Find a, b and c so that the quadrature formula has the highest degree of precision integral f(x)dx zaf(1) + bf (4) + cf(5)

Answers

Answer 1

The coefficients for the quadrature formula with the highest degree of precision are a = -2, b = -1/2, and c = -2/7.

To obtain the quadrature formula with the highest degree of precision for the integral ∫f(x)dx, we need to determine the coefficients a, b, and c in the formula zaf(1) + bf(4) + cf(5).

The highest degree of precision in a quadrature formula is achieved when it accurately integrates all polynomials up to a certain degree. In this case, we want the formula to integrate all polynomials up to degree 2 exactly.

To determine the coefficients a, b, and c, we can use the method of undetermined coefficients. We construct three linear equations by substituting polynomials of degree 0, 1, and 2 into the quadrature formula and equating them to their respective exact integrals.

Let's denote the function f(x) as f(x) = c₀ + c₁x + c₂x², where c₀, c₁, and c₂ are constants.

For the polynomial of degree 0, f(x) = 1, we have:

zaf(1) + bf(4) + cf(5) = zaf₁ + bf₄ + cf₅,

where f₁ = 1, f₄ = 1, and f₅ = 1.

For the polynomial of degree 1, f(x) = x, we have:

zaf(1) + bf(4) + cf(5) = zaf₁ + 4bf₄ + 5cf₅,

where f₁ = 1, f₄ = 4, and f₅ = 5.

For the polynomial of degree 2, f(x) = x², we have:

zaf(1) + bf(4) + cf(5) = zaf₁ + 16bf₄ + 25cf₅,

where f₁ = 1, f₄ = 16, and f₅ = 25.

Solving the system of equations formed by these three equations will give us the values of a, b, and c.

By solving the system of equations, we find:

a = 6/(-3) = -2,

b = 6/(-12) = -1/2,

c = 6/(-21) = -2/7.

Therefore, the coefficients for the quadrature formula with the highest degree of precision are a = -2, b = -1/2, and c = -2/7.

To know more about quadrature formulas , refer here:

https://brainly.com/question/31475940#

#SPJ11


Related Questions

Please help.

a+67a+3ab-2ab-1=​

Answers

Answer:

68a+ab-1

Step-by-step explanation:

Have a good day!

X Kawika had to raise the flag this morning. The 15 ft flag pole casted at
shadow with the ground at a 35° angle. What is the length of the
shadow? (Round answers to the nearest tenth) *
Answer with JUST THE NUMBER, without writing out the unit after the number.

Answers

Add 15 + 35 then take that and subtract it from the answer you get

Picking a purple marble from a jar with 3 green and 3 purple marbles. What is the probability of picking a purple marble?

Answers

Answer:

1/2

Step-by-step explanation:

The total number of marbles in the jar is equal to 6

Since we have 3 purple marbles and 3 green marbles,

The probability of picking a purple marble =

Number of purple marbles in the jar / total number of marbles

= 3/6

= 1/2

From this calculation the probability of picking a purple marble is 1/2 or 0.5

24 Hour Fitness charges svara spatee plus so per months to poun thensyn time has podszes por s gym membership so farHow many monohis has he been a member at 24 Hour Fitness monks​

Answers

Answer:

4 months

Step-by-step explanation:

Equation:

y = 55 + 30x

y = gym membership

x = per month

Work:

y = 55 + 30x

175 = 55 + 30x

30x = 175 - 55

30x = 120

x = 4

4 months

Help there are five people at the carnival they are 15 people at the other carnival how many people are there

Answers

I think there are 20 people

Please help! if do you will get 'Brainliest' (Right answers only, and please show your work)

Answers

Answer:

The answer should be B

[tex]3c \: + \: 43 \: \geqslant \: 100[/tex]


The circle graph shows how William spends his day on average. If he sticks
to this schedule, how many hours will William spend sleeping over the
course of a week (7 days)? ()
17% 11%
10%
А
A) 75.6 hours
B) 78.2 hours
C) 814 hours
Watching TV
Video Games
Fating
Working
45 %Sleeping
27%
D) 848 hours

Answers

Answer:

d

Step-by-step explanation:

i did the math


Is x = 5 a solution to the equation 19 - x = 14?

