find the radius of convergence, r, of the series. [infinity] 9nxn n4 n = 1

Answers

Answer 1

The radius of convergence, r, is infinity, meaning the series converges for all values of x.

To determine the radius of convergence, we can use the ratio test.

The ratio test states that if the limit of the absolute value of the ratio of consecutive terms in a series is L, then the series converges if L is less than 1, and diverges if L is greater than 1.

Let's apply the ratio test to the series:

∑(n=1 to infinity) 9n/(n^4)

To apply the ratio test, we need to calculate the limit of the absolute value of the ratio of consecutive terms:

L = lim(n→∞) |(9(n+1)/(n+1)^4) / (9n/n^4)|L

= lim(n→∞) |9(n+1)n^4 / (n+1)^4 * n|L

= lim(n→∞) |9n(n+1)n^4 / n^4(n+1)^4|L

= lim(n→∞) |9(n+1) / (n+1)^4|L

= lim(n→∞) 9/(n+1)^3

As n approaches infinity, the term (n+1)^3 dominates the denominator, so we can simplify the expression to:

L = 9/∞^3

Since the denominator approaches infinity, the ratio L becomes 0.L = 0 < 1

Since the limit of the ratio is less than 1, the series converges.

Therefore, the radius of convergence, r, is infinity, meaning the series converges for all values of x.

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Related Questions

3(4g-6)>6(g+2) solve each inequality.

Answers

Answer:

5

Step-by-step explanation:

12g - 18 > 6g + 12

12g > 6g + 30

6g > 30

g = 5

Have a great day!

Please rate!

Which is a perfect square?
61
62
63
65​

Answers

Answer:

None

Step-by-step explanation:

None of these, but \(\sqrt{64}=8\) so if 64 is an option than that's the correct option

\(\sqrt{61} =7.81 \\\sqrt{62}=7.87\\\sqrt{63} =7.93\\\sqrt{65} =8.06\)

Use the surface integral in Stokes Theorem to calculate the circulation of the field F around the curve C in the indicated direction. F=yi+xzj+x²k C The boundary of the triangle cut from the plane 8x+y+z=8 by the first octant, counterclockwise when viewed from above. The circulation is (Type an integer or a fraction) Is

Answers

To calculate the circulation of the vector field F = yi + xzj + x²k around the curve C in the indicated counterclockwise direction, we can apply Stokes' Theorem.

Stokes' Theorem relates the circulation of a vector field around a closed curve to the surface integral of the curl of the vector field over the surface bounded by that curve.

The curve C is the boundary of the triangle cut from the plane 8x + y + z = 8 in the first octant, counterclockwise when viewed from above. To apply Stokes' Theorem, we need to find the curl of the vector field F. The curl of F is given by ∇ × F, which is equal to (partial derivative of F₃ with respect to y - partial derivative of F₂ with respect to z)i + (partial derivative of F₁ with respect to z - partial derivative of F₃ with respect to x)j + (partial derivative of F₂ with respect to x - partial derivative of F₁ with respect to y)k.

Once we have the curl of F, we can calculate the surface integral of the curl over the surface bounded by the curve C. This integral will give us the circulation of the field F around the curve C in the specified counterclockwise direction.

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The difference of the same side interior angles of two parrelels lines is 50 degrees find all angles

Answers

Answer:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Step-by-step explanation:

Angle 1: Same-side interior angle of Line 1

Angle 2: Same-side interior angle of Line 2

We know that the difference between the angles is 50 degrees. Since the angles are supplementary, we can write the equation:

Angle 1 + Angle 2 = 180

Now, we need to express the difference between the angles in terms of Angle 1 or Angle 2. We can choose either angle, so let's express it in terms of Angle 1:

Angle 1 - Angle 2 = 50

We can rewrite this equation as:

Angle 1 = 50 + Angle 2

Now substitute this expression for Angle 1 into the first equation:

(50 + Angle 2) + Angle 2 = 180

Combine like terms:

