For what values of r does the sequence {r"} converge? Diverge? Select the correct choice below and fill in any answer boxes in your choice. A. The sequence {r"} converges for and diverges otherwise. E. The sequence {r") converges for all real values of r. F. The sequence {r") diverges for all real values of r.

Answers

Answer 1

The sequence {r"} converges for |r| < 1 and diverges otherwise

The question requires us to consider the sequence {r"} and determine whether it converges or diverges for different real values of r.

We can use the following test to determine if a series converges or diverges:

If limn→∞ an=0 and an is a decreasing sequence, then the series converges.

If an is not decreasing, then the series diverges.

For the given sequence {r"}, we have:

rn = r × r × r × ... × r (n times) = rn-1 × r

Since rn-1 is a real value, we can see that this sequence is just the geometric sequence with a common ratio of r. For the geometric sequence, the sum of n terms is given by:

S_n = a(1 - rⁿ) / (1 - r)

where a is the first term.

So, if |r| < 1, then the sequence {r"} converges, and if |r| ≥ 1, then the sequence diverges.

Hence, option (A) is the correct choice.

To know more about  series please visit :

https://brainly.com/question/26263191

#SPJ11


Related Questions

I need help just did all of this and still lost :D

I need help just did all of this and still lost :D

Answers

Answer:

It's the last one...I think... I'm 99.99% sure...

Step-by-step explanation:

Quadrant IV

a color print 21 pages in 7 minutes How many minutes does it take per page?

Answers

Answer:

3

Step-by-step explanation:

Cause you would divide 21 by 7 and 7 can only go into 21 3 times

Solve for b

a) 2b x 3 = 6 c) 6 + 7b = 41

b) 32 - 3b = 2 d) 100/ 5b = 2

Answers

a) The solution for b in the equation 2b × 3 = 6 is b = 1.

b) The solution for b in the equation 32 - 3b = 2 is b = 10.

c) The solution for b in the equation 6 + 7b = 41 is b = 5.

d) The solution for b in the equation 100/5b = 2 is b = 10.

a) To solve for b in the equation 2b × 3 = 6, we can start by dividing both sides of the equation by 2 to isolate b.

2b × 3 = 6

(2b × 3) / 2 = 6 / 2

3b = 3

b = 3/3

b = 1

Therefore, the solution for b in the equation 2b × 3 = 6 is b = 1.

c) To solve for b in the equation 6 + 7b = 41, we can start by subtracting 6 from both sides of the equation to isolate the term with b.

6 + 7b - 6 = 41 - 6

7b = 35

b = 35/7

b = 5

Therefore, the solution for b in the equation 6 + 7b = 41 is b = 5.

b) To solve for b in the equation 32 - 3b = 2, we can start by subtracting 32 from both sides of the equation to isolate the term with b.

32 - 3b - 32 = 2 - 32

-3b = -30

b = (-30)/(-3)

b = 10

Therefore, the solution for b in the equation 32 - 3b = 2 is b = 10.

d) To solve for b in the equation 100/5b = 2, we can start by multiplying both sides of the equation by 5b to isolate the variable.

(100/5b) × 5b = 2 × 5b

100 = 10b

b = 100/10

b = 10.

Therefore, the solution for b in the equation 100/5b = 2 is b = 10.

In summary, the solutions for b in the given equations are:

a) b = 1

c) b = 5

b) b = 10

d) b = 10

For similar question on equation.

https://brainly.com/question/30451972  

#SPJ8

what is the result of 2.130 x 10³ - 6.6 x 10² =

Answers

Answer:

The answer you're looking for is 1470.

Step-by-step explanation:

The method I used was PEMDAS

Since there was no parenthesis, I simplified the exponents.

2.130 x 10³ - 6.6 x 10² = ?
2.130 x 1000 - 6.6 x 100 = ?

After that, I multiplied all terms next to each other.

2.130 x 1000
- 6.6 x 100 = ?
2130 - 660 = ?

The final step I did was to subtract the two final terms and ended up with 1470 as my final answer.

1470 = ?

I hope this was helpful!



