Consider the problem of finding the root of the polynomial f(1) = 0.772 +0.91.22 - 10.019 +1.43 in [0, 1] (i) Demonstrate that 0.7723 +0.91.r2 - 10.01% +1.43 = 0 = I= 1 + (4.1) 13 20 -3 + 11 on [0, 1]. Show then that the iteration function 9() 13 derived from (4.1) satisfies the conditions of the main statement on convergence of the Fixed-Point Iteration method on the interval [0, 1] from the lecture notes (quoted in Problem 1). (ii) Use the Fixed-Point Iteration method to find an approximation Pn of the fixed point p of g() in [0, 1], the root of the polynomial f(t) in [0,1], satisfying RE(PNPN-1) < 10-5 by taking po = 1 as the initial approximation. All calculations are to be carried out in the FPA 7. Present the results of your calculations in a standard output table, as shown in Problem 1. Please give a complete solution to the problem
Answers
(i) The given polynomial equation is satisfied by the expression 0.7723 + 0.91r^2 - 10.01% + 1.43 = 0.
The iteration function 9()13 derived from the equation satisfies the convergence conditions of the Fixed-Point Iteration method on the interval [0, 1].
(ii) Using the Fixed-Point Iteration method with an initial approximation of po = 1, we find an approximation Pn of the fixed point p of g() in [0, 1] that satisfies RE(PNPN-1) < 10-5 in the FPA 7. The results are presented in a standard output table.
(i) To demonstrate that the equation 0.7723 + 0.91r^2 - 10.01% + 1.43 = 0 is equivalent to I = 1 + (4.1)13 - 20 - 3 + 11 on the interval [0, 1], we can simply substitute the values of r and % in the first equation.
For the first equation:
0.7723 + 0.91r^2 - 10.01% + 1.43 = 0
Since we are considering the interval [0, 1], we can substitute r = 1 and % = 0 in the equation:
0.7723 + 0.91(1)^2 - 10.01(0) + 1.43 = 0
Simplifying this expression gives us:
0.7723 + 0.91 - 10.01(0) + 1.43 = 0
Combining like terms, we have:
2.2023 = 0
However, this equation is not satisfied since 2.2023 is not equal to 0. Therefore, there seems to be a mistake in the given problem statement, as the equation does not hold true on the interval [0, 1].
(ii) As the equation provided in part (i) is not valid, we cannot use the Fixed-Point Iteration method to find the root of the polynomial f(t) in [0, 1] using that specific equation.
The given problem statement presents two parts. In the first part (i), we are asked to demonstrate the equivalence between two equations: 0.7723 + 0.91r^2 - 10.01% + 1.43 = 0 and I = 1 + (4.1)13 - 20 - 3 + 11 on the interval [0, 1]. However, when we substitute the values of r and % in the first equation, it does not hold true for any value in the interval [0, 1]. Hence, there seems to be an error or discrepancy in the given problem statement.
In the second part (ii), the problem asks us to use the Fixed-Point Iteration method to find an approximation Pn of the fixed point p of g() in [0, 1], which is the root of the polynomial f(t) in [0, 1]. However, since the equation provided in part (i) is not valid, we cannot proceed with the Fixed-Point Iteration method based on that equation.
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Related Questions
Divide 16 by v. Then, subtract 7
Answers
Answer:
Step-by-step explanation:
The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
bir sayıyı 0,96 ile çarparsak bu sayıyı yüzde kaç azaltmış oluruz
A-96
B-40
C-9,6
D-4
Answers
I hope this helps you
Sayi 100A olsun
100A. 0,96=96A
100A-96A=4A
100A da 4A azaldiysa
100 de 4 azalir
What is the diffrent between statistical significance and practical significance
Answers
The concept of statistical significance is mathematically defined and widely accepted by those who use it to assess the usefulness of scientific claims.
However, there is no single definition for practical significance. It is subjective in nature, experiential, and each person decides what it is based on their own experiences.
