Consider the series 12 ta) Find the stadius and interval of convergence (b) For what values of these converge absolutely (c) For whates of x does the series convorbe conditionally In) Find the interval of convergence Find the radius of convergence RE {b} For wat also does the series converge about fel For what values of x. does the series coworo conditionaty Select the cornect choice below and necessary in the war box to compete your choice O A The sensores conditionally at se acomo parte answers as needed) OB. The series does not convorge conditionally 1 #1 *
Answers
a) The series converges conditionally for -1 < x < 1) and the radius of convergence is 1.
b) The series converges absolutely for |x| < 1.
c)The series converges conditionally for -1 < x < 1.
d) The interval of convergence is (-1, 1) and the radius of convergence is 1
e)The series converges about x = 0 because the series of 12x^n converges to 0 as n → ∞.
f) The series converges conditionally for -1 < x < 1
(a) To find the radius of convergence (or stadius), we can use the ratio test:
lim n→∞ |12x^n+1 / 12x^n| = lim n→∞ |x| = |x|
So, the series converges if |x| < 1, and diverges if |x| > 1. When |x| = 1, the ratio test is inconclusive and we need to use another method to determine convergence.
Therefore, the interval of convergence is (-1, 1) and the radius of convergence is 1.
(b) The series converges absolutely if the series of |12x^n| converges. This series is a geometric series with ratio |x|, so it converges if |x| < 1 and diverges if |x| > 1. When |x| = 1, the series diverges.
So, the series converges absolutely for |x| < 1.
(c) The series converges conditionally if it converges but the series of |12x^n| diverges. We already know that the series converges for |x| < 1, so we need to check if the series of |12x^n| diverges for some values of x in that interval.
The series of |12x^n| is a geometric series with ratio |x|, so it diverges if |x| ≥ 1. Therefore, the series converges conditionally for -1 < x < 1.
(d) The interval of convergence is (-1, 1) and the radius of convergence is 1, as found in part (a).
(e) The series converges about x = 0 because the series of 12x^n converges to 0 as n → ∞. This is the only point outside the interval of convergence where the series converges.
(f) The series converges conditionally for -1 < x < 1, as found in part (c).
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Related Questions
The baseball team is raising money by selling cheesecakes. The players plan to sell an entire cheesecake for $24.00 each and slices of cheesecake for $3.50 each. If they want to raise at least $700, how many of each could
they sell?
Answers
Answer:
200 slices or 30 cakes
Step-by-step explanation:
Divide 700 by 3.5 = 200
Divide 700 by 24 = 29.16
Roberto owed his credit card $1000 dollars after
8 weeks. He decides to start paying it off.
After 10 weeks, he only owns $750. Calculate the
rate of change to figure out how much he was paying
per week after week 8.
Answers
wwwwwwwwwwwwwwwwwwww
(URGENT!) The function g is defined by the following rule. Complete the function table. g(x)=4x-2 (The table is in the image)
Answers
Put each value in the place of x for the function g(x)=4x-2.
g(-5) = 4(-5)-2 = -20-2 = -22
g(-2) = 4(-2)-2 = -8-2 = -10
g(1) = 4(1)-2 = 4-2 = 2
g(3) = 4(3)-2 = 12-2 = 10
g(5) = 4(5)-2 = 20-2 = 18
The stingray population in a particular reef is decreasing at a rate of 1.4% per year. The population was 3800 in the year 2008. What is the best prediction of the population in the year 2013? Round to the nearest whole number. (no need to label your answer :
Answers
Answer:
Population in 2013 = 3541
Step-by-step explanation:
if u and v are in r n , how are u t v and v t u related? how are uv t and vu t related?
Answers
They are related as u^T transposes of each other. v and v^T u are scalar values that represent the dot product of u and v. uv^T and vu^T are matrices of size n x n that represent the outer product of u and v.
