I need answers ASAP please

I Need Answers ASAP Please
I Need Answers ASAP Please

Answers

Answer 1

Answer:

22

Step-by-step explanation:

Just count the units around it,

it's kind of blurry so you should just double check in case.


Related Questions

Bandhan Bank employee salary after 10 years

Answers

Answer:

- Banking Operations salary in India with less than 1 year of experience to 10 years ranges from ₹ 1.4 Lakhs to ₹ 7 Lakhs with an average annual salary of ₹ 3.1 Lakhs based on 261 latest salaries

A bag of marbles has 12 green marbles, 5 red marbles, 8 blue marbles and 7 yellow marbles. What is the probability of randomly selecting a blue marble?

Answers

Probability = # of desired options / # of total options

Our desired option is blue and there are 9 blue marbles in the bag.

There are 32 total marbles (options) in the bag.

P(blue) = 9 / 32 = 0.28125 = 28.125%

Hope this helps!


Find the difference
884,283-349,407

Answers

The difference between 884,283 - 349,407 is calculated to be 534,876

How to find the difference

The difference is a term used to represent subtraction, hence in the problem is solved using the mathematical operation known as subtraction

To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it.

The operation is done as follows

= 884,283 - 349,407

= 534,876

The subtraction gives 534,876

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What is the quotient of 30 and 0.08

Answers

Answer:

30 divided by 0.08 will get you 375

Step-by-step explanation:

11. Which of the following are not meaningful?
(b) XXXI
(a) VXXIX
(C) XLIV
12. Write 'Divide the difference of 91 and 7 by 6' using brackets and solve.
(d) CXCLXV

Answers

The answer to question 11 is (d) CXCLXV. Roman numerals are not meaningful when they are repeated more than three times.

The answer to question 12 is [(91 - 7) ÷ 6] = 14.

Your firm purchases a business copier that costs $14,000 and requires $3,000 in maintenance for each year of its four-year life. After four years, the copier will be replaced. The copier falls into the MACRS three-year class life category. Use table 12.8 on page 415 in your textbook for DDB depreciation. If the tax rate is 32 percent, whats the depreciation tax shield for this project in year 4?

Answers

Answer:

The depreciation tax shield for this project in year 4 is $178.24.

Explanation:

To calculate the depreciation tax shield for this project in year 4, we need to first determine the depreciation expense for year 4 using the MACRS three-year class life category and the double-declining balance (DDB) method.

From Table 12.8 on page 415 of the textbook, we can see that the depreciation rate for year 1 is 33.33%, for year 2 it is 44.45%, for year 3 it is 14.81%, and for year 4 it is 7.41%.

Using the DDB method, we can calculate the depreciation expense for each year as follows:

Year 1: Depreciation expense = $14,000 x 33.33% = $4,667

Year 2: Depreciation expense = ($14,000 - $4,667) x 44.45% = $3,554

Year 3: Depreciation expense = ($14,000 - $4,667 - $3,554) x 14.81% = $830

Year 4: Depreciation expense = ($14,000 - $4,667 - $3,554 - $830) x 7.41% = $557

The total depreciation expense over the four years is the sum of the individual year's depreciation expenses, which is:

$4,667 + $3,554 + $830 + $557 = $9,608

Now, we can calculate the depreciation tax shield in year 4. The depreciation tax shield is the amount of the depreciation expense that reduces the firm's taxable income, multiplied by the tax rate. In year 4, the depreciation tax shield is:

Depreciation tax shield = Depreciation expense in year 4 x Tax rate

Depreciation tax shield = $557 x 32% = $178.24

Therefore, the depreciation tax shield for this project in year 4 is $178.24.

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U thought this was a professional answer?!!!!??????

You're wrong!!!!!!!!!!!!!!!!!

But the answer is correct though...

:))

PEW PEW PEW

Bing Chilling

It's over...

No more to read

Happy birthday if it's ur birthday...

Have a nice day my king:)

How many ninth does it take to make the same amount as one third

Answers

We just need to multiply the number by 3

Answer:

3

Step-by-step explanation:

you have 1/3, to find out how many ninths you have, you must multiply the denominator by three (because 3*3=9). whatever you multiply on the bottom you must multiply on the top (if you don't do that then it's not the same as 1/3 anymore)

therefore 1/3 == (1*3)/(3*3) == 3/9

if you want to know how many twelves it was then you multiply by 4 to get 12 on the bottom:

1/3 == (1*4)/(3*4) == 4/12

therefore 1/3 == 3/9 == 4/12. they are all the same fraction

De los 12 jugadores del equipo 2/8 son delanteros

Answers

There are a total of 3 forwards on the team.