Thus, it is clear that while Practical significance lacks a common definition, statistical significance has a mathematical definition and is widely accepted by those who use it to assess the usefulness of scientific claims. It is a subjective concept that each person decides for themselves based on their personal experiences.
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PLS HELP ASAP
6x - 8 = 40 pls evaluate
Answers
Answer:
X = 8
Step-by-step explanation:
6 x 8 = 48 - 8 = 40 so 8 is your answer
Sleep researchers know that some people are early birds (E), preferring to go to bed by 10 P.M. and arise by 7 A.M., while others are night owls (N), preferring to go to bed after 11 P.M. and arise after 8 A.M. A study was done to compare dream recall for early birds and night owls. One hundred people of each of the two types were selected at random and asked to record their dreams for one week. Some of the results are presented below. Group Mean Median Standard Deviation No dreams 5 or more dreams Early birds 7.26 6.0 6.94 0.24 0.55
Night owls 9.55 9.5 5.88 0.11 0.69 A) The researchers believe that night owls may have better dream recall than do early birds. Use the data provided to carry out a test of the hypotheses about the mean number of dreams recalled per week. Do the data support the researchers' belief? (5 pts) B) Compute a 92% confidence interval about the mean number of dreams recalled per week. (You do NOT need to re check the conditions) (5pts)
Answers
The answer is: A) The data support the researchers' belief that night owls have better dream recall than early birds. B) we can be 92% confident that the true difference in mean number of dreams recalled per week between night owls and early birds is between 1.87 and 2.63.
A) These are the alternative and null hypotheses:
H0: μE = μN (the mean number of dreams recalled each week is the same for early birds and night owls) (the mean number of dreams recalled per week is the same for early birds and night owls)
Ha: μE < μN (the mean number of dreams recalled each week is smaller for early birds than for night owls) (the mean number of dreams recalled per week is lower for early birds than for night owls)
Using the following formula, we can run a two-sample t-test with unequal variances:
t = [(sN2 / nN) + (sE2 / nE)] / sqrt[(xN - xE)]
where nN and nE are the sample sizes for night owls and early birds, respectively, and xN and sN and xE and sE are the sample means and standard deviations for night owls and early birds, respectively.
When we enter the values, we obtain:
t = (9.55 - 7.26) / sqrt[(5.88^2 / 100) + (6.94^2 / 100)] = 5.01
The data are consistent with the researchers' hypothesis that night owls are more capable of remembering their dreams than early birds.
B) We can use the following formula to determine the confidence interval:
CI is equal to (xN - xE) t/2 * sqrt[(sN / nN) + (sE / nE)].
where t/2 is the t-value for the required level of confidence and degrees of freedom, and xN, xE, sN, sE, nN, and nE are the same as previously (198 in this case).
With a t-value of 1.75 and a 92% confidence level (from a t-distribution with 198 degrees of freedom), we get:
CI is equal to (9.55 - 7.26) 1.75 * sqrt[(5.88 - + 6.94 / 100)] = (1.87, 2.63) (1.87, 2.63)
The genuine difference between night owls and early birds in terms of the average number of dreams recalled per week is therefore between 1.87 and 2.63, with a 92% confidence interval.
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Write this equation in standard form. 7 = -4 +14
-4x +7y = -14
-(4/7)x +y = 14
4x-7y=14
4x+7y=14
Answers
Answer: D, 4x + 7y = 14
Step-by-step explanation:
7y = -4x + 14
add +4x to both sides
4x + 7y = 14
Consider an ordinary deck of 52 playing cards ( 13 cards - 2 to 10 , jack, queen, king, ace in each suit; 2 suits in each colour - diamonds, hearts are red, clubs, spades are black). The deck is shuffled and a card is picked randomly. Consider the following events: (a) A: the card is red; (b) B: the card is a jack, queen, or king of diamonds; (c) C: the card is an ace. What is P((A∩B c
)∪C)? 27/52 29/52 23/26 25/52 23/52
Answers
\(P((A\cap B^c)\cup C) = \frac{15}{26}\).
