For any positive integer k, the radius of convergence R is: If k ≥ -2, R = 0 (the series diverges for all x). If k < -2, R = ∞ (the series converges for all x).
To find the radius of convergence,
R, of the series Σ[tex][n!^{k+3} / ((k + 3)n)!][/tex][tex]x^n[/tex] (n = 0 to infinity),
we can use the ratio test.
Step 1: Apply the ratio test
Consider the ratio of consecutive terms:
L = [tex]\lim_{n \to \infty}[/tex] |[tex](n+1)!^{k+3}[/tex] / ((k + 3)(n + 1))!| / [tex]n!^{k+3}[/tex]/ ((k + 3)n)!|
= [tex]\lim_{n \to \infty}[/tex] |[tex](n+1)!^{k+3}[/tex] / [tex]n!^{k+3}[/tex] × ((k + 3)n)! / ((k + 3)(n + 1))!|
= [tex]\lim_{n \to \infty}[/tex] |[tex]n+1^{k+3}[/tex]/ ((k + 3)(n + 1))|
Step 2: Simplify the ratio
L =[tex]\lim_{n \to \infty}[/tex][tex]|(n + 1)^k / (k + 3)|[/tex]
= ∞ if k ≥ -2 (the limit diverges)
= 0 if k < -2 (the limit converges to 0)
Step 3: Determine the radius of convergence
According to the ratio test, the series converges if L < 1,
and diverges if L > 1.
Since the limit L depends on the value of k,
the radius of convergence R varies accordingly:
If k ≥ -2, the series diverges for all values of x.
If k < -2, the series converges for all values of x.
Learn more about limit converges here:
https://brainly.com/question/31489380
#SPJ4
What is the value of
[tex] \sqrt{100 \times 4} [/tex]
Answer:
√{100×4)=√20²=±20 is your answer
Ben wants to buy a new car stereo and he has already saved some money. He used this inequality to represent the amount he still has to save to be able to buy the stereo, where a represents the amount still left to save.
a + 212 greater-than-or-equal-to 365
If Ben saves $15 a week for the next 10 weeks, will he be able to buy the stereo and why?
Answer:
Since Ben would have $362, he won't be able to buy the stereo as he needs to have an amount greater than or equal to 365.
Step-by-step explanation:
First, you need to determine the amount that Ben would have after saving $15 for the next 10 weeks:
$15*10=$150
Now, the inequality indicates that the amount left to save plus 212 should be greater than or equal to 365, so you have to add up 212 plus the amount Ben will save in the next 10 weeks to be able to determine if he would be able to buy the stereo:
150+$212=$362
Since Ben would have $362, he won't be able to buy the stereo as he needs to have an amount greater than or equal to 365.
Four times a first number decreased by a second number is 19. The first number increased by four times the second number is −8. Find the numbers.
Answer:
a = 4
b = -3
Step-by-step explanation:
Let a and b be the two numbers.
According to question,
4a - b = 19........(i)
And,
a + 4b = -8........(ii)
From (i),
4a - b = 19
or, b = 4a - 19
Replacing b in (ii),
a + 4(4a - 19) = -8
a + 16a - 76 = -8
17a = -8 + 76
17a = 68
a = 68/17
a = 4
And,
b = 4a - 19
= 4 x 4 - 19
= 16 - 19
= -3
Which function is equivalent to (x)=-7(x+4)2-1?
a : f(x)=-7x2 + 8x+15
b : F(x)=-7x2-56x-113
C : f(x)=-7x2-56x-105
d : f(x)=-7x2 + 111
Answer:
answer : b
Step-by-step explanation:
hello :
calculate : f (x)=-7(x+4)²-1
f(x) = -7(x²+16+8x) -1 use identity : (a+b)² = a²+b²+2ab
f(x) = -7x²-112 -56x -1
f(x) = -7x²-56x -113
5 in=? feet fraction form
You just obtained a credit card. You immediately purchase a stereo system for $200. your credit limit is $1000. Let's assume that you make no payments and purchase nothing more and there are no other fees. The monthly interest rate is 1.42%.
What is the growth rate of your credit card balance?
A. 0.42
B. 0.0142
C. 14.2
D. 142
Answer:
its b
Step-by-step explanation:
have a great day <3
The growth rate of your credit card balance is approximately 0.0142.
Therefore, the correct option is B.
