5) = 65

Since there are no negative powers of (z + 3), the Laurent series of the function is simply the constant term:

f(z) = 65

(b) To evaluate the integral ſc[−3,3] (z²−9)(z+3) dz, we can first simplify the integrand:

(z² - 9)(z + 3) = (z - 3)(z + 3)(z + 3) = (z - 3)(z + 3)²

Now, let's integrate the simplified expression:

∫[(z - 3)(z + 3)²] dz

Expanding the expression:

∫[z³ + 6z² + 9z - 27] dz

Integrating each term:

(1/4)z⁴ + (2/3)z³ + (9/2)z² - 27z

Now, we can evaluate the integral over the given interval [−3, 3]:

∫[−3,3] (z²−9)(z+3) dz = [((1/4)z⁴ + (2/3)z³ + (9/2)z² - 27z)] evaluated from z = -3 to z = 3

Substituting the upper and lower limits into the expression and simplifying, we get:

[((1/4)(3)⁴ + (2/3)(3)³ + (9/2)(3)² - 27(3))] - [((1/4)(-3)⁴ + (2/3)(-3)³ + (9/2)(-3)² - 27(-3))]

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Answer:

no but choose b if u don't know it it usually works for me sorry if I don't help :(

Answer:

y=-3x is the bottom right one

y=4x is the top middle

y=x-3 is the top right one

Step-by-step explanation:

The closest measurement in square inches to the overall surface area of the candle is 87.92 square inches.

To find the total surface area of the candle, we need to calculate the lateral surface area (excluding the top and bottom) and then add the areas of the two circular bases.

1. Lateral Surface Area:

The formula for the lateral surface area of a cylinder is given by A = 2πrh, where r is the radius of the base and h is the height of the cylinder.

Given that the diameter of the candle is 4 inches, we can calculate the radius by dividing the diameter by 2:

Radius (r) = 4 inches / 2 = 2 inches

Height (h) = 5 inches

Using the formula, we can calculate the lateral surface area:

Lateral Surface Area = 2π(2 inches)(5 inches) = 20π square inches

2. Base Area:

The formula for the area of a circle is given by A = πr^2, where r is the radius of the circle.

Using the radius calculated earlier (r = 2 inches), we can calculate the area of each circular base:

Base Area = π(2 inches)^2 = 4π square inches

3. Total Surface Area:

To find the total surface area, we add the lateral surface area and the areas of the two circular bases:

Total Surface Area = Lateral Surface Area + 2(Base Area)

Total Surface Area = 20π + 2(4π) = 20π + 8π = 28π square inches

Approximating the value of π to 3.14, we can calculate the approximate total surface area:

Total Surface Area ≈ 28(3.14) = 87.92 square inches

Therefore, the closest measurement to the total surface area of the candle in square inches is 87.92 square inches.

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Answer:

45 m^2

Step-by-step explanation:

Answer:

v = 9x9x0.5x5 = 202.5 ft^3

Step-by-step explanation:

Answer:

25 cents

Step-by-step explanation:

1.) Set up an equation you can solve from the wording of the question:

(2/3)*m = 50, where "m" represents the money in your pocket.

2.) Solve for that equation:

m = 50*(3/2) = 150/2 = 75, so now you know the money you have in your pocket is 75 cents

3.) Multiply the money you have in your pocket by 1/3 to find 1/3 of the money you have in your pocket:

75*(1/3) = 25

Answer:

The volume of the cone is 3140cm³

Step-by-step explanation:

Volume of come = 1/3 × πr²h

r = diameter/2 = 20/2 = 10cm

h = 30cm

π = 22/7

Volume = 1/3 × 22/7 × 10² × 30

Volume = 1/3 × 22/7 × 100 × 30

Volume = 3142.86cm³

Volume = 3140cm³

The only solution of the initial-value problem y" + x^2y = 0, y(0) = 0, y'(0) = 0 is y(x) = 0, where y(x) represents the unknown function and x represents the independent variable.

To determine the solution of the initial-value problem, we consider the given second-order linear homogeneous differential equation y" + x^2y = 0 along with the initial conditions y(0) = 0 and y'(0) = 0.

First, we solve the differential equation by assuming a solution of the form y(x) = Ax^n, where A is a constant and n is an exponent to be determined. Substituting this into the differential equation, we obtain the characteristic equation n(n-1) + x^2 = 0.

Solving the characteristic equation, we find that the roots are n = 0, which corresponds to the solution y(x) = A, and n = 1, which corresponds to the solution y(x) = Bx. However, when we apply the initial conditions y(0) = 0 and y'(0) = 0, we find that both solutions are equal to zero.

Therefore, the only solution that satisfies both the differential equation and the initial conditions is y(x) = 0, indicating that the function y(x) is identically zero for all values of x.

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Answer:

it is x=4÷2

Step-by-step explanation:

I just known the answer who cares about the steps

The minimum of Brown's badly scaled function, f(x) = (x₁ - 10^6)² + (x₂ − 2 × 10^-6)² + (x₁x₂ - 2)², can be found using Powell's method.

Powell's method is an optimization algorithm used to find the minimum of a function. It is an iterative method that searches for the minimum by successively approximating the direction of the minimum along each coordinate axis.