Answers

Answer:

Yes

Step-by-step explanation:

Test the equation by substituting 5 in for x:

19- 5 =14

14=14

TRUE

If I helped, a brainliest would be greatly appreciated!

Answer: If you replace x with 5 then 19-5=14

Step-by-step explanation:

The diameter of a circle is 4 feet. What is the circumference?
d=4 ft
Give the exact answer in simplest form.

I need the answers

Answers

Answer: 4π

Step-by-step explanation: C= 2πr; 2r=d; C=dπ; C=4π!

Answer:

4π  ft

Step-by-step explanation:

C = 2πr  (Circumference formula for a circle)

diamater = 4, so  diamter = 2 x radius,  4 = 2 x r , so r = 2

Use formula:

C = 2π(2) = 4π

4π ft (Exact answer)

Multiplication and division questions that equal -8?
And another one for -15?

Pls and thank u <3

Answers

For negative 8

1. -4 x 2

2. -48 ÷ 8

For negative 15

1. -5 x 3

2. -60 ÷ 4

( Sorry if they aren't complex enough)

Help me please with the answer

tell me how to answer this

Answers

The mid point of the line segment is (-2, 5 / 2).

How to find the mid point of a line segment?

The midpoint of a line segment is a point that lies exactly halfway between two points.

Therefore, let's find the mid point of the line segment indicated above.

Hence, using (-4, 0) and (0, 5)

Hence,

mid point = (x₁ + x₂ / 2, y₁ + y₂ / 2)

Therefore,

mid point = (0 - 4 / 2, 5 + 0 / 2)

mid point = (-4  /2, 5 / 2)

mid point = (-2, 5 / 2)

learn more on mid point here: https://brainly.com/question/22241594

#SPJ1

what is the first 5 cubic numbers​

Answers

Answer:

1,8,27,64,125

Step-by-step explanation:

1, 6 8 27 64 125 is the answer

The center and a point on a circle are given. Find the circumference to the nearest tenth.

center:(−15, −21);
point on the circle: (0, −13)

The circumference is about ?

Answers

Answer:

Circumference ~ 106.8

Step-by-step explanation:

Use the distance formula to find the radius of the circle with the two coordinates given. The radius of this circle is 17. Plug 17 into the formula 2(pi)r to find the Circumference. The answer is 106.8 rounded to the nearest tenth.

pls help i’m so confused omg!!

Answers

Answer:

C or B

Step-by-step explanation:

Answer:

Your answer is A.

Step-by-step explanation:

You can count the arrow lines as the 2s. Such as, 2, 4, 6, 8 and 10.

So, the line 'x' is being divided by how many lines touching it.

Therefore, it is 1.

Then you add x and 6, the number which the line is ending with.

Your final answer is, F(x) =      1      

                                                x+6

Hope this helped!

       

7 + k = 11 step explanation

Answers

Answer:

k = 4

Step-by-step explanation:

11 - 7 = 4

What's the equation to use to solve x?

Answers

Total Speed = total distance/total time
= 290/2
= 145km/hr
145-15=x
= 130km/hr

Using mirrors installed on the moon by Apollo astronauts to reflect laser waveforms, its possible to measure the distance from earth to moon to high precision. Due to the physics of the detectors, the measurement errors have a uniform distribution of -3.0 to + 5.0 cm

a. What is the probability that a particle measurement will be accurate to within +- 1.0 cm?

b. Find the mean of the measurement errors

c. Find the standard deviation of the measurement errors

Answers

A.the probability that a particle measurement will be accurate to within +- 1.0 cm is  0.25 B. the mean of the measurement errors is 1 cm. C.  the standard deviation of the measurement errors is 2.311 cm.

a. For a uniform distribution of -3.0 to + 5.0 cm, the total distance is 5.0 - (-3.0) = 8.0 cm.

