Proof that the formula Fn = Fn-1 + Fn-2 works
Fibonacci python

Answers

Answer 1
Umm— fn-1+Fn-2?? Fibonacci python
Answer 2
= f6 .

IV. The sum of the first n Fibonacci numbers with even indices is

f2 + f4 + ... + f2n = f2n+1 - 1.

Proof:

From II,

f1 + f2 + f3 + ... + f2n = f2n+2 - 1.

When we subtract the result from III, we get the desired result.

Example:

f2 + f4 + f6 + f8 + f10 + f12 = 1 +3 + 8 + 21 +55 +144

= 232

= f13 - 1 .

V. The sum of all (fn+1)/ (fn )

converges to the Golden Ratio.

3/1 + 5/3 + 8/5 + 13/8 .... converges to ) / 2.

Proof that Rn converges to the Golden Ratio:

Let R = lim Rn as n approaches infinity

= lim f n+1 / f n as n approaches infinity

= lim fn + fn-1 /fn as n approaches infinity

= lim (1 + fn-1/ fn) as n approaches infinity

= 1 + lim (fn-1 /fn ) as n approaches infinity

= 1 + 1/ lim (fn-1 /fn ) as n approaches infinity

= 1 + 1/R

So, R = 1 + 1/R,

or R^2 = R + 1,

R^2 - R - 1 = 0,

R = ( ) / 2

= ( ) / 2

Since Rn is positive, Rn = ( ) / 2 .

Thus, Rn converges to the Golden Ratio.

Related Questions

Which of the following is a step in simplifying the expression x multiplied by y to the power of 2 over x to the power of negative 3 multiplied by y to the power of 3, the whole to the power of negative 4.? (5 points)

x to the power of negative 4 multiplied by y to the power of negative 2, the whole over x to the power of negative 7 multiplied by y to the power of negative 1.
x to the power of negative 4 multiplied by y to the power of negative 8, the whole over x to the power of 12 multiplied by y to the power of negative 12.
x to the power of negative 4 multiplied by y to the power of negative 8, the whole over x to the power of negative 3 multiplied by y to the power of 3.
x to the power of negative 4 multiplied by y to the power of negative 2, the whole over x to the power of negative 3 multiplied by y to the power of 3.

Answers

Answer:

x to the power of negative 4 multiplied by y to the power of negative 8, the whole over x to the power of negative 3 multiplied by y to the power of 3

Step-by-step explanation:

B because when you multiply 4 times 2 8

How would you do this?

Answers

it would be 6.0x4 because the square is 6.0 on each side
The answer is 6.0 x 4

negative3.5 degree F, 5 degree F, 1.5 degree F, negative 0.5 degree F, negative 2 degree F, 2.5 degree F, negative 4 degree F. Part 1: Weather Analysis Plot and label the temperatures on a number line. You can create the number line by using a drawing program, by drawing it by hand and sending in a picture, or by describing in detail how the completed number line should look.

Answers

A thermometer can help us determine how cold or hot a substance is. Temperature is in most of the world measured and reported in degrees Celsius (°C). In the U.S. it is common to report temperature in degrees Fahrenheit (°F). In the Celsius and Fahrenheit scales the temperatures where ice melts (water freezes) and water boils are used as reference points.

Rewrite 24.5 as a mixed number in lowest terms.



Rewrite 0.85 as a fraction in lowest terms.

Answers

Answer:

49/2, 17/20

Step-by-step explanation:

24.5=245/10=245÷5/10÷5=49/2

0.85=85/100=85÷5/100÷5=17/20

Answer:

Mixed numbers

a)  24  1/2  

b) 85/100 = 17/20

Step-by-step explanation:

a) as they asked mixed number we only have to create a fraction for the decimal 0.5 = 1/2 and rewrite 24 1/2 = 24.5

If the question asked for lowest terms 24/5 then 24.5% = 245/1000 = 49/200

b) rewrite 0.85 as a fraction in lowest terms

0.85 = 85% = 85/100 = 17/20

simplify

(x^a.x^b)^a-b*(x^b.x^c)^b-c*(x^c.x^a)^c-a

step by step..

Answers

Answer:

= x(a+b)(a-b) . x(b+c)(b-c) .x(c+a)(c-a)

Answer:

x(a+b)(a-b) . x(b+c)(b-c) .x(c+a)(c-a)

Hope it helped!

