4 When a ball bounces, the heights of consecutive bounces form

a geometric sequence. The height of the first bounce is

121 centimeters and the height of the third bounce is

64 centimeters. To the nearest centimeter, what is the height of the

fifth bounce?

Answers

Answer 1

Answer:

34 cm

Step-by-step explanation:

The nth term of a geometric progression Tₙ = arⁿ⁻¹ where a = first term, and r = common ratio.

Given that our first term, T₁ = ar¹⁻¹ = a = 121 cm and our third term T₃ = ar³⁻¹ = ar² = 64 cm

Then, T₃/T₁ = ar²/a = r²

r² = T₃/T₁

r² = 64 cm/121 cm

r = √64/121

r = 8/11

So, the height of our fifth bounce T₅ = ar⁵⁻¹

= ar⁴

= 121 cm × (8/11)⁴

= 121 × 4096/14641

= 4096/121 cm

= 33.9 cm

≅ 34 cm to the nearest cm

Answer 2

Using a geometric sequence, it is found that the height of the fifth bounce is of 33.85 cm.

In a geometric sequence, the quotient between consecutive terms is always the same, and it is called common ratio r.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1r^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

In this problem:

The height of the first bounce is of 121 cm, hence [tex]a_1 = 121[/tex].The height of the third bounce is of 64 cm, hence [tex]a_3 = 64[/tex], and this is used to find r.

[tex]a_n = a_1r^{n-1}[/tex]

[tex]64 = 121r^{2}[/tex]

[tex]r^2 = \sqrt{\frac{64}{121}}[/tex]

[tex]r = \frac{8}{11}[/tex]

Hence:

[tex]a_n = 121\left(\frac{8}{11}\right)^{n-1}[/tex]

The height of the fifth bounce is of [tex]a_5[/tex], hence:

[tex]a_5 = 121\left(\frac{8}{11}\right)^{4} = 33.85[/tex]

The height of the fifth bounce is of 33.85 cm.

You can learn more about geometric sequences at https://brainly.com/question/11847927


Related Questions

A farmer sells 6.7 kilograms of pears and apples at the farmer's market. 3/5 Of this weight is pears, and the rest is apples. How many kilograms of apples did she sell at the farmer's market?

Answers

Answer: She sold 2.68kg of apples in the market

Step-by-step explanation:

Weight of pears and apples= 6.7 kg

weight of pears = 3/5 x 6.7 kg= 4.02 kg

Weight  of apples = Total weight of the fruits -  weight of pears

= 6.70kg- 4.02kg =2.68 kg

1. The fare of 12 kg of luggage for a distance of 36km is 24 rupees
How much fare will be charged for a luggage of 18kg for a distance
of 12km?​

Answers

Answer:

16 rs maybe not sure sry if wrong

Is 299 in the sequence of 2 5 8 11 14 with 3n-1 as the term

Answers

Answer:

yes

Step-by-step explanation:

Equate

3n - 1 = 299 ( add 1 to both sides )

3n = 300 ( divide both sides by 3 )

n = 100

Then 299 is the 100 th term of the sequence

Un escalador sube 225m de altura. El asenso lo hizo en 3 etapas. En la primera subio un quinto en la, en la tercera un cuarto. ¿cuanto hizo en la segunda?

Answers

Answer:

Segunda etapa= 123.75 metros

Step-by-step explanation:

Altura total= 225 metros

En la primera estapa subió el 20% (un quinto):

Primera etapa= 225*0.2= 45 metros

En la tercera etapa subió 25% (un cuarto):

Tercera etapa= 225*0.250 56.25 metros

Ahora debemos determinar cuánto subió en la segunda etapa:

Segunda etapa= altura total - total subido

Segunda etapa= 225 - (45 + 56.25)

Segunda etapa= 123.75 metros

Rectangle A has a length of 6 and width of 4. Rectangle A prime has a length of 9 and width of 6. Find the scale factor of the dilation shown. 1/2 3/2 2 2/3

Answers

Answer: The scale factor of the dilation [tex]=\dfrac32[/tex]

Step-by-step explanation:

[tex]\text{Scale factor}=\dfrac{\text{Side in image}}{\text{Corresponding side in preimage}}[/tex]

Given: Rectangle A has a length of 6 and width of 4.