2Angle 2 + 50 = 180

Subtract 50 from both sides:

2Angle 2 = 130

Divide by 2:

Angle 2 = 65

Now substitute this value back into the equation for Angle 1:

Angle 1 = 50 + Angle 2

Angle 1 = 50 + 65

Angle 1 = 115

Therefore, the angles are as follows:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

7. A cell phone was marked at 40% above the cost price and a
discount of 30% was given on its marked price. Find the gain or
loss percent made by the shopkeeper.
K​

Answers

Answer:

loss

Step-by-step explanation:

The curved surface area of a cylinder of height 28cm is 352sq.cm. Find the diameter of the base of the cylinder​

Answers

Answer:

d = 4cm

Step-by-step explanation:

curved surface area (CSA) of cylinder = \(2\pi rh\)

h = 28cm and CSA = 352\(cm^{2}\)

\(2\pi rh\) = 352

2 * \(\frac{22}{7}\) * r * 28 = 352

\(r = \frac{352*7}{2*22*28}\)

after calculating, you will get r = 2cm

so diameter = 4cm

David deposits $4,300 in an account that pays 5% annual simple interest for 7 years. How much interest is earned?

Answers

Answer:

4300 x 5/100 = 215

215 x 7 = 1 505

4300 + 1505 = 5 805

A key feature of a case-control study is that: (Select that all apply) A. It is generally used to explore rare diseases B. It is limited to health exposures and behaviors rather than health outcomes C. The comparison groups are those with a disease and those without the disease D. Once the comparison groups are identified, the exposure history will be obtained.

Answers

The main features of a case-control study is that:
A. It is generally used for exploring the rare diseases
C. The comparison groups are those with a disease and those without the disease
D. Once the comparison groups are identified, the exposure history can be obtained easily.

The correct answers are C and D. A case-control study compares individuals with a particular disease (cases) to those without the disease (controls) and investigates the potential exposures or behaviors that may have contributed to the development of the disease.

Therefore, the comparison groups are those with the disease and those without the disease, and once these groups are identified, the exposure history is obtained. The study is not limited to health exposures and behaviors but rather focuses on any potential risk factors. Case-control studies are often used to explore rare diseases because they are more efficient in identifying potential risk factors than cohort studies.
While case-control studies can be limited in some aspects, they are valuable for examining health exposures and behaviors in relation to health outcomes, rather than being limited to only one or the other.

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What is the minimum angle of rotation lin degrees that will carry the six-sided star onto itself?
What’s the degree

Answers

Answer:

120 degrees

Step-by-step explanation:

If it's a 6 sided star, that means that it will be divided into 3 parts (think about how a normal 5-point star has 10 sides). That means that we divide 360 (total number of degrees in a full rotation) by 3 (number of sections) = 120

Look at the graph of a function below.
Which set builder notation represents the domain of the function in the graph?

Look at the graph of a function below.Which set builder notation represents the domain of the function

Answers

The domain of the function in the graph is {yl1≤y≤9}.  Option b is the correct answer.

Graph:

The domain of a function is the collection of all conceivable values that can be used as inputs, or alternatively, it is the full range of potential values for independent variables.

A graph is an organized visual representation of any data in mathematics. The relationship between the variable quantities is depicted on the graph. In a graph theory, the set of items that are somehow connected to one another is represented by a graph. The vertices or nodes of the objects are essentially mathematical notions, and the edges between the nodes represent the relationships between the nodes. In mathematics and statistics, there are various types of graphs that are used to visually display data. The study of points and lines is known as graph theory. It is a branch of mathematics that focuses on the investigation of graphs. The mathematical truth is shown visually in this picture. Relationships are studied using graph theory.

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The urface area of a cylinder i 24π m². The ditance around the bae of the cylinder i 3π meter and the diameter of a bae of the cylinder i 4 meter. What i the height of the cylinder? Enter your anwer, a a implified fraction, in the box

Answers

After solving, the height of the cylinder is 6 meters.

