Help me! I need help with my homework! Ty! :)

The complex integral of [tex]\frac{zdz}{(z-a)^2}[/tex] over the unit circle C is [tex]\frac{-4\pi i}{a}[/tex] if a < 1, and 0 if a > 1.

From the question, we are to evaluate the given complex integral when a <1 and a > 1

We can evaluate the complex integral of [tex]\frac{zdz}{(z-a)^2}[/tex] over the unit circle C using the residue theorem. Since the function has a pole of order 2 at z = a, we need to compute the residue of the function at that point.

If a < 1, then the point a is inside the unit circle C. To compute the residue at z = a, we can expand the function in a Laurent series centered at z = a:

[tex]\frac{zdz}{(z-a)^2}= (\frac{1}{(z-a)})^2 d(z-a)[/tex]

= (1/(z-a))^2 dz - (2/(z-a))^1 da + ...

[tex](\frac{1}{(z-a)})^2dz -(\frac{2}{(z-a)})^1 da + ...[/tex] (Laurent series expansion)

The residue of the function at z = a is given by the coefficient of the [tex](z-a)^{-1}[/tex] term in this expansion, which is:

[tex]Res[z=z0] \frac{z dz}{(z-a)^2} = \frac{-2}{(a - 0)^1} = \frac{-2}{a}[/tex]

Therefore, by the residue theorem, the value of the integral is given by:

[tex]\oint \frac{c zdz}{(z-a)^2} = 2\pi i \times \frac{-2}{a} = \frac{-4\pi i}{a}[/tex]

If a > 1, then the point a is outside the unit circle C. Since the function is holomorphic on and inside the unit circle, it has no singularities inside C and the integral is zero:

[tex]\oint \frac{c zdz}{(z-a)^2} = 0[/tex]

Hence, the complex integral is [tex]\frac{-4\pi i}{a}[/tex] when a < 1, and 0 if a > 1.

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Answer: 1945

Step-by-step explanation:

Answer:

Harriet Tubman was born in 1820.

Step-by-step explanation:

Showing how brave and resourceful she was in running such a dangerous operation. A black woman operating in slave territory could be highly noticeable. It is a testament to her courage, brains, and fortitude that she was successful. Also, kudos to the many white persons who manned the stations along the Underground Railroad who coordinated with her.

Her impact on America—demonstrating an individual with struggle can accomplish much and correct wrongful structures in our land.

The commercial message that need to be run on every medium to maximize the audience is x = 15, y = 7 and z = 12.

A mathematical method called linear programming is used to maximise a linear objective function under the restrictions of linear equality and inequality. Finding choice variable values that maximise or decrease the objective function while meeting the limitations is required.

Let us suppose the number of advertisement run on television = x.

Let us suppose the number of advertisement run on radio = y.

Let us suppose the number of advertisement run on online = z.

Then,

140,000x + 18,000y + 30,000z

The constraints on the ads run on are as follws:

1,500x + 200y + 550z <= 24,100 (budget constraint)

x <= 15 (television usage limit)

y <= 19 (radio usage limit)

z <= 12 (online usage limit)

y <= 0.45(x+y+z) (radio usage limit as a percentage of total usage)

x >= 0.15(x+y+z)

Using the linear programming model we have:

x = 15, y = 7 and z = 12.

Substitute the value of x, y, and z:

140,000(15) + 18,000(7) + 30,000(12) = 2,910,000

Hence, the commercial message that need to be run on every medium to maximize the audience is x = 15, y = 7 and z = 12.

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122 degrees Fahrenheit is equal to 50 degrees Celsius.

Fahrenheit is a temperature scale where water freezes at 32 degrees and boils at 212 degrees under standard atmospheric pressure.

It is primarily used in the United States, the Bahamas, Belize, and the Cayman Islands.

For example, a typical comfortable room temperature of 72 degrees Fahrenheit would be 22.2 degrees Celsius on the Celsius scale.

Using the formula F = (9/5 x C) + 32, we can find the temperature in Fahrenheit when the temperature is 50 degrees Celsius.

F = (9/5 x C) + 32

F = (9/5 x 50) + 32

F = (90) + 32

F = 122

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Answer: To satisfy the given condition, we need to place the numbers in the boxes in a way that the sum of any three adjacent boxes is divisible by 3.

We can divide the boxes into three groups as follows:

Group 1: Boxes {1, 4, 7}

Group 2: Boxes {2, 5, 8}

Group 3: Boxes {3, 6, 9}

For any three boxes in a group, the sum of their contents must be divisible by 3. We can place any multiple of 3 in the middle box of each group, and the other two boxes will have to be filled accordingly.

