Answer:
The first thing you want to d is find out how many centimeters are in 1 foot, because if a flat bar cost 2 pesos per centimeter, and they want 1 foot, then you will multiply how many centimeters in 1 foot, by how much each centimeter cost: 2 pesos:
There are exactly 30.48 centimeters in 1 foot, so you will multiply that by 2:
2 * 30.48 = 60.96
It will cost 60.96, or rounded up to 61 pesos for a 1 foot flat bar.
Step-by-step explanation:
Hope it helps! =D
If f(x)=3x^2+1 and g(x)=1-x, what is the value of (f-g)(2)?
Answer:
14
Step-by-step explanation:
To find the value of (f-g)(2), we first need to compute the function (f-g), which is defined as the difference between f(x) and g(x), and then evaluate it at x=2.
So, (f-g)(x) = f(x) - g(x)
Substituting the given functions, we get:
(f-g)(x) = (3x^2 + 1) - (1-x)
(f-g)(x) = 3x^2 + x
Now, to find (f-g)(2), we substitute x=2 into the expression we just obtained:
(f-g)(2) = 3(2)^2 + 2
(f-g)(2) = 3(4) + 2
(f-g)(2) = 12 + 2
(f-g)(2) = 14
Therefore, the value of (f-g)(2) is [14.]
What ordered pair is asolution to y=x+5 and x-5y=-9
Therefore , the solution of the given problem of ordered pair comes out to be system of equations is the ordered pair (-4, 1).
What are ordered pairs exactly?Two independent variables that are grouped in a fashion that suggests a particular order are known as "ordered pairs." The 1 and 2 parts each indicate one of an order pair's y-coordinates. The ordered pair is shown in close parenthesis in the example that follows.
Here,
We can solve this system of equations by substitution or elimination.
Here's how to do it using the substitution method:
From the first equation, we know that y = x + 5. We can substitute this expression for y in the second equation to get:
$x - 5y = -9
$x - 5(x + 5) = -9
$x - 5x - 25 = -9
Simplifying the equation, we get:
$-4x = 16$
$x = -4$
Now that we know the value of x, we can substitute it back into the first equation to find y:
y = x + 5 = -4 + 5 = 1$
Therefore, the solution to the system of equations is the ordered pair (-4, 1).
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MY BROTHER NEEDS HELP FAST OR HE'S GONNA FAIL!!
what is 4,007 + 981 = ???
Show your work
Answer: The correct answer is 4988.
Step-by-step explanation: 4007+981 = 4988 Add the one to the eight then add the 8 to the tens place and add the 9 to the hundreds place.
THIS IS THE CORRECT ANSWER.
A nurse can visit 5 patients each hour. If he has 37 patients to visit in a day, which of the following lengths of time worked will allow him to visit all of his patients.
If a nurse can visit 5 patients each hour. If he has 37 patients to visit in a day. the nurse can visit all of his patients if he works for at least 8 hours in a day.
How to find the number of hours?Let's start by figuring out how many hours the nurse would need to visit all 37 patients, assuming he could work for a continuous period of time without taking a break:
37 patients ÷ 5 patients/hour = 7.4 hours
However, since the nurse cannot work a fraction of an hour, we need to round up to the nearest hour. Therefore, the nurse would need to work for 8 hours in order to visit all 37 patients.
So, the nurse can visit all of his patients if he works for at least 8 hours in a day.
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18. If the points A and B are 16 m apart and points A and Care 22 m apart, find the distance between B and C
After doing some thinking, I believe it's 6 m.
The equation for the photo I just uploaded I need help please
Maura will have 5, 206 points at either hotel by booking 301 nights.
How to find the number of points ?To find the number of points, we shall assume that nights are denoted as n. The number of points for Hotel Elegance will be shown as :
= Signing up points + ( Number of points per night x Number of nights)
= 89 + 17 n
The number of points for Hotel Paradiso is:
= 691 + 15 n
The number of nights that Maura needs to stay for the points to be the same is :
89 + 17 n = 691 + 15 n
17 n - 15 n = 691 - 89
2 n = 602
n = 602 / 2
n = 301 nights
The number of points would be :
= 691 + 15 n
= 691 + 15 x 301
= 5, 206 points
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Como resuelvo esto
X/5=2
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{x}{5} = 2}[/tex]
[tex]\large\textbf{Multiply 5 to both sides:}[/tex]
[tex]\mathsf{\dfrac{x}{5} \times 5= 2\times 5}[/tex]
[tex]\large\textbf{Simplify it:}[/tex]
[tex]\mathsf{x = 2\times 5}[/tex]
[tex]\mathsf{x = 10}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x = 10}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day\bf !}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
What is 1/2 divided by 1/10
Answer: 2
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
[tex]\frac{1}{2} *\frac{10}{1} = \frac{10}{2} = 5[/tex]
An engine supplies 110 hp to an electric generator, and the generator delivers 90 hp of electrical power. What is the
efficiency of the generator?