In which line is an error first made when solving the equation below? -18 = 19z -9
Line One = z -9
Line Two = 11 = z
Line Three = z = 11
* Choose one of the following, A, B, C, D.*
A) no mistake was made
B) line 3
C) line 2
D) line 1

Answers

It’s line 3. Hope that helps :)

lets evaluate 81^-3/4.

Answers

Answer:

1/ 27

Step-by-step explanation:

[tex] = 81^{ \frac{-3}{4} } [/tex]

[tex] = (\frac{1}{81}) ^{ \frac{3}{4} } [/tex]

[tex] = (\frac{1}{3}) ^3 [/tex]

[tex] = \frac{1}{27} [/tex]

1/27 because that the answer

15 POINTS!!!
Identify the initial value and rate of change for the graph shown

A coordinate plane graph is shown. A line passes through the y-intercept at 1 and through the point 5 comma 4.

Initial value: 1, rate of change 3 over 5.
Initial value: 3 over 5., rate of change: 0
Initial value: 1, rate of change 5 over 3.
Initial value: 5 over 3., rate of change: 0

Answers

Answer:

Step-by-step explanation:

y=mx+b

y-intercept= 1

b=1

point (5,4)

x=5

y=4

y=mx+b

4=m(5)+1

5m=3

m=3/5

rate of change = 3/5

The blue shape is a dilation of the black shape. What is the scale factor of the dilation? Simplify your answer and write it as a fraction or whole number.

Answers

Answer:

3 or 3/1 (the 1 is the denominator)

Step-by-step explanation:

the shape got 3 times bigger. let me know

I believe this would be 3/1. The size was multiplied 3xs thus in factor form is 3/1

PLEASE HELP THIS QUESTION IS SO ANNOYING!!

Answers

ANSWER- 23 , 76


Explanation- just did it :)
THE ANSWER IS 23,76 !!!

Identify the initial value and rate of change for the graph shown

A coordinate plane graph is shown. A line passes through the y-intercept at 1 and through the point 5 comma 4.

Initial value: 1, rate of change 3 over 5.
Initial value: 3 over 5., rate of change: 0
Initial value: 1, rate of change 5 over 3.
Initial value: 5 over 3., rate of change: 0

Answers

initial value: 1. rate of change: 3 over 5.
Initial value:1,rate of change 3 over 5

does this make sence to anyone

Answers

What the dude above you said
The answer would be 490 one because the surface area is just the area of the whole figure so you’d find the area of each figure and add them all up

Evaluate 4 - x, when x = -6

Answers

Answer:

10

Step-by-step explanation:

4--6

4+6=10

Answer

10

step-by-step

4–6

4+6

can anyone help me I'm confused?

Answers

Answer: 10 inches

Step-by-step explanation:

If the two triangles are similar, that means their sides are proportional to each other.

JK = 15JL = 15 + 6 = 21JM = 14

The proportion would look like this:

[tex]\frac{JK}{JL} =\frac{JN}{JM}\\[/tex]

Substitute in the values:

[tex]\frac{15}{21} =\frac{JN}{14}[/tex]

Cross-multiply and solve for JN:

[tex]21*JN=15*14\\JN=\frac{15*14}{21} =\frac{210}{21} =10[/tex]

Answer:

10 inches

Step-by-step explanation:

JM=14<JL=21

And you know that JN=X<JK=15

You also know that JM=14>JN=x

KL=6 so NM=4

JM= (14) - NM (4)= 10

Hope this makes sense, and can help!

Leon used the number line below to show -5 + 4. explain what is wrong with his model.

Answers

Well since he used -5, then it should be +5.
Step by step:
Hope that help a little I guess.

Help me please! It’s due in like 10 minutes and I’m barely on the 8th question !!!

Answers

Answer:A

Step-by-step explanation:campbella helped

Answer:

A

Step-by-step explanation:

6(5-3x) -5(3x+2)

multiply each expression by the number outside the bracket

6×5=30,6×-3x=-18x -5×3x=-15x,-5×+2=-10

30-18x-15x-10

group the like terms

30-10-18x-15x

20-33x

A) what is the simplified product of seven-fourths divided by eight-fifths as an improper fraction

B) what is this number as a mixed number

Answers

Answer:

A) 

First were going to put our numbers in perspective.

[tex]\frac{7}{4}[/tex] ÷ [tex]\frac{8}{5}[/tex]

But to find the improper fraction, we have to cross multiply these numbers.