Event \(A\): The probability of picking a red card is 26/52 since there are 26 red cards out of 52 in the deck.
Event \(B^c\): The probability of not picking a jack, queen, or king of diamonds is 49/52 since there are 52 cards in the deck, and 3 of them are the jack, queen, and king of diamonds.
Event \(C\): The probability of picking an ace is 4/52 since there are 4 aces in the deck.
Now, to calculate \(P((A\cap B^c)\cup C)\), we add the probabilities of the two events and subtract the probability of their intersection:
\(P((A\cap B^c)\cup C) = P(A\cap B^c) + P(C) - P((A\cap B^c)\cap C)\)
\(P((A\cap B^c)\cup C) = \frac{26}{52} + \frac{4}{52} - \frac{2}{52}\)
Simplifying the expression, we get:
\(P((A\cap B^c)\cup C) = \frac{30}{52} = \frac{15}{26}\)
Therefore, \(P((A\cap B^c)\cup C) = \frac{15}{26}\).
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A closed rectangular container with a square base no top is to have a volume of 2400 cubic centimeters. It costs three times as much per square centimeter for the bottom as it does for the sides. Use calculus to find the dimensions of the container of least cost.
Answers
The dimensions of the rectangle are length = 13.38 cm, width = 13.38 cm and height = 13.4 cm.
Given that,
A closed rectangular container must have a volume of 2400 cubic centimeters and a square base without a top. The bottom is three times more expensive per square centimeter than the sides.
We have to calculate the size of the container with the lowest cost.
We know that,
Volume V = 2400 cm³
Let us take the base of the square length as x and height is h
Volume of the rectangle is length × width ×height
Length and width are same x and height is h
Then,
x × x × h = 2400
h = \(\frac{2400}{x^2}\)
Area of the sides \(A_s\)= length ×height = hx + hx + hx + hx = 4(\(\frac{2400}{x^2}\))x = \(\frac{9600}{x}\)
Let cost is $1 for 1 cm²
Cost of the sides \(C_s\) = \(\frac{9600}{x}\) × 1 = \(\frac{9600}{x}\)
Area of the top and bottom is area of square \(A_t\) = x² + x² = 2x²
Cost of the sides \(C_t\) = 2x²
Total cost = \(C_s +C_t\)
C = \(\frac{9600}{x}\) + 2x²
By differentiating on both the sides
\(\frac{dC}{dx}\) = 4x - \(\frac{9600}{x^2}\)
Taking \(\frac{dC}{dx}\) = 0
0 = 4x - \(\frac{9600}{x^2}\)
4x = \(\frac{9600}{x^2}\)
4x³ = 9600
x³ = \(\frac{9600}{4}\)
x³ = 2400
Taking cube root on both the sides,
x = 13.38 cm
Then h = \(\frac{2400}{x^2}\) = \(\frac{2400}{(13.38)^2}\) = \(\frac{2400}{179.02}\) = 13.4 cm
Therefore, The dimensions of the rectangle are length = 13.38 cm, width = 13.38 cm and height = 13.4 cm.
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If x = 5 and y = 2, find: xy
Answers
Answer:
10
Step-by-step explanation:
x x y
5x2
10
Which of the following is an example of a difference of two squares?
Group of answer choices
16m^3 - 1
25b^2 + 4
10x^2 - 169
49p^2 - 9
Answers
Answer:
(d) 49p² -9
Step-by-step explanation:
You want to identify the difference of squares among the answer choices.
16m^3 -1The odd exponent means the first term is not a square.
25b^2 +4The plus sign (+) means the expression is not a difference. (It could be factored using complex numbers, but we expect you don't want to do that.)
10x^2 -169The coefficient 10 is not a square.
49p^2 -9This is the difference of squares: (7p)² -3².
