Answers
Step-by-step explanation:
(a) Fₙ₋₁ > 0, so Fₙ₊₁ > Fₙ. Each term is bigger than the one before it, so the function is increasing, meaning the series will diverge to infinity.
(b) Fₙ₊₁ / Fₙ = (Fₙ + Fₙ₋₁) / Fₙ
Divide.
Fₙ₊₁ / Fₙ = 1 + (Fₙ₋₁ / Fₙ)
Rewrite the second fraction using negative exponent.
Fₙ₊₁ / Fₙ = 1 + (Fₙ / Fₙ₋₁)⁻¹
Take the limit of both sides as n approaches infinity.
lim(n→∞) Fₙ₊₁ / Fₙ = 1 + lim(n→∞) (Fₙ / Fₙ₋₁)⁻¹
Substitute with φ.
φ = 1 + φ⁻¹
Solve.
φ² = φ + 1
φ² − φ − 1 = 0
φ = [ -(-1) ± √((-1)² − 4(1)(-1)) ] / 2(1)
φ = (1 ± √5) / 2
Since the ratio can't be negative:
φ = (1 + √5) / 2
Related Questions
George desposit is as follows: Checks: $63.21, $37.79, and $15.50; cash: 24 one-dollar bills, 11 ten-dollar bills, 20 quarters, 22 dimes, and 40 pennies; less $20.00 as chas recevied. What is his total deposit?
Answers
Answer:
$258.10
Step-by-step explanation:
A school dance sold 2 types of tickets: one for freshman/sophomores (9th/10th graders), and one for juniors/seniors (11th/12th graders). The freshman/sophomore tickets cost $8, and the junior/senior tickets cost $6. They sold a combined total of 525 tickets, and earned a total of $4600. How many tickets of each type did the school sell? Write and show all algebra work; you cannot use graphing to solve this.
Answers
9514 1404 393
Answer:
freshman/sophomore: 725junior/senior: -200Step-by-step explanation:
It is convenient to let a variable represent the number of the highest-price tickets sold. We'll use x for that. Then the number of lower-price tickets sold is 525 -x and the total revenue is ...
8x +6(525 -x) = 4600
2x = 1450 . . . . . . . . . . . . subtract 3150
x = 725
525 -x = -200
__
The school sold 725 freshman/sophomore tickets and -200 junior/senior tickets.
_____
Comment on the question
There is apparently an error in the question somewhere. The average revenue per ticket is ...
$4600/525 ≈ $8.76
You cannot sell $6 and $8 tickets and earn more than $8 per ticket sold. (Average revenue must be between $6 and $8 per ticket.)
__
If we assume a typo in revenue, and that it should be $3600, then the sales will be 225 freshman tickets and 300 senior tickets.
determine which operation is needed in the blank so that the expression simplifies to 25.
40_10_4_(8_2_3)_5^2
Answers
Answer:
÷ - × ÷ - +
Step-by-step explanation:
40 ÷ 10 - 4 × (8 ÷ 2 - 3) + 5^2
Will give brainliest answer, so please help!!
Answers
Answer:
Step-by-step explanation:
10x+8+6x-3
10x+6X+8-3
16x+5
Answer:
16x+5
Step-by-step explanation: That’s the expression (answer)
Solve the system of linear equations by graphing y = -4x + 2 ; y = -x - 1
What is the solution?
Answers
Answer:
Step-by-step explanation:
Easiest way would be to substitute points into the given equations and plot your answers.
E.g. if you substitute points into your first equation you get:
If x = 0, y = -4(0) +2 = 2
If x = 1, y = -4(1) +2 = -2
If x = -1, y = -4(-1) +2 = 6
Etc.
Second equation:
If x = 0, y= -(0) -1 = -1
If x = 1, y = -1 -1 = -2
If x = -1, y = -(-1) -1 = 0
Pretty much just plug in values for x into the equations to find y.
Once you have your points, draw a line :)
Where the two lines intercept would be the solution.
1.A cook has 2 3/4 pounds of ground beef.How many quarter-pound burgers can he make?
2.A child needs to take 1/6 tablespoons of medicine per day in 4 equal doses.How much medicine is in each dose?
3.How many 5/6 cup salt shakers can be filled from 24 cups of salt?