The probability that a particle measurement will be accurate to within +- 1.0 cm is given by:

P(-1.0 ≤ X ≤ 1.0) = (1/(8.0)) * (1.0 - (-1.0))= (1/8.0) * 2= 0.25

b. Find the mean of the measurement errors

The formula to calculate the mean (μ) of the measurement errors is:μ = (a + b) / 2

where, a is the lower limit of the distribution, and b is the upper limit of the distribution.μ = (-3.0 + 5.0) / 2= 2 / 2= 1

Therefore, the mean of the measurement errors is 1 cm.

c. Find the standard deviation of the measurement errors

The formula to calculate the standard deviation (σ) of a uniform distribution is:σ = (b - a) / √12

where, a is the lower limit of the distribution, b is the upper limit of the distribution, and √12 is the square root of 12.σ = (5.0 - (-3.0)) / √12= 8 / 3.464= 2.311

Therefore, the standard deviation of the measurement errors is 2.311 cm.

Know more about  probability here,

https://brainly.com/question/31828911

#SPJ11

"






Perform the following test of hypothesis. H0: μ 10.70, H1: μ # 10.70, n = 47, t = 12.234, = H0 is
"

Answers

Based on the given information, we have sufficient evidence to conclude that the population mean (μ) is not equal to 10.70.

To perform the test of hypothesis, we can use a t-test to determine whether there is sufficient evidence to reject the null hypothesis (H0) in favor of the alternative hypothesis (H1).

The given hypotheses are:

H0: μ = 10.70 (null hypothesis)

H1: μ ≠ 10.70 (alternative hypothesis)

The sample size is n = 47, and the test statistic is t = 12.234.

To conduct the test, we need to compare the calculated test statistic to the critical value(s) based on the desired significance level (α).

The steps to perform the hypothesis test are as follows:

Step 1: Set the significance level (α)

Let's assume a significance level of α = 0.05. This means we want to be 95% confident in our decision.

Step 2: Determine the critical value(s)

Since the alternative hypothesis is two-sided (μ ≠ 10.70), we need to find the critical values for a two-tailed t-test.

Since n = 47, we have n - 1 = 46 degrees of freedom (df). Looking up the critical values in the t-distribution table or using a statistical calculator, the critical values for a two-tailed test with α = 0.05 and df = 46 are approximately ±2.013.

Step 3: Calculate the p-value

The p-value is the probability of obtaining a test statistic as extreme as the one observed (t = 12.234), assuming the null hypothesis is true.

Using a t-table or statistical software, we can determine the p-value associated with the given t-value and degrees of freedom. The p-value turns out to be very small (p < 0.001).

Step 4: Make a decision

If the p-value is less than the significance level (α), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Since the p-value is smaller than α (p < 0.001), we reject the null hypothesis (H0).

Learn more about hypothesis here:

https://brainly.com/question/29576929

#SPJ11

Solve for n. 2n+3/4n = 3/4

Answers

Answer: n=3/11

Step-by-step explanation:

1. You want to simplify both sides of the equation.

2n+3/4n=3/4.

(2n+3/4n)=3/4 (combine like terms).

11/4n=3/4.

2. Multiply both sides using 4/11.

(4/11)x(11/4n)=(4/11)x(3/4)

3. You get your answer which is n=3/11.

Hoped I help :)

PLEASE HELP PLEASE

Write a clear explanation summarizing what you have learned about defining expressions that have zero or a negative integer as an exponent. Then explain, using examples, why these definitions makes sense. Give as many reasons as you can. Also indicate which exclamation makes the most sense to you.

Answers

Answer:

Any number raised to zero is one.

Examples:

[tex]4^{0} = 1\\\\178^0=1\\\\15^0 = 1[/tex]

Any number raised to a negative integer is 1 over that exponential term without the negative exponent.

Examples:

[tex]5^{-1} = \frac{1}{5}\\\\324^{-13}=\frac{1}{324^{13}}\\\\17^{-6} = \frac{1}{17^{6}}[/tex]

Someone please help me.

Answers

Answer:

with what life

Step-by-step explanation:

Emily is making a flag with the dimensions shown. What is the minimum amount of material needed for the flag?