The surface area of a cylinder is 24π m².

The distance around the base of the cylinder is 3π meter.

The diameter of a base of the cylinder is 4 meter.

Now the radius of the cylinder = diameter/2

The radius of the cylinder = 4/2

The radius of the cylinder = 2 meter.

The formula of surface area of cylinder:

S = 2πrh

From the question:

2πrh = 24π

Now putting the value of r

2π × 2 × h = 24π

4πh = 24π

Divide by 4π on both side, we get

h = 6

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The complete question is:

The surface area of a cylinder is 24π m². The distance around the base of the cylinder is 3π meter and the diameter of a base of the cylinder is 4 meter. What is the height of the cylinder? Enter your answer, in a simplified fraction, in the box.

Consider the line 7x+6y=5.
What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?
Slope of a perpendicular line:
005
x 5
?
Slope of a parallel line:
a

Answers

Answer:

Slope of parallel line: -7/6

Slope of perpendicular line: 6/7

Step-by-step explanation:

7x + 6y = 5

6y = -7x + 5

y= -7/6x + 5/6

a sphere has a radius of 6 centimeters. what is the volume of the sphere?

Answers

Question  

A sphere has a radius of 6 centimeters. What is the volume of the sphere

Given:  

r = 6 cm

Formula:

V = (4/3)πr

Solution:  

V = (4/3)πr

V = (4/3)(3.14)(6)

V = 25.12 cm³

Final Answer:  

25.12 cm³

Which of the sets of ordered pairs represents a function?

A = {(−5, 5), (−2, 2), (2, −2), (5, −5)}

B = {(4, 2), (3, −2), (9, 4), (11, −3)}

Only A
Only B
Both A and B
Neither A nor B

Answers

Answer:

Both A and B

Step-by-step explanation:

They both pass vertical line test

Each week jake gets an allowance of $8 plus $3 for each chore he does at
home. His younger sister bella gets an allowance of $6 plus $2 per each chore
she does. Write an expression for how much their parents give them each week if
they do the same number of chores.

Answers

Answer:

y = 5x + 14

Step-by-step explanation:

y represents the total money their parents give them. X represents the number of chores. 5 is the sum of 3 + 2 since Jack gets $3 for each chode while Bella gets $2 for each chore. 14 is the set amount of money the receive each week since 8 + 6 is 14.

you need a piece of paper to measure 65.31 cm. if you tape two together that each measure 38.9 cm, how much do you need to cut off?

Answers

Answer:

you would need to cut off 12.49 cm. of the paper

Alexander is raking leaves to earn money to buy a bicycle that costs $300 including tax.

He currently has $75 and will spend $50 on supplies.

He charges $15 per yard he rakes.

What is the fewest number of yards Alexander will have to rake to have enough money to buy the bicycle?

Answers

Answer:

19 yards

Step-by-step explanation:

75 - 50 = 25

15 * 19 = 285

285 + 25 = 310

If there are 360 g of radioactive material with a half life (decreased by half or 50% )of 1 hour, how much of the radioactive material will be left after 4 hours ?

Answers

After 1 hour, 360 g decays to 180 g.

After another hour (total 2 hours), 180 g decays to 90 g.

After another hour (total 3), 90 g decays to 45 g.

After one more (total 4), 45 g decays to 22.5 g.

More quickly, with a half-life of 1 hour, the 360 g of starting material decays to

(360 g) / 2⁴ = 22.5 g

In general, if the half-life is 1 hour, then after n hours, an initial amount A of this substance decays according to

A / 2

The length of the sides of the base of the largest of the Great Pyramids of Giza, near Cairo, Egypt, is 230 m. This square pyramid is 147 m tall.



What is the lateral area of the pyramid?



Round the slant height to the nearest hundredth, and round your final answer to the nearest whole number

Answers

The lateral area of the pyramid is 125660 m². Rounding the final answer to the nearest whole number, we get the lateral area of the pyramid to be 125660 m².