Answers
2- 1/24 is a dose
3- 20 salt shakers
plsss help me! I’m stuck :(
Answers
Answer:15 = 2 16 = -1.25
Step-by-step explanation:If you need any more help I'm usually available between 9 a.m - 3:50 pm
A bird goes from a higher location to a lower location at a
rate of 2 meters per second,
Which equation models the change in the bird's position at 30 seconde?
A. (-30)(-2) = -60
B. 30(-2) = -60
C. 30.2 = 60
D. 30(-2) = 60
Answers
Answer: It's B.
Step-by-step explanation: I took the test.
|2x+1| < 5
help please
Answers
Answer:
3
Step-by-step explanation:
Answer: x=2 and x=-3
Step-by-step explanation:
|2x+1|=5>|2x+1|=-5
2x+1=5 > 2x+1=-5
2x+1-1=5-1 > 2x+1-1=-5-1
2x=4 > 2x=-6
2x÷2=4÷2 > 2x÷2=-6÷2
x=2 > x=-3
A graph titled Calories in Strawberries. The x-axis shows the number of strawberries, numbered 1 to 9, and the y-axis shows the number of calories, numbered 3 to 27. A straight line with a positive slope begins at point (0, 0) and ends at point (6.8, 27). The graph shows the relationship between the number of strawberries eaten and the approximate number of calories consumed. Which statement is true? Each strawberry contains 4 calories. Each strawberry contains 3 calories. Twenty-four strawberries contain 6 calories. Four strawberries contain 15 calories
Answers
Answer:
the answer is edge 2020 A
Step-by-step explanation:
each strawberry contains four calories
gaming legend
Answer:
Its A
Step-by-step explanation:
got it right on Edge
Which of these is NOT an example of a property tax?
F) Tax paid on the value of a farm a person owns
G) Tax paid on the value of a piece of land a person owns
H) Tax paid on the value of a piece of furniture a person owns
J) Tax paid on the value of a home a person owns
Answers
Answer:
H i think
Step-by-step explanation:
Answer:
H
Step-by-step explanation:
HOPE THIS HELPS
if x=-3 is the only x-incercept of the graph of a quadratic equation which statement best describes the discrinant of the equation
Answers
Answer:
The discriminant must be zero.
Step-by-step explanation:
Quadratic Equation
The standard representation of a quadratic function is:
[tex]f(x)=ax^2+bx+c[/tex]
where a,b, and c are constants.
The zeros, roots, or x-intercepts can be found by solving the equation:
[tex]ax^2+bx+c=0[/tex]
We can use the quadratic formula to find the roots:
[tex]\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Note this formula gives us two different roots if the square root is non-zero.
The only way there can be only one x-intercept is because the square root is zero.
If the square root is zero, then
[tex]b^2-4ac =0[/tex]
The expression is called the discriminant.
Thus, if x=-3 is the only x-intercept of the graph of a quadratic function, then the discriminant must be zero.
Each student in the fifth grade at Bonchon elementary bought 15 to the book fair they bought 1245 altogether how many fifth grade students go to Boston elementary
Answers
Answer:
83 fifth grade students
Step-by-step explanation:
the total amount was 1,245
they each bought 15
equation is 1,245/15=?
answer is 83
Answer:
3 students went to the book fair
Step-by-step explanation
Doing inverse operations so you do 1245 divided by 15 and that would be your answer.
The diagram was constructed with straightedge and compass tools.
Select all segments that have the same length as segment AC.
Answers
Answer:
AB and AC
Step-by-step explanation:
Because they are the same length
Jane Little rents a car for $39.00 a week. She pays $15.00 per week for the insurance, and spends $17.50 weekly on gas. What will her cost be per month (four weeks)?
Answers
Answer: Her cost will be $286 per month.
Step-by-step explanation: $39.00 times 4 is $156. $15.00 times 4 is $60. And $17.50 times 4 is $70. Adding all that together is $286
Answer:
$286.00
Step-by-step explanation:
First, you add 39.00 + 15.00 + 17.00 because that is for one week and you get $71.50 Then, you multiply 71.50 x 4 because there are 4 weeks in a month and you get $286.00 Hope This Helps :)
solve for y in the equation -y+9=23
Answers
Answer:
y=-14
Step-by-step explanation:
-y+9=23
-y=14
y=-14
Solve for x.
16x^2- 9=0
Answers
Step-by-step explanation:
Hey there!
