Write a function trapezium_integrator(f, start, end, num_traps) that uses the Trapezium Rule to evaluate the integral ∫endstartf(x)dx where f, start, and end are defined in the formula above, and num_traps is the number of trapeziums that the integration interval should be divided into.

Notes:

You may assume num_traps >= 1
Hint: This should be a simple modification of your code from the last question.
We are still expecting you to compute the width of each trapezium and then use a for loop to solve this problem, iterating over the trapeziums to sum their areas. A more efficient approach, using numpy and avoiding any explicit loops, is the topic of one of the challenge questions.

Answers

Answer 1

The function trapezium_integrator uses the Trapezium Rule to approximate the value of a definite integral. It takes four parameters: f, which represents the function to be integrated, start and end, which specify the interval of integration, and num_traps, the number of trapeziums used to approximate the integral.

In the Trapezium Rule, the interval of integration is divided into multiple trapeziums of equal width. The area of each trapezium is calculated as the sum of the lengths of its parallel sides divided by 2, multiplied by its height (the difference between the function values at the two endpoints of the trapezium). The areas of all trapeziums are then summed to obtain an approximation of the integral.

The function calculates the width of each trapezium by dividing the interval length by the number of trapeziums. It then uses a for loop to iterate over the trapeziums, accumulating their areas. The final result is returned as the approximation of the integral.

By dividing the interval into smaller trapeziums, the Trapezium Rule provides a reasonably accurate estimate of the integral. However, for highly oscillatory or irregular functions, a large number of trapeziums may be required to achieve sufficient accuracy. In such cases, more sophisticated numerical integration methods may be more appropriate.

Learn more about definite integral here:

https://brainly.com/question/30760284

#SPJ11


Related Questions

According to this partial W-2 form, how much money was paid in FICA taxes? Use the partial sample of a W-2 form to answer a question. $823.73 $4345.89 $6817.08 $11,162.97

Answers

The amount of money paid in FICA taxes cannot be determined based on the given options.

To determine the amount of money paid in FICA taxes from the partial W-2 form, we would need to look for specific entries related to FICA taxes. Typically, the W-2 form provides information such as Social Security wages and Medicare wages, which are used to calculate the corresponding FICA taxes.

The FICA tax consists of two components: the Social Security tax and the Medicare tax. The Social Security tax is calculated based on a fixed percentage (e.g., 6.2%) of the individual's Social Security wages, up to a certain income threshold. The Medicare tax is calculated based on a different fixed percentage (e.g., 1.45%) of the individual's Medicare wages, with no income threshold.

Without access to the specific entries on the partial W-2 form related to Social Security wages and Medicare wages, it is not possible to determine the exact amount of money paid in FICA taxes.

To learn more about amount click here :

brainly.com/question/31009592

#SPJ11

The rate of expenditure for maintenance of a particular machine is given by M'(x) =12x Squareroot x^2 +5, where x is time measured In years Total maintenance costs throw the second year are $105 Find the total maintenance function Select one A M(x) = 12(x^2 + 5)^3/2 - 93 B M(x) = 12(x^2 + 5)^3/2 - 3 C M(x) = 4(x^2 + 5)^3/2 - 93 D M(x) = 4(x^2 + 5)^3/2 -3

Answers

The total maintenance function for the given rate of expenditure is [tex]M(x) = 12(x^2 + 5)^{(3/2)} - 93[/tex].

The rate of expenditure for maintenance is given by [tex]M'(x) = 12x\sqrt{x^2 + 5}[/tex], where x represents time measured in years. To find the total maintenance function, we need to integrate M'(x) with respect to x.

Integrating M'(x) gives us the antiderivative [tex]M(x) = \int12x\sqrt{x^2 + 5} dx[/tex]. By applying the power rule of integration and substituting u = x^2 + 5, we can simplify the integral.

After simplification, we obtain [tex]M(x) = 4(x^2 + 5)^{(3/2)} - 93[/tex]. Therefore, the total maintenance function is [tex]M(x) = 12(x^2 + 5)^{(3/2)} - 93[/tex].