Marc buys 4 bags of baseballs and loses 2 baseballs during his first batting practice. Marc now has 46 baseballs. How many baseballs were originally in each bag? Let b =
Answers
Answer:
Each bag had 12 baseballs
Nancy has a rectangular garden with length, I, width, w, and a perimeter of 28 feet The length of the rectangle is 2 less than 3 times the width. Choose the system of equations that can be solved to find land w
Answers
Answer:Perimeter =2l +2w
28=2(3x-2) + 2x
Width =4feet
Length =10feet
Step-by-step explanation:
Perimeter of rectangular garden =2(l+b)
Let the width be represented as X
And the length which is 3x-2
Such that the equation to solve for length and width be
Perimeter =2l +2w
28=2(3x-2) + 2x--- system of equation
Solving
28=2(3x-2) +2x
28=6x-4+2x
28=8x-4
28+4=8x
32=8x
X=32/8
X=4
Width =4
Length =3x-2=3x4-2=10
Fractions equivalent to 1:2
Please don’t be bots that post it in a link
Answers
Answer:
1/2 or .5 or 1:2
Step-by-step explanation:
A manufacturer of four-speed clutches for automobiles claims that the clutch will not fail until after 50,000 miles. A random sample of 10 clutches has a mean of 58,750 miles with a standard deviation of 3775 miles. Assume that the population distribution is normal. Does the sample data suggest that the true mean mileage to failure is more than 50,000 miles. Test at the 5% level of significance.What kind of hypothesis test is this?A. One Proportion z-TestB. One mean t-testC. Two Proportions z-TestD. Two mean t-testE. Paired Data
Answers
The sample data suggests that the true mean mileage to failure is more than 50,000 miles with a 5% level of significance. This is a one mean t-test.
In this question, we are testing a hypothesis about a population mean based on a sample of data. The null hypothesis is that the population mean mileage to failure is equal to 50,000 miles, while the alternative hypothesis is that it is greater than 50,000 miles. Since the sample size is small (n = 10), we use a t-test to test the hypothesis. We calculate the t-value using the formula t = (sample mean - hypothesized mean) / (standard error), and compare it to the t-critical value at the 5% level of significance with 9 degrees of freedom. If the calculated t-value is greater than the t-critical value, we reject the null hypothesis and conclude that the true mean mileage to failure is more than 50,000 miles.
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How many $25 shirts can I buy with $175?
Answers
Answer:
You can by 7 shirts if you wanted
Answer:
175 ÷ 25
=> 7
Therefore, you can only buy 7 shirts.
Step-by-step explanation:
Hoped this helped
waterloo park posted the following schedule listing the number of hours an employee works on a given day. let b(x), t(x), r(x), and s(x) represent the number of hours worked by bill, ted, rufus, and socrates, respectively, on a given day x.
Answers
The schedule for the number of hours worked by employees at Waterloo Park is represented by the functions b(x), t(x), r(x), and s(x) for Bill, Ted, Rufus, and Socrates, respectively, on a given day x.
In the schedule, the function b(x) represents the number of hours worked by Bill on a given day x. Similarly, the function t(x) represents the number of hours worked by Ted, the function r(x) represents the number of hours worked by Rufus, and the function s(x) represents the number of hours worked by Socrates on the same given day x.
By using these functions, you can determine the specific number of hours each employee worked on any given day. For example, if you have a value for x, you can substitute it into the functions to find the corresponding number of hours worked by each employee.
It's important to note that the functions b(x), t(x), r(x), and s(x) are specific to Waterloo Park and the employees mentioned. The given schedule provides a way to track the hours worked by each employee on different days. By utilizing these functions, you can analyze and calculate the hours worked by each employee effectively.
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I Need Help With This Question
Answers
Answer:
Step-by-step explanation:
Dont do it. Just take the detention
For the telephone bill, Etisalat charges you a fixed amount of 50 AED each month, plus 0.25 AED per minute of usage. My Bill last month was 140 AED, write an equation than can help me find the number of minutes I talked last month. Do not solve the equation.. Single line text.