By completing the square, work out the coordinate of the turning point of the curve y= x²+ 16x -7

Answers

Answer:

(-8,-71)

Step-by-step explanation:

I assume by turning point it means the vertex:

\(y=x^2+16x-7\\y+71=x^2+16x-7+71\\y+71=x^2+16x+64\\y+71=(x+8)^2\\y=(x+8)^2-71\)

Now that we converted our equation to vertex form \(y=(x+h)^2+k\), we can see our vertex, or turning point, is (h,k)=(-8,-71)

Draw a rhombus with diagonals 4 and 6. What is the area of the rhombus?

Answers

first of all you have to draw a rhombus

area (d+d)/2

(4+6)/2

5

What is the sum of the measures of the interior angles of an octagon?

Answers

Answer:

1080

Step-by-step explanation:

(n-2) × 180

(8-2) × 180= 1080

the u.s.post office will accept a box for shipment only if the sum of height and girth(distance around of bottom) is at most 108 in. find the dimensions of the largest volume of acceptable box with square bottom.

Answers

The dimensions of the box of height 36in and the side of the square is 18in.

A topological measure of the size of an object's covering properties is its dimension. It is roughly the number of coordinates required to specify a point on the object.

Given that the u.s.post office will accept a box for shipment only if the sum of height and girth(the distance around of bottom) is at most 108 in.

We must first determine the box's dimensions.

Let s be the side of the square base and h be the height of the box

So , h + 4s = 108

H = 108 – 4s -----(1)

Volume = s^2 h

V = s^2(108-4s)

= 108s2 – 4s3

V’ = 216s – 12s2

Let v’ = 0

S[216-12s] = 0

216 – 12s = 0

12s = 216

S = 216/12

S = 18

V” = 216 – 24s for s =18

V” = 216 – 432

= -216(-ve)

Volume is maximum when s =18

So h= 108-72

=36 in

Therefore the dimensions of the box of height 36in and the side of the square is 18in.

To learn more about dimensions visit

https://brainly.com/question/8286598

#SPJ4

48 mouse traps/6 people = X mouse traps/1 person

Answers

Answer:

8 mousetraps

Step-by-step explanation:

to find how many mousetraps per person, we need to divide 48 by 6, which gives us 8.

EMERGENCY! Please give me the correct answer!​

EMERGENCY! Please give me the correct answer!

Answers

Answer:

6^10

Step-by-step explanation:

6^0 is 1 so 6^10 x 1 is just 6^10

The solid below is similar to a larger solid.

The surface area and volume of the smaller solid is given along

with the scale factor between the two solids. Find the surface area (S) and Volume (V) of the larger solid. Show

all your work.

Answers

Surface Area of Larger Solid: S2 = k^2 * S1 and Volume of Larger Solid: V2 = k^3 * V1. Substitute in the given values for S1, V1, and k before solving for S2 and V2.

To solve this problem, we need to use the fact that similar solids have corresponding sides that are proportional in length.  

Let's call the scale factor between the two solids "k". This means that if the smaller solid has a side length of "s", then the corresponding side length in the larger solid is "ks".

Now let's use the given information to find the surface area and volume of the larger solid. Let's call the surface area and volume of the smaller solid "S1" and "V1", respectively.

Surface Area:
The surface area of a solid is proportional to the square of its linear dimensions. Since the scale factor between the two solids is "k", the surface area of the larger solid is k^2 times the surface area of the smaller solid. Therefore, the surface area of the larger solid (S2) can be found using the formula:

S2 = k^2 * S1

Volume:
The volume of a solid is proportional to the cube of its linear dimensions. Using the same logic as above, the volume of the larger solid (V2) can be found using the formula:

V2 = k^3 * V1

Learn more about surface area brainly.com/question/29298005

#SPJ11

-1/5 x 15/16 get 70 pts if u answer thisss tysmmm<3

Answers

Answer:

\(\frac{-3}{16}\)

Step-by-step explanation:

\(\frac{-1}{5}\) × \(\frac{15}{16}\)

=> \(\frac{-15}{80}\)

=> \(\frac{-3}{16}\)

Hoped this helped.

find the area (in square feet) of a trapezoid with height $h$h and bases $b_1$b1 and $b_2$b2 . h=6

b1=9
b2=12

The area is
square feet.

