(x+y-¹)²÷(1+x-¹y-¹)​

Using Richardson extrapolation, the computed first derivative of f(x) at x = 2 is approximately -0.052.

The absolute error with respect to the true solution is 22.348.

To compute the accuracy gain using Richardson extrapolation, we'll use the central difference formula for the first derivative, which is given by:

f'(x) = [f(x + h) - f(x - h)] / (2h)

h₁= 0.02 and h₂ = 0.03, and then apply Richardson extrapolation.

Calculate the derivative using h₁ = 0.02

x = 2

h₁ = 0.02

f(x + h₁) = f(2 + 0.02) = f(2.02) = 5sin(10 × 2.02) + (2.02)³ - 2(2.02)² - 6(2.02) + 10

= 5sin(20.2) + 8.120808 - 8.162808 - 12.12 + 10

= -3.5799

f(x -h₁) = f(2 - 0.02) = f(1.98)

= 5sin(19.8) + 7.783608 - 7.844808 - 11.88 + 10

= -3.4758

f'(x) = [-3.5799 - (-3.4758)] / (2 × 0.02)

= -0.052

Calculate the derivative using h₂ = 0.03

x = 2

h₂  = 0.03

f(x + h₂ ) = f(2 + 0.03) = f(2.03) = 5sin(10 × 2.03) + (2.03)³ - 2(2.03)² - 6(2.03) + 10

= -3.5998

f(x - h₂) = f(2 - 0.03) = f(1.97)

= -3.3943

f'(x) = [-3.5998 - (-3.3943)] / (2 × 0.03)

= -0.052

Richardson extrapolation is given by the formula:

\(f'(x) = (2^p \times f'(x, h_2) - f'(x, h_1)) / (2^p - 1)\)

Here, p is the order of the method. Since we're using the central difference formula, which is second-order accurate, p = 2.

f'(x) = (2² × -0.052 - (-0.052)) / (2² - 1)

= (4 × -0.052 + 0.052) / 3

= -0.052

Therefore, using Richardson extrapolation, the first derivative of f(x) at x = 2 is approximately -0.052.

To compute the absolute error with respect to the true solution, we need to find the true derivative of f(x) and evaluate it at x = 2.

f(x) = 5sin(10x) + x³ - 2x² - 6x + 10

f'(x) = 50cos(10x) + 3x² - 4x - 6

f'(2) = 50cos(20) + 3(2)^2 - 4(2) - 6

= 50(-0.408) + 12 - 8 - 6

= -22.4

Absolute error = |(-22.4) - (-0.052)|

= |-22.4 + 0.052|

= 22.348

Therefore, the absolute error with respect to the true solution is  22.348.

To learn more on Differentiation click:

https://brainly.com/question/24898810

#SPJ4

Answer: 24 goals

Step-by-step explanation:

Melissa makes 2 goals out of every 12 shots on goal.

This means that the amount of shots needed to score a goal for her is:

= Number of shots / Number of goals

= 12 / 2

= 6 shots

She scores a goal every 6 shots.

If she makes 144 shots therefore, she will score:

= Number of shots / Number of shots needed per goal

= 144 / 6

= 24 goals

Answer:

y= 32x

Step-by-step explanation:

Use slope formula

192-128/6-4= 64/2

M=32x

Find y-intercept (if any)

128=32(4)+b

128=128+b

B=0

total number of tickets sold = x + y = 9 + 18 = 27. So, Darius sold 27 tickets altogether.

what is an algebraic expression?

In mathematics, an algebraic expression is a combination of variables, constants, and mathematical operations (such as addition, subtraction, multiplication, and division) that represent a quantity.

Let x be the number of children's tickets sold, and let y be the number of adult tickets sold.

From the problem statement, we know that:

The price of a children's ticket is $4.50

The price of an adult ticket is $6.50

The total amount collected is $157.50

The number of adult tickets sold is twice the number of children's tickets sold

Using this information, we can set up the following system of equations:

x + y = total number of tickets sold (equation 1)

4.5x + 6.5y = 157.5 (equation 2)

y = 2x (equation 3)

We can use equation 3 to substitute y in terms of x in equations 1 and 2:

x + 2x = total number of tickets sold (substitute y = 2x from equation 3 into equation 1)

4.5x + 6.5(2x) = 157.5 (substitute y = 2x from equation 3 into equation 2)

Simplifying these equations, we get:

3x = total number of tickets sold (simplifying the left side of the first equation)

17.5x = 157.5 (simplifying the second equation)

x = 9 (dividing both sides of the second equation by 17.5)

Therefore, the number of children's tickets sold is x = 9, and the number of adult tickets sold is y = 2x = 2(9) = 18.