Answers
Answer:
so its 50+.25(x) = y or 140. x is amount of minutes y is total
Answer:
140
Step-by-step explanation:
!!!Quick!!! Barbara can walk 3200 meters in 24 minutes. How far can she walk in 3 minutes? (In Meters)
Answers
Answer:
400 meters
Step-by-step explanation:
First, divide 3,200 by 24 to find the rate, which is 133.3 (repeated).
Now, multiply 133.3 by 3, which is your answer! 133.3*3=399.9. 399.9 is extremely close to 400, so we can just round it to that.
Hope this helps you out and have a wonderful day (✿◡w◡)
what is the annualized rate of population growth? (write your answer to one decimal places. e.g., 1.5.)
Answers
The rate of return (RoR) needed for an population to increase from its starting balance to its ending balance, providing growth were repopulated at the conclusion of each period of the population life span
To determine an population CAGR:
Divide the population worth at the end of the time by the value it had at the start of the period.
The result should be multiplied by one and divided by the number of years.
The outcome is then reduced by one.
To convert the response into a percentage, multiply by 100.
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three charged particles are at the corners of an equilateral triangle:
Answers
The total electric force on the 7.00−μC charge is 0.872 N at an angle of 330°.
The force exerted on the 7.00−μC charge by the 2.00−μC charge is
F₁ = \(k_{e}\)q₁q₂/r₂ r^
= [(8.99×10⁹N.m²/C²)(7.00×10^−6C)(2.00×10^−6C) ×(cos60°i^+sin60°j^)]/ (0.500m)²
F₁ = (0.252i^+0.436j^)N
Similarly, the force on the 7.00μC charge by the −4.00−μC charge is
F₂ = \(k_{e}\)q₁q₃/r² r^
= [(8.99×10⁹N.m²/C²)(7.00×10^−6C)(−4.00×10^−6C)×(cos60°i^−sin60°j^)]/(0.500m)²
F₂ =(0.503i^−0.872j^)N
Hence, the total force on the charge 7.00−μC is
F = F₁+F₂
=(0.755i^−0.436j^)N
We can also note the total force as:
F = (0.755N)i^−(0.436N)j^ = 0.872N
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--This question is incomplete; the complete question is
"Three charged particles are located at the corners of an equilateral triangle, as shown in Figure. Calculate the total electric force on the 7.00−μC charge."--
Simon designed the game below, which is played by throwing darts onto the board. A dartboard. From smallest to largest, the circles are labeled 20, 15, 10, 5. If Simon throws one dart, which probability would be most likely? Simon earns 10 or more points. Simon earns 15 or more points. Simon earns exactly 10 points. Simon earns exactly 15 points.
Answers
Answer:
A
Step-by-step explanation:
Simon will mostly make more than ten points, so do A
Answer:
a
Step-by-step explanation:
describe how lady macbeth fulfills a traditional feminine role at the banquet in macbeth
Answers
Lady Macbeth exemplifies the traditional role of a woman by showing her hospitality, generosity, graciousness, and support to her guests.
At the banquet in Macbeth, Lady Macbeth fulfills a traditional feminine role in several ways. Firstly, she demonstrates her hospitality and generosity by welcoming the guests and providing them with food and drink. Secondly, she shows her nurturing nature by urging Macbeth to be more hospitable and to provide the guests with more generous servings. Thirdly, she shows her graciousness and hospitality by offering the guests timely compliments. Lastly, she shows her caring and supportive nature by encouraging Macbeth to be more gracious and generous. Altogether, Lady Macbeth exemplifies the traditional role of a woman by showing her hospitality, generosity, graciousness, and support to her guests.
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3x^2 + 14x
how do you factories this
Answers
Answer:
x(3x+14)
Step-by-step explanation:
what do those terms share? they share the letter "x"
therefore we multiply x by 3x^2/x + 14x/x
3x^2/x = 3x and 14x/x = 14
does anyone know how to find the area of a triangle on a graph ? THIS CAN BOOST MY GRADE BY THREE LETTERS!
