Mathematics College

NO LINKS!! Determine whether the sequence is geometric.
2, 4/√(3) , 8/3, 16/3√(3) , . . .

Choose:
1. Yes, the sequence is geometric
2. No, the sequence is not geometric

If so, find the common ratio. (if the sequence is not geometric, enter NONE)

Answers

Answer 1

Geometric sequence has a common ratio.

Let's verify is the ratio of subsequent terms is common:

[tex]r=t_2/t_1=(4/\sqrt{3})/2 = 2/\sqrt{3} =2\sqrt{3}/3[/tex][tex]r=t_3/t_2=(8/3)/(4/\sqrt{3}) = 2/\sqrt{3} =2\sqrt{3}/3[/tex][tex]r=t_4/t_3=(16/3\sqrt{3})/ (8/3) = 2/\sqrt{3} =2\sqrt{3}/3[/tex]

As wee se the ratio is common, it confirms that the sequence is geometric.

Common ratio is:

[tex]r=2\sqrt{3}/3[/tex]
Answer 2

Answer:

Yes, the sequence is geometric.

[tex]\textsf{Common ratio}=\dfrac{2\sqrt{3}}{3}[/tex]

Step-by-step explanation:

Given sequence:

[tex]2, \; \dfrac{4}{\sqrt{3}},\; \dfrac{8}{3},\;\dfrac{16}{3\sqrt{3}},\;...[/tex]

A geometric sequence has a common ratio.

Therefore, to check if the given sequence has a common ratio, divide each term by the previous term:

[tex]\boxed{\begin{aligned}\dfrac{16}{3\sqrt{3}} \div \dfrac{8}{3}&=\dfrac{16}{3\sqrt{3}} \times \dfrac{3}{8}\\\\&=\dfrac{48}{24\sqrt{3}}\\\\&=\dfrac{2}{\sqrt{3}}\\\\&=\dfrac{2\sqrt{3}}{3}\end{aligned}}[/tex]

[tex]\boxed{\begin{aligned}\dfrac{8}{3} \div \dfrac{4}{\sqrt{3}}&=\dfrac{8}{3} \times \dfrac{\sqrt{3}}{4}\\\\&=\dfrac{8\sqrt{3}}{12}\\\\&=\dfrac{2\sqrt{3}}{3}\end{aligned}}[/tex]

[tex]\boxed{\begin{aligned} \dfrac{4}{\sqrt{3}} \div 2&= \dfrac{4}{\sqrt{3}} \times \dfrac{1}{2}\\\\&= \dfrac{4}{2\sqrt{3}} \\\\&=\dfrac{2}{\sqrt{3}}\\\\&=\dfrac{2\sqrt{3}}{3}\end{aligned}}[/tex]

As there is a common ratio, the sequence is geometric.

The common ratio is:

[tex]\dfrac{2\sqrt{3}}{3}[/tex]

Related Questions

Neil swam 4 2/3 lengths of the pool. Mia swam 6 1/2 lengths of the pool. How many more lengths did Mia swim than Neil

Answers

Answer:

1 5/6

Step-by-step explanation:

Find the range for the set of data: 22, 25, 25, 27, 32​

Answers

Answer: Range for set is 10

Hope this help!

Are these ratios equivalent?
1 newspaper every 4 days
3 newspapers every 12 days

Answers

Yes. The ratio above has just been multiplied times 3.
1 newspaper every 4 days as a ratio is - 1:4

3 newspapers every 12 days as a ratio is - 3:12


3:12 / 3 = 1:4

Therefore the ratios are equivalent

what is the definition of corresponding sides​

Answers

Answer:

Corresponding sides touch the same two angle pairs.

Step-by-step explanation:

Answer:

In a pair of similar triangles, the corresponding sides are proportional. Corresponding sides touch the same two angle pairs.

When the sides are corresponding it means to go from one triangle to another you can multiply each side by the same number.

Can someone please help me I will give you brainleist but please don’t put no links

Answers

Answer:

You already have the needed numbers to find the area for each rectangle.

