Rohan dropped a lacrosse ball from a building.



After each bounce, the height of the ball is measured and recorded in the table.

Bounce Number Height (cm) After Bounce
1 10,240
2 2,560
3 640
4 160
Write an explicit and recursive formula to represent the sequence of the height of the ball after each bounce.

What is the height of the ball after bounce 8? Explain your answer by using one of the formulas you created.

Answers

Answer 1

Answer:

The nth bounce a sub n is 0.25 (a sub n-1)

0.625 cm

Answer 2

  Recursive formula of the sequence[tex]T_n=10240(\frac{1}{4})^{n-1}[/tex]

  Explicit formula of the sequence → [tex]T_1=10240, \\T_{n+1}=T_n(0.25)[/tex]

  Height of the ball after 8th bounce will be 0.625 cm.

Geometric sequence and its explicit and recursive formula,If a sequence is in the form of [tex]ar,ar,ar^2,ar^3.....[/tex] n terms,

        Sequence will be the geometric sequence and the explicit formula

        of the sequence will be,

        [tex]T_n=ar^{n-1}[/tex]

        Here, [tex]a=[/tex] First term

        [tex]r=[/tex] Common ratio

        [tex]n=[/tex] Number of terms

Similarly, recursive formula will be,

        [tex]a=[/tex] First term

        [tex]T_{n+1}=T_n(r)[/tex]

From the table attached,

There is common ratio between the successive term and previous term under the column (height after the bounce) is,

[tex]\frac{T_2}{T_1}=\frac{2560}{10240}=\frac{1}{4}[/tex]

[tex]\frac{T_3}{T_2}=\frac{640}{2560}=\frac{1}{4}[/tex]

Therefore, height of the ball after each bounce will represent a geometric sequence.

Explicit formula of a geometric sequence will be given by the expression,

[tex]T_n=10240(\frac{1}{4})^{n-1}[/tex]

Recursive formula for the sequence will be,

[tex]T_1=10240[/tex]

[tex]T_{n+1}=T_n(\frac{1}{4})[/tex]

By using recursive formula,

Height of the ball after 8th bounce,

[tex]T_8=10240(\frac{1}{4})^{8-1}[/tex]

    [tex]=10240(0.25)7[/tex]

    [tex]=0.625[/tex] cm

      Therefore, explicit formula to represent the height of the ball will be [tex]T_n=10240(\frac{1}{4})^{n-1}[/tex]recursive formula will be, [tex]T_1=10240\\T_{n+1}=T_n(0.25)[/tex]

       And height of the ball after 8th bounce will be 0.625 cm.

Learn more about the geometric sequence here,

https://brainly.com/question/25250161?referrer=searchResults


Related Questions

The scatter plot shows how much puppy weighs within a certain time period. about how much did the puppy gain during this time period?

Answers

Where is the picture to answer it?

Find the volume of the cuboid, length= 7mm, b= 5mm, h= 6mm
.. Please anwser fast.. ​

Answers

Answer:

Volume = lbh

Volume = 7 × 5 × 6

Volume = 7 × 30

Volume = 210 mm³

Therefore

Volume is 210 mm³

[tex] \\ [/tex]

Given:-

[tex] \bullet [/tex] Length (l) of the cuboid = 7mm

[tex] \bullet [/tex] Breadth (b) of the cuboid = 5mm

[tex] \bullet [/tex] Height (h) of the cuboid = 6mm

To Find:-

The volume of the cuboid.

Solution:-

We know the formula of the volume of the cuboid is ( Length × Breadth × Height ) cubic units.

[tex] \therefore [/tex] Volume of the cuboid is ( 7 × 5 × 6 ) mm³

Volume of the cuboid is 210 mm³.

The volume of the cuboid is 210 mm³. [Answer]

Plsss help ASAP

Will mark brainleist

Answers

Answer:

hello! Your answer would be, 1: B) AND 2: D)

Step-by-step explanation:

Hope I helped! Brainiest plz!♥ Have a nice afternoon. Hope you make a 100%! -Amelia

Find the slope of the line graphed below.​

Answers

Answer:

Step-by-step explanation:

What is the slope of y= -7/5x +4

Answers

Y= -7/5x + 4

To find -intercept/zero, substitute

Multiply both sides of the equation by

0= -7/5x +4

Move the variable to the left-hand side and change its sign

0= -7x +20

Divide both sides of the equation by

7x=20
20/7 = 2 6/7 = x 2.857

Answer: I hope this helps!

brainliest or a thank you pls :)) <33

Tom scored double what Ali scored. Bob scored 6 less then Ali. If together they scored 60 points. How many points did they each score?

