I need help with this question

The Test of convergence of series, helps us to check the given series are absolutely convergent

divergent, conditionally convergent.

Using the convergence test we get,

a) The lim. 72 = 5 is divergent. The correct option is option( C).

b) lim 0:2 = 0.5 is absolutely convergent. The correct option is option ( A).

Firstly , we discuss how to check absolutely convergent , divergent or conditionally convergent.

Steps to Determine :

Step 1: Take the absolute value of the series. Then determine whether the series converges.

If it converges, then we say the series converges absolutely.

If it does not converge, then we say it does not converge absolutely and we follow to Step 2

Step 2: Use the Alternating Series Test to determine whether the original series converges or diverges.

If it converges, then we say the series converges conditionally.

If the Alternating Series Test fails, we attempt another test.

Absolute Convergence Test :

If ∑∞ |an| converges, then ∑∞ aₙ converges

n = 1 n =1

We say that ∑∞ aₙ converges absolutely

n=1

if this case is true. If a series does not converge absolutely but converges by another test, we say that the series converges conditionally.

The Alternating Series Test: An alternating series, ∑∞( −1)⁽ⁿ⁻¹⁾aₙ , converges if the following 3

n=1

conditions are satisfied:

n→∞

Geometric Series Test: a series of the form

∑∞ ar⁽ⁿ⁻¹⁾ , the series converges if |r|< 1 and

n=1

diverges if |r | ≥1 nᵗʰ Term Test/Divergence Test

∑∞ aₙ , diverges if lim aₙ

n=1 n→ ∞

does not exist or does not equal zero.

p-series Test : The series ∑∞ (1/nₚ) converges if

n=1

p>1 and diverges if p ≤1.

we have given that

a) ∑∞ |aₙ₊₁/aₙ| = 5 >1

n = 1

Ratio Test: If 0 < aₙ and limn→∞(aₙ₊₁/aₙ) < 1, then an converges.If the limit is greater than 1, then

the series diverges. And if the limit is equal to 1, then the test gives no information.

so, it is divergent

b) ∑∞ |aₙ₊₁ /aₙ| = 0.5 <1

n = 1

: If 0 < an and limn→∞(aₙ₊₁/aₙ) < 1, then series converges. So, it is absolutely convergent .

To learn more about convergence of series , refer:

https://brainly.com/question/23804543

#SPJ4

The derivative of g(x) is (-4x²-3x+1)cos(1+2x) - (2x³ - 2x^2 + x)tcos(1+2x) + t(1+2x)sin(1+2x) + C, where C is a constant of integration.

The derivative is a mathematical concept that represents the rate at which a function changes. It is essentially the slope of the tangent line to the curve of the function at a given point.

Integration is the process of finding the integral of a function, which involves calculating the area under its curve. It is the reverse of differentiation and is used in calculus and mathematical analysis.

According to the given information:

To find the derivative of g(x), we first need to evaluate the integral:

g(x) = ∫[1, 2x+1] (1-2t)sin(t) dt

Using the product rule of differentiation, we have:

g'(x) = (d/dx) [∫[1, 2x+1] (1-2t)sin(t) dt]

= (2-2x)sin(2x+1) - ∫[1, 2x+1] 2sin(t) dt

Simplifying the second term, we get:

g'(x) = (2-2x)sin(2x+1) - 2[cos(2x+1) - cos(1)]

Therefore, the derivative of g(x) is g'(x) = (2-2x)sin(2x+1) - 2[cos(2x+1) - cos(1)].

To know more about derivative and integration visit:

https://brainly.com/question/29210692

#SPJ1

Answer:

I believe the answer is D:56.52 feet (hopefully I helped you)

Step-by-step explanation:

Radius: 18/2= 9 feet

Circumference: 2(pi)9

Circumference: 18(pi)

Circumference: 56.54

Answer: 56.52

Step-by-step explanation:

Answer:

5, 9,13,17

Step-by-step explanation:

5 +4 +4+4

The first 10 terms sum in the geometric series is 5115.

The first term of geometric series = 5

Common ratio = 2

First, let us discuss how to calculate the sum of n terms of GP. Assume the sum of the first n terms of a GP with first term a and common ratio r. Then the first 'n' terms of GP are of form a, ar, ar², ... ar^(n-1). Let S be the sum of the GP of n terms. Then:

Sₙ = a + ar + ar² + ... + ar^(n-1) ... (1)

Multiply both sides by r:

rSₙ = ar + ar² + ... + arⁿ ... (2)

Subtracting equation (1) from equation (2):

rSₙ - Sₙ = (ar + ar² + ... + arⁿ) - [a + ar + ar² + ... + ar^(n-1)]

Sₙ (r - 1) = arⁿ - a

Sₙ (r - 1) = a(rⁿ - 1)

Sₙ = a(rⁿ - 1)/(r - 1)

Note that, here, r ≠ 1.