(Type a whole number or decimal rounded to two decimal places as needed)
Answer:
the efficiency of the generator is 81.82%.
Step-by-step explanation:
The efficiency of a generator is defined as the ratio of the electrical power output to the mechanical power input. In this problem, the electrical power output is given as 90 hp, and the mechanical power input is the power supplied by the engine, which is 110 hp. Therefore, the efficiency of the generator can be calculated as follows:
Efficiency = Electrical power output / Mechanical power input
Efficiency = 90 hp / 110 hp
Simplifying the fraction, we get:
Efficiency = 0.8182
To convert this decimal to a percentage, we multiply by 100:
Efficiency = 0.8182 * 100
Rounding to two decimal places, we get:
Efficiency = 81.82%
Therefore, the efficiency of the generator is 81.82%.
Which event is most likely to occur?
O Rolling a multiple of 4 on a eight-sided die, numbered from 1 to 8.
Spinning a spinner divided into four equal-sized sections colored
red/green/yellow/blue and landing on pink.
Winning a raffle that sold a total of 100 tickets, if you buy 53 tickets.
Reaching into a bag full of 50 strawberry chews and 10 cherry chews without
looking and pulling out a strawberry chew.
The event with the highest probability is "reaching into a bag full of 50 strawberry chews and 10 cherry chews without looking and pulling out a strawberry chew", with a probability of 5/6 or approximately 0.83. Option D
How to find the Which event is most likely to occurTo determine which event is most likely to occur, we need to compare the probabilities of each event happening.
Rolling a multiple of 4 on an eight-sided die:
There are 8 possible outcomes when rolling an eight-sided die, and 2 of them are multiples of 4 (4 and 8). So, the probability of rolling a multiple of 4 is 2/8, or 1/4.
Spinning a spinner and landing on pink:
There are 4 possible outcomes when spinning the spinner, and only one of them is pink. So, the probability of landing on pink is 1/4.
Winning a raffle that sold a total of 100 tickets, if you buy 53 tickets:
The total number of possible outcomes is the total number of tickets sold, which is 100. The number of favorable outcomes is the number of tickets the person bought, which is 53. So, the probability of winning the raffle is 53/100.
Reaching into a bag full of 50 strawberry chews and 10 cherry chews without looking and pulling out a strawberry chew:
The total number of possible outcomes is the total number of candies in the bag, which is 50 + 10 = 60.
The number of favorable outcomes is the number of strawberry chews in the bag, which is 50. So, the probability of pulling out a strawberry chew is 50/60, which simplifies to 5/6.
Comparing the probabilities, we can see that the event with the highest probability is "reaching into a bag full of 50 strawberry chews and 10 cherry chews without looking and pulling out a strawberry chew", with a probability of 5/6 or approximately 0.83. Therefore, this event is the most likely to occur.
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Booth's fixed assets were used to only 50% of capacity during 2019, but its current assets were at their proper levels in relation to sales. All assets except fixed assets must increase at the same rate as sales, and fixed assets would also have to increase at the same rate if the current excess capacity did not exist. Booth's after-tax profit margin is forecasted to be 5% and its payout ratio to be 60%. What is Booth's additional funds needed (AFN) for the coming year
Booth's additional funds needed (AFN) for the coming year is $365.
What is additional funds?
Additional Funds Needed (AFN) is a way of calculating how much new funding will be required, so that the firm can realistically look at whether or not they will be able to generate the additional funding and therefore be able to achieve the higher sales level.
Use the following formula to calculate Booth's additional funds needed (AFN) -
AFN = (A*/S)ΔS - (L*/S)ΔS - MS1(RR)
where -
A* = Total assets excluding spontaneous liabilities
S = Sales
ΔS = Increase in sales
L* = Total spontaneous liabilities
MS1 = Net income (1 - RR), where RR is the retention ratio (1 - payout ratio)
Start by calculating A* and L*.