To apply Powell's method to find the minimum of Brown's badly scaled function, we start with an initial guess for the minimum point. Then, we iteratively update the guess by evaluating the function at different points and adjusting the guess based on the obtained results.

The iterative process continues until a convergence criterion is met, indicating that the minimum has been sufficiently approximated. The final guess represents the minimum point of the function.

By applying Powell's method to Brown's badly scaled function, we can determine the coordinates of the minimum point, which correspond to the values of x₁ and x₂ that minimize the function. The specific values of x₁ and x₂ will depend on the initial guess and the convergence criteria used in the optimization process.

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Answer:

205

Step-by-step explanation:

5^2 = 25

8.2 * 25 = 205

wth ..

Answer:

205 hope this helps

Step-by-step explanation:

5^2= 25

8.2×25= 205 hope

8,99,999 in international system:-

899,999= Eight hundred ninety-nine thousand nine hundred ninety-nine

Using area under normal curve and z-score, approximately 21.32% of shafts have a diameter between 19.987 mm and 20.000 mm.

To find the proportion of shafts with a diameter between 19.987 mm and 20.000 mm, we need to calculate the probability that a randomly selected shaft falls within this range.

Given that the diameters of the shafts are normally distributed with a mean of 20.003 mm and a standard deviation of 0.005 mm, we can use the properties of the normal distribution to determine the desired proportion.

To calculate this proportion, we need to find the area under the normal curve between the values of 19.987 mm and 20.000 mm.

Let's denote the random variable X as the diameter of the shafts. We want to find P(19.987 ≤ X ≤ 20.000).

To do this, we can standardize the values by converting them to z-scores using the formula:

z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation.

For 19.987 mm:

z₁ = (19.987 - 20.003) / 0.005

For 20.000 mm:

z₂ = (20.000 - 20.003) / 0.005

We can then use a standard normal distribution table or calculator to find the corresponding probabilities associated with these z-scores.

Using a standard normal distribution table, we find that P(Z ≤ z₁) ≈ 0.2119 and P(Z ≤ z₂) ≈ 0.4251.

To find the proportion of shafts between 19.987 mm and 20.000 mm, we subtract the probabilities:

P(19.987 ≤ X ≤ 20.000) = P(Z ≤ z₂) - P(Z ≤ z₁) ≈ 0.4251 - 0.2119

P(19.987 ≤ X ≤ 20.000) ≈ 0.2132

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Answer:

i think it is A CiNiyah

Step-by-step explanation:

Answer:  x = √105

Step-by-step explanation:

a² + b² = c²

8² + x² = 13²

64 + x² = 169

x² = 105

x = √105

Step-by-step explanation:

What is the measure of angle B in the triangle?

Enter your answer in the box.

m∠B=

°

A triangle labeled ABC with angle A as one hundred twenty degrees, angle B as X degrees and angle C as parenthesis X plus sixteen parenthesis degrees

the answer in the photo

Answer:

8

x

3

+

2

x

2

−

3

x

+

18

Step-by-step explanation:

simply the answer thought bc i didn't simplify

Answer:

From the given information, we can see that when x = -3, f(x) = 1 and g(x) = -3. Since g(x) = kf(x), we can substitute the values of f(x) and g(x) to solve for k: g(x) = kf(x) -3 = k(1) k = -3 So the value of k is -3, which corresponds to answer choice D.

For a graph with seven vertices, a minimum degree of 3 (8 = 3), and a maximum degree of 5 (Δ = 5), it can be shown that the graph must contain at least 12 edges. The largest number of edges possible in this graph is determined by the Handshaking Lemma, which states that the sum of the degrees of all vertices in a graph is equal to twice the number of edges.

(a) To show that the graph must contain at least 12 edges, we can use the Handshaking Lemma. The sum of the degrees of all vertices in the graph is equal to twice the number of edges. In this case, with seven vertices and a minimum degree of 3, the sum of the degrees is at least 7 * 3 = 21. Therefore, the minimum number of edges is 21/2 = 10.5, which rounds up to 11. So the graph must contain at least 11 edges, but since the number of edges must be an integer, it must be at least 12.

(b) The largest number of edges possible in this graph can be determined by considering the maximum degree. In this case, the maximum degree is 5. Since the sum of the degrees of all vertices is equal to twice the number of edges, the sum of the degrees is at most 7 * 5 = 35. Therefore, the largest possible number of edges is 35/2 = 17.5, which rounds down to 17. So the largest number of edges possible in this graph is 17.

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Answer:

this is the answer for 4th question

and it is a collinear

Answer:

C=20

Step-by-step explanation:

This is for question 3

For perpendicular lines , the product of their gradient should give -1 for the answer and thus,

3×x=-1

x=-⅓, the gradient for the line.

Therefore c =

-2-3/c- 5 =-⅓

-1(c-5)=3(-2-3)

-c+5=-6-9

-c=-6-9-5

-c=-20

The negatives cancel each other leaving c as 20

A) Logical vector diagram of the flight is drawn below. B) The aircraft's ground velocity is approximately 260.2 km/hr at a bearing of -153.7°. C) The vacation island is approximately 1301 kilometers from the airport of departure.

