The sum of the first 6 terms of a geometric series is 9 times the sum of the first 3 terms, find the common series.​

Answers

Answer 1

The exponential function y = a · 2ⁿ ⁻ ¹, where a is any real number, is generates the geometric series.

How to derive the formula of a geometric series

Geometric series are sets of elements generated by exponential functions of the form:

y = a · bⁿ ⁻ ¹, where a and b are real numbers and n is a natural number.

Where:

a - Value of the first element of the series.b - Increase rate.n - Index of the n-th element.y - Value of the n-th element.

According to the statement, we derive the following expression between the two sums:

9 · a · (1 + b + b²) = a · (1 + b + b² + b³ + b⁴ + b⁵)

Now we proceed to simplify and find the value of b:

8 · a · (1 + b + b²) = a · (b³ + b⁴ + b⁵)

8 · (1 + b + b²) = b³ + b⁴ + b⁵

b⁵ + b⁴ + b³ - 8 · b² - 8 · b - 8 = 0

Then, the value of b by numerical methods is equal to 2.

The geometric series is generated by the exponential function y = a · 2ⁿ ⁻ ¹, where a is any real number.

To learn more on geometric series: https://brainly.com/question/21087466

#SPJ1

The Sum Of The First 6 Terms Of A Geometric Series Is 9 Times The Sum Of The First 3 Terms, Find The

Related Questions

(b) If the radius of wheel is 7cm, how far it travels in three rotation​

Answers

The wheel will travel 131.8cm in 3 rotations.

The radius of the wheel, r = 7cm

Number of rotations, n= 3

distance covered in 1 rotation= circumference of circle=2πr

distance covered in 3 rotation= 2πr x 3

where π=3.14(fixed)

=2 x 3.14 x 7 x 3

Distance=131.88cm

Therefore, the distance covered in 3 rotations is 131.88cm

To learn more about rotation visit:

https://brainly.com/question/24463763

Answer:

132cm

Step-by-step explanation:

use formula 22/7 *diameter which is 7*2 getting the answer as 44.For three rotations multiply the answer by three

What are 3 horizontal lines?

Answers

The 3 horizontal line refers the equivalent relation.

The term horizontal line in math defined as a straight line that is mapped from left to right and it is parallel to the X-axis in the plane coordinate system.

Here have to find the meaning of 3 horizontal line.

As per the definition of horizontal line, the three horizontal line also known as triple line defines the equivalent relation of the term.

Here the equivalent that is not the same as 'equals'

Where the double bar is more common and generally implies equality on the other hand the triple bar or equal sign with three lines means congruent or, more generally, an arbitrary equivalence relation.

To know more about Horizontal line here

https://brainly.com/question/10863938

#SPJ4

A lacrosse 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

the total of 29 cheesecake and 2 slices of cheesecake will be making $703.

What is the arithmetic operation?

The four basic arithmetic operations are addition, subtraction, multiplication, and division of two or more quantities. They all fall under the umbrella of mathematics, and among them is the study of numbers, particularly the order of operations, which is crucial for all other branches of the subject, such as algebra, data organisation, and geometry. To solve the problem, you must be familiar with the fundamentals of mathematical operations.

A lacrosse 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.

A multiplier of 24 close to 700 is 29

So 29 cheesecake will cost 696.

Now they need more 4 dollars to raise so they have to sell 2 slices, which will be 7$.

So the total of 29 cheesecakes and 2 slices of cheesecake will be making $703.

Learn more about arithmetic, by the following link.

https://brainly.com/question/13181427

#SPJ4

Help Pls
Figure ABCD is similar to figure EFGH. What is the sequence of transformations that maps ABCD to EFGH?

Answers

The transformation used to map ABCD to EFGH is rotation of 180 degrees about the origin.

What is transformation?

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

The transformation used to map ABCD to EFGH is rotation of 180 degrees about the origin.

Find out more on transformation at: https://brainly.com/question/4289712

In Ellen's math class, there were 2 boys to every 3 girls. Which of the following could be the ratio of girls to boys in the class? As a fraction

Answers

Answer:

A . 17/21

B . 14/21

C . 7/14

D. 11/17

Step-by-step explanation:

Answer:

Answer is B: 14 to 21

Step-by-step explanation:

The ratio "2 to 3" was multiplied by 7 to get this ratio. All the other following are incorrect.

Rewrite 16r²s² as a power of a product.
The solution is

Answers

[tex]16r^2s^2[/tex] as the product of power is written as [tex](4rs)^2[/tex]

How would you characterize a product's strength?

