a circular diaphragm 58.06 cm in diameter oscillates at a frequency of 15.69 khz as an underwater source of sound used for submarine detection. far from the source, the sound intensity is distributed as the diffraction pattern of a circular hole whose diameter equals that of the diaphragm. take the speed of sound in water to be 1450. m/s, and find the angle (in degrees) between the normal to the diaphragm and a line from the diaphragm to the first minimum.

The radius of convergence, R, of the series (-1)nx^n-1 can be found using the ratio test the interval of convergence is (-1, 1) in interval notation. .

We have
lim |(-1)^(n+1)x^(n) / (-1)^nx^(n-1)| as n approaches infinity
= lim |x|

Since the limit exists only when |x| < 1, the radius of convergence is R = 1.
To find the interval of convergence, we need to check the endpoints x = -1 and x = 1.
When x = -1, the series becomes (-1)^n(-1)^n-1 = (-1)^2n-1 which diverges.

When x = 1, the series becomes (-1)^n1^n-1 = (-1)^(n-1) which also diverges.
Therefore, the interval of convergence is (-1, 1) in interval notation.

Note that the endpoints are not included in the interval of convergence because the series diverges at those points.

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The radius of convergence is R = 1 and the interval of convergence is (-1, 1).

To find the radius of convergence, we can use the ratio test:
lim┬(n→∞)⁡|(-1)^(n+1)x^n|/|(-1)^(n)x^(n-1)| = lim┬(n→∞)⁡|x|/1 = |x|
The series converges if |x| < 1 and diverges if |x| > 1. So the radius of convergence is R = 1.
To find the interval of convergence, we need to test the endpoints x = -1 and x = 1. When x = -1, the series becomes (-1)^n(-1)^n = 1, which is a divergent series. When x = 1, the series becomes (-1)^n, which is an oscillating series that does not converge.
Therefore, the interval of convergence is (-1, 1), where -1 is excluded and 1 is included, since the series converges for -1 < x < 1 and diverges for x ≤ -1 and x ≥ 1.
In summary, the radius of convergence is R = 1 and the interval of convergence is (-1, 1).

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The solution to the given differential equation, x²y'' + xy' - y = ln(x), using variation of parameters is: y(x) = C₁x + C₂x ln(x) + x ln²(x)/2,

where C₁ and C₂ are constants.

To solve the differential equation using variation of parameters, we first find the solutions to the homogeneous equation x²y'' + xy' - y = 0. Let's denote these solutions as y₁(x) and y₂(x).

Next, we find the Wronskian W(x) = y₁(x)y₂'(x) - y₁'(x)y₂(x) and calculate the integrating factors u₁(x) = -∫(y₂(x)ln(x))/W(x) dx and u₂(x) = ∫(y₁(x)ln(x))/W(x) dx.

Using these integrating factors, we can determine the particular solution yₚ(x) = -y₁(x)∫(y₂(x)ln(x))/W(x) dx + y₂(x)∫(y₁(x)ln(x))/W(x) dx.

Finally, the general solution is given by y(x) = yₕ(x) + yₚ(x), where yₕ(x) is the general solution to the homogeneous equation.

Solving the homogeneous equation x²y'' + xy' - y = 0 gives the solutions y₁(x) = x and y₂(x) = x ln(x).

After calculating the Wronskian W(x) = x² ln(x), we obtain the integrating factors u₁(x) = -ln(x)/2 and u₂(x) = -x/2.

Plugging these values into the particular solution formula, we find yₚ(x) = C₁x + C₂x ln(x) + x ln²(x)/2.

Hence, the general solution is y(x) = C₁x + C₂x ln(x) + x ln²(x)/2, where C₁ and C₂ are arbitrary constants.

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The book is opened to pages 11 and 12.

How to get the product of the page

x * (x + 1) = 132

Expanding the equation, we get:

x² + x = 132

To solve for x, we need to rewrite the equation as a quadratic equation:

x²+ x - 132 = 0

Now, we can factor the quadratic equation:

(x - 11)(x + 12) = 0

This equation has two solutions for x:

x = 11

x = -12

Since page numbers cannot be negative, we discard the second solution. Thus, the left-hand page number is 11, and the right-hand page number is 11 + 1 = 12.

So, the book is opened to pages 11 and 12.

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For this visualization, a bar chart would be the best choice.

A bar chart is an effective way to visually compare different categories or groups. In this case, the data analyst can create a bar chart where each bar represents a city, and the height of the bar corresponds to the population of that city. The analyst can include only the top ten most populous cities in North Carolina and color the bars differently based on whether the population is below or above 250,000 people. By doing so, it becomes easy to identify which cities fall below the threshold, as they will have shorter bars compared to those above the threshold. The clear distinction between the bar heights allows for quick visual comparison and provides a straightforward representation of the population distribution among the top ten cities in North Carolina.

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Answer:it is the 2 one

Step-by-step explanation: trust me

The distance between the lower whisker and the minimum value and the distance between the upper whisker and the maximum value indicate the range of the leg lengths of the insects in millimeters.

A box plot, also known as a box-and-whisker plot, is a graphical representation of a dataset that displays the distribution of a continuous variable. It shows the minimum and maximum values, the first and third quartiles, and the median of the data. The length of the box in a box plot represents the interquartile range (IQR), which is the range between the first and third quartiles. The whiskers extend from the box to show the range of the data, excluding outliers.
In the context of the question, the box plot displays the leg lengths, in millimeters, of a sample of insects. To determine the range of lengths of the insects, we need to examine the whiskers of the box plot. The whiskers extend from the box to the minimum and maximum values of the dataset, and their length represents the range of the data.
Therefore, to answer the question, we need to look at the length of the whiskers in the box plot.
In conclusion, the range of lengths of the insects can be determined by looking at the length of the whiskers in the box plot. The answer will depend on the specific values displayed in the plot.

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The answers for the new work

Answer:

Solution C HOPE THIS HELPS! Have A nice day

Step-by-step explanation:

According to the plot, the spread of the data is

A. 21 to 29 years

The spread of data is also known as data dispersion or variability. this refers to the extent to which data points are scattered or spread out around the central tendency (such as the mean or median) in a dataset.

It provides information about the distribution and the degree of variability within the dataset. there are several common measures used to describe the spread of data

The range is the simplest measure of spread and represents the difference between the largest and smallest values in the dataset.

This is used hear and the highest is 29 years while the lowest is 21 years hence making a the best choice

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It will take 7 men 42 hours to complete the job if they work at the same rate.

If it takes 4 men 6 hours to repair a road, it means that the total work done is 1 job.

The number of man-hours required to complete the job is the product of the number of men and the number of hours

= 4 men x 6 hours

= 24 man-hours

Now, let's find out how many hours it will take for 7 men to do the same job. We can set up a proportion using the man-hours:

4 men / 24 hours = 7 men / x hours

4x = 7 (240)

4x = 168

x = 168 / 4

x = 42

Therefore, it will take 7 men 42 hours to complete the job if they work at the same rate.

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The cost of 1 pencil and 1 eraser is $0.10 and 3 pencils and 5 erasers is $0.38.

To clear up this problem, we are able to use simultaneous equations to locate the value of 1 pencil and 1 eraser. Let x be the price of 1 pencil and y be the price of 1 eraser. Then we are able to write  equations based totally on the given records:

1x + 2y = 0.14 and 2x + 3y = 0.24

To take away y, we can multiply the first equation by using -3 and add it to the second equation:

-3x - 6y = -0.42 and  2x + 3y = 0.24

-x - 3y = -0.18

Then we can divide both sides by way of -1 to get:

x + 3y = 0.18

To dispose of x, we are able to multiply the first equation through -2 and upload it to the second equation:

-2x - 4y = -0.28 and  2x + 3y = 0.24

-y = -0.04

Then we are able to divide both sides by -1 to get:

y = 0.04

This method that one eraser fee of $0.04. To locate the cost of one pencil, we can replace y in both equations. For instance, the usage of the primary equation:

1x + 2(0.04) = 0.14

1x + 0.08 = 0.14

1x = 0.14

- 0.08 1x = 0.06

This approach is that one pencil is priced at $006.

Therefore, the cost of:

i.) one pencil and one eraser is $0.06 + $0.04 = $0.10

ii.) 3 pencils and 5 erasers is 3($0.06) + 5($0.04) = $0.18 + $0.20 = $0.38.

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Answer:

4

Step-by-step explanation:

R + the 4 spaces to T

Let's calculate the profit made by the owner on each branch at the end of the season. The owner buys a wooden branch for $2. After marking up the price by 75%, the selling price becomes:

$2 + ($2 * 0.75) = $2 + $1.50 = $3.50

However, at the end of the season, the owner sells the branches for 30% off. So the selling price after the discount is:

$3.50 - ($3.50 * 0.30) = $3.50 - $1.05 = $2.45

To calculate the profit made on each branch, we subtract the original cost from the selling price:

$2.45 - $2 = $0.45

Therefore, the owner makes a profit of $0.45 on each branch at the end of the season.

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Answer:

  ≈ 0.14159265359

Step-by-step explanation:

You want the value of f(x) = |x| when x = 3-π.

The function value is ...

  f(3-π) = |3-π| ≈ |-0.14159265359| = 0.14159265359

The absolute value function changes the sign from negative to positive. Pi is irrational, so the actual value is irrational. It is rounded up to the value shown.

<95141404393>

Answer:

Therefore

a=12

<B=66°

<C=24°

Step-by-step explanation:

Hyp²=opp²+adj²

x²=5²+11²

x²=25+121

x²=126

[tex] \sqrt{ {x}^{2} } = \sqrt{146} [/tex]

x=12

sinß=opp/hyp

sinß=11/12

[tex] \beta = { \sin( \frac{11}{12} ) }^{ - 1} [/tex]

ß=66°

<A+<B+<C=180°

90+66+<C=180

<C+156=180

<C=180-156

<C=24°

So the points on the ellipse that are farthest away from the point (1,0) are: (1/15)(2 + sqrt(394)), ±sqrt(4 - 4(1/15)(2 + sqrt(394))^2 )and (1/15)(2 - sqrt(394)), ±sqrt(4 - 4(1/15)(2 - sqrt(394))^2).

We want to find the points on the ellipse that are farthest away from the point (1,0). The distance between two points (x1, y1) and (x2, y2) is given by the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

So, we need to maximize the distance d, subject to the constraint that the point (x, y) lies on the ellipse 4x^2 + y^2 = 4.

Using Lagrange multipliers, we set up the following system of equations:

f(x, y) = (x - 1)^2 + y^2 = λg(x, y) = λ(4x^2 + y^2 - 4)

Taking the partial derivatives with respect to x, y, and λ, we get:

fx = 2(x - 1) = 8λx

fy = 2y = 2λy

g(x, y) = 4x^2 + y^2 - 4 = 0

From the second equation, we can see that y = 0 or λ = 1. If y = 0, then the first equation simplifies to:

(x - 1)^2 = λ(4x^2 - 4)

Solving for λ and substituting into the equation for g(x,y), we get:

4x^2 - (x - 1)^2 - 4 = 0

Simplifying, we get:

15x^2 - 2x - 11 = 0

Using the quadratic formula, we get:

x = (1/15)(2 ± sqrt(394))

Substituting into the equation for the ellipse, we get the corresponding y-values:

y = ±sqrt(4 - 4x^2)

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The largest area that can be enclosed with 100 meters of fencing is 1250 square meters.

To find the largest area that can be enclosed with 100 meters of fencing, we need to determine the dimensions of the rectangular area that would maximize the area.

Let's assume the length of the rectangle is L and the width is W. We are given that the total amount of fencing available is 100 meters, which means the perimeter of the rectangle should equal 100 meters:

2L + W = 100

To express the area of the rectangle in terms of L and W, we can use the formula:

Area = L * W

We want to maximize the area, so we can rewrite the equation in terms of a single variable using the perimeter equation:

W = 100 - 2L

Substituting this expression for W in the area equation:

Area = L * (100 - 2L)

Expanding and rearranging:

Area = 100L - 2L²

To find the maximum area, we can take the derivative of the area equation with respect to L and set it to zero:

d(Area)/dL = 100 - 4L = 0

Solving for L:

4L = 100

L = 25

Substituting this value back into the perimeter equation to find W:

W = 100 - 2L

= 100 - 2(25) = 50

Therefore, the dimensions of the rectangle that would maximize the area are L = 25 meters and W = 50 meters. To find the maximum area, we can substitute these values back into the area equation:

Area = L * W = 25 * 50 = 1250 square meters

Thus, the largest area that can be enclosed with 100 meters of fencing is 1250 square meters.

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The health center needs to survey approximately 196 students to estimate the proportion of students experiencing depression or anxiety with a 95% confidence level and a margin of error of 5%.

To estimate the proportion of students experiencing depression or anxiety, the health center at the college will need to conduct a survey of a random sample of students. With a confidence level of 95%, they can be 95% confident that the true proportion of students experiencing depression or anxiety falls within the range of the estimated proportion plus or minus the margin of error of 5%.

To determine the sample size needed for the survey, the health center will need to use a formula that takes into account the population size (number of students at the college), the desired confidence level, and the margin of error. With a population size of, say, 10,000 students, the sample size needed would be around 385 students.

If prior research shows that the prevalence of mental illness in college students is about 15%, then the health center can expect the proportion of students in their sample experiencing depression or anxiety to be around 15%. However, with the margin of error of 5%, the estimated proportion could range from 10% to 20%.

Overall, by conducting a survey with a random sample of students and using a confidence level of 95% and a margin of error of 5%, the health center at the college can estimate with a high degree of confidence the proportion of students experiencing depression or anxiety.

To estimate the proportion of students experiencing depression or anxiety at the college, the health center can follow these steps:

1. Use the prior research that shows the prevalence of mental illness in college students is about 15%. This will be used as the initial proportion (p) for the calculation.

2. Determine the desired confidence level (95%) and margin of error (5%). In this case, the confidence level is 95%, which corresponds to a z-score of 1.96 for a standard normal distribution. The margin of error is 5% (0.05).

3. Calculate the sample size required for the estimation using the formula:

n = (Z^2 * p * (1-p)) / E^2

where n is the sample size, Z is the z-score (1.96 for 95% confidence level), p is the initial proportion (0.15), and E is the margin of error (0.05).

4. Plug in the values and calculate the sample size:

n = (1.96^2 * 0.15 * (1-0.15)) / 0.05^2
n ≈ 196

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The series of transformations that correctly maps rectangle ABCE to LMNO is: Translate rectangle ABCD right 9 units, then dilate the result by a scale factor of 3 centered at the origin.

Based on the diagram, translation is by adding 9 to the x-coordinates of all the points in the rectangle.

Also,the dilation us by multiplying the coordinates of all the points in the translated rectangle A'B'C'D' by a factor of 3.

Hence, the series of transformations that correctly maps rectangle ABCE to LMNO is to teanslate rectangle ABCD right 9 units, then dilate the result by a scale factor of 3 centered at the origin.

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Answer:

The correct answer is: Age and height are positively correlated.

Positive correlation means that as one variable increases, the other variable also increases. In this case, as a child ages, they also get taller. There are many factors that contribute to a child's height, including genetics, nutrition, and health. However, age is one of the most important factors.

Here are some additional details about the relationship between age and height:

The correlation between age and height is positive and strong. This means that there is a strong relationship between the two variables.

The correlation between age and height is linear. This means that the relationship between the two variables is straight.

The correlation between age and height is not perfect. This means that there are some children who are taller or shorter than expected for their age.

Overall, the relationship between age and height is positive and strong. This means that as a child ages, they also get taller.

Step-by-step explanation:

1. Lines that have different slopes and intersect at one point have one solution.

2. Lines that have the same slope and different y-intercepts (they do not intersect) have no solution.

3. Lines that have the same slope and the same y-intercepts have infinitely many solutions.

The number of ways to choose five articles to read is given as follows:

21 ways.

The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The combination formula is used in the context of this problem as the order in which the articles are read does not matter.

Five articles are chosen from a set of seven, hence the number of ways to choose the articles is given as follows:

[tex]C_{7,5} = \frac{7!}{5!2!} = 21[/tex]

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The exact value of tan(tetha) is 4/3

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

The hypotenuse is the side facing the right angle and the opposite is the side facing the acute angle and the adjascent is the third side.

The opposite side = √ 5²-3²

= √ 25 -9

= √16

= 4

Therefore ;

Tan(tetha) = 4/3

the exact value of tan(tetha) is 4/3

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Answer:

(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)

Step-by-step explanation:

To find MED, we can use the distance formula between points D and E:

MED = √[(x2 - x1)^2 + (y2 - y1)^2]

Using the coordinates for points D and E:

MED = √[(-4 - 2)^2 + (-4 - 5)^2]

= √[(-6)^2 + (-9)^2]

= √[36 + 81]

= √117

≈ 10.82

To find MEF, we can use the distance formula between points E and F:

MEF = √[(x2 - x1)^2 + (y2 - y1)^2]

Using the coordinates for points E and F:

MEF = √[(0 - (-4))^2 + (2 - (-4))^2]

= √[(4)^2 + (6)^2]

= √[16 + 36]

= √52

≈ 7.21

Based on these calculations, we can conclude that:

The distance between points D and E (MED) is approximately 10.82 units.

The distance between points E and F (MEF) is approximately 7.21 units.

As for the points D, E, and F, we can conclude that they do not form a straight line since the distances between them (MED and MEF) are different. They are likely to be non-collinear points.

Rounding to the appropriate number of significant figures, the final volume of the cube is 7.99x10^-6 m^3.

The change in volume of a material under pressure can be calculated using the formula:

ΔV/V = -P/β

where:

ΔV = change in volume

V = original volume

P = pressure

β = bulk modulus

In this case, the original volume of the cube is (2cm)^3 = 8cm^3 = 8x10^-6 m^3.

Plugging in the given values, we get:

ΔV/V = -P/β

ΔV/8x10^-6 = -(3.0x10^5)/(3.5x10^9)

ΔV = -8.57x10^-11 m^3

Therefore, the final volume of the cube is:

V + ΔV = 8x10^-6 - 8.57x10^-11 = 7.99143x10^-6 m^3

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Answer:

JE

Step-by-step explanation:

found it online

Answer:

6 games on each of the three shelves

Step-by-step explanation:

The total of  22 books minus the 4 books on the top shelf leaves 18 remaining books. You take that 18 and divide by 3 since there are three more shelves. This will leave you with a total of 6 books on each of the other shelves

22 - 4 = 18

18 / 3 = 6