Since we are told that spontaneous liabilities increase at the same rate as sales, we can use the percentages provided to calculate the required increases in each account -
Accounts receivable: ΔAR = 0.5(S1 - S0) = 0.5(2000 - 1000) = 500
Inventories: ΔINV = 0.5(S1 - S0) = 0.5(2000 - 1000) = 500
Accounts payable: ΔAP = 0.5(S1 - S0) = 0.5(1000 - 500) = 250
Accruals: ΔACC = 0.5(S1 - S0) = 0.5(1000 - 500) = 250
A* = Total assets - spontaneous liabilities
= $1000 - ($200 + $50 + $250 + $50 + $250)
= $200
L* = Spontaneous liabilities
= $200 + $50 + $250 + $50
= $550
Next, calculate the increase in fixed assets that would be required if Booth operated at full capacity -
ΔFA = (FCR)(ΔS)
where FCR is the fixed assets capacity ratio, given by -
FCR = Actual sales / Full capacity sales
= $1000 / (2 x $1000)
= 0.5
ΔFA = (0.5)(1000)
= 500
Now calculate AFN using the formula -
AFN = (A*/S)ΔS - (L*/S)ΔS - MS1(RR)
= ($200 / $1000)(1000) - ($550 / $1000)(1000) - ($30)(0.5)
= $365
Therefore, the value is obtained as $365.
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The Booth Company's sales are forecasted to double from $1,000 in 2016 to $2,000 in 2017. Here is the December 31, 2016, balance sheet:
Cash $ 100 Accounts payable $ 50
Accounts receivable 200 Notes payable 150
Inventories 200 Accruals 50
Net fixed assets 500 Long-term debt 400
Common stock 100
Retained earnings 250
Total assets $1000 Total liabilities and equity $1000
Booth's fixed assets were used to only 50% of capacity during 2016, but its current assets were at their proper levels in relation to sales. Spontaneous liabilities and all assets except fixed assets must increase at the same rate as sales, and fixed assets would also have to increase at the same rate if the current excess capacity did not exist. Booth's after-tax profit margin is forecasted to be 3% and its payout ratio to be 50%. What is Booth's additional funds needed (AFN) for the coming year? Round your answer to the nearest dollar.
You work as a tailor. You are provided with 5(3/4) yards of cloth for making curtains. You use 4(1/4) yards of cloth for that purpose.
How many yards of cloth remain?
A 1 (1/4)
B 1(1/2)
C 1(3/4)
D 10
E 11
The answer is option B, 1(1/2) yards.
How to determine the total amount?
We apply the following total sales calculation to get the total sales amount.
Total sales = original price + original price * sales tax rate
To find out how many yards of cloth remain, we need to subtract the amount used for making curtains from the total amount provided:
Total amount of cloth provided = 5(3/4) yards
Amount of cloth used for curtains = 4(1/4) yards
Remaining amount of cloth = Total amount of cloth provided - Amount of cloth used for curtains
= 5(3/4) - 4(1/4) yards
= 5 yards + 0.75 yards - 4 yards - 0.25 yards
= 1(1/2) yards
Therefore, the answer is option B, 1(1/2) yards.
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Exercice 1:
Sur 100 étudiants, on considère les ensembles M de ceux qui étudient les mathématiques, E de ceux qui étudient
l'économie et G de ceux qui étudient la gestion. Sur ces 100 étudiants, 55 étudient les mathématiques, 9 les mathéma-
tiques et la gestion, 7 les mathématiques et l'économie, 8 l'économie et la gestion, 6 les mathématiques et la gestion
mais pas l'économie, 80 les mathématiques ou la gestion et 12 l'économie seulement.
(a) Combien d'étudiants suivent les trois matières ?
(b) Combien sont-ils a étudier les mathématiques ?
(c) Combien sont-ils a étudier la gestion?
(d) Combien sont-ils a étudier l'économie?
(e) Combien n'étudient aucune de ces trois matières ?