Answers

Given, the height \($h=6$, the base $b_1=9$ and $b_2=12$.\)

The area of the trapezoid is given by the formula,

\(\[A = \frac{1}{2}h(b_1+b_2)\]\)

Substitute the given values,  

\(\[A = \frac{1}{2} \times 6 \times (9+12)\]\\\)

Simplifying the above expression,

\(\[A = 45 \text{ square feet}\]\)

Therefore, the area of the trapezoid is $45$ square feet.

The perimeter of a two-dimensional geometric shape is the entire length of the boundary or outer edge. It is the sum of the lengths of all the shape's sides or edges.

The perimeter of a square, for example, is calculated by adding the lengths of all four sides of the square.

Similarly, to find the perimeter of a rectangle, sum the lengths of two adjacent sides and then double the result because there are two pairs of adjacent sides.

To know more about perimeter visit:

https://brainly.com/question/6465134

#SPJ11

solve for y. 9=5-y/3

Answers

Answer:

y = -1.3 or y = -22

Step-by-step explanation:

5-y/3=9

5/3     9/3

1.66666666667 = 1.7

1.7-y=3

-y/-1=1.3/-1

y=-1.3

or

5-y/3=9

5-y=27

5=27+y

5-27=y

-22=y

Find the value of x

 Find the value of x

Answers

Answer:

A) 33

Step-by-step explanation:

180 - 105= 75

75 + 72 + x = 180

147 + x = 180

x= 33

Which expression is not equivalent to (5^2x)^3

Which expression is not equivalent to (5^2x)^3

Answers

Answer:

#3

Step-by-step explanation:

For this... you just multiply the exponents together to get 6x

   any of the others that do NOT have 6x as a product of exponents is not equiv    ..... so #3 is not equivalent  

Option 3 is not equivalent to the given expression.

What is an equivalent expression?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given expression is (5²ˣ)³.

Now, (5⁶ˣ)

(5ˣ)⁶

(5²)³ˣ

Therefore, option 3 is not equivalent to the given expression.

To learn more about an equivalent expression visit:

https://brainly.com/question/28170201.

#SPJ2

In parallelogram ABCD, AB = 7x + 6, BC = 2x + 16, CD = 3x + 10. What is the length of AD?
O 1
O 13
O 18
O 20

In parallelogram ABCD, AB = 7x + 6, BC = 2x + 16, CD = 3x + 10. What is the length of AD?O 1O 13O 18O

Answers

20 I think sry if I’m wrong

graph the equation using slope-intercept form.

y=3/4x-1

where would i place the dot in the graph ?

Answers

So one dot you could make is at -1 on the y axis because your y intercept (the -1 in y=3/4x-1). Another dot you could make if you follow the slope is a point up three and over 4 (slope is rise over run).
Picture explanation:
Hope this helps!
graph the equation using slope-intercept form. y=3/4x-1where would i place the dot in the graph ?

Can someone heeeeelp???​

Can someone heeeeelp???

Answers

X = 23

23+44=67

23+35=58

67+58+55=180

PLZ HELP IM TIMMED 50 POINTS The total sales for June at Jim’s Candy Store were $7,785. The total sales for June and July
were $12,603. What were the total sales for July?

Answers

Answer:

the answer is 4818 pls give me brainliest

Step-by-step explanation:

if the dot product of two nonzero vectors is zero, the vectors must be perpendicular to each other. a) true b) false

Answers

The statement "if the dot product of two nonzero vectors is zero, the vectors must be perpendicular to each other" is true. The dot product of two vectors is zero if and only if the vectors are perpendicular.

The dot product of two vectors is defined as the product of their magnitudes and the cosine of the angle between them. When the dot product is zero, it means that the cosine of the angle between the vectors is zero, which occurs when the vectors are perpendicular.

In other words, the dot product being zero indicates that the vectors are at a 90-degree angle to each other, supporting the statement that they are perpendicular.