How many forwards are there on the team?

A fraction represents a part of the whole or group of objects.In a fraction, numerator and denominator are separated by a horizontal bar known as the fractional bar

Given:

2/8 of the players are forwards.

Total number of players on the team = 12

We will determine the total number of forwards on the team by multiplying the total number of players by the fraction representing the forwards.

Fraction representing the forwards:

= 2/8

= 1/4

Total forwards on the team:

= 12 * (1/4)

= 3.

Translated question:

Of the 12 players on the team, 2/8 are forwards. What are the total forward in the team?

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What is 3.4 divided by 10?

Answers

Answer:0.34 or .34

Step-by-step explanation:

Find the root of the function f(x)=−4x+1.

Find the root of the function f(x)=4x+1.

Answers

Answer: A

Step-by-step explanation:

\(-\frac{4}{x}+1=0\\\\1=\frac{4}{x}\\\\x=4\)

Writing linear equations in slope-intercept form. Write the equation of each linear below:

Writing linear equations in slope-intercept form. Write the equation of each linear below:

Answers

The linear equations in slope-intercept form are  y=2x+3 ,  y=-1x-2 , y=-3x+4 and y = 3x .

What is linear equation ?

Linear equation can be defined as equation in which highest degree is one.

Given ,

We have to write linear equations in slope intercept form.

So,

An equation in the slope-intercept form is written as

y = mx + b

Where m is the slope of the line and b is the y-intercept. You can use this equation to write an equation if you know the slope and the y-intercept.

So, from given graphs we can say that

y - 3 = 2x

y=2x+3

y + 2 = -x

y=-1x-2

y - 4 = -3x

y=-3x+4

y - 0 = 3x

y=3x+0

y = 3x

Therefore, The linear equations in slope-intercept form are  y=2x+3 ,  y=-1x-2 , y=-3x+4 and y = 3x .

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6lbs of apples for 33.60

Answers

Answer:

If that's the whole question then what exactly are we trying to solve here?

Step-by-step explanation:

1. An acrobat is on a platform that is 25 feet in the air. She jumps down at an initial vertical velocity of 4 ft/s. Write a quadratic function to
represent the height h of the acrobat t seconds after the jump. If a safety net is placed 5 feet above the ground, how long will it take for her to land safely on the net?

Answers

Since we are only interested in the positive solution, the time it will take for her to land safely on the net is:

t = 1 second.

To write a quadratic function to represent the height h of the acrobat t seconds after the jump, we can use the following formula:

\(h(t) = -16t^2 + vt + h0\)

Where h0 is the initial height of the acrobat, which is 25 feet, and v is the initial vertical velocity, which is 4 ft/s. Plugging in these values, we get:

\(h(t) = -16t^2 + 4t + 25\)

To find how long it will take for her to land safely on the net, we need to find the time at which h(t) = 5. In other words, we need to solve the equation:

\(-16t^2 + 4t + 25 = 5\)

Simplifying this equation, we get:

\(-16t^2 + 4t + 20 = 0\)

Dividing both sides by -4, we get:

\(4t^2 - t - 5 = 0\)

Now we can use the quadratic formula to solve for t:

\(t = (-b ± \sqrt(b^2 - 4ac)) / 2a\)

Where a = 4, b = -1, and c = -5. Plugging in these values, we get:

\(t = (1 ± \sqrt(1 + 4(4)(5))) / 8\)

Simplifying this equation, we get:

\(t = (1 ± 9) / 8\)

So, the two solutions are:

\(t = 1 and t = -5/4\)

Since we are only interested in the positive solution, the time it will take for her to land safely on the net is:

t = 1 second.

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HELP PLZ and thank you

find the measure of the arc or central angle indicated. assume that lines which appear to be diameters are actual diameters.

HELP PLZ and thank you find the measure of the arc or central angle indicated. assume that lines which

Answers

Answer:

Step-by-step explanation:

Circle degrees total 360 .  