[tex]\frac{7}{4}[/tex] × [tex]\frac{8}{5}[/tex]

7 x 5 = 35.  

4 x 8 = 32.

Now we have our improper fraction is  [tex]\frac{35}{32}[/tex]

B)  

To turn our improper fraction into a mixed number, we will use division.

We know that the 32 can only go into 35 one time.  We also know that the bottom number always stays the same.  So our equation will look somewhat like this.

[tex]1\frac{?}{32}[/tex]

Now to fine the top number we will have to subtract 35 from 32 because we already know that 32 can go into 35 one time, so 35 - 32 = 3.  So are mixed number will look like this.

[tex]1\frac{3}{32}[/tex]

This is our answer!

Answer:

7/4 ÷ 8/5

A. First, we need to do the reciprocal of 8/5.

7/4 x 5/8 = 35/32

B. Now, we need to convert it into a mixed number. Divide 35 by 32. 32 goes into 35 one time. 35 - 32 = 3, so remainder 3. We use 1 as the whole number since 32 goes into 35 one time. We use the remainder 3 as the numerator, and 32 as the denominator.

1 3/32

Hope this helps u have a great day :)

find the value of a and be when x is 12 a= 5x^2/2 b= 2x^2(x-5)/10x

Answers

Answer:

a=360

b=168

Step-by-step explanation:

a=5×12×12/2=5×12×6=360

b=2×12×12×(12-5)/10×12=2×12×7=14×12=164

answer a is 360 and answer b is 180 :)

Marly gets 5 gems every 5 minutes. If Marely has 180 gems, how many minutes have passed?

Answers

Find out how many gems Marly can get in a minute.

5 gems = 5 minutes

1 gems = 5 divided by 5 = 1 minute

180 gems = 1 x 180 = 180 minutes

180 minutes have passed.



Answer:

180

Step-by-step explanation:

It is one gem per minute.

Which of the equations is graphed below?

Answers

Answer:

D

Step-by-step explanation:

Slope of -2 that's going through y=1

so y=-2x+1

d is the correct answer bc if you plug in 0 you get 1 which is a point on the graph

Which sequence of transformations will change figure PQRS to figure P′Q′R′S′? (5 points)

A coordinate grid is labeled from negative 5 to 0 to 5 on both x and y axes at increments of 1. Figure PQRS has P at ordered pair 1, 2, Q at 2,1, R at 3,2, S at 3,3.

Figure P prime Q prime R prime S prime has P prime at ordered pair 1,negative 2, Q prime at 2,negative 1, R prime at 3,negative 2 and S prime at 3,negative 3.
Counterclockwise rotation about the origin by 180 degrees followed by reflection about the x-axis
Counterclockwise rotation about the origin by 180 degrees followed by reflection about the y-axis
Counterclockwise rotation about the origin by 270 degrees followed by reflection about the x-axis
Counterclockwise rotation about the origin by 270 degrees followed by reflection about the y-axis

Answers

Answer:

Counterclockwise rotation about the origin by 180 degrees followed by reflection about the x-axis

Step-by-step explanation:

Please help! I’m confused.

Answers

Step-by-step explanation:

We need to use the formula :-

2 (l + b) × h ---> For Lateral surface area

2(30+30) h = 7200

2×60×h = 7200

120 × h = 7200

h = 7200/120

h = 60 cm

Now, volume = l×b×h

= 30×30×60

= 54000 cm³ is the required answer.

Hope it helps! :D

Answer:

54000cm³

Step-by-step explanation:

7200=4*30x,so x=60

In other words, the length of the vertical side is equal to 60cm

The volume inside the kite=60*30*30=54000cm³

(08.05)The box plot shows the number of years during which 24 colleges have participated in a local college fair:
Years of Participation
0
10
5
Years
At least how many schools have participated for 2 years or fewer?
2schools
4schools
6schools
7 schools

Answers

Where is the plot (Unnecessary Stuff)
The answer is 7 schools or d

find the first four terms and the tenth term
a) 3n^2

Answers

Step-by-step explanation:

3n^2

First term => n=1 => 3(1)^2 =>3

Second term => n=2 => 3(2)^2 =>3x4=12

Third term => n=3 => 3(3)^2 =>3x9=27

Fourth term => n=4 => 3(4)^2 =>3x16=48

Tenth term => n=10 => 3(1)^2 =>3x10=300

Answer:

{3, 12, 27, 48, 300}

Step-by-step explanation:

For the first four terms, n = {1, 2, 3, 4}.  For the tenth, n = {10}.