To find the total number of tickets sold, we can add x and y:

therefore, total number of tickets sold = x + y = 9 + 18 = 27

So, Darius sold 27 tickets altogether.

To learn more about algebraic expression from given link:

https://brainly.com/question/19245500

#SPJ1

Answer:

25

Step-by-step explanation:

35 to 75

x to 105

To get from 75 to 105 you would multiply 75 by 5/7 so you would do the same to 35. So 35 x 5/7 is 25.

Answer:

the answer is $5

Step-by-step explanation:

The amount of money that Brandon would have more than Julian is $16,564.

The formula for calculating future value when there is continuous compounding is :

FV = A x e^r x N

Where:

Future value of Brandon's investment = $1,100 x 2.718^0.0775 x 18 = $21,395.36

The formula for calculating future value when there is monthly compounding:

FV = P (1 + r)^nm

Where:

FV = 1100 x (1 + 0.006875)^(18 x 12) = $4,831.85

Difference in the amount that Brandon and Julian has  = $21,395.36 - $4,831.85 = $16,563.51≈ $16,564

To learn more about continuous compounding, please check: https://brainly.com/question/26476328

#SPJ1

The Laplace domain equation X(s) is found to be X(s) = (s + 2)/(s^2 + 5s + 6). The time domain equation x(t) can be obtained by applying the inverse Laplace transform to X(s), resulting in x(t) = e^(-t) - e^(-2t).

Given the Laplace domain equation X(s), we need to substitute the given parameters and find its expression in terms of s. The equation provided is X(s) = (s + 2)/(s^2 + 5s + 6).

To obtain the time domain equation x(t), we need to apply the inverse Laplace transform to X(s). The inverse Laplace transform of X(s) will give us x(t) in terms of t.

Applying the inverse Laplace transform to X(s) involves finding the inverse transform of each term separately. The inverse Laplace transform of (s + 2) is simply 1, representing the unit step function. The inverse Laplace transform of (s^2 + 5s + 6) is e^(-t) - e^(-2t), which can be obtained through partial fraction decomposition.

Therefore, the time domain equation x(t) is given by x(t) = e^(-t) - e^(-2t), where t represents time.

Learn more about Laplace transform here:

https://brainly.com/question/30759963

#SPJ11

Answer:

x=15

Step-by-step explanation:

Answer:

x=15

Step-by-step explanation:

See image below

The slope formula is m= y2-y1/x2-x1.

m= 4-0/2-5

m=4/-3

Therefore, 4/-3 is the slope.

Answer:

The first option, incase something happens to the president, they’re next in line.

Step-by-step explanation:

Answer: Hello how are you doing today?

Step-by-step explanation: How may I help you?

There are 60 f-words that can be made using all the letters of the word "AGAIN".

To find the number of f-words that can be made using all the letters of the word "AGAIN", we need to use the concept of permutations.

There are five letters in the word "AGAIN". To find the number of f-words that can be made using all these letters, we need to find the number of permutations of these letters.

The number of permutations of a set of n elements is given by n!. However, in this case, we have two "A"s in the word "AGAIN". This means that we cannot simply use n! to calculate the number of permutations.

Instead, we need to use the formula for permutations with repeated elements, which is:

\($\frac{n!}{n_1!n_2!\cdots n_k!}$$\)

where n is the total number of elements, and n1, n2, ..., nk are the number of times each element is repeated.

In this case, we have two "A"s and one of each of the other letters. Therefore, we can plug in the values into the formula:

\($\frac{5!}{2!1!1!1!} = \frac{120}{2} = 60$$\)

This means that there are 60 f-words that can be made using all the letters of the word "AGAIN".

To know more about Permutation visit;

brainly.com/question/13715183

#SPJ1

Answer:

$12 discount

Step-by-step explanation:

$40x0.30=12

Answer:

A = -7.5   B = -17.5

Step-by-step explanation:

A + B = -25

A = B + 10

Plug the second equation into the first equation:

B + 10 + B = -25

2B = -35

B = -17.5

Plug that value into the first equation:

A - 17.5 = -25

A = -7.5

The probability of getting 0 lemons in the sample is 0.8836, the probability of getting 1 lemon in the sample is 0.1060, and the probability of getting 2 lemons in the sample is 0.0564.

The probability distribution of x can be calculated as follows:

Given that 6% of all cars produced at a large auto company are lemons. This means that out of every 100 cars manufactured at the company, 6 of them are lemons.Let x denote the number of lemons in this sample. Then, x can take the values 0, 1, or 2. To find the probability of each value of x, we use the binomial probability formula, which is:

P(x) = (nCx) * p^x * (1-p)^(n-x)

where n is the sample size, p is the probability of success, and x is the number of successes.