Step-by-step explanation:

For Group 1:

If we place 3 in the middle box, then the boxes 1 and 7 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {1, 2}, {1, 5}, {4, 2}, {4, 5}, {7, 2}, {7, 5}. This gives us 6 possible ways to fill the boxes in Group 1.

If we place 6 in the middle box, then the boxes 1 and 7 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {1, 5}, {1, 8}, {4, 5}, {4, 8}, {7, 5}, {7, 8}. This gives us another 6 possible ways to fill the boxes in Group 1.

For Group 2:

If we place 3 in the middle box, then the boxes 2 and 8 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {1, 2}, {1, 5}, {4, 2}, {4, 5}, {7, 2}, {7, 5}. This gives us 6 possible ways to fill the boxes in Group 2.

If we place 6 in the middle box, then the boxes 2 and 8 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {1, 8}, {1, 5}, {4, 8}, {4, 5}, {7, 8}, {7, 5}. This gives us another 6 possible ways to fill the boxes in Group 2.

For Group 3:

If we place 3 in the middle box, then the boxes 3 and 9 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {2, 9}, {2, 6}, {5, 9}, {5, 6}, {8, 9}, {8, 6}. This gives us 6 possible ways to fill the boxes in Group 3.

If we place 6 in the middle box, then the boxes 3 and 9 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {2, 6}, {2, 3}, {5, 6}, {5, 3}, {8, 6}, {8, 3}. This gives us another 6 possible ways to fill the boxes in Group 3.

Therefore, the total number of ways to fill the boxes is:

6 x 6 x 6 x 6 = 1296.

Thus Bian can write the integers 1 to 9 in these ways.

hope it helps...

Answer:

Sin 60°

Sin 60°

Cos 30°

Cos 30°

The answer to this question is 4 Gallons and 1 quart or we can say 17 quarts.

The US Customary System defines a unit of liquid volume or capacity as 4 quarts (3.79 liters).

we have to find the value of 10 gallons and 11 quarts in gallons and quarters after dividing by 3.

As we know,

1 gallon = 4 quarts

10 gallons = [tex]10 * 4[/tex]=40 quarts

so 40 quarts + 11 quarts= 51quarts

It must be divided by 3 (According to the question we have to divide by 3 )

So, it becomes,

[tex]\frac{51}{3} =17[/tex]

Now we get 17 quarts.

And 17 quarts= 4 gallons and 1 quarts

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Answer:321.125 and i think the R that you are trying to say stands for remainder

Step-by-step explanation:

The height of the rock is described by the quadratic equation:

h = -16t² + 79t + 50.

a. The rock will be 125 feet above the beach for approximately 3.66 and 1.28 seconds.

b. The rock will reach its maximum height in about 2.5 seconds, reaching a height of around 147.5 feet.

An equation of the form f(x) = ax² + bx + c, where a 0 and a, b, and c are numbers, is a quadratic equation.

a. The following is how the rocket's height function is presented:

h(t) = -16·t² + 79·t + 50

The time at which the height is 125 feet is as follows:

h(t) = 125 feet

h(t) = 125 = -16·t² + 79·t + 50

-16·t² + 79·t + 50 - 125 = 125 - 125 = 0

-16·t² + 79·t - 75 = 0

The quadratic formula indicates:

t = (-79 ± √(79² - 4 × (-16) ×(-75)))/(2 × (-16)) = (79 ± √(1441))/32

t = (79 ± √(1441))/32

t = (79 + √(1441))/32 ≈ 3.66

t = (79 - √(1441))/32 ≈ 1.28

Therefore, the times at which the height of the rock is 125 feet above the beach are t ≈ 3.66 seconds, and t ≈ 1.28 seconds.

b.The formula for determining the input value at the maximum value of a quadratic function, which is: at the maximum height, x = -b/2a, can be used to determine the time at which the rock is at the maximum height.

Consequently, we obtain at the highest height;

t = -79/(2 (-16)) = 2.46875 is the time.

The rock climbs to its highest point in 2.46875 seconds, or 2.5 seconds.

Hence, h (2.46875) = -162.46875² + 792.46875 + 50 = 147.515625 147.5 is the maximum height.

The rock can rise up to a height of approximately 147.5 feet.

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Carlo should consider the sample size, sampling method, response rate, and sampling frame when determining which survey result is likely to be more accurate. By investigating these factors, Carlo can make an informed decision as to which survey result is likely to be more accurate.

Sample size is the number of participants or observations in a given study or experiment. It is an important factor in determining the validity and accuracy of the results. Large sample sizes are typically needed for experiments that involve multiple variables and for research with a small population. Sample size also affects the power of a test, which is the probability of correctly rejecting the null hypothesis.