360 - 126 -54-54 (other side of vertical angles) equals 126 degrees left for the other two remaining sections.  

14x+4  +15x+6 =126

19x+10 = 126

29x = 116

x=4 .  answer .

Solve for 2. Round to the nearest tenth, if necessary.
B
U
67
T
x
142°

Solve for 2. Round to the nearest tenth, if necessary.BU67Tx142

Answers

Tan(angle) = opposite/ adjacent


tan(42) = 67/x


x =67/tan(42)

X = 74.411


rounded to nearest tenth : x = 74.4

Find a factorization of x² + 2x³ + 7x² - 6x + 44, given that
−2+i√√7 and 1 - i√/3 are roots.

Answers

Surely you mean

\(x^4 + 2x^3 + 7x^2 - 6x + 44\)

The coefficients are integers, so the conjugate of any complex root to the quartic is also a root. In particular,

\(-2 + i\sqrt7 \text{ and thus } -2 - i\sqrt7\)

are roots, as are

\(1 - i\sqrt3 \text{ and } 1 + i\sqrt3\)

Then the complete factorization is

\(\boxed{(x - (-2 + i\sqrt7)) (x - (-2 - i\sqrt7)) (x - (1 + i\sqrt3)) (x - (1 - i\sqrt3))}\)

which we can simplify to get a factorization involving only integer coefficients,

\((x^2 + 4x + 11) (x^2 - 2x + 4)\)

A factorization of \(x^4+2x^3+7x^2-6x+44\) is \((x^2+4x+11)(x^2-2x+4)\).

What are the properties of roots of a polynomial?The maximum number of roots of a polynomial of degree \(n\) is \(n\).For a polynomial with real coefficients, the roots can be real or complex.The complex roots of a polynomial with real coefficients always exist in a pair of conjugate numbers i.e., if \(a+ib\) is a root, then \(a-ib\) is also a root.

If the roots of the polynomial \(p(x)=ax^4+bx^3+cx^2+dx+e\) are \(r_1,r_2,r_3,r_4\), then it can be factorized as \(p(x)=(x-r_1)(x-r_2)(x-r_3)(x-r_4)\).

Here, we are to find a factorization of \(p(x)=x^4+2x^3+7x^2-6x+44\). Also, given that \(-2+i\sqrt{7}\) and \(1-i\sqrt{3}\) are roots of the polynomial.

Since \(p(x)=x^4+2x^3+7x^2-6x+44\) is a polynomial with real coefficients, so each complex root exists in a pair of conjugates.

Hence, \(-2-i\sqrt{7}\) and \(1+i\sqrt{3}\) are also roots of the given polynomial.

Thus, all the four roots of the polynomial \(p(x)=x^4+2x^3+7x^2-6x+44\), are: \(r_1=-2+i\sqrt{7}, r_2=-2-i\sqrt{7}, r_3=1-i\sqrt{3}, r_4=1+i\sqrt{3}\).

So, the polynomial \(p(x)=x^4+2x^3+7x^2-6x+44\) can be factorized as follows:

\(\{x-(-2+i\sqrt{7})\}\{x-(-2-i\sqrt{7})\}\{x-(1-i\sqrt{3})\}\{x-(1+i\sqrt{3})\}\\=(x+2-i\sqrt{7})(x+2+i\sqrt{7})(x-1+i\sqrt{3})(x-1-i\sqrt{3})\\=\{(x+2)^2+7\}\{(x-1)^2+3\}\hspace{1cm} [\because (a+b)(a-b)=a^2-b^2]\\=(x^2+4x+4+7)(x^2-2x+1+3)\\=(x^2+4x+11)(x^2-2x+4)\)

Therefore, a factorization of \(x^4+2x^3+7x^2-6x+44\) is \((x^2+4x+11)(x^2-2x+4)\).

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During a single day at the radio station WMZH, the probability that a particular song is played is 1/6. What is the probability that this song will be played on exactly 6 days out of 7 days? Round your answer to the nearest thousandth.

Answers

Around 0.000125 or 0.0125% of the time, the song will be played exactly six out of seven days.

Every day represents a trial in this binomial probability issue, and there are only two potential results:

either the music is played (a success), or it is not (failure). We're looking for the likelihood that exactly 6 out of 7 trials will be successful.

The likelihood of success (performing the song) is 1/6, while the likelihood of failure (not playing the song) is 1 - 1/6 = 5/6, on any given day.

