[tex]f(n)=3^n[/tex]
find expressions for [tex]f(n+3)[/tex] and [tex]f(n+1)[/tex]
hence find the value of [tex]k[/tex] such that [tex]f(n+3)-f(n+1)= kf(n)[/tex] where k ∈ N

Answers

Answer 1

Answer:

[tex]24(f(n))[/tex]

Step-by-step explanation:

[tex]f(n+3) = 3^{n+3}\\f(n+1) = 3^{n+1}[/tex]

so

[tex]f(n+3) - f(n+1) = 3^{n+3} - 3^{n+1}[/tex]

[tex]= 27(3^n) - 3(3^n)[/tex]

[tex]= 24(3^n)[/tex]

[tex]= 24(f(n))[/tex]

hope this helped! :)


Related Questions

How many yards is 6 inches

Answers

Answer:  6 inches equals 0.16666667 yards, or about 0.2 yards.

Step-by-step explanation: 1 yard equals 36 inches. By that reasoning, we can divide 6 by 36, since we are trying to find out how many yards are in 6 inches.

6/36 = 0.16666667

The answer is 0.16666667 yards, or about 0.2 yards.


What is the range of the data set?

Answers

Answer:

In statistics, the range is the spread of your data from the lowest to the highest value in the distribution.

Step-by-step explanation:

Answer:

The range of a set of data is the difference between the highest and lowest values in the set.

If you divide a number by 8, the answer is
20. What is the number?

Answers

Answer:

160

Step-by-step explanation:

160 divided 8 =20

Answer:

The answer is 160

Step-by-step explanation:

Let the unknown number be x.

x/8=20

x and 8 are linked by a division so if 8 crossed the equality sign it becomes multiplication. So we'll have

x=20*8

x=160

Therefore x is equal to 160.

LET'S CHECK IF IT'S CORRECT

160/8=20

A recipe calls for 1 ¼ cups of sugar and 1 ¾ cups of flour to make one batch of cookies. How much sugar and flour would it take to make 3 batches of cookies?

Answers

Answer:

It will take 3 3/4 cups of sugar and 5 1/4 cups of flour.

Step-by-step explanation:

Multiply 1 1/4 and 1 3/4 by three, because 3 batches of cookies are being made.

1 1/4x3= 3 3/4 cups of sugar

1 3/4x3= 5 1/4 cups of flour

A car traveled 200 miles on 8 1/2 gallons of gas. How much gas will it take to drive 1 mile?

Answers

Answer:

23 1/2 gallons of gas to travel one mile

Step-by-step explanation:

Given the car can travel 200 miles on 8 1/2 gallons of gas, we divide 200 by 8 1/2.

8 1/2 = 8.50 = 8.5

200/8.5 = 23.5 = 23.52 = 23 1/2

Answer:

17/400 gallons or 0.0425 gallons

Step-by-step explanation:

Take the ratio of the scale and the actual values :

200 miles : 8 1/2 gallons = 1 mile : x gallons200/(8.5) = 1/x400/17 = 1/xx = 17/400 gallons or 0.0425 gallons

Can you solve all please

Answers

A) 3
B) 3
C) 3
D) 3
I think those are the first four

Answer:

A) 3

B) 3

C) 3

D) 3

I think those are the first four

Step-by-step explanation:

What is the volume, in cubic meters, of a rectangular prism with a height of 14 meters, a width of 12 meters, and a length of 2 meters?

Answers

Answer:

The volume of a rectangular prism with a height of 14 m, a width of 12 m, and a length of 2 m is equal to 336 .

General Formulas and Concepts:
Geometry

Volume Formula [Rectangular Prism]:
[tex]\displaystyle V = lwh[/tex]

l is lengthw is widthh is height

Step-by-step explanation:

Step 1: Define

Identify given variables.

h = 14 m

w = 12 m

l = 2 m

Step 2: Find Volume

[Volume Formula - Rectangular Prism] Substitute in variables:
[tex]\displaystyle V = (14 \ \text{cm})(12 \ \text{cm})(2 \ \text{cm})[/tex]Evaluate:
[tex]\displaystyle V = \boxed{ 336 \ \text{cm}^3 }[/tex]

∴ the volume of the rectangular prism with the given dimensions is equal to 336 cm³.

