Answer:
The nth bounce a sub n is 0.25 (a sub n-1)
0.625 cm
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
What is the value of x? Show me how you got that answer.
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
Volume of Cylinders, Cones, and Spheres
I NEED HELP ASAP!!
Answer:
8) 144pi
9) 196pi
11) 18pi
12) 298.67pi
Step-by-step explanation:
CylindersThe 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]
SphereThe 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]
ConeThe 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]
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?
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.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.
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.
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
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 slope of the line graphed below.
Answer:
Step-by-step explanation:
please give a full explanation:)
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
Based on the timeline, which of the following statements is true?
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
Please help I do not know how to do this
Can someone help me with my homework its experimental and theorectical probability
Answer:
Step-by-step explanation:
fjfjgjgjghg
(0,2) (1,0) what is the equation of this line in slope intercept form
What is the slope of y= -7/5x +4
Answer: I hope this helps!
brainliest or a thank you pls :)) <33
Which expression is equivaien. to 6 (3x + 4)?
Answer:
18x + 24
Step-by-step explanation:
6(3x + 4)
combine like terms
18x + 24
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.
Answer:
A, C, and D
Step-by-step explanation:
PLEASE HELP WILL MAKE BRAIN IF YOU HELP!
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
Find the area of the shaded region. Round your answer to the nearest tenth.
You need to include the Image
qué número entero está entre -2 y 5
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).
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
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
Evaluate 32. (4 + 2) - 1 + (2.3)
A
15
В
23
C
54
D
57
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.
Lamborghini rental company charges a rate to rent a Lamborghini of $85 plus an additional fee of five dollars per mile you drive a car wouldn’t ultimate ticket or geometric sequence best model the situation what explicit formula models the situation how much would you have to pay if you drive 150 miles
Answer:
835$
Step-by-step explanation:
5$ for each extra mile
5 x 150 = 750
750 + 85 = 835
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?
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
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?
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
xy + 4y - 2x - 8 thanks
Answer:
(x+4)(y-2)
Step-by-step explanation:
Hope this helped!!!!
Answer:
xy + 4y
Step-by-step explanation:
good luck!!!! hope this helps
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
Answer:
she spent like 40% of her time easy
Step-by-step explanation:
that was like 3rd grade
Find the volume of the cuboid, length= 7mm, b= 5mm, h= 6mm
.. Please anwser fast..
Answer:
Volume = lbh
Volume = 7 × 5 × 6
Volume = 7 × 30
Volume = 210 mm³
Therefore
Volume is 210 mm³
[tex] \\ [/tex]
[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
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
The scatter plot shows how much puppy weighs within a certain time period. about how much did the puppy gain during this time period?
Express 130 and 325 as the sum of two squares in two different ways.
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.
85°
152
Find the value of the missing angle
Answer:
67°........................
Answer:
x=67
Step-by-step explanation:
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
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.