We can use the binomial probability formula to find the probability of exactly 6 successes in 7 trials:

P(6 successes) = (7 choose 6) * (1/6)⁶ * (5/6)¹

where (7 choose 6) is the number of ways to choose 6 days out of 7 to play the song, and is calculated as:

(7 choose 6) = 7! / (6! * 1!) = 7

Plugging in the values, we get:

P(6 successes) = 7 * (1/6)⁶ * (5/6)¹

P(6 successes) ≈0.00012502

Therefore, the probability that the song will be played on exactly 6 days out of 7 is approximately 0.000125 or 0.0125%.

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If M2BAC = (3x – 1)º, m_chD = (6x + 10)°, m2DAE (2x + 6)°, and m_BAE = 103°, then find the mZCAD​

Answers

Answer:

mZCAD=310°

Step-by-step explanation:

M2BAC=1,m2DAE=3 and m-BAE=0 therefore solution will be 310°

What is the solution to the equation?
2(x + 7) 2/3 = 8

Answers

Answer: x = -1

Step-by-step explanation:

simplify 2(x + 7) 2 / 3 = 8 to 4x + 28 = 24 and then solve it from there

Pls help me I CANT DO THIS AT ALL PLS

Pls help me I CANT DO THIS AT ALL PLS

Answers

2 is the gcf because 24 and 26 has 2 in common


\( \frac{2}{3} \times \frac{1}{2} \)
ayuda por favor en español ​

Answers

1/3
Reduces los números usando el máximo común divisor= 2

12a-12b+12c please help to simplify

Answers

Answer:

12(a+b+c)

Step-by-step explanation:

how to verify:

Distribute 12 and you'll get the original expression

I hope my answer was helpful!

What are the values of x in the equation x2 – 6x + 9 = 25? x = –2 or x = 8 x = –1 or x = –11 x = 1 or x = 11 x = 2 or x = –8

Answers

Answer:

x = 8 or x = -2

Step-by-step explanation:

x^2 - 6x + 9 = 25

x^2 - 6x - 16 = 0

The formula to solve a quadratic equation of the form ax^2 + bx + c = 0 is equal to x = [-b +/-√(b^2 - 4ac)]/2a

with a = 1

b = -6

c = -16

substitute in the formula

x = [-(-6) +/- √(-6^2 - 4(1)(-16))]/2(1)

x = [6 +/- √(36 + 64)]/2

x = [6 +/- √10]/2

x = [6 +/- 10]/2

x1 = [6 + 10]/2 = 16/2 = 8

x2 = [6 - 10]/2 = -4/2 = -2

Answer:

x = 8,-2

Step-by-step explanation:

First, complete the square on LHS (Left-Handed Side).

\(\displaystyle \large{x^2-6x+9=(x-3)^2}\)

Make sure to recall the perfect square formula. Rewrite another equation with (x-3)² instead.

\(\displaystyle \large{(x-3)^2 = 25}\)

Square both sides of equation.

\(\displaystyle \large{\sqrt{(x-3)^2}=\sqrt{25}}\)

Because x² = (-x)² which means that it’s possible for x to be negative. Thus, write plus-minus beside √25 and cancel square of LHS.

\(\displaystyle \large{x-3=\pm \sqrt{25}}\\ \displaystyle \large{x-3=\pm 5}\\ \displaystyle \large{x=\pm 5+3}\)

Therefore, x = 5+3 or x = -5+3

Thus, x = 8,-2

The method above is called completing the square method.

Identify the property of the quadratic function.
1. Zeros:
2. Axis of Symmetry: X =
3. Vertex: (-
4. Circle: Up or Down
5. Circle: Minimum or Maximum
6. Identify the Minimum or Maximum Value:
T
7
T

Identify the property of the quadratic function.1. Zeros:2. Axis of Symmetry: X =3. Vertex: (-4. Circle:

Answers

1. The zeros of the given quadratic function are -4 and 0

2. The axis of symmetry is at x = -2

3. The vertex of the quadratic function is (-2, 4)

4. The quadratic function opens down

5. Maximum

6. The maximum value is y = 4

Determining the properties of a quadratic function from the graph

From the question, we are to determine the given properties of the quadratic function

1. The zero(s) of a quadratic function is(are) the point(s) where the curves intersect(s) with the x-axis

The zeros of the given quadratic function are -4 and 0

2. The axis of symmetry is at x = -2

3. The vertex of a quadratic function is the coordinates of the lowest or highest point of the function. The vertex of the quadratic function is (-2, 4)

4. The quadratic function opens down

5. Maximum

6. The maximum value is y = 4

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A zip wire runs between two posts, 25m apart. The zip wire is at an angle of 10∘ to the horizontal. Calculate the length of the zip wire.