Step-by-step explanation:

You have to find the area for the needed triangles by multiplying the width by length.

This data shows the number of sit-ups done by 27 students in a gym class.
58 62 49 52 75 86 88 54 56 61 85 48 77 60
47 58 62 73 78 69 65 84 59 67 53 84 50
Which histogram represents the data?

Answers

Answer:

C

Step-by-step explanation:

Answer:

The Answer is C

Step-by-step explanation:

There are three 40s and eight 50s none of the others have these


4, 2, 1, 2, ...
O Arithmetic
O Geometric
O Neither

Answers

Answer:

Step-by-step explanation:

Neither...there is no common difference nor a cmon ratio do neither

a car company uae the symbol shown below for their logo. if the inside space of the logo is a rhombus,what is the length of FJ?​

Answers

Answer:

F has a new version of this book that is designed for the same as if you can use it to get a yellow one

helppppppp will give BRAINLIEST!!!

Answers

Answer:

c

Step-by-step explanation:

range is the largest -the smallest

median is the line between 9 and 10

first quartile is on 6

I’m working on these as well! Hope this helps! Happy Friday! <3

Answer:

Should be the 3rd quartile.

Step-by-step

Because the first quartile ends at 10.5, because of the line, I believe, and 18 is past 11. So, it should be the 3rd quartile.

what is the value of A when we rewrite (32/5)^-2x as A^x​

Answers

Answer:

[tex](\dfrac{25}{1024})^x[/tex]

Step-by-step explanation:

The given expression is :

[tex](\dfrac{32}{5})^{-2x}[/tex]

We need to rewrite it in the form of [tex]A^x[/tex].

We know that, [tex](\dfrac{1}{x})^{-a}=x^a[/tex]

So,

[tex](\dfrac{32}{5})^{-2x}=(\dfrac{5}{32})^{2x}\\\\=(\dfrac{5^2}{32^2})^x\\\\=(\dfrac{25}{1024})^x[/tex]

So, [tex]A=\dfrac{25}{1024}[/tex]. Hence, this is the required solution.

Answer: A = (32/5)^-2

Step-by-step explanation:

If the Volume of a Cylinder is 287 and the radius is 5, what is the height "h"?
Round your answer to the nearest tenth if needed.

Answers

Answer:

3.7 is the height

Step-by-step explanation:

so the volume is 287 radius is 5 . The formula Volume = base area x height which we come to equate 287 =3.142x5x5 to get 287 divides by 78.55 answers round off to the nearest tenths 3.653 round off 3.7

Need the answer fast question is on the problem will mark brainliest
NO LINKS PLEASE

Answers

It’s the last one & the second one

Simplify the following polynomial expression.
(534 – 933 + 73 – 1) + (-804 + 4.12 – 3x + 2) - (-413 + 51 – 1)(21 – 7)
OA. 504 – 3723 - 612 + 411 - 8
OB. 524 – 3723 - 6x2 + 411 - 6
OC. 11,4 – 21.13 + 14x2 + 331 - 6
OD. 11,4 – 2113 + 14.2 + 33.3 - 8

Answers

Answer:

This equals:

3949.12

Letter C is the closest since all the rest of the letters eqaul negative sums and C is the only one that's positive.

Step-by-step explanation:

Decrease 48 by 75% answer please

Answers

Answer:

75/100 × 48= 36

48-36= 12

help...........................

Answers

Answer:

1.54

Step-by-step explanation:

The problem asks for the absolute value of -1.54. Absolute value refers to the magnitude of a number regardless of its sign, so the negative sign is dropped.

A jet flies at an altitude of 43,280 feet. What is the height of the jet in miles?

Answers

Answer:

about 8 miles

Step-by-step explanation:

There are 5280 ft in a mile, so divide the number of miles by that:

43,280/5,280 = 8.196 . . .