Given that you got a credit card, you purchased a stereo system for $200. your credit limit is $1000.
The monthly interest rate is 1.42%.
We need to determine the growth rate of your credit card balance,
To calculate the growth rate of your credit card balance, we need to consider the monthly interest rate and the initial purchase amount.
The monthly interest rate is 1.42%, which can be expressed as a decimal by dividing it by 100: 0.0142.
The initial purchase amount is $200.
Assuming no payments are made and no additional purchases are made, the credit card balance will increase each month due to the accrued interest.
To calculate the growth rate, we can divide the accrued interest by the initial purchase amount.
Accrued interest = Monthly interest rate x Initial purchase amount
= 0.0142 x $200
= $2.84
Growth rate = Accrued interest / Initial purchase amount
= $2.84 / $200
≈ 0.0142
Therefore, the growth rate of your credit card balance is approximately 0.0142, which corresponds to option B.
Learn more about Credit cards click;
https://brainly.com/question/30940802
#SPJ2
Can you say a coefficient is
significantly different from zero at 5% level if the coefficient of
a variable is twice as large as its estimated standard error?
Explain.
A coefficient is significantly different from zero at 5% level if the coefficient of a variable is twice as large as its estimated standard error. This is because, at the 5% level of significance, the critical value for the t-distribution, when a two-tailed test is used, is equal to 1.96. To be significantly different from zero, the calculated t-value has to be greater than 1.96 or less than -1.96.
Suppose the estimated standard error is SE and the coefficient of the variable is β. The standard error of β, denoted by SE(β), is equal to SE/√n, where n is the sample size. Thus, if the coefficient of the variable is twice as large as its estimated standard error, then β > 2SE.
And, the calculated t-value would be greater than (β/SE) > 2, which is greater than 1.96. Therefore, we can say that the coefficient is significantly different from zero at the 5% level.
Know more about coefficient:
https://brainly.com/question/1594145
#SPJ11
Use series to approximate the definite integral to within the indicated accuracy:
the integral from from 0 to 0.4 of e^?x^3 dx with an error <10?4
Note: The answer you derive here should be the partial sum of an appropriate series (the number of terms determined by an error estimate). This number is not necessarily the correct value of the integral truncated to the correct number of decimal places.
We evaluate S_n by substituting x = 0.4 into the nth partial sum and obtain our approximation for the integral.
To approximate the definite integral ∫(0 to 0.4)
[tex] {e}^{-x^3} [/tex]
dx with an error less than
[tex] {10}^{ - 4} [/tex]
we can use a Taylor series expansion for
[tex]{e}^{-x^3} [/tex]
The Taylor series expansion of
[tex]{e}^{-x^3} [/tex]
centered at x = 0 is:
[tex] {e}^{-x^3} = 1 - x^3 + (x^3)^2/2! - (x^3)^3/3! + ...[/tex]
By integrating this series term by term, we can approximate the integral. Let's denote the nth partial sum of the series as S_n.
To estimate the number of terms needed for the desired accuracy, we can use the error estimate formula for alternating series:
|Error| ≤ |a_(n+1)|, where a_(n+1) is the absolute value of the first omitted term.
In this case, |a_(n+1)| =
[tex]|(x^3)^{n+1} /(n+1)!| ≤ {0.4}^{(3(n+1)} /(n+1)!
[/tex]
By setting
[tex]{0.4}^{(3(n+1))} /(n+1)! < 10^(-4)[/tex]
and solving for n, we can determine the number of terms required.
Learn more about integral here:
https://brainly.com/question/31433890
#SPJ4
What is the slope, m, of the line? Enter your answer as a decimal.
Round to the nearest hundredth.
Answer:
4.56
Step-by-step explanation:
The slope (m) of the line given in the graph is -0.332.
In the given graph coordinates of the line are given, that is (2,0) and (-4, 2).
How to find the slope of the line?Pick two points on the line and determine their coordinates. Determine the difference in y-coordinates of these two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).
Now, the slope of the line=m=0-2/2-(-4)=-2/6=-0.33333
-0.33333≈-0.332
Therefore, the slope (m) of the line given in the graph is -0.332.
To learn more about the slope of the line visit:
https://brainly.com/question/28108658.