Answers

The length of the zip wire is approximately 25.42 meters.

To calculate the length of the zip wire, we can use trigonometry and the given information about the angle and the distance between the two posts.

Given:

Distance between the two posts: 25m

Angle of the zip wire to the horizontal: 10°

We can use the trigonometric function cosine (cos) to find the length of the zip wire. Cosine relates the adjacent side to the hypotenuse of a right triangle.

In this case, the adjacent side is the distance between the two posts (25m) and the hypotenuse is the length of the zip wire that we want to calculate.

Using the cosine function:

cos(angle) = adjacent/hypotenuse

cos(10°) = 25m/hypotenuse

To find the hypotenuse (length of the zip wire), we can rearrange the equation:

hypotenuse = 25m / cos(10°)

Using a calculator or trigonometric tables, we can find the value of cos(10°) to be approximately 0.9848.

Therefore, the length of the zip wire is:

hypotenuse = 25m / 0.9848 ≈ 25.42m

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Geometric Sequence S = 1.0011892 + ... + 1.0012 + 1.001 + 1

Answers

Answer:

\(S_{1893} =5632.98\)

Step-by-step explanation:

The correct form of the question is:

\(S = 1.001^{1892} + ... + 1.001^2 + 1.001 + 1\)

Required

Solve for Sum of the sequence

The above sequence represents sum of Geometric Sequence and will be solved using:

\(S_n = \frac{a(1 - r^n)}{1 - r}\)

But first, we need to get the number of terms in the sequence using:

\(T_n = ar^{n-1}\)

Where

\(a = First\ Term\)

\(a = 1.001^{1892}\)

\(r = common\ ratio\)

\(r = \frac{1}{1.001}\)

\(T_n = Last\ Term\)

\(T_n = 1\)

So, we have:

\(T_n = ar^{n-1}\)

\(1 = 1.001^{1892} * (\frac{1}{1.001})^{n-1}\)

Apply law of indices:

\(1 = 1.001^{1892} * (1.001^{-1})^{n-1}\)

\(1 = 1.001^{1892} * (1.001)^{-n+1}\)

Apply law of indices:

\(1 = 1.001^{1892-n+1}\)

\(1 = 1.001^{1892+1-n}\)

\(1 = 1.001^{1893-n}\)

Represent 1 as \(1.001^0\)

\(1.001^0 = 1.001^{1893-n}\)

They have the same base:

So, we have

\(0 = 1893-n\)

Solve for n

\(n = 1893\)

So, there are 1893 terms in the sequence given.

Solving further:

\(S_n = \frac{a(1 - r^n)}{1 - r}\)

Where

\(a = 1.001^{1892}\)

\(r = \frac{1}{1.001}\)

\(n = 1893\)

So, we have:

\(S_{1893} =\frac{1.001^{1892} *(1 -\frac{1}{1.001}^{1893})}{1 -\frac{1}{1.001} }\)

\(S_{1893} =\frac{1.001^{1892} *(1 -\frac{1}{1.001}^{1893})}{\frac{1.001 -1}{1.001} }\)

\(S_{1893} =\frac{1.001^{1892} *(1 -\frac{1}{1.001}^{1893})}{\frac{0.001}{1.001} }\)

\(S_{1893} =\frac{1.001^{1892} *(1 -\frac{1}{1.001^{1893}})}{\frac{0.001}{1.001} }\)

Simplify the numerator

\(S_{1893} =\frac{1.001^{1892} -\frac{1.001^{1892}}{1.001^{1893}}}{\frac{0.001}{1.001} }\)

\(S_{1893} =\frac{1.001^{1892} -1.001^{1892-1893}}{\frac{0.001}{1.001} }\)

\(S_{1893} =\frac{1.001^{1892} -1.001^{-1}}{\frac{0.001}{1.001} }\)

