standard form. (-3,0) and (0,8)

According to given function the final value is [tex]$f=\frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}(x-i y)}{x^2+y^2} ; \quad x \neq-i y$[/tex]

[tex]$$f(x+i y)=\sum_{k=1}^{\infty} \frac{1}{k}(x+i y)$$[/tex]

[tex]$$f(x+i y)=\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}$$[/tex]

Divide both sides by [tex]$x+i y ; \quad x \neq-i y$[/tex]

[tex]\frac{f(x+i y)}{x+i y}=\frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}}{x+i y} ; \quad x \neq-i y$$[/tex]

Simplify

[tex]\frac{f(x+i y)}{x+i y}=\frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}}{x+i y}$$[/tex]

Simplify[tex]$\frac{f(x+i y)}{x+i y}: f$[/tex]

Simplify [tex]$\frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}}{x+i y}: \frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}(x-i y)}{x^2+y^2}$[/tex]

[tex]f=\frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}(x-i y)}{x^2+y^2} ; \quad x \neq-i y$$[/tex]

[tex]f=\frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}(x-i y)}{x^2+y^2} ; \quad x \neq-i y$$[/tex]

The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x.

In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

To learn more about function visit:https://brainly.com/question/12431044

#SPJ1

Answer:

It is arithmetic, the common difference is 5

Step-by-step explanation:

What an arithmetic sequence has to have is a common difference meaning you are adding or subtracting the same number each time, in this case you are adding 5 every time so it is arithmetic

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$4500\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &1 \end{cases} \\\\\\ I = (4500)(0.08)(1) \implies I = 360~\hfill \underset{monthly~payment}{\stackrel{360 ~~ \div ~~ 12}{\text{\LARGE 30}}}[/tex]

c.

PRT/100

4500×8×1/100=360

per month=360÷12

=30

The coordinate that represent the solution of the equation -

x² - 3x = x² - 1 is (0.333, -0.8889).

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given is the following equation -

x² - 3x = x² - 1

In order to solve it using intersect method, we will plot the graphs of both functions and find the point of intersection of graphs of both the equations.

Assume -

f(x) = x² - 3x

g(x) = x² - 1

Now, the point of intersection of both the graphs will be the solution to the equation given by -

f(x) = g(x)

It can be seen from the graph that, both the graphs intersect at the coordinate (0.333, -0.8889). This coordinate will be the solution set of the equation -

f(x) = g(x)

Therefore, the coordinate that represent the solution of the equation -

x² - 3x = x² - 1 is (0.333, -0.8889).

To solve more questions on solving equation by graphs , visit the link below-

https://brainly.com/question/16604883

#SPJ2

Answer:

n ≥ -5

Step-by-step explanation:

-2n ≤ 10

Divide both sides by -2. Remember to flip ≤ to ≥.

-2n/(-2) ≥ 10/(-2)

n ≥ -5

The use the numbers 5, 6, and 7 and the operations of addition, subtraction, multiplication, and/or division to create three different number expressions with three different values will be:

1. 5 × 6 + 7 = 37

2. 5 + 6 - 7 = 4

3. 5 + 6 + 7 = 18

Addition simply means the sum of the numbers that are given. It should be noted that addition is represented by the sign +.

In this case, we are told to use 5, 6 and 7 to create different values. These are represented above. The addition of 5, 6, and 7 gives 18.

Learn more about addition on:

brainly.com/question/24536701

#SPJ1

The law of mathematical logic that was used to derive the given conclusion is; Law of Syllogism

The law of syllogism is defined as a type of logical argument using deductive reasoning.

Now, In mathematical logic, the Law of Syllogism states that if the following two statements are true:

(1) If a , then b .

(2) If b , then c .

Then we can derive a third true statement:

(3) If a , then c .

Now, applying that law to our question, we see that;

1) If I'm a student, then I go to school.

2) If I go to school, then I learn.

Then we can derive a third true statement:

3)  If I'm a student, then I learn.

Read more about Law of Syllogism at; https://brainly.com/question/28560796

#SPJ1

Triangle LMN is an obtuse angle then, the angle at vertex L is acute, the angle at vertex N is acute.

The triangle LMN is an obtuse angle at the vertex M. So by the definition of obtuse angle triangle LMN is an obtuse angle.

As ∠M is an obtuse angle

So 90° < m∠M < 180°

By the property of a triangle,

m∠L + m∠M + m∠N = 180°

m∠M = 180° - (m∠L + m∠N)

90° < 180° - (m∠L + m∠N) < 180°

90° - 180° < -(m∠L + m∠N) < 0

-90° < -(m∠L + m∠N) < 0

90° >(m∠L + m∠N) > 0

90° > m∠L  and 90° > m∠N

Therefore both angles L and N are acute angles.