Answer:
(a) Pour trouver le nombre d'étudiants qui suivent les trois matières, on peut utiliser la formule suivante:
fill in blanks below chart
The solution is,
y = 2(x+1)^2+6
The vertex (−1,6)
Equation of axis of symmetry is x = -1
minimum at (-1,6)
y = -(x-1)^2/2 -4
The vertex (1,-4)
Equation of axis of symmetry is x = 1
maximum at (1,-4)
What is graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
here, we have,
y = 2(x+1)^2+6
The vertex (−1,6)
Equation of axis of symmetry is x = -1
minimum at (-1,6)
y = -(x-1)^2/2 -4
The vertex (1,-4)
Equation of axis of symmetry is x = 1
maximum at (1,-4)
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How do I solve the inequality 15<4+x
15 < 4 + x
15 - 4 < x
11 < x
Therefore, the solution to the inequality is x > 11.
use the multiplier method to decreae £56 by 14%
Answer:
New value =
56 - Percentage decrease =
56 - (14% × 56) =
56 - 14% × 56 =
(1 - 14%) × 56 =
(100% - 14%) × 56 =
86% × 56 =
86 ÷ 100 × 56 =
86 × 56 ÷ 100 =
4,816 ÷ 100 =
48.16
56 decreased by 14% = 48.16
Absolute change (actual difference):
48.16 - 56 = - 7.84
Mark me as a brainlist thankyou
What is the answer to this question?
8(x-3)+-4-4+x+1+-2(x+2)+6+7x+-8x=?
Answer:
X = -29/22
Step-by-step explanation:
I used PEMDAS to solve the question
60% of the students in Math 6 are currently mastering their math lessons. If 300 students are currently mastering their math lessons, how many students are in Math 6? A. Joey thinks that 180. Do you agree with Joey? Why or why not? B. What method do you think Joey used to arrive at his answer? Is it the right way to solve this? C. Show the work for how to set up and solve the problem correctly. You may either use a percent equation, set up a table, or use a model. Work: Final Answer:
Final answer is that there are 500 students in Math 6.
what is percentage ?
Percentage is a way of expressing a number as a fraction of 100. It is often denoted using the % symbol. For example, 50% means 50 out of 100, or 0.5 as a decimal.
According to question:
A. Joey's answer of 180 is not correct. If 300 students are currently mastering their math lessons and this represents 60% of the total number of students in Math 6, we can use the following equation to find the total number of students in Math 6:
60% of the total number of students = 300
0.6 × Total number of students = 300
Total number of students = 300 ÷ 0.6
Total number of students = 500
Therefore, there are 500 students in Math 6, not 180.
B. It is possible that Joey used a method called "guess and check" to arrive at his answer of 180. This method involves guessing a number, plugging it into an equation or problem, and checking to see if it is the correct answer. While this method can be useful in some cases, it is not a reliable method for solving this problem since there are an infinite number of numbers to guess from and the probability of guessing the correct answer is low.
C. To solve this problem correctly, we can use a percent equation. We know that 60% of the students in Math 6 are mastering their math lessons, so we can write:
0.60 × Total number of students = 300
To solve for the total number of students, we can divide both sides of the equation by 0.60:
Total number of students = 300 ÷ 0.60
Total number of students = 500
Therefore, the final answer is that there are 500 students in Math 6.
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Money should be rounded to 2 decimal places. Your salary is to be increased by 8%. Currently you’re paid $12.50 an hour. What will your pay be after the increase?
Using arithmetic operations it is obtained that after the increase, the pay will be $13.50 per hour.
What is arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
To calculate the increase in pay, start by multiplying the current hourly rate of $12.50 by the percentage increase of 8% -
Increase in pay = $12.50 x 8/100
Increase in pay = $12.50 x 0.08
Increase in pay = $1.00
So, the increase in pay is $1.00 per hour.
To find the new hourly rate after the increase, add the increase in pay to the current hourly rate -
New hourly rate = $12.50 + $1.00 = $13.50
Therefore, the increased, pay will be $13.50/hr.
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You are thinking of conducting a one-sample t test about a population mean
�
μ
using a 0.05 significance level. Which of the following statements is correct? (a) You should not carry out the test if the sample does not have a Normal distribution. (b) You can safely carry out the test if there are no outliers, regardless of the sample size. (c) You can carry out the test if a graph of the data shows no strong skewness, regardless of the sample size. (d) You can carry out the test only if the population standard deviation is known. (e) You can safely carry out the test if your sample size is at least 30.
Answer:
The correct statement is (B), You can safely carry out the test if your sample size is large and there are no outliers.