Learn more about dot product here: brainly.com/question/23477017
#SPJ11

snowdon has a height of approximately 1100 metres above the sea
assuming that the temperature decreases by 1 oc for every 100m above sea level, work out the temperature at the summit of snowdon when the sea level temperature is 4oc

snowdon has a height of approximately 1100 metres above the sea assuming that the temperature decreases

Answers

Answer:

\(-7^\circ C\)

Step-by-step explanation:

Let

x -----> the height in meters

y ----> the temperature in Celsius degree

we know that

The linear equation in slope intercept form is equal to

\(y+mx+b\)

where

m is the slope or unit rate

b is the y-intercept or initial value

In this problem we have

The slope or unit rate is equal to

\(m=-\dfrac{1}{100} \dfrac{^\circ C}{m}\) ---> is negative because is a decreasing function

The y-intercept or initial value is equal to

\(b=4^\circ C\) ----> value of y when the value of x is equal to zero (sea level)

substitute

\(y=-\dfrac{1}{100} x+4\)

For x=1,100 m

substitute in the linear equation and solve for y

\(y=-\dfrac{1}{100} (1,100)+4\)

\(x=-7^\circ C\)

Solve the equation for the specified variable. Y=AB-2, For A

Answers

Answer:

b = 1

b = -1

a = 0

Step-by-step explanation:


What is A in degrees?
Sin (A)= 0.7721

Answers

Answer:

angle

Step-by-step explanation:

it means angle. no prob

It’s means an angle hopefully you get an a

2, 10, 50, 250, 1250

Write the explicit form of the sequence above.

Answers

The explicit function of the sequence is a(n) = 2(5)^n-1

How to determine the explicit function of the sequence

The definition of the function is given as

2, 10, 50, 250, 1250

The above definitions imply that we simply multiply 5 to the previous term to get the current term

Using the above as a guide,

So, we have the following representation

a(1) = 2

Common ratio, r = 5

So, we have

a(n) = a * r^n-1

This givs

a(n) = 2(5)^n-1

Hence, the sequence is a(n) = 2(5)^n-1

Read more about sequence at

https://brainly.com/question/29431864

#SPJ1

Alicia and Leah are making cookies for a fundraiser.
Leah made 10% more cookies than Alicia.
They are selling the cookies for $1.00 each.
They sold 90% of the cookies they made.
Write an equation to represent the total amount of money

Answers

You’ll do % over 100 and than divide

Find all EXACT solutions of the equation given below in the interval \( [0, \pi) \). \[ \sin (3 x)=-\frac{\sqrt{3}}{2} \] If there is more than one answer, enter them in a list separated by commas. En

Answers

The required exact solutions of this equation are \($$\boxed{\frac{4\pi}{9}, \frac{5\pi}{9}, \frac{16\pi}{9}, \frac{17\pi}{9}}$$\)

The given equation is

\($\sin(3x)=-\frac{\sqrt{3}}{2}$.\)

The first step to solving this equation is to solve for \($3x$\).

We know that

\($\sin(60^o) = \frac{\sqrt{3}}{2}$,\) so we need to find the angle whose sine is

\($-\frac{\sqrt{3}}{2}$\) (since $\sin$ is negative in the third and fourth quadrants).

This angle will be \($240°$\) since \($\sin(240^o) = -\frac{\sqrt{3}}{2}$\).

The reference angle for $240°$ is $60°$, which is the same as the reference angle for \($\frac{\sqrt{3}}{2}$\).

Since the sine function is negative in the third and fourth quadrants, we must add $180°$ to each solution to get the angles in the interval $[0, \pi)$.

Hence, we have:

\($$\begin{aligned} 3x&=\frac{4\pi}{3}+360^on\\ 3x&=\frac{5\pi}{3}+360^om \end{aligned}$$\)

where $n, m$ are any integer.

Find exact solutions by solving for \($x$\) in each equation.

We get: \($$\begin{aligned} x&=\frac{4\pi}{9}+120^on\\ x&=\frac{5\pi}{9}+120^om \end{aligned}$$\)

where $n, m$ are any integer.  

Since the interval is\($[0, \pi)$\), we only need to consider the values of \($[0, \pi)$\) and \($m$\) that make \($x$\) in this interval.