Answers

Answer:

A = 16.5

T = 33

B = 10.5

Step-by-step explanation:

T = 2A

B = A-6

T + B + A = 60

(2A) + (A-6) + A = 60

4A - 6 = 60

4A = 66

A = 16.5

T = (16.5)*2 = 33

B = 10.5

Based on the timeline, which of the following statements is true?​

Answers

Answer:

Answer B.

Step-by-step explanation:

If you check each answer, only B works since it is the only one that would place everything correctly on the timeline

Which expression is equivaien. to 6 (3x + 4)?

Answers

Answer:

18x + 24

Step-by-step explanation:

6(3x + 4)

combine like terms

18x + 24

please give a full explanation:)

Answers

Answer:

x = 5, y = 2.5

Step-by-step explanation:

Because the original image is scaling down 4, it means all of the values of the shape will be scaled down, or divided by 4.

20, which divided by 4, will make x equal 5.

10, which divided by 4, will make y equal 2.5

In the diagram, AP is a tangent and PBC is a secant in a circle O. If PC = 12 and BC = 9, what is AP?

Answers

Answer:

6

Step-by-step explanation:

AP^2 = PC * PB

We have PC and BC. We need PB.

PC = 12

BC = 9

PB + BC = PC

PB + 9 = 12

PB = 3

AP^2 = 12 * 3

AP^2 = 36

AP = 6

Answer: 6

Answer:

Hey!

AP will be 6cm.

Step-by-step explanation:-

to solve this, the equation  PB X PC = [tex]AP^{2}[/tex]  can be used

In the ques, its given that PC= 12cm and BC = 9.

To solve this, WE NEED TO FIND PB, SO:-

PB + BC = PC

PB + 9 = 12

PB = 3cm.

Now, we can substitute this in the equation:- PB X PC = [tex]AP^{2}[/tex]

[tex]AP^{2}[/tex] = PB x PC

[tex]AP^{2}[/tex] = 3 X 12

[tex]AP^{2}[/tex] = 36

AP = [tex]\sqrt{36}[/tex]

AP = 6cm.

during a debate Bonnie used 9 minutes to present her opinion 6 minutes to rebut the opposing opinion and 5 minutes to summarize what percent of the time did she spend summarizing

Answers

Answer:

she spent like 40% of her time easy

Step-by-step explanation:

that was like 3rd grade

85°
152

Find the value of the missing angle

Answers

Answer:

67°........................

Answer:

x=67

Step-by-step explanation:

Can someone help me with my homework its experimental and theorectical probability

Answers

Yes sure what’s the question?

Answer:

Step-by-step explanation:

fjfjgjgjghg

PLEASE HELP WILL MAKE BRAIN IF YOU HELP!​

Answers

Answer:

60

Step-by-step explanation:

The sum of two interior angles in a triangles is equal to one exterior angle that is supplementary to the third interior angle

3x+4x = 10x - 45

7x = 10x - 45 transfer 45 to the other side of equation and subtract 7x from 10 10

45 = 10x - 7x

45 = 3x divide both sides by 3

15 = x angle B is 4*15 = 60

A rectangle has a perimeter of 10 meters.
Choose all the possible dimensions of the rectangle.
D A
1 meter by 4 meters
B.
1 meter by 9 meters
C. 2 meters by 3 meters
OD. 3 meters by 2 meters
O E. 4 meters by 1 meter
OF. 5 meters by 5 meters
G. 9 meters by 1 meter

Answers

Answer:

DA

C

OD

OE

Step-by-step explanation:

Answer:

DA

1 meter by 4 meters

Step-by-step explanation:

To find the perimeter of a rectangle, you add up all four sides.

if a rectangles dimensions are 1 by 4, you would add 4 + 4 + 1 + 1 = 10

Hope this helps

It is customary to leave a 15% tip for a waiter/waitress. Suppose your meal costs $22.50, What would you tip the wait person? How much totalwould you pay for the meal?

Answers

Answer:

$25.88

Step-by-step explanation:

Given data

Cost of meal= $22.50

Tip= 15%

Let us find 15% of $22.50

=15/100*22.50

=0.15*22.50

=3.375

Hence the amount you would pay in total is

=3.375+22.5

=$25.88

Consider two circular swimming pools. Pool A has a radius of 24 feet, and Pool B has a diameter of 14.82 meters. Complete the description for which pool has a greater circumference. Round to the nearest hundredth for each circumference. 1 foot ≈ 0.305 meters The diameter of Pool A is meters. So, the diameter of Pool (select) is greater, and the circumference is (select) by meters.