___

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Topic: Geometry

Help me please help me

Answers

Answer:

g= 8/21

Step-by-step explanation:

[tex]g=\frac{5}{7} -\frac{1}{3} \\g=\frac{15}{21} -\frac{7}{21} \\g=\frac{8}{21}[/tex]

Write 8.6 x 10^-9 in Standard Form

Please help :)

Answers

Answer:

8.6 × 10-9

Step-by-step explanation:

x2 + 3x + 1 = 5. know the answer but need to understand how?

Answers

Answer:

[tex]x=-4,\: x=1[/tex]

Step-by-step explanation:

[tex]x^2+3x+1=5\\\\x^2+3x-4=0\\\\(x+4)(x-1)=0\\\\x=-4,\: x=1[/tex]

Make sure you use the Zero Product Property to solve for each factor when the equation is set equal to 0 and can be factored.

The area of a DVD is 36π cm. What is the diameter of the DVD?

Answers

Answer:

12 cm

Step-by-step explanation:

shape of DVD is circle

Area of circle = 36π

πr² = 36π

r² = 36

r = √36

r = 6

Diameter (d) = 2r = 2(6) = 12cm

A can has a height of 11cm and a volume of 486cm^3 . Find the radius of each can . Correct to two decimal places

Answers

If the height is 11 cm and the volume is486 cubic cm. Then the radius of the can will be 3.75 cm.

What is a cylinder?

A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.

A can has a height of 11 cm and a volume of 486 cubic cm.

Then the radius of the can will be

We know that the volume is given as

Volume = πr²h

     486 = π r² x 11

         r² = 14.06

           r = 3.75 cm

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Part A: Sydney made $18.50 selling lemonade, by the cup, at her yard sale. She sold each cup for $0.50 and received a $3 tip from a neighbor. Write an equation to represent this situation. (4 points)

Part B: Daria made a profit of $21.00 selling lemonade. She sold her lemonade for $0.75 per cup, received a tip of $3 from a neighbor, but also had to buy each plastic cup she used for $0.10 per cup. Write an equation to represent this situation. (4 points)

Part C: Explain how the equations from Part A and Part B differ. (2 points)

Please help (Ithink imma fail a math exam if not)

Answers

Answer:

Part A answer: 0.5x + 3 = 18.50
How I got the answer: 0.5 means how much money she made from each cup. the variable x = how many she sold. 3 equals the tip from the neighbor. and 18.50 is the total price

Part B answer: (0.75x - 0.10x) + 3 = 21.00
How i got the answer: 0.75 is how much money she make from each cup. 0.10 means how many she paid for each cup she used. x = how many cups were sold/bought (should be the same number!). 3 is the tip. and 21.00 is the total price made.

Part C answer: The equations differ because Sydney didn't have to pay for the cups she used, while Daria did. Although they did have the same amount for a tip, Daria made more money than Sydney.
------------------------------------------------------------------------------------------

this should be correct! hopes this help and i wish you good luck on your math exam!

LAST CHANCE FOR TONS OF POINTS!!!!!!! AND BRAINLIEST!!!
A boat can travel 28 miles up a river in the same amount of time it takes to travel 36 miles down the same river. If the current is traveling at 2 miles per hour, what is the speed of the boat in still water?

Answers

Answer:

6

Step-by-step explanation:

Verify each trigonometric identity

Answers

Answer:

hope it helps you.......

The Kakkar family is building a circular swimming pool. If the radius of the pool is 6 feet, What is its circumference? Use π = 3.14 to solve.

Answers

Answer:  37.68 feet

Work Shown:

C = 2*pi*r

C = 2*3.14*6

C = 37.68

is 2-3y a binomial or a trinomial or polynomial or monomial

Answers

Answer:

binomial

Step-by-step explanation:

i learned about binomials

What is the cot⁡θ in the right triangle shown?