Step-by-step explanation:
Step 1: Given Information
A one-sample test about a population mean using a significance level.
Next, OR Step 2
To identify the correct statement:
(a) False, because if a distribution is moderately skewed, then you can still carry out the test if the sample size is large ( or more).
(b) True, because if the sample size is larger ( or more) and there are no outliers, then you can still safely carry out the test.
(c) False, the sample size should be large ( or more) since the distribution is moderately skewed.
(d) False, the one-sample test can only be used if the population standard deviation is unknown. You apply the onesample test if the population standard deviation is known.
(e) False, -procedures are not robust, because they are heavily influenced by outliers.
Thus the answer to your problem is, B.
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When testing for current in a cable with 10 color-coded wires, the author used a meter to test 2 wires at a time. How many different tests are required for every possible pairing of 2 wires?
what is combination ?
In mathematics, a combination is a way of selecting items from a collection, such that the order of selection does not matter. The combination formula gives the total number of ways to choose k items from a set of n distinct items without regard to the order in which they are chosen.
The combination formula is given by:
n choose k = n! / (k! * (n-k)!)
Explanation:
If we have 10 color-coded wires, we can choose 2 wires out of them in (10 choose 2) ways.
(10 choose 2) is a combination formula given by:
(10 choose 2) = 10! / (2! * (10-2)!)
= (10 * 9) / 2
= 45
This means that we need to perform 45 tests to cover all possible pairings of 2 wires from 10 color-coded wires.
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my son is having trouble with this problem he (6) can you tell him the answer 9+10
Answer:
19
Step-by-step explanation:
111111111
+
1111111111
count how many 1ns are there.
ans is 19
Find y.
A. 6√3
B. 3
C. 2√3/3
D. 3√3
Answer:
B 3
notice that beside the 30 degree there is also 90 degree. please see the attachment.
A study in a journal found that 8% of children younger than age 18 in a country have at least one food allergy. Among those with food allergies, about 38% had a history of severe reaction. (Enter your answers to four decimal places.) (a) If a child younger than 18 is randomly selected, what is the probability that he or she has at least one food allergy and has a history of severe reaction? (b) It was also reported that 31 % of those with an allergy are allergic to multiple foods. If a child younger than 18 is randomly selected, what is the probabilty that he or she is allergic to multiple foods?
0.0248 is the probabilty that he or she is allergic to multiple foods .
What is probability and its formula?
The probability serves as a gauge for the possibility that an event will occur. It quantifies the certainty of the event.
The probability equation is stated by the following notation: P(E) = Number of Favorable Outcomes/Number of Total Outcomes.
P(food allergy and history of severe reaction) = 0.08 x 0.38
= 0.0304
b) P(allergic to multiple foods) = 0.08 x 0.31
= 0.0248
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let X be a random variable with support {1,2,3,5,15,25,50}, each point of which has the same probability 1/7. Argue that c = 5 is the value that minimizes h(c) = E( | X - c | ). Compare c with the value of b that minimized g(b) = E[( X - b )^2]
To minimize h(c) = E( | X - c | ), we need to find the value of c that makes the difference between X and c as small as possible.
One way to do this is to find the median of the support set. The median is the middle value when the values are arranged in ascending order.
In this case, the median is 5, so c = 5 is the value that minimizes h(c).
To compare c with the value of b that minimized g(b) = E[( X - b )^2], we need to find the value of b that makes the difference between X and b as small as possible squared. One way to do this is to find the mean of the support set.
The mean is the sum of the values divided by the number of values. In this case, the mean is (1 + 2 + 3 + 5 + 15 + 25 + 50) / 7 = 14.57, so b = 14.57 is the value that minimizes g(b).
Comparing c and b, we can see that c = 5 is closer to the median of the support set, while b = 14.57 is closer to the mean of the support set. This is because the median is a measure of central tendency that is less affected by extreme values, while the mean is a measure of central tendency that is more affected by extreme values.
Therefore, c = 5 is the value that minimizes h(c) = E( | X - c | ), while b = 14.57 is the value that minimizes g(b) = E[( X - b )^2].
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find two possible values for the geometric mean of 16 and 36
Answer:
The geometric mean of 16 and 36 is 24
HOW Do this please help omg omg omg omg
it would take approximately 11 hours to complete the order if the number of working machines increased by a factor of 2.
