A ball is dropped and bounces to a height of 5 feet. The ball rebounds to 70% of its previous height after each bounce The function that could be used to model the nth term in the sequence of heights of the ball after the initial drop is

Answers

Answer 1

Answer:

[tex]T_n = 7.143(0.7^n)[/tex]

Step-by-step explanation:

If a ball bounces to a height of 5feet, the initial drop = 5feet

If the ball rebounds to 70% of its previous height after each bounce, the next height after rebouncing will be expressed as;

= 70% of 5

= 70/100 * 5

= 0.7*5

= 3.5 feet

The next height will be 0.7*3.75 = 2.45 and so on

The  heights wil form a sequence as thus;

5, 3.5, 2.45...

This sequence forms a geometric progression.

To get the function that could be used to model the nth term in the sequence of heights of the ball after the initial drop, w will find the nth term of the sequence

[tex]T_n = ar^{n-1}[/tex]

a is the first term of the sequence

n is the number of terms

r is the common ratio

From the sequence:

a = 5

[tex]r = \frac{3.5}{5} = \frac{2.75}{3.5} = 0.7[/tex]

Substitute the given values into the formula

[tex]T_n = 5(0.7)^{n-1}\\T_n = 5(\frac{0.7^n}{0.7^1} )\\T_n = \frac{5}{0.7}\times 0.7^n \\T_n = 7.143(0.7^n)[/tex]

The nth tern=m required is [tex]T_n = 7.143(0.7^n)[/tex]


Related Questions

You buy a gallon of milk. How many cups can you pour from it?

Answers

Answer: 16 cups!

Step-by-step explanation: Hopefully this helped :D

Answer:

16

Step-by-step explanation:

Step 1:

1 gallon = 16 cups     Conversion

Answer:

16 cups

Hope This Helps :)

Find the additive inverse of -1/8​

Answers

Answer:

1/8

Step-by-step explanation:

(Dont mind me, just need to add more characters LOL)

An ant with a mass of 4 x 10-6 kg is carrying a bread crumb back to its anthill . The bread crumb has a mass of 8 x 10-5 kg. The mass of the bread crumb is how many times the mass of the ant?​

Answers

Answer:

Mass of bread crumb is 20 times the mass of the ant..

Step-by-step explanation:

Mass of an ant = [tex]4\times 10^{-6}[/tex] kg

Ant carries a weight of bread crumb to its anthill.

Mass of the bread crumb = [tex]8\times 10^{-5}[/tex] kg

Ratio of their masses,

[tex]\frac{\text{Mass of the ant}}{\text{Mass of bread crumb}}=\frac{4\times 10^{-6}}{8\times 10^{-5}}[/tex]

[tex]\frac{\text{Mass of the ant}}{\text{Mass of bread crumb}}=\frac{1}{2\times 10^{(-5+6)}}[/tex]

[tex]\frac{\text{Mass of the ant}}{\text{Mass of bread crumb}}=\frac{1}{20}[/tex]

Mass of the bread crumb = 20×(Mass of the ant)

Therefore, mass of the bread crumb is 20 times the mass of the ant.

Which of the binomials below is a factor of this Torinomial? X2 + 12x + 32

Answers

x2+12x+32

Factor out 2 from the expression

2(x+6x+16)

Collect like terms

2(7x+16)

Now we do the same thing only different way ok

x+6x

If a term doesn't have a coefficient , it is considered that the coefficient is 1

1x+6x

Collect like terms by adding their coefficients

(1+6)x

Add the numbers

7x

1+6=7

To add the numbers using a number line, start from zero.

Since 1 is positive, move the point 1 unit to the right.

Since 6 is positive, move the point 6 units to the right

The result is 7

Answer : 2(7x+16)

That's it . Hope it  wasn't too hard to understand?

Please give me as brainliest

What is the measure in degrees of angle R?

Answers

r=90 degrees i think

A contractor purchases ceramic tile to remodel a kitchen floor. Each tile cost $4 and the adhesive/grouting material costs $17.82. If the contractor pays a total of $545.82 how many ceramic tiles did the contractor purchase

Answers

Answer:

132 tiles

Step-by-step explanation:

Each tile cost $4

The adhesive/grouting material costs $17.82.