Rectangle A prime has a length of 9 and width of 6.

Scale factor = [tex]\dfrac{9}{6}\ \ \ or \ \ \dfrac{6}{4}[/tex]

[tex]=\dfrac32[/tex]

Hence, the scale factor of the dilation [tex]=\dfrac32[/tex]

Answer:

3/2

Step-by-step explanation:

Michael sells 136 newspapers each week. If there are 52 weeks in a year, how many newspapers does Michael sell in a year?

Answers

Answer:

7,072

Step-by-step explanation:

136 times 52 = 7,072

Answer:

7,072 newspaper in a year

Step-by-step explanation:

Multiply: 136*52=7,072

(I would put a picture of my work but I'm lazy right now lol)

Hope this helped!! :)

Stay safe and have a wonderful day/night!!!!!

Brainliest?!?!

Finding a percentage of o total amount without a calculator...
An item is regularly priced at $35. It is on sale for 40% off the regular price. How much (In dollars) Is discounted from the regular price?
Amount discounted: si
х
5
?
Help

Answers

35 - 0.80*35 = x

35 - 28 = x

7 = x

x = 7

He paid $7

Pls help middle school math!!

Answers

Answer:

r = √A/π      (radius = square root of a over pi)

Explanation:

There is a radius and a diameter. Diameter is the length of the whole circle across. The radius is half of the circle's length across, so half of the diameter.

hope this answers your question!

Please help I need it for today

Answers

Step-by-step explanation:

Disculpe pero de qué grado es usted para ayudarle un poquito más mejor

Find the slope/
please help me
х
y
Rise =
6
-3
Run =
0
1
0 -3
3
3
m =
-6
5

Answers

Use this to answer

Using two of the points on the line, you can find the slope of the line by finding the rise and the run. The vertical change between two points is called the rise, and the horizontal change is called the run. The slope equals the rise divided by the run

The relationship between the postage rate and the weight of a letter can be defined by a piecewise function. The graph shows the 2018 postage rates for using regular service to mail a letter. Kiran and Mai wrote some rules to represent the postage function, but each of them made some errors

Answers

Kiran equation is incorrect because there are two rates when the weight is 1,2, and 3 ounces, also, the first symbol is incorrect; on the other hand, Mai is incorrect because the prices for 1, 2, and 3 ounces are not correctly expressed.

What is a function?

A function is an expression that shows how two factors, in this case, rate and weight are related. These functions are usually created based on specific data and they should relate the data correctly.

What was Kiran's mistake?

1. There are two rates for 1, 2, and 3 ounces: The use of symbols Kiran used to explain the rate for 1, 2, and 3 ounces is incorrect. Let's examine an example:

0.71  1  ≤  w ≤ 20.92  2  ≤ w  ≤ 3

It seems the rate for 2 pounds can be both 0.71 and 0.92 because in the first line if the weight is less or equal to 2, the rate is 0,71 and this also happens in the second line.

2. The first symbol he used is incorrect because it seems like there is a charge even if the weight is 0, which is impossible.

0.50 0  ≤ w  ≤ 1 (The rate if the weight is less or equal to 0 is 0.50)

What is Mai's mistake?