Answers

9514 1404 393

Answer:

  B  80 square inches

Step-by-step explanation:

The area of a parallelogram has the same formula as the area of a rectangle:

  A = bh . . . . . b is the base; h is the height

  A = (10 in)(8 in)

  A = 80 in²

The minimum amount of material needed is 80 square inches.

Answer:

The answer is 80

Step-by-step explanation:

Hope this helps

please please I really need help this depends on my life​

Answers

Answer:

39.4 divided by (-7.2)= -5.472

6.7-39.31=-32.61

Step-by-step explanation:

write the equation of a function whose parent function, f(x) = x 8, is shifted 2 units to the right.

Answers

To find the equation of a function whose parent function, f(x) = x^8, is shifted 2 units to the right, we can use the formula given below: g(x) = f(x - a) + bwhere f(x) is the parent function, a is the horizontal shift (positive for right and negative for left), b is the vertical shift (positive for up and negative for down), and g(x) is the new function.So, in this case, we need to shift the parent function f(x) = x^8 two units to the right.

This means that a = 2 and b = 0 (since there is no vertical shift).So, substituting these values in the formula, we get:g(x) = f(x - 2) + 0g(x) = (x - 2)^8Thus, the equation of the new function, g(x), is (x - 2)^8 when the parent function, f(x) = x^8, is shifted 2 units to the right.

To shift the parent function f(x) = x^8 two units to the right, we need to modify the equation by replacing 'x' with 'x - 2'. This will shift the graph horizontally to the right by 2 units.

Therefore, the equation of the shifted function, let's call it g(x), becomes:

g(x) = (x - 2)^8

To shift the parent function, f(x) = x^8, two units to the right, we can use the transformation equation:

g(x) = f(x - h)

where h represents the horizontal shift. In this case, h = 2 because we want to shift the function two units to the right. Substituting the values into the equation, we get:

g(x) = (x - 2)^8

Therefore, the equation of the function after shifting the parent function, f(x) = x^8, two units to the right is g(x) = (x - 2)^8.

To know more about horizontal shift visit:

https://brainly.com/question/30285734

#SPJ11

The given parent function is f(x) = x 8. We are supposed to write the equation of a function that is shifted two units to the right. It can be done by taking a new function g(x) and writing it as g(x) = f(x − 2).

Therefore, the equation of the new function g(x) is g(x) = (x − 2)8.

Step-by-step explanation: The given parent function is f(x) = x 8. We are supposed to write the equation of a function that is shifted two units to the right. It can be done by taking a new function g(x) and writing it as g(x) = f(x − 2).

The value of f(x) = x 8

Write it as follows:

when x is 0, 0 8 = 0 and

when x is 1, 1 8 = 8.

Now, we can write the equation for g(x) by using f(x) = x 8.

We have g(x) = f(x − 2)

= (x − 2)8.

Therefore, the equation of the new function g(x) is g(x) = (x − 2)8.

To know more about equation visit

https://brainly.com/question/29538993

#SPJ11

For a hypothesis test using the single-factor ANOVA formula:

The obtained overall F ratio = MS between treatments divided by MS within treatments.

Calculate the obtained overall F ratio for: MS between treatments= 8 and MS within treatments = 2.

Then describe the null hypothesis decision for = .05, df numerator: 3, and df denominator: 4.

Reject of fail to reject null hypothesis?

Answers

We can conclude that there is not enough evidence to suggest that the means of the different groups are different.

The obtained overall F ratio for MS between treatments = 8 and MS within treatments = 2 can be calculated using the formula for a hypothesis test using the single-factor ANOVA. The formula is given below: Obtained overall F ratio = MS between treatments/MS within treatments Substituting the values in the above formula, we get, Obtained overall F ratio = 8/2 = 4

The obtained overall F ratio for MS between treatments = 8 and MS within treatments = 2 is 4.Now, let's describe the null hypothesis decision for α = .05, df numerator: 3, and df denominator: 4.The null hypothesis decision can be made using the F-distribution table. Using the table, the critical value of F is 9.49.

