The approximation of I = * cos(x3 - - dx using composite Simpson's rule with n=3 is:

Answers

Answer 1

The approximation of I = * cos(x³ - - dx using composite Simpson's rule with n=3 is 4

To approximate the integral ∫cos(x³) dx using composite Simpson's rule with n = 3, we need to divide the integration interval into smaller subintervals and apply Simpson's rule to each subinterval. The formula for composite Simpson's rule is:

I ≈ (h/3)  [f(x₀) + 4f(x₁) + 2f(x₂) + 4f(x₃) + 2f(x₄) + ... + 2f([tex]x_{n-2}[/tex]) + 4f([tex]x_{n-1}[/tex]) + f([tex]x_{n}[/tex])]

where h is the step size, n is the number of subintervals, and f(xi) represents the function value at each subinterval.

In this case, n = 3, so we will have 4 equally-sized subintervals.

Let's assume the lower limit of integration is a and the upper limit is b. We can calculate the step size h as (b - a)/n.

In our case, the limits of integration are not provided, so let's assume a = 0 and b = 1 for simplicity.

Using the formula for composite Simpson's rule, the approximation becomes:

I ≈ (h/3)  [f(x₀) + 4f(x₁) + 2f(x₂) + 4f(x₃) + f(x₄)]

For n = 3, we have four equally spaced subintervals:

x₀ = 0, x₁ = h, x₂ = 2h, x₃ = 3h, x₄ = 4h

Using these values, the approximation becomes:

I ≈ (h/3)  [f(0) + 4f(h) + 2f(2h) + 4f(3h) + f(4h)]

Substituting the function f(x) = cos(x^3):

I ≈ (h/3)  [cos(0³) + 4cos((h)³) + 2cos((2h)³) + 4cos((3h)³) + cos((4h)³)]

Now, we need to calculate the step size h and substitute it into the above expression to find the approximation. Since we assumed a = 0 and b = 1, the interval width is 1.

h = (b - a)/n = (1 - 0)/3 = 1/3

Substituting h = 1/3 into the expression:

I = (1/3) [cos(0)³ + 4cos((1/3)³) + 2cos((2/3)³) + 4cos((1)³) + cos((4/3)³)]

I = 1/3[1 + 4 + 2 + 4 +1]

I = 4

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Related Questions

The person who answers has an explanation that doesn't have a link, and isn't incorrect gets brainiest. Ok here is the question "What are the first 30 characters in pi aka ~3.141592653589793238462643383 is all I remember."

Answers

Answer:

3.14152628283829299348473929

I need help thank you

Answers

Answer: 4x-3

Step-by-step explanation: use the slope formula to calculate the slope, then add the y-int to the equation and ur done hope this helps

What is the value of x in this equation?

2x + 2 = -52
pls someone help

Answers

Answer: x= −27 or x = 27

Step-by-step explanation:

Answer:

-27

Step-by-step explanation:

Subtract 2 from both sides

2x= -54

Divide both sides by 2

x = -27


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Answer:

this is hard to tell and sorry if I'm wrong but I would say it is only a

Step-by-step explanation:

Aanything in the shaded area is correct if it's not it's wrong

You measure a wound to be 2.5 inches long. How many millimetres long is the wound? Round to the nearest tenth.

You measure the depth of a wound to be 0.25 inches. How many millimetres is this? Round to the nearest whole number.

Answers

(a) If you measure a wound to be 2.5 inches long, the corresponding length in millimeters is 63.5 mm.

(b) If you measure the depth of a wound to be 0.25 inches, the corresponding length in millimeters is 6.35 mm.

What is the measure of the lengths?

If you measure a wound to be 2.5 inches long, the corresponding length in millimeters is calculated as follows;

1 in = 25.4 mm

2.5 in = ?

? = 2.5 x 25.4 mm

? = 63.5 mm

If you measure the depth of a wound to be 0.25 inches, the corresponding length in millimeters is calculated as follows;

1 in = 25.4 mm

0.25 in = ?