The power of a product rule states that [tex](a^m)(a^n) = a^(m+n)[/tex], where "a" is the base, "m" is the exponent of the first term, and "n" is the exponent of the second term. This rule allows us to simplify expressions where multiple variables are being raised to a power and multiplied together by adding the exponents.

For example, [tex](a^2)(a^3) = a^(2+3) = a^5[/tex].

It is also important to remember that when we are using the power of a product rule, the bases must be the same. If we have different bases, we cannot use this rule.

For example, [tex](a^2)(b^3) = a^2 * b^3, not a^(2+3) = a^5[/tex].

Rewritten as power of product:

[tex]16r^2 s^2= 4*4*r*r*s*s\\16r^2s^2= 4^2*r^2*s^2\\16r^2s^2=(4rs)^2[/tex]

To know more about exponents visit:-

brainly.com/question/30066987

#SPJ1

someone please help me with this

Answers

I think the answer Is 1430

Answer:

[tex]area = 4 \times ( \frac{1}{2} \times base \times height) \\ =2 \times ( \frac{1}{2} \times 16.3 \times 42.7) + 2 \times ( \frac{1}{2} \times 16.3 \times 22.5) \\ = 696.01 + 366.75 \\ = 1062.76 \\ = 1063[/tex]

12 POINTS!!!
Write the equation of the exponential function (y=ab^x) through the point (2,36) and (5,972).

Answers

Answer:

Step-by-step explanation:

Review the graph of complex number z. On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point z is at (negative 7, negative 6). What is the conjugate of z?

Answers

The conjugate is -7+6i. The correct option is third.

What is conjugate?

When two binomials have the same terms but different arithmetic operators in the center of these related words, they are said to be conjugate. For instance, the conjugate of p + q is p - q.

Given:

On a coordinate plane,

the y-axis is labeled imaginary and the x-axis is labeled real.

Point z is at (negative 7, negative 6).

Z(-7, -6)

So, the equation,

-7-6i

So, the conjugate of the equation is,

-7+6i

Therefore, -7+6i is the conjugate of the points.

To learn more about the conjugate;

https://brainly.com/question/29081052

#SPJ1

for each mentor artist, write an equation and a graph showing the proportional relationship between the art sold and your total commission.

Sara's pieces of art sell for $25 each your commission is 60%

Ravi's pieces of art sell for $2000 each your commission is 25%

x represents the number of pieces of art sold

y represents the total commission

K represents the commission per piece of art

Answers

The equations of the commissions are

Sara: y = 15xRavi: y = 500x

How to determine the equations and the graph

From the question, we have the following parameters that can be used in our computation:

Sara's pieces of art sell for $25 and  commission is 60%Ravi's pieces of art sell for $2000 and commission is 25%

Also from the question, we have:

x represents the number of pieces of art soldy represents the total commission

This means that:

Commission = Unit rate * Commission proportion * Number of pieces

Using the above as a guide, we have the following:

Sara: y = 25 * 60% * x

Ravi: y = 2000 * 25% * x

Evaluate

Sara: y = 15x

Ravi: y = 500x

See attachment for the graph of the commission equations

Read more about linear equations at

https://brainly.com/question/4074386

#SPJ1

Simplifying algebraic expression

Answers

Answer:

42

Step-by-step explanation:

2 + 3(5) + 5(5)

2 + 15 + 25

Which equals..

42

Answer:

42

Step-by-step explanation:

IF b=5

Now,

2+3b+5b

=. 2 + 3*5 + 5*5

=. 2 + 15 + 25

=. 42

Find the least common denominator for these
two rational expressions.
-8/s^2 -4/s^2

Answers

Answer:

Step-by-step explanation:

a) Write down the mathematical name of this shape.
what is the shape called ​

Answers

Answer:

What shape? i don't see no shape

Answer:

What shape? Can you add in a picture or something? That would be very helpful in trying to figure out what shape we're dealing with.

What is the solution to –2(8x – 4) < 2x + 5?

x > x is greater than StartFraction 1 Over 6 EndFraction.
x < x is less than StartFraction 1 Over 6 EndFraction.
x > 6
x < 6

Answers

Answer:

x > [tex]\frac{1}{6}[/tex]

Step-by-step explanation:

Given

- 2 (8x - 4) < 2x + 5 ← distribute left side

- 16x + 8 < 2x + 5 ( subtract 2x from both sides )

- 18x + 8 < 5 ( subtract 8 from both sides )

- 18x < - 3

Divide both sides by - 18, reversing the symbol as a result of dividing by a negative quantity.

x > [tex]\frac{-3}{-18}[/tex] , that is

x > [tex]\frac{1}{6}[/tex]

Using the five digits 7, 7, 8, 8, and 8 once each, how many positive five-digit integers can be formed?