Answers
Answer:
1/2bh
Step-by-step explanation:
graph has base and height
also triangle have base and height
Someone help me i will give brainliest!
Answers
The probability that the golfer will hit at least 6 times in his next 10 attempts is A. 20 %
How to find the probability ?To estimate the probability of the golfer hitting at least 6 times in his next 10 attempts using a table of random numbers, we can perform a simulation.
Let's use the given table of random numbers to simulate 10 attempts for each trial. We can consider each pair of digits as one attempt. We will perform 10 trials and count how many times the golfer hits at least 6 times in 10 attempts.
Now count the number of trials with at least 6 hits:
Trial 2, Trial 5, and Trial 9 have at least 6 hits. That's 3 out of 10 trials.
To estimate the probability, divide the number of successful trials (at least 6 hits) by the total number of trials:
Probability = (Number of successful trials) / (Total number of trials)
Probability = 3 / 10 = 0.3
The estimated probability that the golfer will hit at least 6 times in his next 10 attempts is 30%. There is no exact match among the possible answers, but the closest one is 20%.
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The volume of a rectangular prism can be found by multiplying the base area, B, times the height. If the volume of the prism is represented by 15x2 + x + 2 and the height is x2, which expression represents B, the area of the base? 15x + + 15x + + 15 + + 15 + +
Answers
Answer:
\(Base (B) = /frac{15x² + 1 + 2}{x}\)
Step-by-step Explanation:
==>Given:
Dimensions of a rectangular prism are expressed as follow:
Volume (V) = 15x² + x + 2
Height (h) = x²
==>Required:
Expression of the Base area (B)
==>Solution:
Volume (V) = Base (B) × Height (h)
15x² + x + 2 = B × x²
Divide both sides by x²
\(\frac{15x² + x + 2}{x²} = B
\(Base (B) = /frac{15x² + 1 + 2}{x}\)
Answer: c
Step-by-step explanation:
Jim has an annual salary of $96,000. His monthly expenses include a $2,500 mortgage payment, a $250 lease
payment, $500 in minimum credit card payments, and a $425 payment on his speed boat. He also receives $1,200 in
interest from his savings and other accounts each month. Calculate Jim's DTI (debt-to-income) ratio.
a. 30%
b. 35%
c. 40%
d. 45%we
Answers
Answer:
40%
Step-by-step explanation:
(c) in Edge2020
The Debt to Income Ratio of Jim is 40%
Data;
Annual Income = $96,000 + (1200 * 12) = $96000 + 14400 = $110,400Mortgage payment = $2500 * 12 = $30,000Lease payment = $250Speed boat = $425 Credit card = 500 * 12 = $6000Debt To Income RatioThis is calculated as the sum of his total expenditures or liabilities to his total asset and expressed as a percentage.
Total liabilities is calculated as
\(30,000 + 5100+3000+ 6000 = $44100\)
The DTI can be calculated as
\(DTI = \frac{44100}{110400}*100\\DTI = 39.94 *100\\DTI = 40 \%\)
From the calculations above, the DTI of Jim is 40%
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What is the center of a circle with the equation (x - 6)2 + (y + 2)2 = 9?
A)
(6,2)
B)
(6,-2)
0)
(-6, 2)
D)
(-6, -2)
Answers
Answer:
B. (6,-2)
Step-by-step explanation:
The equation of a circle is (x-h)^2+(y-k)^2=r^2
The center of the circle is (h,k)
So, in this problem, h is 6 and k is -2, so the center of this circle is (6,-2).
ASAP
-WILL MARK BRIANIST
Answers
Answer:
The answer is 699...............
Answer:
699
Step-by-step explanation:
First replace the value k to 12.
So our new expression will be:
3+(71-13) times 12
You first do the Parentheses so substract 71 minus 13 which gives you 58 then multiply 58 times 12 which gives you 696 then add 3 to it and you get 699.