To know more about the obtuse angle refer to the link given below:

https://brainly.com/question/3250447

#SPJ1

Answer:

1, 2 and 5

Step-by-step explanation:

see picture

The graph of the defined piece-wise function is sketched at the end of the answer.

A piecewise-defined function is a function that has different definitions, depending on the input of the function.

In the context of this problem, the function has three definitions, as follows:

For the first definition, to the left of x = -3, the function assumes a constant value of 3, hence it is an horizontal line at y = 3.

For the second definition, between x = -3 and x = 4, the function is a increasing linear function, with intercept 1 and slope 2, due to the rule y = 2x + 1.

For the third definition, to the right of x = 4, the function assumes a constant value of -2, hence it is an horizontal line at y = -2.

With each of these definitions, the graph of the function is given at the end of the answer.

More can be learned about piece-wise functions at https://brainly.com/question/19358926

#SPJ1

Answer:

1. 12hrs

2. 2hrs

Step-by-step explanation:

4:00pm is 2 hrs from 6:00pm

5:00am is 12hrs from 5:00pm

The values of a, b and c are a = 2, b = -10 and c = -20

The equation is given as

(ax + 2)(5x + b) = 10x^2 + bx + c

Open the brackets

So, we have

5ax^2 + 10x + abx + 2b = 10x^2 + bx + c

By comparing the above equation.

We have the following set of equations

5a = 10

10 + ab = b

2b = c

By solving the equations, we have

a = 2

Substitute a = 2 in 10 + ab = b

10 + 2b = b

So, we have

b = -10

Substitute b = -10 in 2b = c

2(-10) = c

Evaluate

c = -20

Hence, the values of the variables are a = 2, b = -10 and c = -20

Read more about quadratic equations at

https://brainly.com/question/1214333

#SPJ1

Answer: The value of the house when it was purchased was 120,000

Step-by-step explanation:

1) Set up the equation. Let x be the house.

x-x*35%= 78,000

First, the house decreases 35% of the cost of the original house. It now costs 78,000.

2) Solve the equation.

x-x*0.35 = 78,000

x-0.35x=78,000

0.65x = 78,000

x= 120,000

In linear equation, 864 is distance the flowerbed from the hive .

What are a definition and an example of a linear equation?

a) The equation is so called "time equation"

      D%2F12 + 16*60 + D%2F8 = 19*60 seconds

(b) To determine the distance D, solve the equation

D%2F12 + D%2F8 = 19*60 - 16*60 = 3*60,

multiply both sides by 24

2D + 3D = 3*60*24

5D = 4320

D = 4320/5 = 864

Learn more about linear equation

brainly.com/question/11897796

#SPJ13

Answer:

40

Step-by-step explanation:

5*(2^3)=40

At 1000 seconds the graph shows the height of 3500 meter.

The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.

Following the creation of a research question, data is continuously gathered through observation. The information is subsequently arranged, condensed, categorised, and visually portrayed.

In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.

Usually, data that varies over time is represented with a line graph.

Given:

The graph gives the relation between Elevation and Time.

As, if at 400 seconds the height is 6500 meters.

and, at 800 seconds the height is 4500 meters.

Thus, at 1000 seconds the graph shows the height of 3500 meter.

Learn more about graph here:

https://brainly.com/question/17267403

#SPJ1

Answer:

Step-by-step explanation:

x cannot be -3 or 2

Step-by-step explanation:

f(g(x)) = 1 / (( x-2) +5)

        = 1/ (x+3)

g(x) cannot have x=2

The domain is restricted where

f(x) has an restriction that x cannot be 5

so g(x) cannot be -5

-5 = x-2

Add 2 to each side

-5+2 = x

-3

In the above question, we need to from 3 probability questions and then give solutions for them

Example 1 : A coin is tossed three times. What is the probability of getting at least one head?

Solution : A coin is tossed 3 times then

Sample space = [HHH, HHT, HTH, THH, TTH, THT, HTT, TTT]

Total number of ways = 2 × 2 × 2 = 8

Favorable Cases = 7

P (A) = 7/8

OR

Probability (of getting at least one head) = 1 – P (no head)⇒ 1 – (1/8) = 7/8

Example 2 : Three red and four black balls are contained in a bag. Randomly, one ball gets taken out of the bag. Determine the probability that the drawn ball is

(i) black

(ii) not black

Solution :

Total number of balls in the bag are = 3 + 4 = 7 balls

Number of favorable outcomes or number of black balls in the bag = 4

(i) Probability getting black balls = [tex]\frac{number of favorable outcomes}{number of total outcomes}[/tex]

P(black ball) = [tex]\frac{4}{7}[/tex]

(ii)  Probability getting no black balls = 1 - P(black ball)

= 1 - [tex]\frac{4}{7}[/tex]

= [tex]\frac{3}{7}[/tex]

Example 3 : Given two dice, what is the likelihood of receiving the number 7?