Given;
[tex]16 {x}^{2} - 9 = 0[/tex]
[tex]16 {x}^{2} = 9[/tex]
[tex] {x}^{2} = ± \frac{9}{16} [/tex]
[tex]x = ± \sqrt{ \frac{9}{16} } [/tex]
[tex]x =± \sqrt{ \frac{ {3}^{2} }{ {4}^{2} } } [/tex]
[tex]x = ± \frac{3}{4} [/tex]
Therefore, X= ±3/4.
Hope it helps..
t a certain vineyard it is found that each grape vine produces about 10 lb of grapes in a season when about 500 vines are planted per acre. For each additional vine that is planted, the production of each vine decreases by about 1 percent. So the number of pounds of grapes produced per acre is modeled by
A(n) = (500 + n)(10 − 0.01n)
where n is the number of additional vines planted. Find the number of vines that should be planted to maximize grape production.
Answers
Answer: Grape production is maximized for 150 vines planted
Step-by-step explanation:
Javier rounded to the nearest half to estimate the product of 3 2/5 and -3 7/8. How do the estimate and the actual product compare Word problem
Answers
Answer:
Step-by-step explanation:
I really need help with this ?
Answers
Answer:
H: 4 3/4
Step-by-step explanation:
You subtract Aaron's and Siri's ages together and you get 4 3/4
56.4 - 27.3
what is the anwser
Answers
Answer:
the answer is 29.1. hope this helped
Step-by-step explanation:
use a fkn calculator
A car company has three sales people, Anna, Mustapha and Joshua.
During March, Anna sold 21 cars, Mustapha sold 12 cars and Joshua sold 15 cars.
Write down and simplify the ratio of the number of cars they sold during March.
:
Anna : Mustapha : Joshua =
..........
Answers
Answer:
7:4:5
Step-by-step explanation:
21:12:15
7:4:5
Answer:
answer you have chosen in your answer booklet. ... Motor Vehicle's at 5% using the straight line method. Required: (a) ... Note 3: Selling and distribution expenses. K000.
Angie painted 1/20 of a fence in 1/2 an hour. How long will it take Angie to paint one fence
Answers
Answer: 30 minute
Step-by-step explanation:60 diviser par 2
Answer:24 hours
Step-by-step explanation: because 1/2 times 20 will give you 24
If you double 4 and if you double 1/2 then add 1, add 8 +1
Answers
Answer:
19?
Step-by-step explanation:
double of 4 is 8, double of 1/2 is 1 and adding them all together is 19
multiple and divide signed numbers
Answers
Answer:
the answer is 9
Step-by-step explanation:
can sommeone please answer this
Answers
Answer:
x= 8
z= 116 degrees
Step-by-step explanation:
the two given angle measures are vertical angles so they are equal to each other, the equation is: 12x-32 = 11x-24
simplify this to get: x= 8
plug the value of x into either of the given equations, I will use the first one: 12(8) - 32
this means that the angle of one of them is 64
and since z and 12x-32 make a straight angle (180 degrees)
you can subtract 64 from 180 to find z
this gives you 180-64 = 116
Perry is responsible for distributing soccer balls to the kids at soccer camp. During practice, Perry would like each group of 5 children to share two soccer balls. How many soccer balls does Perry need if 25 kids attend camp?
Answers
Q: Perry is responsible for distributing soccer balls to the kids at soccer camp. During practice, Perry would like each group of 5 children to share two soccer balls. How many soccer balls does Perry need if 25 kids attend camp?
A: 20 soccer balls
Hope this helped!
List the integers from greatest to least.
{-23, -17, -4, -3, -15, -18, -26}
Answers
-26,-23,-18,-17,-15,-4, and -3 I’m pretty sure
Answer:
-3, -4, -15, -17, -18, -23, -26
Explanation:
The umbers away from zero are least and the numbers closer to zero are greater
Which Property of Addition does 9 + 0 = 9 illustrate ? A. Distributive Property B. Identity Property C. Zero Property D. Commutative Property
Answers
Answer:
B. Identity Property
Ms. Ramirez is throwing a fundraising event to
raise money for new chromebooks for GWCP.
Ms. Ramirez is charging $35 an an entrance fee
and then additionally guest can buy raffle tickets
for prizes. Ms. Colsant comes to the event,
purchases 4 raffle tickets and spends a total of
$62. How much is Ms. Ramirez charging for raffle
tickets at the event?
Students, write your response!
Pear Deck interest