If the contractor pays a total of $545.82

Let the number of tiles be represented as x

The equation is represented as:

$17.82 + $4 × x = $545.82

17.82 + 4x = 545.82

Collect like terms

4x = 545.82 - 17.82

4x = 528

Divide bother sides by 4

4x/4 = 528/4

x = 132

The number of ceramic tiles the contractor bought = 132 tiles

Can you answer this question for me Thank you For the school cafeteria, 15 pounds of vegetables were ordered by the chef. If each student usually gets 3/8 of a pound of vegetables each day for lunch, how many students could be fed with the vegetables in one day?

Answers

Answer:

The answer could be 40. I might be wrong.

Step-by-step explanation:

15 divided by 3/8 = 40

Match each fraction with its reciprocal.

Answers

Answer:

1/ 4=4

1/3+3/1

3/4=4/

Step-by-step explanation:

Which list contains only composite numbers? 12, 37, 54, 80, 117,
31, 44, 57, 64, 92,
26, 53, 66, 84, 96,
6, 24, 51, 72, 105,​

Answers

Answer:

6, 24, 51, 72, 105

Step-by-step explanation:

6,24,51,72,105

It was right on my work hoops this helps :)

I will give brainliest !!!!!
An office supply store sells notebooks in packs of 15 and folders in packs of 18. A business wants to have one notebook for each folder. What is the least number of notebooks and folders that the business has to buy?

30
270
3
90

Answers

Answer:

90 notebooks and folders

Step-by-step explanation:

Find the least common multiple (LCM) or 18 and 15!

18 x 5 = 90

15 x 6 = 90

Therefore, your answer is 90

Hope this helps!

x+12= -5 helpppp meeeee

Answers

Answer:

The answer is -17.

Step-by-step explanation:

Well since the answer turns out to be a negative, one of the numbers has to be negative.(not all cases but for this one, yes)You have to add 12+5 and you get 17. This has to be a negative because the answer is a negative.

Find the inverse of Function F.
F(x)=9x+7

Answers

Answer:

x - 7/9 = f(x)^-1

Step-by-step explanation:

f(x) = 9x + 7

y - 7 = 9x

y - 7/9 = 9x/9

Interchange!

x - 7/9 = y

HELPP ASAP!! PLS BE SURE THAT THE ANSWER IS CORRECT

Answers

2 inches squared I think

What does extraneous solution mean?

Answers

Answer:

Extraneous solutions are values that we get when solving equations that aren't really solutions to the equation.

Step-by-step explanation: None

Completa las siguientes sucesiones y encuentra su regla general. a) -4, -2, 0, ___, ___,... b) -15, -10, ___, ___,... Y su regla general de todas. Por favor ya había dicho que no se muy bien, Por favor es urgente

Answers

La sucesión es geométrica ya que cada término se obtiene multiplicando el anterior por una cantidad constante (llamada razón), en este caso 1/2

1  *  1/2 = 1/2

1/2 *  1/2 = 1/4

1/4 *  1/2 = 1/8

La fórmula general en este tipo de sucesiones es?

aₙ = a₁ * r ⁿ⁻¹

Donde

aₙ es un término dentro de fórmula general

a₁ es el primer término

r es la razón de la sucesión

n es el índice del término

Con la fórmula podemos obtener los términos que faltan

Término 5

a₅ = 1 * 1/2 ⁵⁻¹

a₅ = 1 * 1/2 ⁴

a₅ = 1 * 1/16

a₅ = 1/16        ======> término 5

Término 8

a₈ = 1 * 1/2 ⁸⁻¹

a₈ = 1 * 1/2 ⁷

a₈ = 1 * 1/128

a₈ = 1/128      =========> término 8

Término 9

a₉ = 1 * 1/2 ⁹⁻¹

a₉ = 1 * 1/2 ⁸

a₉ = 1 * 1/256

a₉ = 1/256  =======> término 9

Study more about GP on https://brainly.com/question/29399287

#SPJ1

(I WILL GIVE BRAINLYIST)

A student solves the inequality -50 > 55. Each step in the student's solution is shown below. Identify where the student made any errors. ​

Answers

Answer: pick b

Step-by-step explanation:

Answer:

Step 2 and 3

Step-by-step explanation:

:)

Amanda owns 9 T-shirts, 4 of which are white. If Amanda randomly selects a T-shirt to wear, what is the probability it will be white? Write your answer as a fraction or whole number.