Describe Algebraic Expression?An algebraic expression is a mathematical phrase that consists of variables, constants, and mathematical operations, but does not contain an equals sign. Algebraic expressions are used to represent mathematical relationships and are an important tool in algebra and other areas of mathematics.
Algebraic expressions can be simple, such as x + 2, which consists of a variable (x), a constant (2), and an addition operation. More complex algebraic expressions can contain multiple variables, constants, and operations, such as 2x² + 3xy - 4.
Variables in algebraic expressions represent unknown values that can vary or change, while constants are fixed values that do not change. Mathematical operations, such as addition, subtraction, multiplication, and division, are used to combine variables and constants in algebraic expressions.
We can use the following formula to solve the problem:
(number of machines) x (time to complete the order) = constant
Let's call the constant k. If six machines working simultaneously can complete the order in 22 hours, we have:
6 x 22 = k
k = 132
Now, let's double the number of machines to 12 and find the new time it would take to complete the order:
12 x t = 132
where t is the new time it would take to complete the order with 12 machines. Solving for t, we get:
t = 132/12
t ≈ 11
Therefore, it would take approximately 11 hours to complete the order if the number of working machines increased by a factor of 2.
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56% of the group did not agree with the proposal. If the group numbered 43, then how many did not agree with the proposal?
Rounding to the nearest whole number, we can conclude that 24 people did not agree with the proposal.
If the idea was rejected by 56% of the group, then 44% of the group, or 100%, agreed with the plan.
Let x be the proportion of the group who rejected the proposition. The percentage of the group that approved of the idea was then 44%, or 0.44 times the total number of group members.
The problem states that there are 43 individuals in the group as a whole. As a result, we may construct the equation shown below:
x + 0.44(43) = 43
When we find x and simplify, we get:
x = 43 - 0.44(43) (43)
x = 23.96
We can estimate that 24, or the nearest whole number, did not support the proposition.
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Can someone please help me with this ;(
The congruent angles in the similar figures are as follows:
∠M ≅ ∠R
∠N ≅ ∠S
∠P ≅ ∠T
∠Q ≅ ∠U
How to find the similar figures?Two figures are said to be similar if they are the same shape. Similar figures have the corresponding sides in proportion to each other.
Similar figures also have the corresponding angles equal to each other.
Therefore, the figures are similar by MNPQ ~ RSTU
Hence,
∠M ≅ ∠R
∠N ≅ ∠S
∠P ≅ ∠T
∠Q ≅ ∠U
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Show that the sequence defined by
a1= 1
an+1 = 3-(1/an)
is increasing and an<3 for all n. Deduce that{an} is convergent and find its limit
Using Monotone Convergence Theorem, {aₙ} is an increasing sequence that is bounded above by 3, and thus it is convergent
How is aₙ convergent and it's limitTo show that the sequence {aₙ} defined by a₁ = 1 and aₙ₊₁ = 3 - (1/aₙ) is increasing, we need to prove that aₙ < aₙ₊₁ for all n.
Let's first prove that aₙ < 3 for all n by induction:
Base case: For n = 1, a₁ = 1 < 3.
Inductive step: Assume aₙ < 3 for some arbitrary n. Then we have:
aₙ₊₁ = 3 - (1/aₙ) < 3 - (1/3) = 8/3
Since aₙ₊₁ is positive (because aₙ < 3), we can also write:
aₙ₊₁ = 3 - (1/aₙ) > 3 - 1 = 2
Therefore, we have:
2 < aₙ < 3 < aₙ₊₁
This shows that {aₙ} is an increasing sequence that is bounded above by 3, and thus it is convergent by the Monotone Convergence Theorem.
To find the limit of {aₙ}, we can take the limit of both sides of the recursive definition:
limₙ→∞ aₙ₊₁ = limₙ→∞ (3 - (1/aₙ))
Since {aₙ} is convergent, we can replace limₙ→∞ aₙ with a to get:
a = 3 - (1/a)
Multiplying both sides by a, we get:
a² = 3a - 1
This is a quadratic equation that can be solved using the quadratic formula:
a = (3 ± √(3² + 4))/2
a = (3 ± √13)/2
Since aₙ < 3 for all n, we have:
a = (3 - √13)/2
Therefore, the limit of {aₙ} is (3 - √13)/2.
Learn more on convergence of series here;
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