Therefore, if the obtained overall F ratio is greater than 9.49, then we reject the null hypothesis. If the obtained overall F ratio is less than or equal to 9.49, then we fail to reject the null hypothesis.Obtained overall F ratio = 4 is less than the critical value of F, i.e., 9.49.Therefore, the null hypothesis is not rejected at α = .05, df numerator: 3, and df denominator: 4.

To know more about critical value visit:

https://brainly.com/question/32607910

#SPJ11

The obtained overall F ratio for MS between treatments = 8 and MS within treatments = 2 will be 4. The null hypothesis decision for α = 0.05, df numerator: 3, and df denominator: 4 is Fail to reject null hypothesis.

Explanation: ANOVA (analysis of variance) is a statistical method used to determine if two or more population means are equal.

It is used to analyze the variation between sample group means and is frequently used in hypothesis testing.

Therefore, we will now calculate the obtained overall F ratio for the given values.

The obtained overall F ratio formula is: Overall F Ratio = MS between treatments / MS within treatments.

Given, MS between treatments = 8 and MS within treatments = 2.

Therefore, Overall F Ratio = MS between treatments / MS within treatments

= 8/2

= 4

Hence, the obtained overall F ratio for MS between treatments= 8 and MS within treatments = 2 is 4.

The null hypothesis decision for α = 0.05, df numerator: 3, and df denominator: 4 is Fail to reject null hypothesis.

The test statistic value, F, is 3.71. The p-value is greater than 0.05. Therefore, we fail to reject the null hypothesis.

To know more about null hypothesis, visit:

https://brainly.com/question/30821298

#SPJ11

1. What is 5,509 rounded to the thousands place?
А
6,000
B
5,500
5,600
D
5,000

Answers

The answer is a. 6000
Your answer would be A

Because the number before the 5 in the thousands place is equal to or greater than 5. Making it round up.

Question Progress
boel
21/40 Marks
Find the area of this parallelogram.
13 cm
15 cm
20 cm

Answers

I think the area of the parallelogram is 260 cm squared. You multiply the 13 by the 20 to get 260. You don’t use the 15 because it is at an angle and you can’t get a proper height using it.

Minh wants to buy a car costing $9,950. She can put $1,000 down and finance the rest at 10.9% APR, making the monthly payments for 3 years. How will Minh pay in finance charges? What will her monthly payments be?

Answers

Answer:

piip;[-p-o-ul0i

Step-by-step explanation:

Tony borrows $7,000 from a friend
at a rate of 5% interest for 4 months.
What is the total that needs
to be repaid after this time
to the nearest dollar?

Answers

Answer:

5%100 ×R200

Step-by-step explanation:

Address and u the one for me please

hejekekkske
sksksksk
sneak

2222222 help me plz plz plz plz

Answers

Answer:

○ B) m∠XOA = m∠OYC

Step-by-step explanation:

Since Point O is circumcentered into the square, we keep it in the midst when we are making comparisons, and since this was simple to identify, this automatically is a false statement. Point O stays in the midst at all times.

- Hope this helps!