Answers

Answer:

There are 5 choices for the first digit, 5 choices for the second digit, 4 choices for the third digit, 3 choices for the fourth digit, and 2 choices for the fifth digit.

PLEASE HELP, i was supposed to be done with this class awhile ago and ive been stuck on this problem and now i have a lot of work to be completed in 5 days, so please it would mean so much to me if someone, anyone could help me!!

Answers

Answer:

Hopefully this makes sense. All you're doing is inputting your X VALUES (or your inputs) and using those numbers to find our what your Y VALUES (or your outputs) are

x: -2     -1      0     1      2      3

y: 49     7       1     [tex]\frac{1}{7}[/tex]       [tex]\frac{1}{49}[/tex]      [tex]\frac{1}{343}[/tex]

b) Suppose that you increase the height of this cylinder by 10 cm.
By how much does the volume increase?

Answers

Answer:

the answer is 5 I think so

3. How many groups 1/2 of days are in 1 week?
groups

Answers

There are 7 groups of 1/2 days in a week.

Given there are 7 days in a week, we can divide 7 by 1/2 to find that:

7 / 1/2 = 14

Hence, 14 groups of 1/2 days are in 1 week.
14 groups because if you split the 7 days in a week by half, you get 14.

i need help with this question?

Answers

Answer:

4.5π[tex]cm^2[/tex] will be your answer!

Step-by-step explanation:

Oki... So the area of a circle is radius x radius x π

So.....

Lemme find what the radius's are

4.5 ÷ 2 = 2.25

2.25 - 1.5 = 0.75

2.25 x 2.25 x π = 5.0625π

0.75 x 0.75 x π = 0.5625π

And subtract.

5.0625π - 0.5625π = 4.5π

What are the factors of 2x^2 7x 3?

Answers

The factors of 2[tex]x^{2}[/tex] + 7x + 3 are ( x + 3) and (2x + 1)

Now, According to the question:

The given function is :

f(x) = [tex]2x^2+7x+3[/tex]

To find the factors of  [tex]2x^2+7x+3[/tex] we need to split the middle term, that is, 7x.

7x = 6x + x

Therefore, 2[tex]x^{2}[/tex] + 7x+ 3 can be written as 2[tex]x^{2}[/tex] + 6x + x + 3 .

On taking '2x' common from first two terms and +1 from next two terms we get

2x (x + 3) +1 (x + 3)

(x + 3) (2x + 1)

Thus, the factors of 2x2 + 7x + 3 are (x+3) and (2x+1)

Learn more about Factorization at:

https://brainly.com/question/2760395

#SPJ4

The complete question is this:

What are the factors of 2x^2+7x +3?

PLEASE I NEED HELP ASAPPPP!!!!!


The scatter plot shows the number of pumpkins that have been picked on the farm during the month of October: A scatter plot with points showing an upward trend with points that are moderately spread out from a line of best fit. The y axis is labeled Number of Pumpkins and the x axis is labeled Days in October

Part A: Using computer software, a correlation coefficient of r = 0. 51 was calculated. Based on the scatter plot, is that an accurate value for this data? Why or why not? (5 points)

Part B: Instead of comparing the number of pumpkins picked and the day in October, write a scenario that would be a causal relationship for pumpkins picked on the farm. (5 points)

Answers

A situation where there might be a causal relationship could be the amount of fertilizer utilized in proportion to the kilograms of pumpkins harvested on the farm.

What is a Scatter Plot?

A scatter plot with a trendline along which the data points are situated can be used to demonstrate the relationship between correlated variables.

Indicating a positive correlation is when the trendline slopes higher from left to right, while the opposite is true.

Part A:

The correlation coefficient of r = 0.51 is valid based on the provided scatter plot.

Part B:

The amount of fertilizer applied in connection to the kilograms of pumpkins harvested on the farm can be a scenario where a causal relationship exists.

Hence, A situation where there might be a causal relationship could be the amount of fertilizer utilized in proportion to the kilograms of pumpkins harvested on the farm.