Sₙ = -a(1 - rⁿ)/(-(1 - r)) = a(1 - rⁿ)/(1 - r).

Sₙ = a[1-rⁿ]/[1-r]

S₁₀ = 5[1-2¹⁰]/[1-2]

S₁₀ = 5[1023]

S₁₀ = 5,115

--The given question is incorrect, the correct question is

"The first term in a geometric series is 5 and the common ratio is 2. Find the sum of the first 10 terms in the series."--

To know more about sum of n terms, here

https://brainly.com/question/16977606

#SPJ4

Answer:

4 balls for $2.50

Step-by-step explanation:

If 4 balls=$2.50

Then,$2.50+2.50= $6.25

$6.25 for 8 balls

Answer:

Step-by-step explanation:

Divide both numbers (30% & 24) by two to get 15% (this will make things easier).         30% / 2 = 15%    &       24 / 2 = 12

Now you know that 15% is 12. To find what value 75% is, you have to divide 75 by 15, which is 5. Multiply 15% and 12 to get your final answer.

15% * 5 = 75%

12 * 5 = 60

Therefore, 75% of this number is 60.

The center of the circle, and consequently the central point of the resort's swimming pool, is located at the intersection of the two legs of the right triangle, approximately 60 feet from one vertex and 120 feet from the other.

The upscale resort has ingeniously designed its circular swimming pool to encompass a central area containing a restaurant. This central area takes the form of a right triangle with legs measuring 60 feet and 120 feet, while the hypotenuse, the longest side of the triangle, spans approximately 103.92 feet. The vertices of the triangle neatly coincide with points on the circumference of the circular pool.

Due to the properties of a right triangle, the hypotenuse is also the diameter of the circle. This means that the circular pool is precisely constructed around the right triangle, with its center located at the midpoint of the hypotenuse.

To determine the exact coordinates of the center of the circle, we can consider the properties of right triangles. Since the legs of the right triangle are perpendicular to each other, the midpoint of the hypotenuse coincides with the point where the two legs intersect.

In this case, the center of the circle is the point of intersection between the 60-foot leg and the 120-foot leg of the right triangle.

For more such questions on center

https://brainly.com/question/1506955

#SPJ8

Answer:

10/12 +4/3b

Step-by-step explanation:

Answer:

look at the photo............

Answer:

x = -3

Step-by-step explanation:

\(\frac{7 - 3x}{2} = 8\)

Multiply both sides by 2, to eliminate the denominator on the left-hand side:

\((2) [\frac{7 - 3x}{2}] = 8 (2)\)

7 - 3x = 16

Next, subtract both sides by 7:

7 - 7 - 3x = 16 - 7

-3x = 9

Divide both sides by -3 to solve for x:

\(\frac{-3x}{-3} = \frac{9}{-3}\)

x = -3

answer

43 minutes

explanation

:)

The following picture represents an explanation to the given question:

CD represents the beacon

We need to find the distance AB

The measure of the angle C = 90

At the triangle BCD,

The measure of the angle CDB = 90 - 21 = 69

Using the sine law, we will find the length of BD

So,

At the triangle ABC

The measure of the angle CDA = 90 - 10 = 80

So, the measure of the angle ADB = angle CDA - angle CDB = 80 - 69 = 11

At the triangle ADB, using sin law:

substitute with the value of BD and CD s

So,

Rounding the answer to the nearest foot

So, the answer will be AB = 346 ft

Beth's statement is incorrect.

The main answer: No.

Using the z-distribution instead of the t-distribution when constructing a confidence interval for a mean with unknown variance can lead to an incorrect interval width. The t-distribution takes into account the sample size, which is particularly important when the sample size is small. By using the z-distribution, which assumes a large sample size or known variance, the resulting interval may be narrower than necessary. This means that the interval might not capture the true population mean with the desired level of confidence.

Learn more about variance

brainly.com/question/31432390

#SPJ11

The solutions to the equation \(x^2 + 10x + 12 = 36\) By factoring or applying the quadratic formula, we find the solutions: x = -4 and x = 6. Hence, the values of x that satisfy the equation are -4 and 6.