#SPJ2
what is the rate of change for y=38x+20
A. 38
B. 20
C.1
D. it has no term
Answer:
A
Step-by-step explanation:
Simplify:
5a+6a^2+2a^0-3a^2-9a
3a^2-4a+2
-a^3+2
-a^2+2
3a^2-4a+1
Answer:
I believe that the answer is '3a^2-4a+2
Find the sum of (6x2 - 9x + 7) and (- 8x2 + 10x - 14)
Answer:
-2x² + x - 7
Step-by-step explanation:
(6x² - 9x + 7) + (-8x² + 10x - 14)
6x² - 9x + 7 - 8x² + 10x - 14
6x² - 8x² - 9x + 10x + 7 - 14
-2x² + x - 7
The Zombie Apocalypse has come to Panama City Beach. It starts when 3 Spring Breakers become zombie after an encounter with a deadly fish. Waking up the next day, each Spring Breaker can infect 4 more people per day before needing a rest. Each of these zombies can, in turn, infect an additional 4 people per day. Write an Exponential Function to represent this situation. Then find out how many crazy Spring Break Zombies will be roaming the beach at the end of the week (Day 7)?
Answer:
By the end of the week there will be 49,152 zombies in Panama City Beach.
Step-by-step explanation:
Since the Zombie Apocalypse has come to Panama City Beach, starting when 3 Spring Breakers become zombie after an encounter with a deadly fish, and since waking up the next day, each Spring Breaker can infect 4 more people per day before needing a rest , and each of these zombies can, in turn, infect an additional 4 people per day, to determine how many crazy Spring Break Zombies will be roaming the beach at the end of the week the following exponential function has to be solved:
3 x 4 ^ 7 = X
3 x 16,384 = X
49.152 = X
Therefore, by the end of the week there will be 49,152 zombies in Panama City Beach.
The number of crazy Spring Break Zombies will be roaming the beach at the end of the week 7 are 49,152 and the equation for the situation is,
[tex]x=3\times(4)^7\\[/tex]
What is an exponential function?Exponential function is the function in which the function growth or decay with the power of the independent variable. The curve of the exponential function depends on the value of its variable.
The exponential function with dependent variable y and independent variable x can be written as,
[tex]y=ba^x+c[/tex]
Here, a, b and c are the real numbers.
The Zombie Apocalypse has come to Panama City Beach. It starts when 3 Spring Breakers become zombie after an encounter with a deadly fish.
In the next morning, each Spring Breaker can infect 4 more people per day before needing a rest. Each of these zombies can, in turn, infect an additional 4 people per day.
As total number of weeks are 7. Thus, for this situation, the exponential function for the variable x can be given as,
[tex]x=3\times(4)^7\\[/tex]
Now to find the number of crazy Spring Break Zombies will be roaming the beach at the end of the week 7, simplify the above equation as,
[tex]x=3\times(4)^7\\\\x=3\times16384\\x=49152[/tex]
Hence, the number of crazy Spring Break Zombies will be roaming the beach at the end of the week 7 are 49,152 and the equation for the situation is,
[tex]x=3\times(4)^7\\[/tex]
Learn more about the exponential function here;
https://brainly.com/question/15602982
Worth five points! it doesnt tell me if what answer is right but if i get 75% or up i will mark the first person who answered with an actual answer brainliest and i don't lie about brainliest!!
What is m∠U?
A. 17
B. 29
C. 46
D. 134
Answer:
A
Step-by-step explanation:
Remarks
The given angle is an exterior angle.It's value is 46 degrees. An exterior angle is the sum of the two remote angles. (A remote angle is one that is not supplementary to the given exterior angle.Solution
46 = <u + <t<t = 2946 = <u + 29 Subtract 29 from both sides.46 - 29 = <u<u = 17 degreesA combination lock with three dials, each numbered 1 through 8, is defective in that you only need to get two of the numbers right to open the lock. (For example, suppose the true combination is 4-2-7. Then 4-2-7 would open the lock, but so would 4-2-5, 4-2-2, 4-8-7 or 4-6-7. But not 2-4-7.)
Answer:
64 combination attempts
Step-by-step explanation:
Since each dial in the lock is numbered from 1-8 then there are 8 possibilities for each dial. Out of the three dials, only 2 actually need to be correct in order for the lock to open therefore, we simply raise the number of possibilities for each dial to the power of 2 which should give us the total number of tries we need in order to guarantee that it opens. Assuming that you are making the combinations in numerical order 1-1-1, 1-1-2, 1-1-3, etc.