In order to determine which survey result is more accurate, Carlo should first consider the sample size of each survey. If the sample size of one survey is significantly larger than the other, it is likely to be more accurate. Additionally, Carlo should consider the sampling method used in each survey. If one survey used a random sampling method while the other was not, then the random sample is more likely to be more representative of the entire population of players in the soccer league. Carlo should also consider the response rate for each survey, as surveys with higher response rates tend to be more accurate. Finally, Carlo should investigate the sampling frame used in each survey. If one survey used a sampling frame that was more representative of the population than the other, then it is likely to be more accurate.

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The symbolic quantified statement is given as:

For all real integers x and y, if x³ = y³, then x = y.

Using quantifiers, this can be written as:

∀x,y∈ℝ, (x³ = y³) → (x = y)

The symbolic quantified statement represents the original sentence using logical symbols and quantifiers.

The universal quantifier (∀) is used to denote "for all," while the implication arrow (→) represents "if... then." The statement asserts that if the cubes of any two real integers x and y are equal, then x and y are equal as well.

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Answer:

i don't know

Step-by-step explanation:

good luck bro

(alright I'm just here for the points so yeah bye)

Answer:

Step-by-step explanation:

Let the profit in 2020 be P.

The profit in 2021 would then be 1.20P (20% increase).

The profit in 2022 would be 0.83(1.20P) = 0.996P (17% decrease from 2021).

We can see that the profit in 2020 was P, while the profit in 2022 was less than P (0.996P).

Therefore, the higher profit was in 2020.

The solution is, the higher profit was in 2020.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

Let the profit in 2020 be P.

The profit in 2021 would then be 1.20P (20% increase).

The profit in 2022 would be 0.83(1.20P) = 0.996P (17% decrease from 2021).

We can see that the profit in 2020 was P, while the profit in 2022 was less than P (0.996P).

Therefore, the higher profit was in 2020.

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Answer:

450

Step-by-step explanation:

270/3=90, 90*5=450

The total cost of buying a postal order of N15 would be N15.50.

To calculate the cost of buying a postal order of N365, we need to determine the commission associated with the value of N365 in the postal order table.

Since N365 is between N100 and N50, the commission for this amount would be N5.50.

Therefore, the total cost of buying a postal order of N365 would be N365 + N5.50 = N370.50.

To find the cost of buying a postal order of N15, we look at the postal order table and find that the commission associated with N15 is 50k.

Therefore, the total cost of buying a postal order of N15 would be N15 + 50k = N15.50.

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Answer:

To find the linear function with the given properties, we need to determine the slope and y-intercept of the function.

We can use the slope-intercept form of a linear function, which is:

y = mx + b

where m is the slope and b is the y-intercept.

First, we can find the slope using the two given points:

slope = (y2 - y1) / (x2 - x1)

slope = (4 - (-12)) / (-7 - (-3))

slope = 16 / (-4)

slope = -4

Now that we have the slope, we can use one of the given points to find the y-intercept. Let's use the point (-3, -12):

y = mx + b

-12 = (-4)(-3) + b

-12 = 12 + b

b = -24

Therefore, the linear function that satisfies the given properties is:

f(x) = -4x - 24

Answer:

Ivanna takes 9.6 minutes per mile.

To find out, you can divide the total time by the total distance:

time per mile = total time ÷ total distance

time per mile = 96 minutes ÷ 10 miles

time per mile = 9.6 minutes/mile

Step-by-step explanation:

Answer:

-7 in binary is -0b111.

-5 in binary is -0b101.

Step-by-step explanation:

Answer:

-111

-101

Step-by-step explanation:

Binary uses powers of 2.

2^0 = 1

2^1 = 2

2^2 = 4

2^3 = 8

2^4 = 16

7 = 4 + 2 + 1

7 = 1 × 2^2 + 1 × 2^1 + 1 × 2^0

7 in binary is 111

-7 in binary is -111

5 = 4 + 1

5 = 1 × 2^2 + 0 × 2^1 + 1 × 2^0

5 in binary is 101

-5 in binary is -101

Answer:

Step-by-step explanation:

x

x  - 1

(x - 1 ) × 3

(x - 1 ) × 3 =

3x - 3

Answer: The range is the best measure of variability for the given data set and its value is 500.

The range is the difference between the maximum and minimum values in a data set, and in this case, the maximum value is 1100 and the minimum value is 600, so the range is 1100-600=500. The range gives us an idea of how spread out the data is, but it can be affected by outliers. In this case, it seems like a reasonable measure of variability since there are no extreme values that would greatly affect the range.

Step-by-step explanation:

From the data of the number of meters swam by students , range is the best measure of variability and equals 500

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.

Given data ,

Let the data set be represented as A

Now , the value of A is

A = { 600, 750, 800, 850, 900, 1100 }

The appropriate measure of variability for the given data is the range. The range is the difference between the largest and smallest values in the data set.