Answers

Pool A =
24 feet => 7.32 meters
circumference = 2 x pi x radius
circumference = 45.99 meters

Pool B =
circumference = pi x diameter
circumference = 46.56 meters

Therefore the diameter of Pool B is greater, and the circumference is 46.56 by meters.

Answer:

The diameter of Pool A is  14.64  meters. So, the diameter of Pool B  is greater, and the circumference is  greater  by  0.56 meters.

Step-by-step explanation:

Identify the diameter of Pool A.

d = 2r

d = 2(24) Substitute 24 for r.

d = 48 ft

Convert from feet to meters. Use the ratio of 1 foot to 0.305 meters. Round to the nearest hundredth.

48 × 0.305 = 14.64

The diameter of Pool A is about 14.64 meters.

Use the formula to find the circumference of Pool A.

C = πd

C = π(14.64) Substitute 14.64 for d.

C ≈ 3.14(14.64) Substitute 3.14 for π.

C ≈ 45.97 Multiply.

The circumference of Pool A is about 45.97 feet.

Identify the diameter of Pool B.

d = 14.82 m

The diameter of Pool B is 14.82 meters.

Use the formula to find the circumference of Pool B.

C = πd

C = π(14.82) Substitute 14.82 for d.

C ≈ 3.14(14.82) Substitute 3.14 for π.

C ≈ 46.53 Multiply.

The circumference of Pool B is about 46.53 feet.

The circumference of Pool B is greater than the circumference of Pool A.

Find how much greater the circumference of Pool B is compared to the circumference of Pool A.

46.53 − 45.97 = 0.56

The circumference of Pool B is greater than the circumference of Pool A by about 0.56 meters.

Lamborghini rental company charges a rate to rent a Lamborghini of $85 plus an additional fee of five dollars per mile you drive a car wouldn’t ultimate ticket or geometric sequence best model the situation what explicit formula models the situation how much would you have to pay if you drive 150 miles

Answers

Answer:

835$

Step-by-step explanation:

5$ for each extra mile

5 x 150 = 750

750 + 85 = 835

hold on i’m working out the problem i will answer it in the comments

(0,2) (1,0) what is the equation of this line in slope intercept form

Answers

The slope intercept form is y= -2x+2

Volume of Cylinders, Cones, and Spheres

I NEED HELP ASAP!!

Answers

Answer:

8) 144pi

9) 196pi

11) 18pi

12) 298.67pi

Step-by-step explanation:

Cylinders

The volume of a cylinder is [tex]V = \pi r^{2} h[/tex], where r represents the radius of the base and h represents the height.

For the first cylinder, the radius of the base is 4 and the height is 9.

[tex]V = \pi (4)^{2} (9)\\V = \pi(16)(9)\\V = 144\pi[/tex]

For the second cylinder, the diameter is 6 and the height is 2. Since the radius is half the diameter, the radius is 3.

[tex]V = \pi (3)^{2} (2)\\V = \pi(9)(2)\\V = 18\pi[/tex]

Sphere

The volume of a sphere is [tex]V = 4\pi r^{2}[/tex], where r is the radius of the sphere.

The diameter is 14, meaning the radius must be 7.

[tex]V = 4\pi (7)^{2} \\V = 4\pi (49)\\V = 196\pi[/tex]

Cone

The volume of a cone is [tex]V = \pi r^{2} (h/3)[/tex], where r is the radius and h is the height.

The radius is 8, and the height is 14.

[tex]V = \pi (8)^{2} (14/3)\\V = \pi (64) (14/3)\\V = \frac{896}{3} \pi\\V = 298.67\pi[/tex]

xy + 4y - 2x - 8 thanks

Answers

Answer:

(x+4)(y-2)

Step-by-step explanation:

Hope this helped!!!!

Answer:

xy + 4y

Step-by-step explanation:

good luck!!!! hope this helps

Express 130 and 325 as the sum of two squares in two different ways.

Answers

Answer:

3^2 + 11^2 = 130

7^2 + 9^2 = 130

---

1^2 + 18^2 = 325

6^2 + 17^2 = 325

Step-by-step explanation:

We want to express 130 and 325 as the sum of two squares in two different ways.