The sample size is 2 because we are selecting two cars at random from the production line. The probability of success (getting a lemon) is 0.06. Using the binomial probability formula, we get:

P(0) = (2C0) * 0.06^0 * (1-0.06)^(2-0) = 0.8836

P(1) = (2C1) * 0.06^1 * (1-0.06)^(2-1) = 0.1060

P(2) = (2C2) * 0.06^2 * (1-0.06)^(2-2) = 0.0564

Therefore, the probability distribution of x is:X P(x) 0. 0.8836 1. 0.1060 2. 0.0564

In conclusion, the probability of getting 0 lemons in the sample is 0.8836, the probability of getting 1 lemon in the sample is 0.1060, and the probability of getting 2 lemons in the sample is 0.0564.

To know more about probability visit:

brainly.com/question/31828911

#SPJ11

Answer:

the area of a circle is equal to pi r square that is 3.14×3×3 = 28.26.

Answer:

The expression representing the perimeter of the platter will be:

P = 10/3x units

Hence, option (D) is true.

Step-by-step explanation:

Let the length l of a rectangular platter will be =  x

As the width of a rectangular platter is 2/3 its length.

so the width w of a rectangular platter will be = 2/3x

As the perimeter of the platter is defined as:

P=2(l+w)

where l is the length, and w is the width

substituting length l = x and width w = 2/3x

\(P=2\left(x\:+\:\frac{2}{3}x\right)\)

    \(=2\cdot \frac{5}{3}x\)             ∵ \(x\:+\:\frac{2}{3}x=\:\frac{5}{3}x\)

    \(=\frac{10x}{3}\) units

Therefore, the expression representing the perimeter of the platter will be:

P = 10/3x units

Hence, option (D) is true.

The amount Bao paid for the pair of shoes is given by A = $ 38.60

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage change is the difference between the measured value and the true value , as a percentage of the true value

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

Given data ,

Let the amount Bao paid for the pair of shoes be represented as A

Now , the initial amount for the pair of shoes be = $ 46

And , the percentage of discount = 30 %

So , the amount for the pair of shoes after discount = ( 70/100 ) x initial amount for the pair of shoes

On simplifying the equation , we get

The amount for the pair of shoes after discount = ( 70/100 ) x 46

The amount for the pair of shoes after discount = $ 32.20

Now , the percentage of processing fee = 20 %

And , the amount after the processing fees = ( 120 / 100 ) x amount for the pair of shoes after discount

On simplifying the equation , we get

The amount after the processing fees = ( 120 / 100 ) x 32.20

The amount after the processing fees = $ 38.64

Hence , the amount for the pair of shoes is $ 38.60

To learn more about percentage click :

https://brainly.com/question/12861068

#SPJ9

Answer:

  9/4

Step-by-step explanation:

You want to know the value required to complete the square in the equation 1 = x² -3x.

Your picture shows the required value: (-3/2)² = 9/4.

<95141404393>

The yy-component of vector a a is -y-direction, which is equal to 0 m/s2.the product of the second term of the vector with unit vector j^j^, which is in the direction of the y-axis.

Given a vector, a⃗ a→ = (5.0 m/s2, −y−direction)Find the yy -component of the given vector a⃗ a→.Solution: The yy-component of the given vector a⃗ a→ = -y-directionTo find the yy-component of the given vector a⃗ a→, we have to take the product of the second term of the vector with unit vector j^j^, which is in the direction of the y-axis.Therefore, the yy-component of vector a⃗ a→ is :a_yy = -y-direction = (-1)(0) = 0 m/s²  Answer: 0 m/s².

To know more about Vector Visit:

https://brainly.com/question/24256726

#SPJ11

The yy-component of vector a⃗ a→ is -y-direction.

The yy-component of a vector represents the magnitude of the vector in the y-direction.

In this case, the vector a⃗ a→ is given as (5.0 m/s2, −y-direction).

Since the yy-component is the magnitude in the y-direction, the yy-component of the vector a⃗ a→ is -y-direction.

https://brainly.com/question/31400182

#SPJ12

The length of the hypotenuse is 9.5 kilometers

From the question, we have the following parameters that can be used in our computation:

Legs = 8,5 and 4.2

The length of the hypotenuse is calculated as

Hyp^2 = Leg 1^2 + Leg 2^2

substitute the known values in the above equation, so, we have the following representation

Hypotenuse^2 = (8.5)^2 + 4.2^2

Evaluate

Hypotenuse^2 = 89.89

So, we have

Hypotenuse = 9.5

Hence, the hypotenuse = 9.5

Read more about right triangles at

https://brainly.com/question/2437195

#SPJ1

Answer: 6 divided by 2/3

Step-by-step explanation:

The division equation which represents the situation is 6 ÷ 2/3 = 9.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

Division equation is the equation involving the operation of division.