A.  a logical vector diagram of the flight is given in image.

B. To determine the aircraft's ground velocity, we need to find the resultant vector of the aircraft's velocity and the wind vector. We can use vector addition to calculate this:

Aircraft's velocity = 250 km/hr at a heading of 170°

Wind velocity = 50 km/hr at a heading of 270° (since it's blowing from the south/west)

To add these vectors, we need to resolve them into their horizontal (x) and vertical (y) components:

Aircraft's velocity:

[tex]V_x[/tex] = 250 km/hr * cos(170°)

[tex]V_{y}[/tex] = 250 km/hr * sin(170°)

Wind velocity:

[tex]V_x[/tex]_wind = 50 km/hr * cos(270°)

[tex]V_y[/tex]_wind = 50 km/hr * sin(270°)

Now, we can add the horizontal and vertical components separately:

[tex]V_{x} total = V_x + V_{x}wind\\V_{y} total = V_y + V_{y}wind[/tex]

To find the magnitude and direction of the resultant vector, we can use the Pythagorean theorem and trigonometry:

Magnitude of the resultant vector (ground velocity):

[tex]V_{total} = \sqrt{V_x total^2 + V_y total^2}[/tex]

Direction of the resultant vector:

[tex]\theta = tan^{-1} 2(V_y total, V_xtotal)[/tex]

Let's calculate the values:

[tex]V_x[/tex] = 250 km/hr * cos(170°) ≈ -235.83 km/hr

[tex]V_y[/tex] = 250 km/hr * sin(170°) ≈ -62.85 km/hr

[tex]V_x[/tex]_wind = 50 km/hr * cos(270°) = 0 km/hr

[tex]V_y[/tex]_wind = 50 km/hr * sin(270°) ≈ -50 km/hr

[tex]V_x[/tex]_total = -235.83 km/hr + 0 km/hr = -235.83 km/hr

[tex]V_y[/tex]_total = -62.85 km/hr + (-50 km/hr) = -112.85 km/hr

[tex]V_{total}[/tex] =  [tex]\sqrt{((-235.83 km/hr)^2 + (-112.85 km/hr)^2) }[/tex] ≈ 260.2 km/hr

θ = [tex]tan^{-1} 2(-112.85 km/hr, -235.83 km/hr)[/tex] ≈ -153.7°

The aircraft's ground velocity is approximately 260.2 km/hr at a bearing of -153.7°.

C. If the entire flight took about 5 hours, we can calculate the distance traveled by multiplying the ground velocity by the time:

Distance = Velocity * Time

Distance = 260.2 km/hr * 5 hours = 1301 km

The vacation island is approximately 1301 kilometers from the airport of departure.

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Answer:

Step-by-step explanation:

This is the equation of a circle with center at (-4, 6) and radius 4√3.

x^2 - x - 6= 0

(x - 3) ( x + 2) = 0

Equating

x - 3 = 0

x = 3

x+ 2= 0

x = -2

Answer: x - 6

Step-by-step explanation:

1. Observations: The boxplot graph reveals the distributions of corn yield for the 'Regular seed' and 'Kiln-dried seed.'

Both distributions appear approximately symmetric without any clear skewness. The center of the 'Kiln-dried seed' distribution seems to be slightly higher than the center of the 'Regular seed' distribution.

2. 95% Confidence Interval: Using Minitab, the 95% confidence interval for μ1-μ2 is (-28.88, -9.66) pounds per acre.

3. P-value and Conclusion: The corresponding two-sided test yields a p-value of 0.003.

Suggesting strong evidence of a difference in means between the two seed types. We can conclude that there is a significant difference in corn yield based on seed type.

4. Dotplots: By comparing the dotplots of 'Regular_seed,' 'Kiln_dried_seed,' and the 'Differences,'

It can be observed that the sample of differences has less variation compared to the two individual samples. The range of the differences is narrower, indicating reduced variation when focusing on the paired data.

5. Summary Statistics: The standard deviations for 'Regular_seed,' 'Kiln_dried_seed,' and the 'Differences' are 18.37, 14.71, and 8.21 pounds per acre, respectively.

Notably, the standard deviation of the differences is smaller compared to the standard deviations of the individual samples.

6. 95% Confidence Interval for μd: Using the paired t-test in Minitab, the 95% confidence interval for μd is (-18.16, -7.38) pounds per acre.

7. Comparison of Confidence Intervals: The confidence interval for μd (paired design) is narrower than the confidence interval for μ1-μ2 (unpaired design) from part 2.

This indicates that considering the pairing reduces the variability and provides a more precise estimate.

8. P-value and Conclusion for μd: The two-sided hypothesis test for μd yields a p-value of 0.001.

Indicating strong evidence of a significant difference in means between the two seed types.

9. Comparison of P-values: The p-value from the paired design (μd) is smaller than the p-value from the unpaired design (μ1-μ2).

This suggests that the paired design is more sensitive and able to detect smaller differences. The advantage of using a paired design becomes evident as it reduces unwanted variation, increases precision, and enhances the ability to detect significant differences.

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