1. Similarly to Kiran she did not express the rate and the pounds correctly. Let's look at one example:

0.71 1 < w < 2 (if the weight is less than 2 the rate is 0.71, which is incorrect because the rate is 0.71 if the weight is less or equal to 2)

Note: This question is incomplete; here is the missing section:

Identify the error in each person's work:

Learn more about rates in: https://brainly.com/question/25565101

1 and 1/3 - 5/6
(ill mark when 2 answers)
(have a good day )
(HELP MEH PLZZ)

Answers

Answer:

1 1/3 - 5/6 = 1/2

Step-by-step explanation:

First we will need to make a common denominator on both sides, so since we have the second side divided in six, we can do the same to the first side as shown;

1/3 = 2/6

now this will help us a lot, now all we have to do is take what we can out of the fraction (2/6) out of the first side so it is equal to 0, NOTE this is not a professional way to do it but it helps me a lot;

5/6 - 2/6 = 3/6

this makes it easy all of a sudden, cause now its in a simpler form, we can tell this because we know that 3/6 is equal to 1/2, so now all we have to do is take 1/2 from our 1 that we are left over with, and VWOLA;

1 - 1/2 = 1/2

GRAND TOTAL;

1 1/3 - 5/6 = 1/2

(note: the space between the 1 and the 1/3 indicates that they are two separate numbers, so you dont have to put the 'and' there)

how much is 28 yards in feet

Answers

it would be 84 feet hope this helped

Answer:

The correct answer is 84 feet.

Step-by-step explanation:

Each yard is  3 feet so then 3 times 28 equals 84.

HAVE A GOOD DAY!

Brainliest????

3 Each expression below shows the length and width of
a rectangle in yards. Write each expression in the
correct box according to the area it represents.

Answers

Answer:

less than 1yd²:

2/3x3/5= 2/5

1/4x5/3= 5/12

1/2x9/10= 9/20

equal to 1yd²

1/4x4/1= 1

4/3x6/8= 1

more than 1yd²

2/3x5/3= 1.1

Step-by-step explanation:

2/3x3/5= 2/5

1/4x4/1= 1

2/3x5/3= 1.1

1/4x5/3= 5/12

1/2x9/10= 9/20

4/3x6/8= 1

Answer:

2..........3

--- x ---

3............5

Step-by-step explanation:

goes to area less than 1square yard

please help me on this will give you brainliest

Answers

Answer:

ST =6.9

SR =15.9

Step-by-step explanation:

radius:
diameter:32 meters
circumference:
area:​

Answers

Given diameter is 32, radius would be 16 bc radius is always half of diameter, and circumference would be 2(pi)*radius, which would be 100.5309649.... and area is (pi)*radius^2 which would be 804.2477193........

Someone help please

Answers

what do you need help with?

um sapato é vendido a r$ 180,00. se a compra for a vista a loja oferece um desconto de 10%. qual o valordo sapato na compra a vista?​

Answers

Preço de um sapato = $ 180,00

Desconto concedido se o sapato for comprado em dinheiro = 10%

Custo do calçado quando comprado à vista :

[tex] =\tt 180 - 10\% \: \: de \: \: 180[/tex]

[tex] = \tt180 - \frac{10}{100} \times 180[/tex]

[tex] =\tt180 - \frac{10 \times 180}{100} [/tex]

[tex] = \tt180 - \frac{1800}{100} [/tex]

[tex] =\tt 180 - 18[/tex]

[tex]\color{plum} =\tt\$162.00[/tex]

▪︎Assim, preço do sapato quando comprado em dinheiro = $ 162,00

A local little league has a total of 60 ​players, of whom 40​% are left​-handed. How many left ​- handed players are​ there?

Answers

Answer:

24 players

Step-by-step explanation:

Answer:

24. 60 X 4/10 is 24

Step-by-step explanation:

Rule: multiply by 2 Pattern: 3,6,12,24,48 Observation: Observation = something similar about the numbers

Answers

Step-by-step explanation:

This numerical sequence corresponds to a geometric progression, which occurs when there is a multiplication of the sequence numbers for a common reason whose result will always be the successor number of the numerical sequence.

Like for example:

3,6,12,24,48

The common reason for the geometric progression is the number 2, so the first term of the sequence multiplied by 2 will be equal to the second term of the sequence and so on:

3x2 = 6

6x2 = 12

12x2 = 24

24x2 = 48

It is necessary to emphasize that the ratio of a geometric progression will always be constant and will always be a number other than zero.