We know that the pyramid is a square pyramid with base side of 230m and height of 147m. We need to find the lateral area of the pyramid.Let us first find the slant height of the pyramid using the Pythagorean theorem. The slant height of the pyramid can be found using the formula: slant height = √(h² + (s/2)²)Where, h = height of the pyramid, s = base side length of the pyramid

Substituting the given values, we get: slant height = √(147² + (230/2)²)≈ 274.24 mRounding it off to the nearest hundredth, we get the slant height to be 274.24 mWe can now find the lateral area of the pyramid. The lateral area of a pyramid can be found using the formula: Lateral area = ½ × perimeter of base × slant heightSince the base of the pyramid is a square, the perimeter of the base = 4 × base side lengthSubstituting the given values, we get:Lateral area = ½ × 4s × slant height= ½ × 4 × 230 × 274.24= 125660 m²Rounding the final answer to the nearest whole number, we get the lateral area of the pyramid to be 125660 m².

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PLEASE help me for this math problem

PLEASE help me for this math problem

Answers

:answer (x+5−4)(x+5+4)(x−4)

how i got it:

(x+5−4)(x−(−

2

2(5+4)

))(x−4)

Bessel polynomials are defined recursively as B(0, x) = 1, B(1, x) = x + 1, and for n > 1 : B(n, x) = (2n − 1)xB(n − 1, x) + B(n − 2, x). Use memoization to define a recursive function B which takes on input an int n and a double x. B(n, x) returns a double, the value of the n-th Bessel polynomial at x.

Answers

The function checks if the result for the current inputs has already been computed and stored in the `memo` cache. If so, it returns the cached result, otherwise it calculates the result using the recursive definition of the Bessel polynomials and stores the result in the `memo` cache for future use.

Memoization is a technique where we store the results of expensive function calls and return the cached result when the same inputs occur again. Here's a recursive function that uses memoization to calculate the n-th Bessel polynomial at x:

```
memo = {}  # Memoization cache

def B(n, x):
   if n == 0:
       return 1
   elif n == 1:
       return x + 1
   elif (n, x) in memo:
       return memo[(n, x)]
   else:
       result = (2 * n - 1) * x * B(n - 1, x) + B(n - 2, x)
       memo[(n, x)] = result
       return result
```

The function checks if the result for the current inputs has already been computed and stored in the `memo` cache. If so, it returns the cached result, otherwise it calculates the result using the recursive definition of the Bessel polynomials and stores the result in the `memo` cache for future use. This approach avoids redundant calculations and can significantly speed up the computation of Bessel polynomials for large values of n.

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350%350, percent of the correct pre-test questions
50
%
50%50, percent of the correct pre-test questions
100
%
100%100, percent of the correct pre-test questions

Answers

The table should be completed to show different percentages of the questions Rita answered correctly on the pre-test as follows;

Number of questions correct           Percentage

7                                                       350% of the correct pre-test questions.

1                                                        50% of the correct pre-test questions.

2                                                       100% of the correct pre-test questions.

What is a percentage?

In Mathematics and Statistics, a percentage refers to any numerical value that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given numerical value.

Based on the information provided about this tape diagram that shows the number of questions Rita answered correctly on the pre-test, we can logically deduce that each of the box represents the number of questions and corresponds to a percentage of 50;

350%  ⇒ 350/50 = 7 questions.

50%  ⇒ 50/50 = 1 question.

100%  ⇒ 100/50 = 2 questions.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

350%350, percent of the correct pre-test questions50%50%50, percent of the correct pre-test questions100%100%100,

One Lump Sum:

Calculate the APR for a $2000 loan that is paid off in one lump sum at the end of the year. The stated annual interest rate is 8%. Show your work.

Answers

The APR for this loan is 8%.

We have,

The formula for calculating APR is:

APR = (r/n) x m

where r is the stated annual interest rate, n is the number of times the interest is compounded in a year, and m is the number of payments made in a year.

In this case,

The loan is paid off in one lump sum at the end of the year, so there is only one payment made in a year (m = 1).