                         ≈ 8

Find the surface area of the cylinder. ROUND YOUR ANSWER TO THE NEAREST TENTH. PLEASE I NEED HELP also if anyone can I need the steps:(

Answers

Answer:

Area = 87.96

Step-by-step explanation:

87.96 square mm, using 3.14 as pi

For surface area of a cylinder:
A = 2(pi)(radius)(height) + 2(pi)(radius squared)


For the first half of that equation:
2(pi)(radius)(height)
2(3.14)(2)(5)
= 62.8

Now the second half of that equation, the area of the circle ends:
2(pi)(radius squared)
= 2(3.14)(2)(2)
= 25.12

Add them up:
62.8 + 25.12 = 87.92


A lock consists of 2 dials, where each dial has 6 letters. What is the probability of guessing the right combination in one try?

Answers

Answer:

i dont know the answer either

Step-by-step explanation:

thanks

Help. Lol 6th grade math.

Answers

Answer:

The first one is howard and the second one is peter

Step-by-step explanation:

Howard is at a higher elevation because he is above the sea level.

Peter is further from sea level because he is 1.1 meters away, whereas Howard is only 0.8 meters away.

Answer:

the first on  is howerd

number two is peter

Step-by-step explanation:

Here is an expression:3.2t solve the equation when t=4

Answers

Answer:

3.2 x 4 = 12.8

therefore your answer will be 12.8

solve for x in the diagram below

Answers

Answer:

15

Step-by-step explanation:

45+15=4x

60=4x

15=x

Pls help it is khan academy :)

Answers

Answer:

4x-12

Step-by-step explanation:

f(x)=3(x-2)^2 +5 Find Vertex of Parabola given.

Answers

The answers (2,5) because

5 Solve the equation sin 2x = 2 cos 2x, for 0°<x< 180°​

Answers

Answer:

Step-by-step explanation:

plot | 2 x = 2 cos(2 x) | x = 0 ° to 180 °

How many plants spaced every 6" are needed to surround a circular walkway with a 25' radius

Answers

Answer:= 2 × 3.14 (25)

= 157.

circumference of circle feet is 157 × 12 inches.

Step-by-step explanation:

consider the following formula to find the circumference of circle

C= 2^_r

here r is radius of circle

the radius of circular is 25 ft.

Therefore circumference is as follows

C = 2^_r

Mrs. Ballesteros students raised $300, Mrs. Garcia's
students raised $210, and Ms. Ramirez students raised
$180. What is the mean, or average, amount of money
raised by the English students?

Answers

Answer:

$230

Step-by-step explanation:

To find the average all you have to do is add all the numbers together in a given set then divide the total by the amount of numbers in the set.

1. Determine the more basic function that has been shifted reflected stretched or compressed.
2. Graph the given function by indicating how the more basic function has been shifted reflected stretched or compressed
[tex] m(x)- 2\sqrt[3]{x } - 4[/tex]
​

Answers

Step-by-step explanation:

kiop

What are the solutions of the equation 9x4 - 2x2 - 7 = 0? Use u substitution to solve.

Answers

Answer: this is what i got hope this helped i took a sceernshot of it

Step-by-step explanation:

ples make brainly

5 (y+2/5)= -13 what is y with explanation

Answers

Answer:

Y= -3

Step-by-step explanation:

Step 1- 5y+2=-13 [move constant to the right]

Step 2- 5y=-13-2 [Calculate]

Step 3- 5y=-15 [Divide both sides]

And with doing these steps you'll end up with the answer Y= -3

I have no idea but in order to keep asking questions I have to answer 2 of them:)

You walk into a store that is closing. The pants normally cost $60.00 but it is discounted 75%. They are also taking an additional 20% off. What is the final price that you pay for the pants? dollars and cents. For example 19 dollars and 25 cents would be written as $19.25​

Answers

Answer:

The final cost that I will pay for the pants is $ 12.

Step-by-step explanation:

Since I walk into a store that is closing, and the pants normally cost $ 60.00 but it is discounted 75%, and they are also taking an additional 20% off, to determine what is the final price that I will pay for the pants se must perform the following mathematical calculation:

 

100 - 20 = 80

(60 - (60 x 0.75)) x 0.80 = X

(60 - 45) x 0.80 = X

15 x 0.80 = X

12 = X

So, the final cost that I will pay for the pants is $ 12.

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