If u and v are vectors in R^n, then:
u^T v and v^T u are related as transposes of each other. Specifically, if
u = [u_1, u_2, ..., u_n]^T
and v = [v_1, v_2, ..., v_n]^T
then:
u^T v = v^T u
= u_1 * v_1 + u_2 * v_2 + ... + u_n * v_n
So, u^T v and v^T u are scalar values that represent the dot product of u and v.
uv^T and vu^T are related as transposes of each other. Specifically, if u = [u_1, u_2, ..., u_n]^T and v = [v_1, v_2, ..., v_n]^T
then:
uv^T = [u_1 * v_1, u_1 * v_2, ..., u_1 * v_n;
u_2 * v_1, u_2 * v_2, ..., u_2 * v_n;
...;
u_n * v_1, u_n * v_2, ..., u_n * v_n]
vu^T = [v_1 * u_1, v_2 * u_1, ..., v_n * u_1;
v_1 * u_2, v_2 * u_2, ..., v_n * u_2;
...;
v_1 * u_n, v_2 * u_n, ..., v_n * u_n]
So, uv^T and vu^T are matrices of size n x n that represent the outer product of u and v.
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Answer in comments pls
Answers
Answer: 7xy+2x^2t
Combine like-terms.
5xy+2xy-x^2t+3x^2t
7xy+2x^2t
:)
Answer:
7xy+2x^2t
Step-by-step explanation:
5xy-x^2t+2xy+3x^2t
Rearrange:
5xy+2xy+3x^2t-x^2t
7xy+2x^2t
in a shipment of 21 smartphones, 2 are defective. how many ways can a quality control inspector randomly test 5 smartphones, of which 2 are defective?
Answers
There are 969 methods for the quality control inspector to randomly check 5 smartphones, of which 2 are defective, from the shipment of 21 smartphones.
We can solve this problem using combinations formula, that is a way of counting the number of ways to select k objects from a fixed of n items without regard to order. The range of combinations of k items from a fixed of n objects is given via:
\(C(n, k) = n! / (k! * (n-k)!)\)
in which:
n: the total number of objects within the setk: the number of objects to pick from the setIn this situation, we want to pick out 2 defective smartphones out of 2 defective smartphones and 19 non-defective smartphones, and we need to pick out out three non-defective smartphones out of the ultimate 19 non-defective smartphones.
Consequently, the number of approaches to choose 2 defective smartphones and 3 non-Defective smartphones from the set of 21 smartphones is:
\(C(2, 2) * C(19, 3) = 1 * (19! / (3! * 16!)) = 191817 / (321) = 969\)
Therefore, there are 969 methods for quality control.
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If using the method of completing the square to solve the quadratic equation x^2+15x+25=0x
2
+15x+25=0, which number would have to be added to "complete the square"?
Answers
Answer:
x = -15/2 ± (1/2)*5√5
Step-by-step explanation:
I will assume that you meant x^2+15x+25=0.
To complete the square, take half of the coefficient of x, square the result, add this square into the equation after '15x,' and then subtract the square from the result:
x^2+15x+25=0 => x^2 + 15x + (15/2)^2 - (15/2)^2 + 25 = 0.
Rewrite the first two terms as (x + 15/2)^2 - 225/4 + 100/4 = 0, or
(x + 15/2)^2 - 125/4 = 0
Taking the square root of both sides, we obtain the solutions:
x + 15/2 ±√[125/4], or
x = -15/2 ± (1/2)*5√5
The quadratic equation x²+15x+25=0, (15/2)² is a number to be added to "complete the square"
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
The quadratic equation x²+15x+25=0
x²+15x+(15/2)²+25-(15/2)²=0
(x+15/2)²+25-225/4
(x+15/2)²+(100-225)/4
(x+15/2)²+(-125/4)
(x+15/2)²-(√125/√4)²
(x+15/2+√125/√4)(x+15/2-√125/√4)
(x+15/2+√125/2)(x-15/2-√125/2)
(x+(15+√125)/2)(x-(15+√125)/2)
Hence (15/2)² is a number to be added to "complete the square"
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It takes 12 minutes to fill an entire bathtub using both cold and hot water. If just the cold water is used, it takes 18 minutes to fill the bathtub. How long would it take to fill the bathtub if just the hot water were used?