? = 0.25 x 25.4 mm

? = 6.35 mm

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The points (x, 3) and (-1, -4) lie on the same line. If the slope of the line is 1, what is
the value of x?
A-3
B 1
C 6
D-6

Answers

Answer:

C)  6

Step-by-step explanation:

use slope formula:

(-4 - 3) / (-1 - x) = 1

cross-multiply:

-7 = -1 - x

-6 = -x

6 = x

[x-2]/4=[3x-7]/10 its x-2 dived by 4 not 2/4 same with other side

Answers

Answer:

x = 4

Step-by-step explanation:

Given

[tex]\frac{x-2}{4}[/tex] = [tex]\frac{3x-7}{10}[/tex] ( cross- multiply )

4(3x - 7) = 10(x - 2) ← distribute parenthesis on both sides )

12x - 28 = 10x - 20 ( subtract 10x from both sides )

2x - 28 = - 20 ( add 28 to both sides )

2x = 8 ( divide both sides by 2 )

x = 4

A part manufactured at a factory is known to be 12.05 cm long on average, with a standard deviation of 0.119. One day you suspect that that the part is coming out a little longer than usual, but with the same deviation. You sample 19 at random and find an average length of 12.25. What is the z-score which would be used to test the hypothesis that the part is coming out longer than usual?

Answers

Z-score is used to test the hypothesis that the part is coming out longer than usual. Z-score is defined as the number of standard deviations away from the mean.

It is calculated using the formula z = (x - μ) / σ, where x is the sample mean, μ is the population mean, and σ is the population standard deviation. In the given problem, the population mean is μ = 12.05 cm and the population standard deviation is σ = 0.119 cm. The sample mean is x = 12.25 cm. The sample size is n = 19.

Therefore, the formula to calculate the z-score is Z = (x - μ) / (σ / √n) Substituting the values, we get z = (12.25 - 12.05) / (0.119 / √19) ≈ 6.586Therefore, the z-score which would be used to test the hypothesis that the part is coming out longer than usual is approximately 6.586.

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If 3 inches represents 25 feet on a scale
drawing, how long will a line segment be
that represents 15 feet?

Answers

Answer:

1.8 inches

Step-by-step explanation:

1. find the # of inches that represents 1 foot.

3/25 = 0.12in

2. to find the length of the line segment that represents 15 feet, multiply 0.12 inches by 15.

0.12*15 = 1.8in

Janna is buying a netbook with a flash drive. The total cost c will include the price p of the netbook plus $12.50 for the flashdrive. Which is the dependent variable?

Answers

The dependent variable would be c (for cost) because the total cost depends on the price of the notebook.

Complete the Square of the quadratic equation in standard form: ax2 + bx + c Treat this like a literal equation where you are solving for x by completing the square. To get started, write the equation in the form: x2 + bx = ?

Answers

Answer:

x = [-b ±√(b² - 4ac)]/2a

Step-by-step explanation:

ax² + bx + c = 0

dividing through by a, we have

ax²/a + bx/a + c/a = 0

x² + bx/a + c/a = 0

x² + bx/a = -c/a

we now add th square of half the coefficient of x to both sides, thus

x² + bx/a + (b/2a)² = -c/a +  (b/2a)²

simplifying the left hand side and right hand side, we have

(x + b/2a)² = -c/a + b²/4a²

re-arranging, we have

(x + b/2a)² = b²/4a² - c/a

taking L.C.M of the right hand side, we have

(x + b/2a)² = (b² - 4ac)/4a²

taking square-root of both sides, we have

√(x + b/2a)² = ±√[(b² - 4ac)/4a²]

x + b/2a = ±√(b² - 4ac)/2a

So, x = -b/2a ±√(b² - 4ac)/2a

taking the L.C.M of the right hand side, we have

x = [-b ±√(b² - 4ac)]/2a

please help, tysm if you do

Answers

Answer: It’s 3

Step-by-step explanation:

Hoped I help :)

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Answers

i believe the answer is 36/100

Answer:

Step-by-step explanation:

To find each probability you will state the probability of the first event happening and multiply it by the chance of the second event happening.  