To learn more about Scatter Plot visit:

brainly.com/question/6592115

#SPJ4

Simplify the polynomial.
3 – 2x + 4 – x5 + 2x

Answers

if u will have more questions like that ,use photo math app helps a lot
The middle box is the answer

Please help! Thanks :DD

Answers

Answer:

A. 58 square cm

Step-by-step explanation:

From the composite figure,

A1 = [tex]\frac{1}{2}[/tex] x base x height

   = [tex]\frac{1}{2}[/tex] x 2 x 3

   = 3 [tex]cm^{2}[/tex]

A2 = length x width

     = 8 x 2

     = 16 [tex]cm^{2}[/tex]

A3 = [tex]\frac{1}{2}[/tex] (a + b) h + [tex]\frac{1}{2}[/tex] x base x height

    = [tex]\frac{1}{2}[/tex] (10 + 12) 3 + [tex]\frac{1}{2}[/tex] x 2 x 3

    = [tex]\frac{1}{2}[/tex] (22) 3 + 3

    = 11 x 3 + 3

A3 = 33 + 3

     = 36 [tex]cm^{2}[/tex]

Total area = A1 + A2 + A3

                 = 3 + 16 + 36

                 = 58 [tex]cm^{2}[/tex]

Given that there are 3 feet or 36 inches in 1 yard, which of the following amounts is greater than 6 feet? Select all that apply. Video A) 2 yards, 3 inches B) 5 feet, 8 inches C) 96 inches D) 3 yards, 2 feet E) 1 yard, 2 feet

Answers

Answer: its D

Step-by-step explanation: 3 yard is bigger then 6 feet because 3 yards equals 9 feet hope this helps

Write the word sentence as an equation. Then solve the equation.
9 is the difference of a number n and 7.
An equation that represents this word sentence is
The solution is n =

Answers

Answer:

see below

Step-by-step explanation:

9 is the difference of a number n and 7.

Let's break this down.

"is" represents the equal sign.

"the difference" represents subtraction.

9 = n - 7

Now let's solve the equation.

9 = n - 7

Add 7 to both sides.

16 = n

Hope this helps!

Please help I beg of you














Will mark brainlist

Answers

160o..................

HELP! THIS IS DUE TODAY, AND I WILL MARK BRAINLEST!!!!

Answers

Answer:

C 2003 and 2004

Step-by-step explanation:

Looking at the graph, you can see that the greatest incline occurs between 2002 to 2003 then 2003 to 2004.This means that the prices grew the most in 2003 and 2004

resuelve la siguiente operacion +1 + (-1)=​

Answers

Answer:

0

Step-by-step explanation:

+ 1 + (-1)

1 + (-1)

1 - 1

Piper is mixing sparkling water and juice. She has 12 liters of sparkling water and 3 liters of juice.
How much sparkling water is there for each liter of juice?​

Answers

Answer:

4/3

Step-by-step explanation:

Answer:

12L/3L

4: 1

four litre of sparkling water for 1 liter juice

What is the value of p so that the line passing through (6, 2) and (10, p) has a slope
of -2?

Answers

Answer:

P = -6

Step-by-step explanation:

y2-y1 / x2-x1 = slope formula

p-2/10-6 =

p-2 over 4

P would be -6 since -6-2 = -8, and -8/4 = -2

Other Questions
If a person has one dominant and one recessive trait for a gene, the allele combination is Does the effective thermal conductivity of an insulation system account for heat transfer by conduction alone 14. A square has a perimeter of 36 units. One vertex of the square is located at (3,5) on the coordinate grid, What could be the x- and y-coordinates of another vertex of the square? Watch this clip from the movie "The Sound of Music"Make 3 observations on how they use the scaleThe song is called Do-Re-Mi A lottery game contains 24 balls numbered 1 through 24. What is the probability of choosing a ball numbered 25 Unit test Which of the x-values are solutions to the following inequality? 2 > 111 What two molecules make up aspartame? What does the unalienable right of liberty mean? Explain the phenomenon of diffussion. Solve each by eliminationx+y =19x - y = -7 What is the formula to find the side? A current-carrying wire is positioned vertically. The current in the wire is moving upward. If you move a compass slowly around the wire, how would the direction of the compass needle change?A.The compass always points in the same direction.B.The compass needle would rotate clockwise.C.The compass needle would rotate counterclockwise.D.The compass needle would spin erratically. What are two way in which early psychological research was biased? Whats an example of bias in psychology? Which characteristic do mushrooms, cats, humans, and trees have in common?A. They have cell walls.B. They are multicellular.C. They have a backbone.D. They make their own food. Can you describe the characteristics of different contemporary art forms? Why is Birdcage Walk called Birdcage? Do nonmetals increase in reactivity when moving from left to right? What is the negative form of he is still there? What is the total number of atoms present in 5Na,PO.? why are light intensity, carbon dioxide concentration and temperature liimiting factors