8^2 = 64 combination attempts
Raymond has two bags of candy. • Bag A has 15 total pieces of candy, 9 are chocolate candies. Bag B has 10 total pieces of candy, 5 are chocolate candies. Which statement is true?
Answer:
The probability of selection of chocolate candy from bag A is ( 10%) bigger than from the bag B
Step-by-step explanation:
From bag A the probability (p₁ ) of selection ( in a random sample) of one chocolate candy is
p₁ = 9/15 p₁ = 0,6
From bag B the probability ( p₂ ) of selection ( in a random sample) of one chocolate candy is:
p₂ = 5/10 p₂ = 0,5
Then the probability of selection of chocolate candy from bag A is bigger than from the bag B
p₁ > p₂ p₁ - p₂ = 0,6 - 0,5 p₁ - p₂ = 0,1 p₁ - p₂ = 10%
p
A running track consists of two parallel lines that are connected at each end but the curved boundary of a semicircle. The parallel lines are 30 meters long and 7 meters apart. Fine the area inside the running track.
Answer:
The area inside the running track is 248.5 m².
Step-by-step explanation:
The area inside the running track is given by the sum of the area of a rectangle and the area of a semicircle:
[tex] A_{t} = A_{r} + 2A_{c} [/tex]
[tex] A_{t} = x*(2r) + 2*(\frac{\pi r^{2}}{2}) [/tex]
Where:
x: is one side of the rectangle = 30 m
r: is the radius = half of the other side of the rectangle = 7/2 m = 3.5 m
Hence, the total area is:
[tex] A_{t} = 30*7 + \pi (3.5)^{2} = 248.5 m^{2} [/tex]
Therefore, the area inside the running track is 248.5 m².
I hope it helps you!
Which quadrilateral's diagonals are congruent and perpendicular bisectors of each other?
Diagonals congruent: rectangle, square, isosceles trapezoid
Perpendicular bisectors: Rhombus, Square
16. Find the perimeter of AJKL.
J
8x - 35
N
5x - 8
77-9
K
Р
M M
2y + 11
o
32
L
Answer:
Parameter OF Δ JKL = 138 unit
Step-by-step explanation:
Given:
JN = 8x - 35
NK = 7y - 9
OK = 2y + 11
OL = 32 - [2y + 11]
JM = 5x - 8
Find:
Parameter OF Δ JKL
Computation:
We know that tangent from same points are always equal
So,
ML = OL
JM = JN
5x - 8 = 8x - 35
8x - 5x = 35 - 8
3x = 27
x = 9
So,
JN = 8x - 35
JN = 8(9) - 35
JN = 37 unit
JM = 5x - 8
JM = 5(9) - 8
JM = 37 unit
NK = OK
7y - 9 = 2y + 11
5y = 20
y = 4
NK = 7y - 9
NK = 7(4) - 9
NK = 19 unit
OK = 2y + 11
OK = 2(4) + 11
Ok = 19 unit
OL = 32 - [2(y) + 11]
OL = 32 - [2(4) + 11]
OL = 13 unit
So,
LM = OL = 13 unit
Parameter OF Δ JKL = JN + NK + OK + OL + LM + JM
Parameter OF Δ JKL = 37 + 19 + 19 + 13 + 13 + 37
Parameter OF Δ JKL = 138 unit
Answer:
Step-by-step explanation:
g
Find the Laplace Transform of number 1 using the definition via integration. F(t) = 5 sin 3t Solve for the Laplace transform using the formula for numbers 2 and 3. G(t) = t^5 — 1/4 e^-9t + 5(t − 1)² F(t) = e^-2t-5
The Laplace Transform of the function F(t) = 5sin(3t) can be found by using the definition of the Laplace Transform, which involves integrating the function with respect to time. The Laplace Transform of F(t) is not a number, but rather a function in the complex domain.
To find the Laplace Transform of F(t) = 5sin(3t) using the definition, we need to integrate the function with respect to time from 0 to infinity. The Laplace Transform is defined as L{F(t)} = ∫[0,∞] F(t)e^(-st) dt, where s is a complex number.
Integrating [tex]5sin(3t)e^(-st)[/tex]with respect to t results in a complex function that depends on s. The integration involves applying the integration rules and evaluating the integral limits. The resulting Laplace Transform is a function of s, denoted as L{F(t)}.