P(2 Nickels):  6/10 x 5/9 = 30/90 (1/3 chance)

P(2 Dimes):  4/10 x 3/9 = 12/90 (4/30 chance)

P(1 nickel and 1 dime): 6/10 x 4/9 = 24/90 (8/30 chance)

I hope this helps :D

Plz help ASAP !!!!!!!! Plzz

Answers

Answer:

option a is the answer to the question

PLEASE HELP ASAP!! WILL GIVE BRANLIEST!!!

Answers

Answer:

Brand A

Step-by-step explanation:

The volume (V) of a cone is calculated as

V = [tex]\frac{1}{3}[/tex]πr²h ( r is the radius and h the height )

Brand A

V = [tex]\frac{1}{3}[/tex]π × 6² × 15 = [tex]\frac{1}{3}[/tex]π × 36 × 15 = π × 12 × 15 = 180π in³

Brand B

V = [tex]\frac{1}{3}[/tex]π × 5² × 18 = π × 25 × 6 = 150π in³

Brand A have the largest volume

A snow removal service in Minnesota is deciding to purchase a new snow removal machine. If they dont purchase the machine, they will make $20,000 if the winter is mild, 530,000 il it is typical, and $50,000 the winter is severe. If they purchase the machine, their profits for these conditions will be $30,000, 535,000 and $40,000, respectively. The probability of a mild winter is 0.3. a typical winter is 0.5 and a severe winter is 0.2. What is the EMV for no machine? 32000 34500 35000 31000

Answers

The Europay, Mastercard and Visa (EMV) for not purchase the snow removal machine is $31,000.

The expected monetary value (EMV) for not purchasing the snow removal machine is $31,000. This value is calculated by multiplying the probabilities of each winter condition by the corresponding profits and summing them up. The probabilities for a mild winter, typical winter, and severe winter are 0.3, 0.5, and 0.2, respectively.

The profits for each condition without the machine are $20,000, $530,000, and $50,000. By multiplying each profit by its probability and adding them together, we get the EMV of $31,000 for not purchase the machine.

In detail, the EMV is calculated as follows:

EMV = (Probability of Mild Winter * Profit for Mild Winter) + (Probability of Typical Winter * Profit for Typical Winter) + (Probability of Severe Winter * Profit for Severe Winter)

EMV = (0.3 * $20,000) + (0.5 * $530,000) + (0.2 * $50,000)

EMV = $6,000 + $265,000 + $10,000

EMV = $31,000

Therefore, the EMV for not purchasing the snow removal machine is $31,000.

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For the following regression model Y = α + βX + u
-Explain how we can test if we adopt the wrong functional forms
of independent variables?

Answers

In order to test if we have adopted the wrong functional forms of independent variables in a regression model Y = α + βX + u, we can use diagnostic plots of the residuals.

Residuals are the differences between the actual values of the dependent variable and the predicted values of the dependent variable. We can plot the residuals against the independent variables to check if there is any functional form that has not been captured by the model, which would indicate that the model has adopted the wrong functional form of independent variables.

If there is no pattern in the residuals when plotted against the independent variables, then it can be concluded that the model has captured the correct functional form of the independent variables. However, if there is a pattern in the residuals, it would indicate that there is some functional form that has not been captured by the model, and we would need to explore different functional forms of the independent variables to see which one fits the data better. This can be done by using different functional forms of the independent variables, such as polynomial, logarithmic, exponential, etc., and comparing the results using various statistical tests.

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If the residuals are normally distributed, then it suggests that the functional form of the independent variable is correct. If they are not, then it suggests that the functional form of the independent variable is incorrect.Overall, it is important to test for the functional forms of independent variables to ensure that the results of the regression model are unbiased and accurate.