Answers

cot is adjacent over opposite. keeping this in mind and looking at the triangle, the answer is C) 11/60

I just need the equation. please help me find it ​

Answers

Answer:

y=5x

Step-by-step explanation:

As you can see for the numbers of minutes on the graph, it goes 2,4,6 and on. If you look at the miles you can see the numbers that connect with the numbers of minutes. You can see a pattern. If you multiple 2 x 5 you get 10, if you multiply 4 x 5 you get 20, and etc etc.

Hope this helps <3

Answer:

y = 5x

Step-by-step explanation:

Here :

y = distance covered (in miles)x = time taken (in minutes)

The standard form of an equation :

y = mx + cm = rate of change = slopec = y-intercept (which is 0 in this graph)

Finding m

Change in rise / Change in run10 - 0 / 2 - 010/2m = 5

Equation of the line

y = 5x

Mrs. Smith gave two classes the same quiz. She randomly selected 5 students from each class to compare the classes. The scores of the five students are shown below.


Class A: 80, 82, 74, 92, 94


Class B: 82, 80, 88, 86, 82


What are the mean and range for each class?
Using the information found in Part A, which class could Mrs. Smith report had the more consistent performance on the unit test? Explain what this means in terms of the situation.

Answers

Answer:

class B because every scores range is withing 6 or less

Answer:

See below ~

Step-by-step explanation:

Class A :

Mean = 80 + 82 + 74 + 92 + 94 / 5Mean = 422/5Mean = 84.4

Range = Highest score - Lowest scoreRange = 94 - 74Range = 20

Class B :

Mean = 82 + 80 + 88 + 86 + 82 / 5Mean = 418/2Mean = 83.6

Range = Highest - LowestRange = 88 - 80Range = 8

Class B had the more consistent performance because the range of scores is significantly less. This means that the students in Class B were more prepared than Class A for a quiz.

a juggler needs both rings and bowling pins no more than 12 of these no less than 5 rings
let x represent the rings and y the pins

Answers

The inequality that represent this scenario is x + y ≤ 12 and y > 5

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the rings and y represent the pin

There were no more than 12 of these, hence:

x + y ≤ 12

and

y > 5

The inequality that represent this scenario is x + y ≤ 12 and y > 5

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Answer:

there right i took the test

Step-by-step explanation:

cant add more because they covered it all

A 10% increase in cigarette prices has been found to result in a _____ decrease of smokers. a. 2% b. 4% c. 10% d. 20% please select the best answer from the choices provided. a b c d

Answers

A 10% increase in cigarette prices has been found to result in a 4% decrease of smokers.

What is the effect of price increase in the demand for cigarettes?

An increase in cigarette price will result in a decrease in the demand for cigarettes.

Since more money needs to be spent to but the same product, less consumers can be able to afford it.

Therefore, a 10% increase in cigarette prices has been found to result in a 4% decrease of smokers.

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Other than temperature, state three examples where similar averages are associated with very different distributions. go deeper with one, and discuss how that might work in more detail

Answers

The examples where similar averages are associated with very different distributions include examination results for students, account management commission and the number of goals scored by teams.

What is average?

It should be noted that average simply means the mean of a given set of numbers that are given in a data.

In this case, the examples where similar averages are associated with very different distributions include examination results for students, account management commission and the number of goals scored by teams

Let's use examination results to butress our point. A good average examination results mean that the students have a good understanding of what was covered in the subject.

Let's say the average pass mark for a subject is 50. In this situation, someone who scores 50 and above is believed to understand the subject and has a pass mark.

On the other hand, someone who scores 49.8 is considered to have failed the class even though the score is identical. This shows the case of variability and how similar average can mean different things.

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8


——-
math



——-
math geniuses pls help!!!

—-


pls check other questions as well thanks,!

Answers

An experimental study involves the researcher seeking to affect the results on purpose. The given situation is an observational study.

What are surveys, experiments, and observational studies?Surveys are one type of observational study since the researchers have no control over the results. Statistical surveys collect data from a sample group in order to learn more about the overall population.The sample population being examined is measured, or surveyed, in observational research. The researcher watches the individuals and measures variables but makes no attempt to influence the population or intervene in the study.In contrast to an observational study, an experimental study involves the researcher seeking to affect the results on purpose. The objective is to find out what influence a certain therapy has on the result.