Other Questions
Which one of the strategies below is more appropriate to be implemented in a company which is trying to increase its market share? a) Sell-out/Divestment strategy b) Profit strategy Liquidation d) Concentric diversification strategy we used the Optional Stopping Theorem to solve the Gambler's Ruin Problem. Specifically, we showed that if Sn So +?=1X; is a biased random walk starting at So = 1, where the steps X; are independent and equal to +1 with probability p1/2 and equal to - 1 with the remaining probability q=1 p, then the probability of hitting N (jackpot") before 0 ("bust") is (g/p) - 1 PJ So = 1) = (g/p)N-1 Recall that the key to this was the martingale Mn = (g/p)Sn, which is only useful when pq. (a) For any pe [0, 1], argue that P(T 1: Sne {0,1}} is the first time that the walk visits 0 or N. Hint: One way is to consider each time that the walk visits 1 before time T, and then compare with a geometric random variable. Note: This is the one condition in the Optional Stopping Theorem that we did not verify during the lecture. (b) Find P(J|So = n) when instead So = n, for some 1 For each of the following situations, indicate whether you agree or disagree with the financial reporting practice employed and state the basic assumption, constraint, or accounting principle that is applied (if you agree) or violated (if you disagree).1.Wagner Corporation adjusted the valuation of all assets and liabilities to reflect changes in the purchasing power of the dollar. do you agreed that cell is a building unit of organism yes explain why?class 9 The cost of a banquet at Nick's Catering is $215 plus $27.50 per person. Ifthe total cost of a banquet was $2827.50, how many people were invited? Gabrielle swam for 142 minutes during her first week of vacation. In her two weeks of vacation, she swam for a total of 347 minutes. How many more minutes did she swim for in the second week than in the first week?Gabrielle swam for ???? more minutes in the second week than in the first week. Which of the fractions is equivalent to 2/3 CAn someone help me plsss Use the information below to prepare closing entries. Cash For the Year Ended December 31, 2021 Accounts Receivable Prepaid Expenses Equipment Adjusted Trial Balance Bristol Company Accumulated Depreciation Accounts Payable Notes Payable Capital Stock Retained Earnings Debit $ 7,030 1,100 700 15,700 Credit $2,100 900 6,200 3,000 10,940 Accumulated Depreciation Accounts Payable Notes Payable Capital Stock Retained Earnings Dividends Fees Earned Wages Expense Rent Expense Utilities Expense Depreciation Expense Miscellaneous Expense Totals 1,790 2,500 1,960 775 250 85 $2,100 900 6,200 3,000 10,940 8,750 $31,890 $31,890 Format: Enter debits and credits as whole numbers WITH commas, but DO NOT add dollar signs. Please use the Chart of Accounts. Don't forget to list expenses in descending order! Listing them ANY OTHER WAY will mark them WRONG!!! Dec 31 Dec 31 Date Account Name Debit Credit Dec 31 When And Where Did Harriet Do This Civil Nursing!? What is the surface area of a cylinder with height 8 ft and radius 4 ft In Ms. Chance's first period class, there are 9 students with hazel eyes, 10 with brown eyes, 7 with blue eyes, and 2 students with green eyes. Ms. Chance picks a student at random. Which color eyes is the student most likely to have? two adaptations in plant that allow them to obtain maximum sunlight an industry in which the firms' cost structures do not vary with changes in production Find the value of the variable.2012A. 10. 13C. 16D.18 When the price of car parking increases from $3 per day to $5 per hour, the number of car park spots rented contracts from 1,200 cars a day to 900 cars per day. Using the mid-point formula, calculate the price elasticity of demand for this price change. 3 marks The money supply that consists of currency, transaction deposits, and traveler's checks is O M1. O M2. O the liquidity approach. O the fiduciary monetary system. Currency consists of O only coins minted by the U.S. Treasury. O coins, Federal Reserve Notes and traveler's checks. O only Federal Reserve notes. O coins minted by the U.S. Treasury and Federal Reserve notes. If a preferred stock from the FIN340 Company pays $1.00 in annual dividends and the required return on the preferred stock is 5.0%, what is the current value of the stock?A fast growing firm paid a dividend of $1.00 per share during the most recent year, The dividend is expected to increase at a rate of 20.0% per year for the next 3 years , Afterwards, a more stable 5.00% annual growth rate should be assumed - If a 10.00% discount rate is appropriate for this stock, what is its value?The FIN340 Company has a net profit margin of 5.00% on annual sales of $1,000,000 and the firm has 50,000 shares outstanding. If the firm's P/E ratio is 10.0X, how much is the stock currently selling for?You want to buy a $9,750 car and the dealer offers you a 7-year loan with an 11.95% APR and no down payment required - Assuming monthly compounding, what will the monthly payments be? For f, g L[a,b], prove the Cauchy-Schwarz inequality |(f,g)| = ||$||||$||. = Hint: Define a function Q(t) = (f + tg, f + tg) for any real number t. Use the rules of inner product to expand this expression and obtain a quadratic polynomial in t; because Q(t) > 0 (why?), the quadratic polynomial can have at most one real root. Examine the discriminant of the polynomial. help pls ill give brainlist