In a regression model, it is important to make sure that the functional forms of the independent variables are correct. If they are not, the results of the model may be biased and incorrect. There are several ways to test if the functional forms are correct or not. Below are some of the methods:Plotting the residuals against the independent variable: If the functional form of the independent variable is correct, then the residuals should be randomly distributed around zero, without showing any patterns. If there are patterns in the residuals, then it suggests that the functional form is incorrect. Testing for linearity: One way to test for linearity is by including the square or cubic terms of the independent variable in the model and testing their significance. If the squared or cubic term is significant, then it suggests that the functional form of the independent variable is incorrect. Testing for additivity: One way to test for additivity is by including interaction terms between the independent variables and testing their significance. If the interaction term is significant, then it suggests that the functional form of the independent variable is incorrect. Testing for normality: One way to test for normality is by examining the normal probability plot of the residuals.

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How many four-digit numbers ABCD have the property that ABCDis equal 26 times BCD?

Note that x1x2...xn represents the n-digit number with digits x1x2...xn.

Answers

9514 1404 393

Answer:

  9

Step-by-step explanation:

There are 9 such numbers:

  1040, 2080, 3120, 4160, 5200, 6240, 7280, 8320, 9360

_____

For each ABCD, where BCD = x, we want ...

  26x = 1000A +x

  25x = 1000A

  x = 40A

The digit A ranges from 1 to 9 for a 4-digit number. That means there are 9 such numbers. For A=1, for example, x = 40·1 = 40, so the number ABCD is 1040. 26·BCD = 26·040 = 1040 as required.

Answer:

9 is correct but if you are here from caribou math it is 7

Step-by-step explanation:

don't dislike what they said because it is the right formula. 25x = 1000A

you get 1040 2080 3120 4160 5200 6240 7280 8320 9360. But since caribou asks for bcd, b > 0 because its a 3 digit number. from that we can eliminate 1040 and 2080 getting 7

A pool has a length that is 3 times the width. Write the algebra radical value of the corner to corner distance

Answers

Answer:

The distance between corner to corner is equal to √10 times the width.

D = √10*W

Step-by-step explanation:

For a rectangle of length L and width W, the distance between two opposite corners can be calculated if we use the Pythagorean's theorem, where we can think on the length as one cathetus, the width as another cathetus and the diagonal as the hypotenuse.

Then the length of the diagonal is:

D^2 = L^2 + W^2

D = √( L^2 + W^2)

In this case we know that the length is 3 times the width, then:

L = 3*W

Replacing this in the equation for the diagonal we have:

D = √( (3*W)^2 + W^2) = √( 9*W^2 + W^2)

D = √( 10*W^2) = √10*√W^2 = √10*W

D = √10*W

The distance between corner to corner is equal to √10 times the width.

20. Solve for x,
(x-2y) = 12
P
mathemat
I
vision oro
How do you do this?

Answers

Answer:

x= 24 and y = 6

Step-by-step explanation:

I think that the right answer

A rectangle has a length of 2x + 1 and a width
of 5x - 4. Which expression best describes the
area of the rectangle?
F 7x - 3
H 10x2 – 3x - 4
J 10x2 + 13x - 4
G 14x - 6

Answers

Answer:

H

Step-by-step explanation:

The rectangle has a length of (2x + 1) and a width of (5x - 4).

And we want to select the expression that represents the rectangle's area.

Recall that a rectangle's area is simply its length multiplied by its width. Thus:

[tex]A=(2x+1)(5x-4)[/tex]

Expand by distributing:

[tex]A=(2x+1)(5x)+(2x+1)(-4)[/tex]

Distribute:

[tex]A=(10x^2+5x)+(-8x-4)[/tex]

Simplify:

[tex]A=10x^2-3x-4[/tex]

Hence, our answer is H.