Since the researcher needs to find if a certain medicine improves the symptoms of the flu, therefore, the objective is to find out what influence a certain therapy has on the result. Hence, the given situation is an observational study.

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Which of the following numbers is irrational?

a fraction with numerator negative 15 and denominator 4, a fraction with numerator negative 7 and denominator 9, square root of 4, π

a fraction with numerator negative 15 and denominator 4
a fraction with numerator negative 7 and denominator 9
square root of 4
π

Answers

Answer:

Pi is an irrational number

Answer:

Square root of 4π

An irrational number is never-ending or a fraction, and pi is almost never-ending, making it the only irrational number here since it cannot be written as a fraction.

Please help ASAP!


George believes the Art Club students at his school have an unfair advantage in being assigned to the art class they request. He asked 500 students at his school the following questions: "Are you in the Art Club?" and "Did you get the art class you requested?" The results are shown in the table below:



Art Club Not in Art Club Total

Received art class requested 100 265 365

Did not get art class requested 65 70 135

Total 165 335 500



Help George determine if all students at his school have an equal opportunity to get into the art class they requested. Show your work, and explain your process for determining the fairness of the class assignment process.

Answers

165 total students in art club. 100 of those got the requested class.

100/165 = 0.6061


335 total students not in art club. 265 got the requested class.

265/335 = 0.7910


the probability was higher for kids not in art club, so all students had an equal opportunity.

Ella jewelry box contains 20 earring: 4 are blue 6 are green,2 are red, and 8 are whit. she took one earring from box and then replaced. she repeated this process 50 times and recorded her result in follwing table

Answers

The complete question

Color Number of times picked from jewelry box

blue      14

green   8

red        16

white      12

What's the theoretical possibility of choosing a red earring?(fraction and percent) What's the Experimental possibility of choosing a red earring?(fraction and percent) What's the theoretical possibility of choosing a blue earring?(fraction and percent) What's the Experimental possibility of choosing a blue earring?(fraction and percent)

The probability values are:

The theoretical probability of selecting a red earring is 25%The experimental probability of selecting a red earring is 10%The theoretical probability of selecting a blue earring is 25%The experimental probability of selecting a blue earring is 20%

How to determine the theoretical probability of red earring?

Here, we use the color of the earrings;

There are 4 colors in total, one of which is red

So, the theoretical probability of selecting a red earring is:

P(Red) = n(Red)/Total

This gives

P(Red) = 1/4 = 25%

Hence, the theoretical probability of selecting a red earring is 25%

How to determine the experimental probability of red earring?

The distribution of the earrings is given as:

Red = 2

Total = 20

The probability of selecting a red earring is:

P(Red) = n(Red)/Total

So, we have:

P(Red) = 2/20

Evaluate

P(Red) = 1/10 or 10%

Hence, the experimental probability of selecting a red earring is 10%

How to determine the theoretical probability of blue earring?

Here, we use the color of the earrings;

There are 4 colors in total, one of which is blue

So, the theoretical probability of selecting a blue earring is:

P(Blue) = n(Blue)/Total

This gives

P(Blue) = 1/4 = 25%

Hence, the theoretical probability of selecting a blue earring is 25%

How to determine the experimental probability of blue earring?

The distribution of the earrings is given as:

Blue = 4

Total = 20

The probability of selecting a blue earring is:

P(Blue) = n(Blue)/Total

So, we have:

P(Blue) = 4/20

Evaluate

P(Blue) = 1/5 or 20%

Hence, the experimental probability of selecting a blue earring is 20%

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An investment of $10,000 is invested for 6 years at r% pa compounded weekly. If the investment grows to $14320.44, calculate the value of r.

Answers

I m sorry I hv no idea

.........

(x - 2)^2/36-(y+1)^2/64=1The vertices for the hyperbola are (2,5) and (2,-7) true or false​

Answers

Answer: False

Step-by-step explanation:

I checked with a graphing app huhu... sorry TT

The vertices are (8, -1) , (-4, -1).

PLEASE HELP ILL MARK BRAINEST!!!!

Answers

Answer:

(-3,8) would NOT fit the table.

Answer: (-3,8)

Step-by-step explanation: click on the file

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