The model shows there are 9 pieces that are each 2/3 feet long.

We can calculate the total length of the pieces using the multiplication equation.

9 × 2/3 = 6

Total length = 6 feet

Length of each piece = 2/3 feet

Number of pieces can be found using the division equation,

6 ÷ 2/3 = 9

Hence the division equation for the given situation is 6 ÷ 2/3 = 9.

Learn more about Division Equation here :

https://brainly.com/question/12066883

#SPJ2

Answer:

1,172.3 cm³

Step-by-step explanation:

Find the volume of one rod, then divide the total volume of steel used by the volume of one rod.  The volume of one rod is

V = (πd²/4)h

d = 4 cm

h = 20 cm

Plugin the numbers and get V in cm³, then divide the given total volume of 28,134.4 cm³ by V.  If the result is not an integer, then round down.

Add

20 + 4 = 24

Then

28,134.4 ÷ 24 = 1172.26

Rounded to the nearest 0.1 or  the Tenths Place = 1,172.3

Therefore, 1,172.3 rods will be made per hour.

The equation of line A is y = 3.5.

The equation of line B is x = 7.5.

What is the equation of the line?

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

Line A is a straight line parallel to the x-axis.

Parallel to the x-axis means that x = 0.

Line B is a straight line parallel to the y-axis.

Parallel to the y-axis means that y = 0.

The equation of line A is y = 3.5.

The equation of line B is x = 7.5.

What is an equation of a line?

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

From the graph, we see that,

Line A and Line B are both straight lines.

Line A is a straight line parallel to the x-axis.

Parallel to the x-axis means that x = 0.

Line B is a straight line parallel to the y-axis.

Parallel to the y-axis means that y = 0.

So,

The equation of line A is the point of the y-intercept.

y = 3.5

The equation of line B is the point of the x-intercept.

x = 7.5

hence,

The equation of line A is y = 3.5.

The equation of line B is x = 7.5.

To learn more about the equation of the line visit:

https://brainly.com/question/18831322

#SPJ1

The complete question is in the attached figure.

Therefore , the solution of the given problem of variable comes out to be the manager will therefore require a total of 41 pie slices when there are 8 visitors.

A quality who can be assessed and expression assigned different values is called a variable. Variables include things like height, age, wages, province of birth, scholastic standing, and type of housing.

Here,

First, let's define our terms.

Suppose there are x visitors. (independent variable).

Let y represent the overall quantity of pie slices required. (dependent variable).

Each guest will receive two slices of pie, and there will be an extra 25 slices, according to the problem. Thus, we can say:

=> y = 2x + 25

Simply enter x = 8 into the equation and calculate to find y when x = 8.

=> y = 2(8) + 25

=> y = 16 + 25

=> y = 41

The manager will therefore require a total of 41 pie slices when there are 8 visitors.

To know more about variable , visit

brainly.com/question/29583350

#SPJ1

Answer: A

Step-by-step explanation: 8 - 5 = 3 not 13

Answer:

A

Step-by-step explanation:

8-5=3 not 13

Answer: Since, m∠2 + m∠1 = 180° [Supplementary angles]

  125° + m∠1 = 180°

  m∠1 = 180° - 125°

  m∠1 = 55°

2). Since ∠7 ≅ ∠12 [alternate interior angles]

  m∠7 = m∠12 = 37°

3). m∠3 = m∠18 = 102° [Alternate exterior angles]

4). m∠8 + m∠3 + m∠7 = 180°

   m∠8 + 102 + 37 = 180

   m∠8 = 41°

5). m∠14 = (m∠7 + m∠8) [Alternate angles]

   m∠14 = 37 + 41 = 78°

6). m∠4 = 180° - m∠3 [Linear pairs]

            = 180 - 102

            = 78°

7). m∠9 = m∠3 = 102° [Vertical angles]

8). m∠15 = m∠2 [Alternate exterior angles]

              = 125°

9). m∠5 = m∠15 [Corresponding angles]

            = 125°

10). m∠10 + m∠5 = 180° [Sum of interior angles on one side of the transversal]

    m∠10 = 180 - 125

              = 55°

10). m∠16 = m∠10 = 55° [Vertical angles]

11). m∠6 = m∠10 = 55° [Alternate interior angles]

12). m∠11 = m∠15 = 125°

13). m∠17 = m∠14 = 78° [Vertical angles]

Step-by-step explanation:

Answer:

Step-by-step explanation: