Find the radius of convergence R of the series. [infinity] n bn (x − a)n, b > 0 n = 1
R= ____
Find the interval of convergence of the series.

[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{28p^5-8p^4 + 40p^2}{4p^3}\implies \cfrac{28p^5}{4p^3}-\cfrac{8p^4 }{4p^3}+\cfrac{ 40p^2}{4p^3}\implies 7p^5 p^{-3}-2p^4 p^{-3}+10p^2p^{-3} \\\\\\ 7p^{5-3}-2p^{4-3}+10p^{2-3}\implies 7p^2-2p+10p^{-1}\implies 7p^2-2p+\cfrac{10}{p}[/tex]

Answer:

side BC and side DF

Step-by-step explanation:

side BC and side DF

An addition inequality to determine how much taller William must be to ride the coaster is, Height of William + x ≥ 42.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, Riders must be at least 42 inches tall to ride the coaster, and 'x' be the variable representing how much taller William should be.

Therefore, Height of William + x ≥ 42 is an inequality that may be used to calculate how much taller William has to be in order to ride the coaster.

learn more about inequalities here:

https://brainly.com/question/28823603

#SPJ1

a = [tex]6\sqrt{5}[/tex] is the right angled triangle's third side when the right angle triangle's opposite sides are 18 and 12, respectively.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric forms. The name given to a triangle with the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

given

by pythagoras theorem

c2 = a2 + b2

18*18 = a2 + 12*12

324  - 144 = a2

a2 = 180

a = [tex]6\sqrt{5}[/tex]

a = [tex]6\sqrt{5}[/tex] is the right angled triangle's third side when the right angle triangle's opposite sides are 18 and 12, respectively.

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

James's house is 24.6 feet tall because he is using a scale of 0.5 inch per 1 foot. To get this measurement, he multiplied 12.3 inches (the height of the doll house) by 2.

1. Take the height of the doll house (12.3 inches).

2. Multiply 12.3 inches by 2.

3. The result is 24.6 feet which is the height of James's house.

James is building a doll house that is proportional to his own house. He is using a scale of

0.5 inch = 1 foot,

which means that for every 0.5 inch in the doll house, 1 foot is represented in his house. To calculate how tall his house is, we need to figure out how many inches the doll house is. The doll house is 12.3 inches tall. To get the height of James's house, we need to multiply this by 2. Thus, 12.3 inches multiplied by 2 equals 24.6 feet, which is the height of James's house. This is because for every 0.5 inch in the doll house, 1 foot is represented in his house. Therefore, with the scale of 0.5 inch = 1 foot, the height of James's house is 24.6 feet.

1. Determine the scale of the doll house (0.5 inch = 1 foot).

2. Measure the height of the doll house (12.3 inches).

3. Multiply 12.3 inches by 2.

4. The result is 24.6 feet which is the height of James's house.

Learn more about measurement here

https://brainly.com/question/4725561

#SPJ4

To add a function in FG, open the functions. php file in your theme folder, add the code for the function at the bottom of the file, save the file, and add the code for the function in the template files where you want it to appear.

To add a function in FG, you first need to open the functions. php file in your theme folder. This is where all the functions for your theme will be stored. Once you have the file open, you can add the code for the function that you want to create. This code should go at the bottom of the file. After you have added the code, save the file. Now, you need to add the code for the function in the template files where you want it to appear. To do this, add the following code: <?php your_function_name(); ?>. This code will call the function that you created in the functions.php file. Once you have added this code, save the file and the function should now appear in your theme.

Learn more about function here

https://brainly.com/question/29633660

#SPJ4

The solution of the equation is x = 1 and y = 0.

We can solve this equation using the substitution method.

First, subtract 5 from both sides of the equation to isolate the x and y terms:8x - 3y = 0

3x - 2y = 0

Next, divide both sides of the first equation by 8:

x = (3/8)y

Substitute this expression for x into the second equation:

3(3/8)y - 2y = 0

Simplify:

(-13/8)y = 0

Divide both sides by -13/8:

y = 0

Now, substitute y = 0 into the first equation:

8x - 3(0) = 0

Simplify:

8x = 0

Divide both sides by 8:

x = 0

Therefore, the solution of the equation is x = 1 and y = 0.

Learn more about equation here

https://brainly.com/question/29657992

#SPJ4

The value of [tex]\lim _{x \rightarrow 2}[/tex] f(x) by Sandwich theorem is 2.

As per the given data the function limits are:

2x − 2 ≤ f(x) ≤ x2 − 2x + 2 for x ≥ 0

Here we have to determine the value of [tex]\lim _{x \rightarrow 2}[/tex] f(x)

Hence by Sandwich theorem:

The sandwich theorem, also known as the squeeze theorem, asserts that if two functions, g (x) and h (x), are squeezed between one another and their respective limits at a given position are both equal to L, then the limit of f (x) at that point is also equal to L.

We can use the theorem to find tricky limits like sin(x)/x at x=0, by "squeezing" [tex]\frac{sin(x)}{x}[/tex] between two nicer functions and ​using them to find the limit at x = 0.

[tex]& \lim_{x \rightarrow 2}(2 x-2) \leq\lim_{x \rightarrow 2} f(x) \leq \lim_{x \rightarrow 2}\left(x^2-2 x+2\right) \\[/tex]

[tex]& \Rightarrow 2 \leq \lim _{x \rightarrow 2} f(x) \leq 2 \\[/tex]

Hence [tex]\lim _{x \rightarrow 2}[/tex] f(x) = 2

For more questions on limits

https://brainly.com/question/28992290

#SPJ4

To find the radius of a circle given the area of a sector and the measure of the central angle of the sector, we can use the formula:

radius = sector area / (central angle measure / 360)

In this case, the sector area is 165.6 cm2 and the central angle measure is 129*. Plugging these values into the formula gives us:

radius = 165.6 / (129 / 360)

= 165.6 / (129 / 360)

= 165.6 / (0.3583)

= 462.9 cm

Rounding this value to the nearest tenth gives us a radius of approximately 463 cm.

Answer:

Step-by-step explanation:

Given isosceles triangle ABC with AB≅AC, altitude AP, and AB=(2x+3), AC=(3y-1), BP=(y+1), and PC=(x+2), you want the values of x and y.

Corresponding parts of ∆ABP and ∆ACP are congruent, so we have ...

  2x +3 = 3y -1

  x +2 = y +1

Subtracting twice the second equation from the first gives ...

  (2x +3) -2(x +2) = (3y -1) -2(y +1)

  -1 = y -3 . . . . simplify

  2 = y . . . . . . add 3

Substituting into the second equation, we have ...

  x +2 = 2 +1

  x = 1 . . . . . . . .subtract 2

The values of x and y are 1 and 2, respectively.

Answer: C, 217

Step-by-step explanation:

Answer: Commutative property.

Step-by-step explanation: Basically, the commutative property can be expressed as a + b = b + a, which matches this scenario pretty well. You are correct.

Let me know if this is right! :)

Only when each iteration is sufficiently time-consuming in terms of CPU usage does parallel programming become more effective.

The term "parallel processing" is used to deliver simultaneous data-processing activities, which is utilized to increase the computing performance of computer systems. Additionally, a parallel processing system has the ability to process input concurrently for quicker execution times.

As an illustration, when an instruction is being carried out in an ALU, the following instruction may be read from memory. The system may be equipped with two or more ALUs and be able to carry out multiple instructions at once.

To know more about parallel processing visit: https://brainly.com/question/28313147

#SPJ4

A slope field for the given differential equation dy/dx = xy/2 at the 9 points indicated is shown below.

We know that a slope field represents the slope of a differential equation at certain vertical and horizontal intervals on the coordinate plane.

First we construct a table which contains the values of slope.

Consider given differential equation dy/dx = xy/2

where -1 ≤ x ≤ 1,

1 ≤ y ≤ 3

Let the slope be m

so, dy/dx = m

For x = -1, y = 1

m = (-1 × 1)/2

   = -1/2

For x = -1, y = 2

m = (-1 × 2)/2

   = -1

For x = -1, y = 3

m = (-1 × 3)/2

   = -3/2

For x = 0, y = 1

m = (0 × 1)/2

   = 0

For x = 0, y =2

m = (0 × 2)/2

   = 0

For x = 0, y = 3

m = (0 × 1)/2

   = 0

For x = 1, y = 1

m = (1 × 1)/2

   = 1/2

For x = 1, y = 2

m = (1 × 2)/2

   = 1

For x = 1, y = 3

m = (1 × 3)/2

   = 3/2

So, the table is:

x/y     1  2    3

-1     -1/2   -1      -3/2

0     0   0   0

1       1/2     1      3/2

Therefore, the slope field is as shown below.

Learn more about the  differential equation here:

https://brainly.com/question/13378403

#SPJ4

There are 10 integers that satisfy 0 < a < 100.

What are integers?

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.

Here, we have

Given: When working modulo m, the notation a⁻¹ is used to denote the residue b for which ab = 1 (mod m), if any exists.

We have to find integers that satisfy 0 < a < 100.

a(a − 1)⁻¹ ≡  4a⁻¹ (mod 20)

a ≡ 4a⁻¹(a − 1)(mod 20)

a² ≡ 4(a-1)(mod 20)

a² - 4a + 4 ≡ 0(mod 20)

(a - 2)² ≡ 0(mod 20)

a = 2 + 10n | for n = (0, 1, 2, 3.....9)

Hence, there are 10 integers that satisfy 0 < a < 100.

To learn more about the  integers from the given link

https://brainly.com/question/929808

#SPJ4

The minimum value of the expression 3x² + 6x + 6 is 3.

Therefore the answer is 3.

A quadratic mathematical expression contains a variable of highest degree of 2 and it is of the general form ax² + bx + c, where a, b and c are constants.

Minimum value of a quadratic equation of form ax² + bx + c is when

x = -b/ 2a

Then minimum value is

a( -b/ 2a )² + b( -b/ 2a ) + c

= (b²a + -2ab² + 4a²c)/ 4a²

= ( - b² + 4ac)/ 4a

= c - b²/4a

In the expression 3x² + 6x + 6, a = 3, b =6 and c = 6. So minimum value is

= 6 - 6²/ (4×3)

= 3

--The question is incomplete, answering  to the question below--

"What will be the minimum value of the expression 3x² + 6x + 6?"

To know more on minimum value

https://brainly.com/question/12416781

#SPJ4

On solving the provided question we can say that the percentage discount will be equal to 20%

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

Tomas wants to buy a new baseball bat. T

he one he likes costs $130, but it is on sale for $104.

The discount percentage will be calculated as:-

( $130 - $104) = $26

( 26 / 130) x 100 = ( 2600 / 130 ) = 20%

the discount will be equal to 20%.

To know more about percentage visit:

https://brainly.com/question/28269290

#SPJ4

Answer: 360,000

Step-by-step explanation: First you would convert 12 kilometers to meters, which is 120,000. Then multiply that by 3. You get 360,000 meters. Therefore, the car can travel 360,000 meters on liters of gas.

If we want to create a truth table , for say expression  (P ∨ Q)∧(~P⇒Q) , then we will create different columns having the column head as , P , Q , ~P , P ∨ Q,~P⇒Q and  (P ∨ Q)∧(~P⇒Q) and then perform the logical operation on them.

Truth table is a medium  used to perform logical operations on expressions. These operations consists of Boolean algebra or Boolean functions expressions.

On performing these logical operation we get to know whether the propositional expression is correct or incorrect, based on the input values. This  entire process is based on Boolean algebra and the table is made up of rows and columns for one or more input values.

To learn more about truth table

brainly.com/question/29155453

#SPJ4

Answer:

She needs 18,731.6 Litres of paint to paint her bedroom.

Step-by-step explanation:

So,

V = l × w × h

V = 10.5 × 7 × 9 feet

V = 661.5 cubic feet

We know that,

So,

661.5 × 28.317 = 18,731.6 Litres

Thus, She needs 18,731.6 Litres of paint to paint her bedroom.

Answer : in California there are 24 volcanoes while in Alaska there are 36 volcanoes.

Step-by-step explanation:

Total number of volcanoes = 60.

40% of the volcanoes where in California.

i.e 100% - 40% = 60%.

60% of the volcanoes were in Alaska.

In California = 40/100 × 60 = 24 volcanoes.

In Alaska = 60/100 × 60 = 36 volcanoes.