To know more about quadrants , visit:

https://brainly.in/question/28784290

#SPJ11

The exact solution is \($x=\frac{2\pi}{9}$\) (in radians). The required solution is: \($\frac{2\pi}{9}$\).

The given equation is:

\($ \sin (3 x)=-\frac{\sqrt{3}}{2} $\)

The interval is \($[0, \pi)$\)

To solve for x, use inverse sine function on both sides:

\(\[\begin{aligned}\sin (3 x)&=-\frac{\sqrt{3}}{2} \\ \sin^{-1} \sin (3 x)&=\sin^{-1} \left( -\frac{\sqrt{3}}{2} \right) \\ 3 x &= -\frac{\pi}{3} + k  \pi \quad \text{or} \quad 3 x = \frac{2\pi}{3} + k \pi, \quad \text{where} \quad k\in \mathbb{Z}\end{aligned}\]\)

To get the values of x in the interval \($[0, \pi)$\):

For

\($3x = -\frac{\pi}{3}$\)

we have \($x = -\frac{\pi}{9}$\),

which is outside the given interval.

For \($3 x = \frac{2\pi}{3}$\),

we have \($x = \frac{2\pi}{9}$\),

which is within the given interval.

So, the exact solution is \($x=\frac{2\pi}{9}$\) (in radians).

Therefore, the required solution is: \($\frac{2\pi}{9}$\).

To know more about inverse sine function, visit:

https://brainly.com/question/24160092

#SPJ11

Given that g(4)=9 and g(-11)=k, find the value of k that would result in a slope of 5 between the two points.

Answers

Answer:

\(k=-66\)

Step-by-step explanation:

So we are given two values:

\(g(4)=9 \text{ and } g(-11)=k\)

They can be interpreted as: (4,9) and (-11,k).

So, we want to find the value of k such that the slope of the line between the two points would be 5.

Recall the slope formula. It is:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Let (4,9) be x₁ and y₁ and let (-11,k) be x₂ and y₂. Substitute 5 for m. Therefore:

\(5=\frac{k-9}{-11-4}\)

Simplify the denominator:

\(5=\frac{k-9}{-15}\)

Multiply both sides by -15. The right side cancels:

\(-15(5)=(-15)\frac{k-9}{-15}\\ -75=k-9\)

Now, add 9 to both sides. The right side cancels.

\((-75)+9=(k-9)+9\\k=-66\)

Therefore, k is -66.

What are the solutions for the equation 2cos0+1=0 ?

Answers

Answer:

2cos0=-1

cos0=-1/2

proved

determine the critical values for a two-tailed test (h1: μ ≠ μ0) of a population mean at the α = 0.05 level of significance based on a sample size of n = 12.

Answers

The critical values for this test are -2.201 and 2.201. If your test statistic falls outside this range, you would reject the nullSo, the critical values for this test are -2.201 and 2.201. If your test statistic falls outside this range, you would reject the null hypothesis in favor of the alternative hypothesis (H1: μ ≠ μ0). in favor of the alternative hypothesis (H1: μ ≠ μ0).

To determine the critical values for a two-tailed test with a sample size of n = 12 and a significance level of α = 0.05, we need to consult a t-distribution table.

First, we need to find the degrees of freedom, which is equal to n - 1 = 12 - 1 = 11.

Next, we look up the t-value for a two-tailed test with a 0.025 level of significance (0.05/2) and 11 degrees of freedom. From the t-distribution table, we find that the t-value is 2.201.

Therefore, the critical values for a two-tailed test of a population mean at the α = 0.05 level of significance based on a sample size of n = 12 are -2.201 and +2.201.

This means that if our calculated t-value falls outside of this range, we can reject the null hypothesis (H0: μ = μ0) in favor of the alternative hypothesis (H1: μ ≠ μ0) at the 0.05 level of significance.

To determine the critical values for a two-tailed test of a population mean at the α = 0.05 level of significance with a sample size of n = 12, you'll need to use a t-distribution table.

Since it's a two-tailed test, you'll need to find the t-score that corresponds to α/2, which is 0.025 in each tail. With a sample size of 12, you have 11 degrees of freedom (df = n - 1).