\(S_{1893} =(1.001^{1892} -1.001^{-1})/({\frac{0.001}{1.001} })\)

\(S_{1893} =(1.001^{1892} -1.001^{-1})*{\frac{1.001}{0.001}}\)

\(S_{1893} =\frac{(1.001^{1892} -1.001^{-1}) * 1.001}{0.001}\)

Open Bracket

\(S_{1893} =\frac{1.001^{1892}* 1.001 -1.001^{-1}* 1.001 }{0.001}\)

\(S_{1893} =\frac{1.001^{1892+1} -1.001^{-1+1}}{0.001}\)

\(S_{1893} =\frac{1.001^{1893} -1.001^{0}}{0.001}\)

\(S_{1893} =\frac{1.001^{1893} -1}{0.001}\)

\(S_{1893} =5632.97970294\)

Hence, the sum of the sequence is:

\(S_{1893} =5632.98\) ----- approximated

EspanolAvicenna, a major insurance company, offers five-year life insurance policies to 65-year-olds. If the holder of one of these policiesdies before the age of 70, the company must pay out $27,400 to the beneficiary of the policy. Executives at Avicenna areconsidering offering these policies for $765 each. Suppose that for each holder of a policy there is a 3% chance that they will diebefore the age of 70 and a 97% chance they will live to the age of 70.00If the executives at Avicenna know that they will sell many of these policies, should they expectto make or lose money from offering them? How much?To answer, take into account the price of the policy and the expected value of the amount paldout to the beneficiary.Avicenna can expect to make money from offering these policies.In the long run, they should expect to make dollars on each policy sold.Avicenna can expect to lose money from offering these policies,

EspanolAvicenna, a major insurance company, offers five-year life insurance policies to 65-year-olds.

Answers

Answer:

Avicenna can expect to lose money from offering these policies. In the long run, they should expect to lose 57 dollars on each policy sold.

Explanation:

If a person lives to the age of 70, they will earn $765. So, there is a 97% chance to earn $765. On the other hand, if a person dies before age of 70, they will lose $26635 because

$27,400 - $765 = 26,635

Then, there is a 3% chance to lose $26635.

Now, we can find the expected value, multiplyion each option by its probability, so:

E = $765(0.97) - (26635)(0.03)

E = $742.05 - $799.05

E = - $57

Since the sign is negative they can expect to lose money, so the answer is:

Avicenna can expect to lose money from offering these policies. In the long run, they should expect to lose 57 dollars on each policy sold.

C is equidistant to which of the following points

C is equidistant to which of the following points

Answers

The point C is equidistant to (b) CL = CM = CN

How to determine the equidistant points

From the question, we have the following parameters that can be used in our computation:

The triangle

From the triangle, we can see that the point C is the centroid of the triangle

As a general rule:

The centroid is the geometric centre of a triangle. It is equidistant from all the points present on the triangle.

This means that point C is equidistant from L, M and N

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10.30, 7.85____, 2.95, 0.50 which of the following should be placed in the blank above to complete the pattern?

6.30
5.40
4.85
3.45

Answers

The answer is C. 4.85

Prove that:-
\( \rm \sum_{n = 1}^ \infty \frac{1}{ {n}^{2} + {x}^{2} } = \frac{\pi x - 1 }{2 {x}^{2} } + \frac{\pi}{x( {e}^{2 \pi x} - 1)} \\ \)​

Answers

Observe that

\(\displaystyle \frac1{e^{2\pi x} - 1} = \frac{e^{-\pi x}}{e^{\pi x} - e^{-\pi x}} = \frac{\cosh(\pi x) - \sinh(\pi x)}{2\sinh(\pi x)} = \frac{\coth(\pi x) - 1}2\)

We have the following series expansion due to Mittag-Leffler:

\(\displaystyle \pi \coth(\pi z) = \frac1z + 2 \sum_{n=1}^\infty \frac z{z^2+n^2}\)

The proof of this is easy to follow. (I'll try to include a link)

With some simple rearrangement, we get the desired result.

\(\displaystyle \sum_{n=1}^\infty \frac1{n^2 + x^2} = -\frac1{2x^2} + \frac{\pi \coth(\pi x)}{2x} \\\\ ~~~~~~~~ = -\frac1{2x^2} + \frac\pi{2x} + \frac\pi{x(e^{2\pi x}-1)}\)

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