A trapezoid has bases of lengths 38 and 52. Find the trapezoids area if it’s height is 8.

Answers

Answer:

360

Step-by-step explanation:

Find the derivative of f(x) = 8x + 4 at x = 9. (6 points)

Answers

Answer:

f(x) = 76

Step-by-step explanation:

All you do is plug-in for x: (x = 9)

f(x) = 8x + 4

f(x) = 8(9) + 4

f(x) = 72 + 4

f(x) = 76

A brand of uncooked spaghetti comes in a box that is a rectangular prism with a length of 9 inches, a width of 2 inches, and a height of 1 1/2 inches. What is the surface area of the box?

Answers

Answer:

SA = 157 in²

Steps:

SA = 2LW + 2WH + 2LH

SA = 2(9×2) + 2(2×11/2) + 2(9×11/2)

SA = 2×18 + 2×22/2 + 2×99/2

SA = 36 + 22 + 99

SA = 157 in²

Han and Andre were comparing the miles they ran during one week of cross country practice Hantan 12 which was three times as much as Andre
How many they run together during the one week

Answers

Answer:

I don't know.

Step-by-step explanation:

Evaluate 3f(2) what is it

Answers

Answer:

the eanswer should be 12

Step-by-step explanation:

i took the test

M is the midpoint of PQ. PM = 7x + 8 and MQ = 5x+ 20. Find the value of x.​

Answers

M is the midpoint, so PM and MQ are equal,
So you would do 7x+8=5x+20
Then it would be 2x = 12
So 12 / 2, which is 6
X = 6

9.20. set s = 2z = {2x : x ∈ z}, the set of even integers. prove that s is equicardinal with z.

Answers

To prove that the set S = 2Z = {2x : x ∈ Z}, the set of even integers, is equicardinal with Z, the set of all integers, we need to show that there exists a one-to-one correspondence (bijection) between the two sets.

A one-to-one correspondence between two sets exists if every element of one set is paired with a unique element from the other set, and vice versa.

Let's define a function f: Z -> S such that f(x) = 2x for every x ∈ Z.

This function assigns each integer x from Z to its corresponding even integer 2x in S.

To prove that f is a bijection, we need to show that it is both injective (one-to-one) and surjective (onto).

Injectivity: Suppose f(a) = f(b) for some a, b ∈ Z. Then, 2a = 2b. Dividing both sides by 2, we get a = b. Hence, f is injective.

Surjectivity: For every y ∈ S, y = 2x for some x ∈ Z. Choosing x = y/2, we have f(x) = 2x = y. Therefore, f is surjective.

Since f is both injective and surjective, it is a bijection. Thus, S and Z are equicardinal sets.

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Mhanifa please help im almost done :)

Answers

Answer:

19)

9/4 = (r - 10)/r9r = 4(r - 10)9r = 4r - 405r = -40r = -8

20)

(x + 6)/x = 10/710x = 7(x + 6)10x = 7x + 423x = 42x = 14

21)

(n - 9)/(n + 5) = 7/47(n + 5) = 4(n - 9)7n + 35 = 4n - 363n = -71n = -71/3

22)

6/(b + 9) = 4/(b + 5)6(b + 5) = 4(b + 9)6b + 30 = 4b + 362b = 6b = 3

23)

8/3 = (v - 9)/(7v + 4)8(7v + 4) = 3(v - 9)56v + 32 = 3v - 2753v = - 59v = -59/53

24)

8/(5x - 4) = 6/(x + 5)8(x + 5) = 6(5x - 4)8x + 40 = 30x - 2422x = 64x = 64/22x = 32/11

Suppose Lucy want to make sure that when she reaches into her drawer, she is certain to take out enough gloves so that she will have one matching pair to wear. HOW MANY GLOVES MUST SHE TAKE?

Answers

Answer:

its 2

Step-by-step explanation:

I have consulted many nice people ( my idiot friends) they all say 2 good luck

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