Looking up the t-distribution table with df = 11 and α/2 = 0.025, you'll find the critical t-value to be approximately ±2.201.

Visit here to learn more about Two Tailed Test:

brainly.com/question/30074072

#SPJ11

Other Questions
which of the following are a solution to be inequality? select all that applyv is less then or equal to 7v=7 v=5 v=9v=12 Question B.1 a) Sketch the variation of crack growth rate (da/dN) with stress intensity range ( AK) for a metallic component. On your diagram label the threshold condition (AKth), fracture toughness (AKC) and the Paris regime. [5 Marks] Given points J(3,3), A(5,4), and R(4,2), graph AJAR and its reflection image across the given line.Rx=1 Name at least 5 joints in the foot and/or ankle and their location (what they connect) Why would it be beneficial to move the Virtual memory to a different physical disk than the (C:) drive? a passive strategy is based on the premise that securities are fairly priced and it avoids the involved in undertaking security analysis. im gonna ask again . please no links and no random answers PLEASE HELP ME WITH THESE QUESTIONS ASAPP Question 1 - How do you feel about the end of the war with Japan and Germany?Question 2 - Do you feel like they should have been punished more or less? Explain. Question 3 - Why do you think we havent seen a war to the scale of World War II since? What are invertebrates? aegisthus stabs his cousin, agamemnon, first, before clytemnestra follows with three more stabs to his chest. T/F? what is bout, the z component of the magnetic field outside the solenoid? Find the volume of the composite figure at the right. " Lugaimighty " is a Food & Beverage company based in Bahrain. It has demands internationally up to Malaysia. Many Malaysian companies import the Bahraini Local Foods from it. The issue is that the Bahraini Dinar and Ringgit Malaysia are fluctuated; hence, it may harm the operation of the international sales of Bahraini Lugaimighty. What is your suggestion to manage this international erationally ? sin(0)=-4 racial 29 over 29 If 0 is an angle in quadrant IV, what is the value of cos(0) Son: Pleae, mum. Can I go out on condition that I (did, do, have done, had done) all my 26 homework before leaving One of our client companies, EA Community Laundry Chain, asked us for a consultation on their company's operations. Based on the accounting information provided by them, please use your professional knowledge to assist them in the preparation of five financial statement based on the information below (Income statement, financial position statement, retained earnings statement, comprehensive income statement, cash flow statement).Sales revenue: $555,080Cost of goods sold: $210,000Financing Costs: $10,000Selling and administrative expenses: $75,000Gain on sale of plant assets: $45,000Unrealized gain on non-trading securities: $15,000Loss on discontinued operations: $20,000Dividends declared and paid: $50,400Allocation to non-controlling interest: $60,000Equipment: $40,000Interest payable: $600Land: $157,320Inventory: $102,000Bonds payable: $78,000Notes payable (due in 5 months): $24,400Buildings: $80,400Share capital: $60,000Accumulated depreciation-equipment: $10,000Prepaid advertising: $5,000Supplies: $1860Taxes payable: $3000Cash: $???(Need to be confirmed in the Financial Position Statement)Salaries and wages payable: $900Accumulated depreciation-buildings: $15,000Please prepare five financial statements based on the data provided by Pizza Mr. Park, Inc Verbos. Fill in the blanks with the appropriate reflexive verb forms (In the present tense).1. irse (t): _______ 2. despertarse (nosotros): _______3. cepillarse (l): _______4. lavarse (yo): _______5. quedarse (nosotros): _______ What is the measure angle of 3PLEASE HELP WORTH 10 points Let Find the Laplace transform F(s) by computing the following integral: f(t) ={t 10 3t7 ; 0 otherwise. P, Q, R and S are points on a circle. PXR and QXS are straight lines. PX = QX. SPX is 29 degrees, QXP is 48 degrees, XQP and XPQ are both 66 degrees and RQX is 29 degrees. Is PR the diameter of the circle? Answer 'Yes' or 'No' and give a reason for your answer. when providing discharge instructions for a patient admitted with diabetic ketoacidosis, with a nurse would include