Answers
Answer:
it takes 36 minutes to fill the bathtub using just hot water.
Which mathematical operation is represented in the phrase "15 less than
p"?
A) +
B) X
C) =
D) -
Answers
Answer:
its (D)
Step-by-step explanation:
Answer:
The answer is D) -
Step-by-step explanation
I have taken the test.
what is the variable in 5 + 12w
Answers
the variable in this question would be........................ W
you are welcom
find the exact length of the curve y=23(x2−1)3/2,1≤x≤3.
Answers
The exact length of the curve y=23(x^2−1)^(3/2), 1≤x≤3, is given by L = (1/9) ∫(sec^(-1)3 to sec^(-1)1) sqrt[9(sec^2θ−1)^2+1] dθ. This integral cannot be evaluated in terms of elementary functions.
To find the length of the curve y = 23(x^2 - 1)^(3/2) from x = 1 to x = 3, we can use the arc length formula:
L = ∫(1 to 3) sqrt[1 + (dy/dx)^2] dx
First, we need to find dy/dx:
dy/dx = 23 * 3/2 * (x^2 - 1)^(1/2) * 2x
= 3x(x^2 - 1)^(1/2)
Now, we can substitute this expression into the arc length formula and integrate:
L = ∫(1 to 3) sqrt[1 + (3x(x^2 - 1)^(1/2))^2] dx
= ∫(1 to 3) sqrt[1 + 9x^2(x^2 - 1)] dx
= ∫(1 to 3) sqrt[9x^4 - 9x^2 + 1] dx
We can solve this integral using trigonometric substitution. Let x = (1/3)secθ, then dx = (1/3)secθ tanθ dθ. Substituting, we get:
L = ∫(θ1 to θ2) [(1/3)secθ * sqrt[9(sec^2θ - 1)^2 + 1]] * (1/3)secθ tanθ dθ
= (1/9) ∫(θ1 to θ2) sqrt[9(sec^2θ - 1)^2 + 1] dθ
where θ1 = sec^(-1)3 and θ2 = sec^(-1)1.
This integral cannot be evaluated in terms of elementary functions, so we can approximate it using numerical methods or leave the answer in this form. Therefore, the exact length of the curve y = 23(x^2 - 1)^(3/2), 1 ≤ x ≤ 3 is:
L = (1/9) ∫(sec^(-1)3 to sec^(-1)1) sqrt[9(sec^2θ - 1)^2 + 1] dθ.
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If you are standing 75 ft away from a tree and looking up at the top at a 40° angle, what is the height of the tree?
Answers
Answer:
Step-by-step explanation:
rewrite each linear expression by factoring out the greatest common factor. -45x+72
Answers
Step 1:
Find the greatest common factor of -45x and +72.
3 | -45x | +72
-----------------------------------------
3 | -15x | +24
-----------------------------------------
| -5x | +8
Therefore, the greatest common factor of -45x and +72 is 3 x 3 = 9
Step 2:
Factor out the greatest common factor
\(\begin{gathered} -45x+72=9(\frac{-45x}{9}+\frac{72}{9}) \\ \text{this implies that} \\ -45x+72=9(-5x+8) \end{gathered}\)Therefore the correct answer 9(-5x + 8)
When it rains I get tired. It's raining today. I'm going to take a nap.
Which law of logic is used to make the conclusion?
Law of Detachment
None of the above
Law of Contrapositive
Law of Detachment
PLEASE HELP
Answers
Answer:
None of the Above
Step-by-step explanation:
Hope this helps
variables that indicate the distance a target is from the level achieved are called
Answers
Variables that indicate the distance a target is from the level achieved are called performance metrics or progress indicators.
Variables that indicate the distance a target is from the level achieved are called performance metrics or progress indicators. These variables help measure and track progress towards a goal by providing a quantitative or qualitative measure of how far the target is from the desired level of achievement.