Then, we want to find two integers a and b such that:

a^2 + b^2 = 130

There is not an analytical way to do this, we just need to try with different integers.

Let's start with 130.

So we start by defining a as a really small integer, for example 1, and try to find b.

1^2 + b^2 = 130

b^2 = 130 - 1

b^2 = √129 = 11.3

This is not an integer, so let's try with another value of a.

a = 2

2^2 + b^2 = 130

4 + b^2 = 130

b^2 = 130 - 4

b = √126 = 11.2

This can be discarded again.

Now let's try with a = 3

3^2 + b^2 = 130

9 + b^2 = 130

b^2 = 130 - 9

b = √121 = 11

Nice.

So we can express 130 as:

3^2 + 11^2 = 130

Now let's find another pair.

In the same way, we can see that for a = 7 we get:

7^2 + b^2 = 130

42 + b^2 = 130

b^2 = 130 - 49

b = √81 = 9

Then we can write:

7^2 + 9^2 = 130

Now for 325:

With the same reasoning than before, we want to find two integers such that:

a^2 + b^2 = 325

Then we start evaluating a by the smallest values:

a = 1

1^2 + b^2 = 325

b^2 = 325 - 1 = 324

b = √324 = 18

Then we can write 325 as:

1^2 + 18^2 = 325

Now to find the next pair we need to keep testing values for a, we will get for a = 6:

6^2 + b^2 = 325

36 + b^2 = 325

b^2 = 325 - 36 = 289

b = √289 = 17

Then we can write:

6^2 + 17^2 = 325.

qué número entero está entre -2 y 5​

Answers

Answer:

1.5

Step-by-step explanation:

-2,-1,0,1,2,3,4,5

Le quitamos un número hasta llegar al medio. En el medio hay dos números, el 1 y el 2. Pues tenemos que buscar el promedio de los dos (1+2=3 y 3÷2=1.5).

The box and whisker plots represent the number of minutes spent by users on two different social media groups. Which THREE statements are correct when comparing the plots?
A) The median time for users of Group B is 40 minutes.

B) Group B has greater median value than Group A.

C) The data for Group B varies slightly more than Group A.

D) The spread of the data for Group A is 25 minutes.

E) The spread of the data for Group A is 40 minutes. ​

Answers

Answer:

A, C, and D

Step-by-step explanation:

Please help I do not know how to do this

Answers

I think it’s Option C.



I think this because I’ve added up all the votes and got 610 which is 100% of the votes


Half of that is 305=50% 1/2

And half of that is 152.5=25% or 1/4

Silver is closer to 1/4 then red and silver is to 1/2

El autobús mide 33,5 pies de largo. El tren de la ciudad es 45,9 pies más largo que el autobús. ¿Cuánto dura el tren de la ciudad

Answers

Respuesta:

79.4 pies

Explicación paso a paso:

Dado que :

Longitud del autobús = 33,5 pies

Longitud del tren = 45,9 pies más largo que el autobús

Por lo tanto, la longitud del tren es igual a:

Longitud del bus + 45,9 pies

33,5 pies + 45,9 pies

Longitud del tren = 79,4 pies

Find the area of the shaded region. Round your answer to the nearest tenth.

Answers

You need to include the Image

Evaluate 32. (4 + 2) - 1 + (2.3)
A
15
В
23
C
54
D
57

Answers

Answer:

7.3

Step-by-step explanation:

Order of operations rules require that any work inside parentheses be done first.  Thus,

(4 + 2) - 1 + (2.3) becomes 6 - 1 + 2.3

This, in turn, becomes 5 + 2.3, and the final result is 7.3.

What is the value of x? Show me how you got that answer.

Answers

Answer:

x = 3

Step-by-step explanation:

The angle measuring 5x and the angle measuring 165° are a linear pair, so they are supplementary. Their measures add to 180°.

5x + 165 = 180

5x = 15

x = 3

Cross elasticity of demand is the percentage change in the quantity __________ of a good divided by the percentage change in __________. Group of answer choices demanded; the price of the good supplied; the price of the good demanded; the price of another good supplied; the price of another good demanded; income

Answers

Answer:

demanded;

the price of another good demanded

Step-by-step explanation:

Cross price elasticity of demand measures the responsiveness of quantity demanded of good A to changes in price of good B.

cross price elasticity of demand = percentage change in quantity demanded of good A / percentage change in price of good B

Price elasticity of demand measures the responsiveness of quantity demanded to changes in price of the good.

Income elasticity of demand measures the responsiveness of quantity demanded to changes in income.

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