The stated annual interest rate is 8%, so r = 0.08.

We need to determine the value of n.

Since the loan is paid off in one lump sum at the end of the year, we can assume that the interest is compounded annually (n = 1).

Using the formula, we get:

APR = (0.08/1) x 1

APR = 0.08

Therefore,

The APR for this loan is 8%.

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find the value of x so that f(x)= 7

Answers

Answer: f (x) =7

Step-by-step explanation:

Find the value of sin J rounded to the nearest hundredth, if necessary.
12
13
K

Find the value of sin J rounded to the nearest hundredth, if necessary.1213K

Answers

The value of the sine of the angle J is equal to 5 / 13 (approx. 0.38).

What is the measure of the missing angle?

The image attached aside shows us a right triangle with two known side lengths (JL, KJ) and a angle measure (m ∠ K). The measure of the missing angle can be found by using the trigonometric function of cosine:

cos m ∠ J = KJ / JL

cos m ∠ J = 12 / 13

m ∠ J = 22.620°

The measure of the angle J within the triangle JKL is approximately 22.620°.

And the sine of the angle J, which helds the same positive sign than cosine as the angle is in the first quadrant on Cartesian plane, is:

sin m ∠J = √(1 - cos² m ∠J)

sin m ∠J = √[1 - (12 / 13)²]

sin m ∠J = 5 / 13

The value of the sine of the angle J is equal to 5 / 13 (approx. 0.38).

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Give the standard form for 900.000 000 + 50 50.000 000 + 9.000 + 600 + 20 + 7

Answers

Answer:

900.000 000 + 5050.000 000 + 9.000 + 600 + 20 + 7

=900+5050+9+600+20+7=6586 is standard one

(Look at screenshot)
7. The graph represents the height of a passenger car on a ferris wheel, in feet, as a
function of time, in seconds.
Use the graph to help you:

a. Find H(0).
b. Does H(t)=0 have a solution? Explain how you know.
c. Describe the domain of the function.
d. Describe the range of the function.

(Look at screenshot)7. The graph represents the height of a passenger car on a ferris wheel, in feet,

Answers

#1

Clear shown in graph

H(0)=5

#2

No

At. no where graph passes through origin so y intercept is not 0 at anywhere

#3

Domain is x values

Domain =[0,oo)

#4

Range is y values set

Range=[5,50]

give an example that shows that the variance of the sum of two random variables is not necessarily equal to the sum of their variances when the random variables are not independent.

Answers

Consider X and Y with Var(X) = Var(Y) = 2/3 and Cov(X, Y) = 2/3. Then, Var(X + Y) ≠ Var(X) + Var(Y) because X and Y are not independent.

Let's consider two random variables X and Y, where X and Y are not independent.
The variance of the sum of X and Y is given by:
Var(X+Y) = Var(X) + Var(Y) + 2Cov(X,Y)
where Cov(X,Y) is the covariance between X and Y.


If X and Y are independent, then Cov(X,Y) = 0 and we have:
Var(X+Y) = Var(X) + Var(Y)


However, if X and Y are not independent, then Cov(X,Y) ≠ 0 and the variance of the sum of X and Y is not necessarily equal to the sum of their variances.
For example, let's say X and Y are the number of heads obtained in two consecutive flips of a biased coin. If the coin is biased such that the probability of obtaining a head on the first flip is 0.6 and the probability of obtaining a head on the second flip is 0.8, then X and Y are not independent.


The variance of X is:
Var(X) = npq = 2(0.6)(0.4) = 0.48
The variance of Y is:
Var(Y) = npq = 2(0.8)(0.2) = 0.32


The covariance between X and Y is:
Cov(X,Y) = E(XY) - E(X)E(Y) = (0.6)(0.8) - (0.6)(0.6)(0.8)(0.2) = 0.048


Therefore, the variance of the sum of X and Y is:
Var(X+Y) = Var(X) + Var(Y) + 2Cov(X,Y) = 0.48 + 0.32 + 2(0.048) = 0.896


As we can see, the variance of the sum of X and Y is not equal to the sum of their variances (0.48 + 0.32 = 0.8). This is because X and Y are not independent and their covariance contributes to the variance of their sum.