Performance metrics can be represented in various forms, such as distance covered, percentage completed, points earned, or even subjective evaluations. For example, in a fitness program, a performance metric could be the number of miles run or the number of push-ups completed.
These metrics enable individuals or organizations to assess their progress and make necessary adjustments to reach their desired outcomes.
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The arcs in the photo at the right appear to
be paths of stars rotating about the North Star, To produce this effect, the
photographer set a camera on a tripod and left the shutter open for an
extended time. If the photographer left the shutter open for a full 24 hours,
each are would be a complete circle. You can model a star's rotation" in the
coordinate plane. Place the North Star at the origin. Let P(1, 0) be the position
of the star at the moment the camera's shutter opens. Suppose the shutter is
left open for 2 h 40 min, with the arc ending at P. a. What angle of rotation
maps Ponto P? b. What are the x and y coordinates of P to the nearest
thousandth? c. What translation rule maps P onto P?
Answers
Answer:
a. What angle of rotation maps Ponto P?
30.25 degrees
b. What are the x and y coordinates of P to the nearest thousandth?
(83.3, 33.3)
c. What translation rule maps P onto P?
Rotation
PLEASE HELP I WILL GIVE YOU BRAINLIEST
Answers
Answer
32
Step-by-step explanation:
fffff
336,765=3,14×0.55×(l+0.55) please help
Answers
Answer:
l = 194999.45
Step-by-step explanation:
I'm going to assume that you meant 3.14 by 3,14.
336,765 = 3.14 × 0.55 × (l + 0.55)
336,765 ÷ (3.14 × 0.55) = l + 0.55
(336,765 ÷ (3.14 × 0.55)) - 0.55 = l
l = 194999.45
The exponential function f(x) has a horizontal asymptote at y=3. What is the end behavior of f(x)?
*photo of graph included*
Answers
Answer:
The answer is A
Step-by-step explanation:
Hope this helps
- What is the density of an object whose mass is 180 grams and whose volume is 45 cm
B. 0.25 g/cm³
A. 4 cm³/g
C. 4 g/cm³
D. 0.25 cm³/g
Answers
The density of an object with a mass of 180 grams and a volume of 45 cm is 0.4 kg/m.
What is density?
How much "stuff" is contained in a specific quantity of space is determined by its density. For instance, a block of the harder, lighter element gold (Au) will be denser than a block of the heavier element lead (Pb) (Au). Styrofoam blocks are less dense than bricks. Mass per unit volume serves as its definition.So the formula will be d = m / v
The mass of the object is 180 g
The volume of the object is 45 cm
Putting the value in the formula
d = 180 g / 45 cm = 0.4 kg/m
Thus, the density of an object will be 0.4 kg/m.
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a curve has slope 2x x^2 a5 3ach point xy on the curve. which is the equation of the curve if it passes through the point 1,3
Answers
The curve is F(x) = x^2 + 3x - 2
From the question, we have
f(x) = 2x + 3
∫f(x) = ∫2x + 3 dx
F(x) = x^2 + 3x + C
2 = (1)^2 + 3(1) + C
2 = 4 + C
C= -2
The curve is F(x) = x^2 + 3x - 2
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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Calculate the distance between the points M=(-1,-2) and C=(-9, 2) in the coordinate plane.
Round your answer to the nearest hundredth.
Answers
Answer:
8.9443
Step-by-step explanation:
d = √((x2-x1)2 + (y2-y1)2)
Step by step procedure:
Find the difference between coordinates:
(x2-x1) = (-9 - -1) = -8
(y2-y1) = (2 - -2) = 4
Square the results and sum them up:
(-8)2 + (4)2 = 64 + 16 = 80
Now Find the square root and that's your result:
Exact solution: √80 = 4√5
Approximate solution: 8.9443
(13.01 LC) What is the value of the expression 7 +(16 - 7) = 3 + 8? (2 points) O 12 O 15 O 17 O 18 Question 3
Answers
Answer:
16 > 11
Step-by-step explanation:
7 + (16 - 7) = 3 + 8
7 + 9 = 3 + 8
16 = 3 + 8
16 ≠ 11
or
16 > 11
when will social security checks be deposited for january 2022
Answers
Answer:
Maybe in June? Mainly the government needs money to send out the security checks
Step-by-step explanation:
Determine the number of solutions that 5x^2 + 3x + 8 has without solving the equation.