By using the ASA Congruence Theorem, Delta PQR is congruent to Delta TSR.

We can prove this by using the fact that triangle PQR and triangle TSR are both right triangles and that R is the midpoint of overline PT and overline PQ is congruent to overline TS. Since R is the midpoint of overline PT, it follows that overline PR is congruent to overline TR (by the midpoint theorem).

Since PQR is a right triangle, and R is the right angle, it follows that angle PQR is congruent to angle TSR (by the definition of a right angle). Since overline PQ is congruent to overline TS, it follows that angle PQS is congruent to angle TSR (by the definition of congruence). Together, these congruences imply that triangle PQR is congruent to triangle TSR by the ASA congruence theorem.

Learn more about the congruence theorem here:

https://brainly.com/question/2102943

#SPJ4

Subtract 0.1 from both sides49x+ 0.10= 117.90

49x+0.1-0.1=117.9-0.1

x=2.404

To learn more about variables refers to:

brainly.com/question/27894163

#SPJ1

The total amount of sales he must make should be of $20800.

Given is that a salesperson works 40 hours per week at a job where he has two options for being paid. Option A is an hourly wage of ​$26. Option B is a commission rate of 5​% on weekly sales

Assume that the amount of sales he needs to make is of ${x}. So, for same amount, we can write -

(26 x 40) = 5% of {x}

(26 x 40) = (5/100) x {x}

{x} = (26 x 40 x 100)/5

{x} = (26 x 40 x 20)

{x} = 26 x 800

{x} = 20800

Therefore, the total amount of sales he must make should be of $20800.

To solve more questions on expressing evaluation, visit the link below -

brainly.com/question/1041084

#SPJ1

The flowers on the float would be 6.000 flowers. The result is obtained by using fraction multiplication.

Fraction represents the part of a set of objects. It has two parts separated by a dividing line, namely numerator at the top and denominator at the bottom.

For example:

It means one of four parts and two of five parts.

We have four thousand two hundred carnations on the float. It was 7/10 of flowers needed. Find the whole flowers on the float!

The carnations of a set of flowers is 7/10. It is 4200 carnations.

The carnations part is 7 and the whole part of flowers is 10.

Using fraction, the whole flowers would be

= 10/7 × 4200

= 6.000 flowers

Hence, the number of flowers needed to be on the float is 6.000 flowers.

Learn more about fraction here:

brainly.com/question/30156711

#SPJ4

The range of f is C.

What is range?
Range is the difference between the highest and lowest values in a set of data. It is a measure of variability, providing an indication of how widely values in the data set are dispersed from one another. In statistics, range is an important tool that helps to describe and summarize data. Range is also used to measure the dispersion of data within a data set, including the degree of spread or variability in the data.

-6<_f(x)<_6. This means that the f(x)-values range from -6 to 6, including -4 and -3. The range of f does not include -3, 3, 6, and 7, which are not within the range of -6 to 6.

To know more about range click-
https://brainly.com/question/2264373
#SPJ1

The beat three options are:  The slope of the line is 1/5, (2) The possible equation if the line is y=1/5x, (3) The slope and the y intercept are the same

Lope is the rate of change of y with respect to x.  slope is also the increase in y over increase in x vice versa

Slope is denoted by rise/run

The Possible solutions from the graph are:

Taking any two points on the graph : (4, 1) and -4, -1,)

We can find the slope as (1--1)/4--4

Therefore, the Slope = 2/3≡1/5

Learn more about slope of a line on https://brainly.com/question/16180119

#SPJ1

Considering that the quadrilateral EFGH is similar to quadrilateral IJKL the side LI is calculated to be

The side LI is calculated using the concept of similar polygons. This concept allows for the sides to be proportionally equal to each other.

This implies that the factor used for any side will produce same result

let the factor be r and using side HG and JK to solve for the factor r

HG * r = JK

where

HG = 16

JK = 51

substituting the values and solving for r

HG * r = JK

16 * r = 51

r = 51/16

and HE * r = LI

where HE = 9.6

LI = 9.6 * 51/16

LI = 30.6

hence side LI = 30.6

Learn more about similar polygons at:

https://brainly.com/question/1493409

#SPJ1