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a price of 300 cedis is shared between Dora and Dorris in the ratio 4:6 respectively. how much is Dorris receive?​

Answers

Answer:

180

Step-by-step explanation:

i don't

Answer: 180 cedis

Step-by-step explanation: 4:6 is 40% for dora and 60% for dorris

The difference between the park and house of a student is 1Km 575m. Every day he walks both ways between the park and his house. Find the total distance covered by him in a week's time?​

Answers

The student covers a total distance of 22.05 kilometers in a week's time, walking between the park and the house each day.

To find the total distance covered by the student in a week's time, we need to calculate the distance covered in one round trip (from the house to the park and back) and then multiply it by the number of round trips in a week.

Given that the difference between the park and house is 1 kilometer and 575 meters, we can convert it to a total distance of 1.575 kilometers.

In a round trip, the student covers twice the distance between the park and the house, which is 1.575 kilometers * 2 = 3.15 kilometers.

Now, we need to determine how many round trips the student makes in a week. Let's assume the student makes one round trip each day.

Since there are 7 days in a week, the total distance covered by the student in a week's time is 3.15 kilometers * 7 = 22.05 kilometers.

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What does George mean when he says I havent any country? Conduct an internet search for information on careers that require geometry. Make a list of professionals who routinely apply geometry in their work. Start with the careers discussed in the lesson. Then, locate one or more resources on the internet to broaden your search and expand your list. 1- a-Girl: Quieres un sndwich? Boy: S, gracias. Girl: De nada 2. b-Woman: Por favor, tienes $1.00? Man: Woman: In general terms, how would you describe land use in the region? 2) If Paul has $5000 in his account at the end of September, how muchdid he have at the end of June rounded to the nearest whole dollar?A) $89B)$178C)$467D) $1,600E) None of the above Find the area of the figure that is blue.A) 116 cm2 B) 220 cm2 C) 276 cm2 D) 284 ft2 The Polygons are similar. Solve for x 109612 If you start with 100 grams of hydrogen-3, how many grams will you have after 24.6 years? How was henry II important to the medieval times?HELP PLEASE AND NO LINKS PLEASEEEE Gary wants to make a circular pond in his yard and put a low fence around the edge. If Gary has 124 feet of fencing, which is closest to the area of the largest circular pond he can make with the fencing? according to piaget how would the problem solving abilites of a 15 year old differ from those of a 30 year old Who of the following are abstract expressionist painters?O Robert MotherwellO Jackson PollockO Silvestre RevueltasO Aaron Copland Evaluate the expression when b = -2 and c = 2. b - 8c units total variable cost 0 $0 1 $12 2 $25 3 $60 4 $120 5 $200 6 $300 what is the average total cost of the 6th unit? what is the first unit of output where diminishing marginal returns have begun? Slope intercept form of an equation of the line with slope 3 and passes through the points (-1,-2) how alleles gets distributed to offspring form parents Which of the following does not fall within the scope of the role of a primary care physician?A. Making initial diagnosis and evaluation of patient's conditionB. Identifying applicable treatment protocols and practice guidelinesC. Providing specialist diagnosisD. Deciding what treatment is warranted Daria is purchasing a $75 appliance for her kitchen. She has threecoupons to the store that she can choose from. Which is a true statementabout Daria's options? *Coupon 1: $10 off purchaseCoupon 2: 15% off purchaseCoupon 3: 1 off purchase Which of the following statement is INCORRECTin describing the purpose of bypass diode for the PV panel? Groupof answer choices It minimizes power loss under heavy shadow Itrestores the PV panel vo What is the potential difference between xi=20cm and xf=30cm in the uniform electric field Ex=1000V/m?Express your answer to two significant figures and include the appropriate units.