Paula salió de su casa rumbo al trabajo avanzo 8km al este y 13km al norte. Si hubiera un camino recto desde su casa a su trabajo ¿Que distancia recorrería por ese camino?

Answers

Answer:

15.26km

Step-by-step explanation:

Con la informacion de la pregunta e hecho un diagrama de la situacion. Podemos ver en el diagrama que el recorido forma un triángulo rectángulo. Entonces para saber la distancia que recorreria por el camino recto desde su casa a su trabajo tendriamos que calcular el valor de x, que se puede calcular usando el teorema de pitagoras que es el siguiente.

[tex]a^{2} + b^{2} = c^{2}[/tex]

donde a y b son el ancho y el alto del triangulo y el c seria x

[tex]8^{2} + 13^{2} = x^{2}[/tex]

[tex]64 + 169 = x^{2}[/tex]

[tex]233 = x^{2}[/tex]

[tex]15.26 = x[/tex]

Finalmente, podemos ver que la distancia seria 15.26km

PLZ HELP WITH MATYHSN

Answers

Answer:

26mm because w=6mm and the perimeter of the smaller triangle is 48mm

HELP ME IT WOULD MEAN A LOT​

Answers

Answer:

123

Step-by-step explanation:

72+51=123

123 - 72 = 51

Answer:

72+51=123

123 - 72 = 51

Step-by-step explanation:

When graphing a system of equations with INFINITE SOLUTIONS,
the SLOPES of the two lines will be__________.

Answers

Answer:

Step-by-step explanation:

Hgbuf7g

The slopes of the two lines will be straight

IVIIxed N
Douglas was planting grape vines. He completed 2-
rows of
grapes
each hour he worked. After completing 140 rows of grapes, how many
hours had he worked?
0000
48 hours
50 hours
52 hours
60 hours

Answers

Answer: He completes 2 4/5 rows per hour

if he completed 140 rows, how many hours did it take?

 

We should divide the work completed by the amount of work done per hour.

So, 140/(2 4/5) =  

2 4/5 is equivalent to 2.8  

so 140/2.8 = 50 hours

Step-by-step explanation:

what is the percent of change from 85 to 64

Answers

Answer:

-24.71%

Step-by-step explanation:

What is the value of x?

Answers

Answer:

x = 22

Step-by-step explanation:

hope I helped!!

23. I hope this helps sorry if it doesn’t ❤️

(5x-8)
+
(2x+19)
Find the value of x.
OA.5
B.7
C.9
D.11

Answers

Answer:

x=9 option C

Step-by-step explanation:

explanation above

Please mark me as brainlist

hola me ayudan pliss como saco el resultado de 584 × (?) =179288 y (?) ÷ 143 = 572​

Answers

1) = 307
2) = 81796

1) 179288/584 = 307
2) 572 x 143 = 81796

Answer:

1)307

2)81796

Step-by-step explanation:

584 × (?) =179288

[tex]\frac{179288}{584}[/tex] =307

(?) ÷ 143 = 572​

572x143 =81796

¡Espero que esto sea de ayuda! :)

Write each fraction as an expression using a negative exponent other than -1. 3. 1 ___________ 4 24. 1 ___________ 100

Answers

Answer:

[tex]\frac{1}{4} = 2^{-2}[/tex]

[tex]\frac{1}{100} = 10^{-2}[/tex]

Step-by-step explanation:

The question is poorly formatted. However, I am able to get:

1. 1/4 and 2. 1/100

Required

Write as an expression of negative expression

1. 1/4.

Express 4 as 2^2

[tex]\frac{1}{4} = \frac{1}{2^2}[/tex]

Apply

law of indices [tex](\frac{1}{a^b} = a^{-b})[/tex]

[tex]\frac{1}{4} = 2^{-2}[/tex]

2. 1/100.

Express 100 as 4^2

[tex]\frac{1}{100} = \frac{1}{10^2}[/tex]

Apply law of indices [tex](\frac{1}{a^b} = a^{-b})[/tex]

[tex]\frac{1}{100} = 10^{-2}[/tex]

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