And , range = 1100 - 600

R = 500

Hence , the range of the data set is R = 500

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The equation of the ellipse is (x - 6)² / 4 + (y - 1)² / (16/9) = 1, the center is (6,1), and the directrices are x = 0 and x = 12.

The center of the ellipse is the midpoint of the major axis. The midpoint of the line segment connecting (4,1) and (8,1) is ((4+8)/2, (1+1)/2) = (6,1). Therefore, the center of the ellipse is (6,1).

The distance between the center and one of the vertices (say, (8,1)) is the length of the semi-major axis, a. This distance is (8-6) = 2. Therefore, the semi-major axis is a = 2.

The eccentricity, e, is given as 1/3.

The distance between the center and one of the foci, c, is related to the semi-major axis and eccentricity by the equation c = ae. Plugging in the values we know, we get c = (1/3)(2) = 2/3.

We can write the equation of the ellipse in standard form:

(x - 6)² / 2² + (y - 1)^2 / b² = 1

where b is the semi-minor axis. We can solve for b using the relationship between the semi-major axis, semi-minor axis, and eccentricity:

So the equation of the ellipse is:

(x - 6)² / 4 + (y - 1)² / (16/9) = 1

The directrices are located a distance of a² / c = (2²) / (2/3) = 6 units away from the center along the major axis. These are the lines x = 6 - 6 = 0 and x = 6 + 6 = 12.

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Answer:

Step-by-step explanation:

zachary climed 9.5 m

erin climed 8.8m

to 2 dp

zachary-9.51

erin-8.76

Answer: 2/7 as a decimal rounded to the nearest thousandth is 0.286.

Answer:

terms:  'k' and '-3d'

coefficient of 'k' is 1

coefficient of '-3d' is -3

Step-by-step explanation:

if a variable exists by itself then its coefficient is 1, otherwise

whatever value precedes a variable is its coefficient

When a is equal to -2, the ordered pair is an equational solution.

The places where the lines representing the intersection of two linear equations intersect are referred to as the solution of a linear equation. In other words, the set of all feasible values for the variables that satisfy the specified linear equation is the solution set of the system of linear equations.

y=3x+7

Ordered pair (-3,a)

introducing x=-3 as a value in the equation

y=3(-3)+7

y=-9+7

y=-2

Hence,value of a is -2 that makes the ordered pair a solution of the equation.

y=3x+7 represents the equation of a straight line. So, it can satisfy infinite ordered pair.

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Answer:

See graph

Step-by-step explanation:

The transformation is as follows

The transformation of h(x) to -h(x) - 4 is a combination of two transformations

1. A reflection around the x -axis. Every point(x, y) in h(x) becomes (x', y') where x' = x and y' = -y so (x, y) → (x, -y)

2. A translation of each reflected point 4 units down; x value does not change but y values are shifted down so the new y is y'-4 = -y -4

The result of both transformations is:
every coordinate (x, y) in h(x) will be transformed to (x, -y -4)

Seeing as the graph consists of two straight lines meeting at the origin, all we need to do is take any 3 points in h(x), find the transformed coordinates and connect them with straight ilnes

h(x0              -h(X) - 4

(-2, 4)    ⇒      (-2, -4-4) = (-2, -8)

(0, 0 )   ⇒       (0, -0 - 4) = (0, -4)

(4, 2)    ⇒       (4, -2 -4)   = (4, -6)

take these three points and plot

Answer:

x ≈ 10.4

Step-by-step explanation:

using the tangent ratio in the right triangle

tan41° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{9}{x}[/tex] ( multiply both sides by x )

x × tan41° = 9 ( divide both sides by tan41° )

x = [tex]\frac{9}{tan41}[/tex] ≈ 10.4 ( to the nearest tenth )

Answer:

x=10.34

Step-by-step explanation:

tanФ=opposite ÷ adjacent

tan41°=9/x

0.87=9/x

x=9/0.87

 =10.34

The equation y = (-2/3)x + 6 represents a line that is decreasing from left to right and intersects the y-axis at the point (0, 6).

The slope refers to the measure of the steepness of a line or a curve. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line or the curve.

The equation of a line can be written as with the help of slope intercept form is given by:

y = mx + b

Where "b" is the y-intercept and "m" is the line's slope of the line.

In the equation y = (-2/3)x + 6, we can see that the slope 'm' is -2/3, which means that for every unit increase in x, the y-value decreases by 2/3 of a unit. This tells us that the line represented by this equation is decreasing (i.e., sloping downwards) from left to right.

The y-intercept 'b' is 6, which means that the line intersects the y-axis at the point (0, 6). This is the starting point of the line, where the value of y is 6 when x is 0.

Therefore, the equation y = (-2/3)x + 6 represents a line that is decreasing from left to right and intersects the y-axis at the point (0, 6).

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