P(white) =

Answers

Step-by-step explanation:

P(white)=4/9 is the probability

Pls help me answer this

Answers

Answer:

number 1 i think if not then 4

Answer:

#3

Step-by-step explanation:

We can't prove any of the others

#3 is stated a bunch of times in the text

They go into dormancy when life gets hard

A shop owner offered a 20% discount off the regular price of a mirror. The amount of the discount is $5. What is the regular price of the mirror?

Answers

Answer:

25 dollars

Step-by-step explanation:

If 20 percent of the initial price was 5, you can create the equation:

0.2x=5, with x being the regular price.

Multiply both sides by 5:

x=25

Answer:

25$

Step-by-step explanation:

20/100 can be rounded down to 1/5 meaning all you have to do is multiply 5 by 5

5 times 5 is 25

25$ was the original price

Find the y-intercept of the equation y = -0.5x - 3

Answers

Answer: -3

Step-by-step explanation: When you graph this that’s what you get

Answer:

-3

Step-by-step explanation:

the y intercept is when x is 0 on the graph. Since you know x has to be zero, you can substitute x for 0 in the equation:

y = -0.5x0 -3

Now you can ignore that first part of the equation because it equates to 0, and so you get:

y= 0 - 3

which equals:

y=-3

Figure B is a scaled copy of Figure A. Select all of the statements that must be true:

Figure B is larger than Figure A.

Figure B has the same number of edges as Figure A.

Figure B has the same perimeter as Figure A.

Figure B has the same number of angles as Figure A.

Figure B has angles with the same measures as Figure A.

Item at position 2
ANSWER QUICKLY PLEASE

Answers

Answer:

Same number of edges

Same number of angles

Angles woth same measures

halp me I need halp plz

Answers

Answer:

3     13/20

Step-by-step instructions

Answer:

The correct equation that is shown is number 3. (edited).

Solve the equation using the Properties of Equality.

Answers

M = 11/24 (hope this helps)

what is the slope of the line that goes through the points (2,-1) and (6,1)

Answers

Answer: The slope is [tex]\frac{1}{2}[/tex].

Step-by-step explanation:

1. You set up your Slope Formula [tex]M=\frac{y2-y1}{x2-x1}[/tex].

2. Substitue your points into the formula.[tex]M=\frac{1--1}{6-2}[/tex].

3. Once you substitute, you will solve the equation[tex]M=\frac{2}{4}[/tex].

4. Simplify the equation if you have to [tex]M=\frac{1}{2\\}[/tex].

Question
Identify the correct graph and solution for the inequality.
10 a <25
(Look at pic)

Answers

i think it is C
explanation:

Answer:

First option

Step-by-step explanation:

First, Solve the inequality:

Divide each side by 10 to cancel out the 10 next to a. It should now look like this: a < 2.5

Find the inequality that matches the solution:

The first option (which literally writes the simplified version of the inequality) is correct, because it matches our simplified inequality above.  

a water turck is filling a swiming pool. the euqation that represents this relationship is y = 19.75x where y is the number of gallons of water in the pool and x is the number of minutes the truck has been filling the pool choose true or false for each statement

Answers

Answer:

True

Step-by-step explanation:

Given the expression

y = 19.75x

let us see the solution from this angle

we know that

speed=distance/time

distance=speed*time

i.e quantity=rate*time

y = 19.75x

y=the quantity =number of gallons

19.5= the rate of flow

therefore

x= the time in  minutes

Point A is at (-6,8) and point M is at (0,0.5).
Point M is the midpoint of point A and point B.
What are the coordinates of point B?

Answers

Answer:

(6,-7)

Step-by-step explanation:

the coordinates of point B are (6-7)

Answer:

the first answer is right

Step-by-step explanation:

is it right? or like idk i’m confused

Answers

This is right                                                                        

The system requires me to have 20 characters in my answer so I am just gonna add this.

The third-grade teachers had a pizza party. They ordered 11 large pizzas and each pizza had 8 slices. There were 4 classrooms in the grade.

Answers

whats the question you only stated the problem

Answer:Not exactly sure what the question is but...

Step-by-step explanation:There would be 88 slices so each classroom would get 22 slices.

Hope this helps

One week, seventy-two percent of the animals that cam to a veterinary hospital were dogs. If there were 230 animals total, how many were dogs?

Answers

Answer:

166/230 or 83/115

Step-by-step explanation:

72/100 converted to  ?/230

100 to 230 is 2.3*100

so 72*2.3=165.6

166/230 simplify 83/115

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