However, for the functions G(t) = [tex]t^5 - (1/4)e^(-9t) + 5(t - 1)^2 and F(t) = e^(-2t - 5)[/tex], the Laplace Transform can be computed using the Laplace Transform formulas. These formulas provide specific transformations for various types of functions, making the calculation more straightforward. By applying the Laplace Transform formulas to G(t) and F(t), we can obtain their respective Laplace Transform expressions, denoted as L{G(t)} and L{F(t)}. These expressions will involve algebraic manipulations and the use of the Laplace Transform tables to identify the corresponding transformations.
Overall, the Laplace Transform is a powerful tool in the field of mathematics and engineering that allows us to transform functions from the time domain to the complex frequency domain, facilitating the analysis and solution of differential equations and systems of equations.
Learn more about function here:
https://brainly.com/question/30721594
#SPJ11
Find the Range of the following set of data. (Round to the
nearest whole number.)
1, 1, 3,0, 7, 2, 0, 3, 1, 6, 8, 1
PLEASE HELP IM DESPERATE
Step-by-step explanation:
put them in least to greatest, so that would be: 0,0,1,1,1,1,2,3,3,6,8,7,8, then do the greatest minus the lowest: 8-0=8
What is the equation of the line shown in the graph?
Answer:
-6
Step-by-step explanation:
it is going through the y axis
A hemisphere with diamater 17 cm
Answer:
not enough information
Step-by-stepexplanation:
Use the following probability distribution to answer questions
x -15 -10 -5 0 5 10 15
P(X=x) 0.05 0.34 0.13 0.24 0.08 0.11 0.05
1. Find P(X=0) a. 0
b. 0.24 c. 0.48 d. 0.52 e. 0.08
The probability P(X=0) is equal to 0.24.
In the given probability distribution, we are provided with the probabilities associated with each value of the random variable X. To find P(X=0), we need to identify the probability assigned to the value 0.
Looking at the table, we see that the probability P(X=0) is given as 0.24. Therefore, the correct answer is option b. 0.24.
The probability distribution assigns probabilities to specific values of the random variable X. In this case, the value 0 has a probability of 0.24. This indicates that there is a 0.24 chance of observing the value 0 when the random variable X is sampled from this distribution.
to learn more about probability click here:
brainly.com/question/14740947
#SPJ11
Need this answer ASAP the last missing square says “take the square root of both sides”
Answer:
add 5 to both sides, divide by 2, take square root, subtract 3/4
Step-by-step explanation:
I think you maybe do the reverse order of operations, which is SADMEP (subtract/add, then divide/multiply, then take care of exponents and square roots, then do that same order for whatever's in parenthesis.)
Factor the expression below. A. (x + 5)(x + 5) B. (x - 5)(x + 5) C. 5(x2 - x + 5) D. (x - 5)(x - 5)
Answer:
A. x² +10x +25
B. x² - 25
C. 5x² -5x + 25
D. x²- 10x + 25
Step-by-step explanation:
A. (x+5)(x+5)
x² + 5x + 5x + 25
x² +10x + 25
B. (x-5)(x+5)
x² + 5x - 5x - 25
x² -25
C. 5(x² -x +5)
5x² -5x + 25
D. (x-5)(x-5)
x² - 5x -5x + 25
x²- 10x + 25
Find the greatest common factor of 24x^2 and 42xy^3 .
Answer:
12y2
Step-by-step explanation:
The cone and cylinder above have the same radius, r, and height, h. The volume of the cone is 69 cubic centimeters. What is the volume of the cylinder?
A. 138 cubic centimeters
B. 207 cubic centimeters
C. 23 cubic centimeters
D. 276 cubic centimeters
Answer:
207 cubic centimeters
Step-by-step explanation:
Given
volume of cone = 9 cubic centimeters
Since the cone and cylinder above have the same radius, r, and height, h, then r = h
volume of the cone = 1/3πr²h
69 = 1/3πr²h
πr²h = 69*3
πr²h = 207cubic cm
Since the volume of the cylinder = πr²h
Hence volume of the cylinder is 207 cubic centimeters
HELP ME PLEASE https://brainly.com/question/22734415
I’m gonnna fail :(
Cheryl moves houses. Her old house is 3 kilometers from her new house. How many meters is it from the old house to the new house?
Answer:
3000 here hope this helps you out