Answers
5x^2 + 3x + 8 has no solutions without solving the equation since the discriminant is negative
How to determine the number of solutions that 5x^2 + 3x + 8 hasUsing the discriminant formula:
The discriminant (D) is given by:
D = b^2 - 4ac
For the equation 5x^2 + 3x + 8, we have:
a = 5, b = 3, and c = 8
Substituting these values into the discriminant formula, we get:
D = (3)^2 - 4(5)(8) = -127
Since the discriminant is negative, the quadratic equation has no real solutions. Therefore, 5x^2 + 3x + 8 has no solutions without solving the equation.
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Please help ASAP please
Answers
Answer:
I would love to help but the image is not there on my screen. :(
Step-by-step explanation:
we assume that with a linear relationship between two variables, for any fixed value of x, the observed ________ follows a normal distribution.
Answers
We assume that with a linear relationship between two variables, for any fixed value of x, the observed residuals follows a normal distribution.
This assumption is based on the Central Limit Theorem, which states that when the sample size is large enough, the distribution of sample means will be approximately normal, regardless of the shape of the underlying population distribution.
In the case of a linear relationship between two variables, we can assume that the residuals (the difference between the observed y values and the predicted values based on the linear regression model) follow a normal distribution with mean 0 and constant variance. This assumption is important because it allows us to use statistical methods that rely on normality, such as hypothesis testing and confidence intervals.
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A bag contains 49 coins consisting of quarters and dimes. There are 2.5 times as many quarters as there are dimes in the bag. Write a system of equations that models this situation. How many dimes are in the bag?
pls write step by step so that I can understand :)
Answers
Answer:
Dimes = 35
Quarters = 14
Step-by-step explanation:
Let
quarters = q
Dimes = d
Total coins = 49
There are 2.5 times as many quarters as there are dimes in the bag
Dimes = 2.5q
Quarters + Dimes = Total
q + 2.5q = 49
3.5q = 49
q = 49/3.5
q = 14
d = 2.5q
= 2.5 * 14
= 35
d = 35
Therefore,
Dimes = 35
Quarters = 14
Answer:
The system of equations that models this equation area:
d + q = 49
q = 2.5d
please help!!
the measure of angle p is _ degrees
the length of NO is _
the value of y is _
the value of x is _
Answers
The measure of angle p is 40 degrees
The length of NO is 13
The value of y is 25/6
The value of x is 47.5/3
What is CPCT?
CPCT is Corresponding Parts of Congruent Triangles.
If two triangles are congruent, their corresponding sides are equal.
Their corresponding angles are equal.
According to the given question:
If ΔITP ≅ ΔNGO then their corresponding sides and corresponding angles are equal.
Hence
IP = NO; IT = NG and TP = GO
∠I = ∠N; ∠T = ∠G and ∠P = ∠O
1) the measure of angle P is _____
Sum of interior angles of a triangle is 180 degrees
∠I + ∠T + ∠P = 180
65 + 75 + ∠P = 180
Therefore, on simplifying we get the measure of angle p as 40 degrees
2) Length of NO is _____
By CPCT,
NO = IP = 13
Hence, length of NO is 13
3) the value of y is ___
By CPCT,
GO = TP
Substituting the values to get
6y - 14 = 11
6y = 25
y = 25/6
4) the value of x is ____
By CPCT,
GN = IT
Substituting the values to get
x - 2y = 7.5
x - 2(25/6) = 7.5
x = 47.5/3
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