Then, applying the formula a(n) = 3n^2 to n = {1, 2, 3, 4, 10}, we get:

{3(1)², 3(2)², 3(3)², 3(4)², 3(10)²} = {3, 12, 27, 48, 300}

Help pls, can you solve for x?

Answers

Answer:

X=1.5, but I may be incorrect, hope this helps!

Step-by-step explanation:

FACTS I KNOW:

X has to be less than 2 but greater than 1

Angle B and D are 90 degrees

The complete bottom side is equal to 10

All triangle angles add up to 180 degrees

All angles in rectangles and squares are 90 degrees

All rectangles have 2 sets of 2 of the same sides.

If you take a piece of the top right you could make a rectangle

It would take about .5 of the 2

Therefore X=1.5 approximately, but I may be wrong.


X=1.5 this is not correct dont mind me pls

50 points !! Select the correct answer.
Which table represents the increasing linear function with the greatest unit rate?
A.
x y
2 16
5 10
B.
x y
2 14
6 12
C.
x y
2 -24
5 -15
D.
x y
2 -12
6 -16
E.
x y
2 -19
6 -17

Answers

Answer:

C.

x y

2 -24

5 -15

Step-by-step explanation:

We need to find the slope for each table

A.

x y

2 16

5 10

m = (y2-y1)/(x2-x1) = (10-16)/(5-2) = -6/3 = -2

B.

x y

2 14

6 12

m = (y2-y1)/(x2-x1) = (12-14)/(6-2) = -2/4 = -1/2

C.

x y

2 -24

5 -15

m = (y2-y1)/(x2-x1) = (-15--24)/(5-2) = (-15+24)/3 = 3

D.

x y

2 -12

6 -16

m = (y2-y1)/(x2-x1) = (-12--16)/(6-2) = (-12+16)/4 = 1

E.

x y

2 -19

6 -17

m = (y2-y1)/(x2-x1) = (-17--19)/(6-2) = (-17+19)/4 = 1

The greatest unit rate is the largest slope

 

 

D is correct answer

Eight hundred tickets are sold for a play. Thirty-five percent of those tickets were sold in advance. Which equation can be used to find the number of tickets sold in advance? StartFraction 800 divided by 8 Over 35 divided by 8 EndFraction = StartFraction 100 Over 4.375 EndFraction StartFraction 100 divided by 8 Over 800 divided by 8 EndFraction = StartFraction 12.5 Over 100 EndFraction StartFraction 35 times 8 Over 800 times 8 EndFraction = StartFraction 280 Over 6400 EndFraction StartFraction 35 times 8 Over 100 times 8 EndFraction = StartFraction 280 Over 800 EndFraction

Answers

Answer:

0.35(800)=x

x=number of tickets sold in advance

Step-by-step explanation:

Answer:

Divide 35÷100 which equals 0.35 then multiply 0.35×800 which equals 280 so the answer is 280 so the equation is 0.35×800=280.

Step-by-step explanation:

Pls help
Spam answers will be reported
Give a good explanation

Answers

Answer:

X = 20

The picture explains my answer

Answer:

The answer is X = 20

Can someone solve this please.

Answers

Answer:

find fist the lcm and gcf for each data

i jus needed some points really quickly

From an 18-pound cut of meat, Mr. Rand cuts off steaks weighting 1 pound 15 ounces, 3 1/8 pounds, and 4 1/2 pounds. He divides up the rest into 9-ounces patties and sells them at 3 for $3.12. How much money does he receive for the patties?

Answers

Answer is in the picture

The amount of money received by him will be $15.60.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division

The amount will be calculated as follows:-

The cut off amount = 18 - ( 1(15/16) -3(1/8)-4(1/2) = 8(7/16)

Now 16 ounces make a pound so divide by 16 we get:-

(135/16) ÷ ( 9 / 16 ) = ( 135/16 ) x ( 16 / 9 ) = 15

Dividing 15 by 3 we get 5 packs of 3 patties for $3.12

So amount = 3.12 x 5 = $15.60

Therefore the amount of money received by him will be $15.60.

To know more about Expression follow

https://brainly.com/question/723406

#SPJ2

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