To solve the equation \(x^2 + 10x + 12 = 36\), we'll follow these steps:

36 should be taken out of both sides of the equation.

\(x^2 + 10x + 12 - 36 = 0\)

Simplifying the left side, we get:

\(x^2 + 10x - 24 = 0\)

To factor the quadratic equation, we need to find two numbers whose sum is 10 (coefficient of x) and whose product is -24 (constant term). These numbers are 4 and -6.

Rewrite the quadratic equation using the found numbers:

(x + 4)(x - 6) = 0

Use the zero product property, which specifies that at least one of the components must be zero if the product of two factors is zero. Set each element to zero and then calculate x as follows:

x + 4 = 0 or x - 6 = 0

For x + 4 = 0:

x = -4

For x - 6 = 0:

x = 6

for such more question on quadratic equation

https://brainly.com/question/17482667

#SPJ8

Answer:

\(x=11\)

Step-by-step explanation:

\(\frac{440}{8} =\frac{605}{x}\)

\(440x=605(8)\)

\(440x=4840\)

\(x=11\)

The calculated value of x given that the streets are parallel to each other is 4760 feet

Given that the street are parallel to each other

We have the following equivalent ratio that can be used to calculate x

x : 2640 = 2380 : 1320

Express the ratio as fraction

So, the above ratio becomes the following equation

x / 2640 = 2380 / 1320

Solving further, we multiply both sides of the equation by 2640

So, we have

2640 * x / 2640 = 2380 / 1320 * 2640

Evaluate the products

x = 4760

Hence, the value of x is 4760 ft

Read more about similar shapes at

https://brainly.com/question/14285697

#SPJ1

Answer:

2184 different combinations

Step-by-step explanation:

To find how many different combinations are possible, multiply all of the values:

3 * 13 * 7 * 4 * 2 = 2184 different combinations

Answer:

2,184 different skateboards.

Step-by-step explanation:

You would have to multiply

3 x 13 x 7 x 4 x 2 = 2184

If it helps you then please mark it as brainliest!

Answer: 42miles to her nephew

the cost of the bike before tax

514.1/106%=$485

Connie's team lost 4 out of 16 games this season. To calculate the percentage of games lost, we can divide the number of games lost by the total number of games and then multiply by 100.

In this case, 4 divided by 16 is equal to 0.25, or 25% as a percentage. Therefore, Connie's team lost 25% of their games this season.

We first note that the total number of games played is 16. Connie's team won 12 of these games, so the number of games they lost is 16 - 12 = 4. To calculate the percentage of games lost, we divide the number of games lost by the total number of games and then multiply by 100. This gives:

(4 / 16) * 100 = 25%

Therefore, Connie's team lost 25% of their games this season.

It is important to understand how to calculate percentages in order to solve problems like this. In this case, we used the formula:

percentage = (part / whole) * 100

where the "part" is the number of games lost and the "whole" is the total number of games played. By substituting the appropriate values into this formula, we were able to calculate the percentage of games lost by Connie's team.

To know more about  games lost refer here:

https://brainly.com/question/29967991#

#SPJ11

Answer:

A

y=3x+11

Step-by-step explanation:

The slope of the line perpendicular to y=-1/3x-4 is 3, and A is the only choice with the slope of 3.

Answer:

4

Step-by-step explanation:

According to the square, we should multiply the respective row by the respective column.

2x * x = 2x^2

2x * 1 = 2x

4 * x = 4x

For the blank we should multiply one by four.

1 * 4 = 4

The blank should be 4.

Hope this helps.

Answer: 133.33%

Step-by-step explanation:

Max invested $5,700 into the new business.

After 7 years this came out to be $13,300.

The total return is calculated as:

= [(Ending investment amount - Beginning investment amount) / Beginning investment amount] * 100

= [(13,300 - 5,700) / 5,700] * 100

= 133.33%

Answer:

28 miles

Step-by-step explanation:

308/11 = 28 miles per gallon of gas

Answer:

a) 54

b) 63

c) 63

d) 36

e) 27

f) 54

m) 72

Step-by-step explanation:

Step-by-step explanation:

y=mx+c

2=(-4)(1)+c

2=-4+c

c=2+4

c=6

therefore the answer is...

y=-4x+6

Hello!

45% of x = 7.2

45x/100 = 7.2

45x = 7.2 * 100

45x = 720

x = 720/45

x = 16

the number = 16

Answer:

0.45

Step-by-step explanation:

You divided 2.25 by 5