Mathematical probability - There are 36 ways in all, or 6 times 6. Favorable scenarios are (1, 6) (6, 1) (2, 5) (5, 2) (3, 4) (4, 3), etc., in six different ways. P (A) = 6/36 = 1/6

To learn more about, probability here

https://brainly.com/question/11034287

#SPJ1

Answer:

The answer is d

Step-by-step explanation:

2/11 has a numerator of 2 but cant be reduced

Answer:

Step-by-step explanation:

I misunderstood the question. So, please disregard this answer. Thank you.

Answer: [tex]10, 20, 30, 40, 50, 60, 70, 80, 90[/tex]

Step-by-step explanation:

If the numbers have at least one 2 and at least one 5, then they are multiples of 10 (since [tex]10=2 \times 5[/tex]).

So, these numbers are [tex]10, 20, 30, 40, 50, 60, 70, 80, 90[/tex].

Answer: A = 452.16 ft²

Step-by-step explanation:

      This gives us the formula to solve for the area.

                     A = πr²

      The radius (r) is the same as the diameter divided by 2.

                     24 ft / 2 = 12 ft

      We will input these given values and solve.

A = πr²

A = (3.14)(12)²

A = 452.16 ft²

Answer:

452.16 ft²

Step-by-step explanation:

To find the radius, you divide the diameter (24) by 2, which equals 12. The area of a circle formula is πr². To find area, you do 12² * 3.14. That equals 144 * 3.14, which equals 452.16.

By using a reflection over the y-axis, the coordinates of the image of the triangle are (- 3, - 3), (- 6, 3) and C'(x, y) = (- 3, 3).

Rigid transformations are transformations applied on geometric loci such that the form of the construction is not altered. Reflections over the y-axis are examples of rigid transformations. In this problem we need to apply this kind of transformation on the three vertices of the triangle: A(x, y) = (3, - 3), B(x, y) = (6, 3), C(x, y) = (3, 3).

The reflection over the y-axis is described by the following formula:

P'(x, y) = P(x, y) + (- 2 · p, 0)

Where:

If we know that A(x, y) = (3, - 3), B(x, y) = (6, 3) and C(x, y) = (3, 3), then the image of the vertices of the triangle:

A'(x, y) = (3, - 3) + (- 6, 0)

A'(x, y) = (- 3, - 3)

B'(x, y) = (6, 3) + (- 12, 0)

B'(x, y) = (- 6, 3)

C'(x, y) = (3, 3) + (- 6, 0)

C'(x, y) = (- 3, 3)

Now we present the picture of the two triangles.

The coordinates of the image of the triangle are A'(x, y) = (- 3, - 3), B'(x, y) = (- 6, 3) and C'(x, y) = (- 3, 3).

To learn more on rigid transformations: https://brainly.com/question/1761538

#SPJ1

Given:

The function

Required:

Find the equation of the tangent at f(x) at x=0.

Explanation:

The slope of f(x),

Now, the slope of function at x = 0 is f'(x) = 2.

The line with slope m = 2 and passing through (0, 0).

Answer:

Equation of tangent of the function at x = 0, f(x) = 2x.

A car salesman earns a 3% commission on sales. If he sells a car for $27,990, how much commission will he earn?

($27,990)*(0.03) = $839.70

The Jones family will pay their insurance broker a commission of $1,750.00.

Commission is an amount of money paid to an employee or company as an incentive to sell more. A straight commission is a percentage of sales.

To know more about Commission

Refer this link:

https://brainly.com/question/957886

#SPJ1

using calculator

Area right to the right of the 2=2.12

P(Z > 2.12)

• P(Z < -2.12)

= 0.0170

Learn more about Standard normal distribution curve:

brainly.com/question/22923352

#SPJ4

Answer:

72.5%

Step-by-step explanation:

Hello!

We can find the percentage by dividing the sale price by the original price, then multiplying that by 100.

The percentage is 72.5%.

The three statement true about the the distance of a dog from a post are-

For the given graph in the question,

Function f gives the distance of a dog from a post, in feet, as a function of time, t in seconds, since its owner left.

The time is denotes on the x axis and the distance covered by the dog on the y axis.

This can be described using the function as.

f(t) = d

Consider values from graph.

When, t = 0, d = 1.5 feet

Function notation ; f(0) = 1.5    ......statement 1

When t = 60, d = 4 feet

Function notation ; f(60) = 4   ......statement 2

Now, the maximum value is 5.

Thus, f(t) < 5    .....statement 3

Therefore, the three statement are formed.

To know more about the function notations, here

https://brainly.com/question/12110934

#SPJ13

The correct question is -

Write three statement that are true about this situation. Use function notations.

Function f gives the distance of a dog from a post, in feet, as a function of time, t in seconds, since its owner left.

Use the = sign in at least one statement and < sign in another statement.