Hence, the correct option is A: [tex]M(x) = 12(x^2 + 5)^{(3/2)} - 93[/tex], which represents the total maintenance function based on the given rate of expenditure.

Learn more about function here:

https://brainly.com/question/30721594

#SPJ11

Romberg integration for approximating -', $(x) dx gives R21 = 6 and R22 = 6.28 then Ru = 0.35 2.15 5.16 4.53

Answers

The required value of Ru is 7.71

Given that Romberg integration for approximating `∫(x) dx` gives `R21 = 6` and `R22 = 6.28`. Then, we need to find `Ru`.

We know that Romberg integration formula is given by:

R_kj = (4^j * R_(k+1),j-1 - R_k,j-1) / (4^j - 1), where, `R_kj` denotes the approximation of integral using `2^(k-1) x 2^(j-1)` points and `R_k,j-1` denotes the approximation of integral using `2^(k-1) x 2^(j-2)` points.

Now, we are given that:

`R21 = 6` and `R22 = 6.28`, we need to calculate `Ru`.

For this, let's use the Romberg integration formula as follows:

`R31 = (4^1 * R22 - R21) / (4^1 - 1)`

Substituting the given values, we get:

`R31 = (4 * 6.28 - 6) / 3 = 7.56 / 3 = 2.52`

Similarly,`R32 = (4^1 * R32 - R31) / (4^1 - 1)`

Substituting the given values, we get:

`R32 = (4 * 6.28 - 2.52) / 3 = 23.12 / 3 = 7.71`

Therefore, `Ru = R32 = 7.71`.Hence, the required value of `Ru` is `7.71`.

To know more about Romberg integration, visit the link : https://brainly.com/question/32552511

#SPJ11

Eiko is wearing a magic ring that increases the power of her healing spell by 30\%30%30, percent. Without the ring, her healing spell restores HHH health points.

Answers

Answer:

Step-by-step explanation:

Answer:

130/100 H  and (3/10 + 1) H

Step-by-step explanation:

Hope this helps!

WILL GIVE BRAINLIEST!
The graph below shows the relationship between distance walked and calories burned.

Find the slope of the line.


Write a sentence that explains the meaning of the slope.
Walking this many miles burns 100 calories.
Walking this many hours burns one calorie.
Walking burns this many calories per hour.
Walking this many miles burns one calorie.
Walking burns this many calories per mile.

Answers

Answer:

70

Step-by-step explanation:

The slope is down 1 over 1.5, so that means Start with the slope formula

m=

(y2 - y1)

(x2 - x1)

Substitute point values in the formula

m=

(140 - 280)

(2 - 4)

Simplify each side of the equation

m=

(140 - 280)

(2 - 4)

=

-140

-2

Solve for slope (m)

m= 70

Booommmm, Im proud of this lol, hope it helps <3

A coin shows heads with probability p. Let Xn be the number of flips required to obtain a run of n consecutive heads. Show that E(Xn) = Ek=p-k.

Answers

To show that E(Xn) = Ek=p-k, we can use the concept of conditional expectation and the law of total expectation.

How to show that E(Xn) = Ek=p-k.

Let's define X as the number of flips required to obtain a run of n consecutive heads.

We can express X as the sum of two random variables: the number of flips required to obtain the first head (H) and the number of additional flips required to obtain a run of n-1 consecutive heads (Xn-1).

We can write the equation as:

X = H + Xn-1

Taking the expectation on both sides, we have:

E(X) = E(H + Xn-1)

Using the linearity of expectation, we can rewrite this as:

E(X) = E(H) + E(Xn-1)

The expected number of flips required to obtain the first head is simply the reciprocal of the probability of getting heads on a single flip, which is 1/p.

So, E(H) = 1/p.

Next, let's consider the expectation of Xn-1. Since Xn-1 represents the number of additional flips required to obtain a run of n-1 consecutive heads, it is equivalent to Xn but with a reduced value of n.

Using the law of total expectation, we can express E(Xn-1) as a conditional expectation:

E(Xn-1) = E(E(Xn-1 | Xn-1 > 1))

In other words, the expected value of Xn-1 can be obtained by conditioning on the event that the first flip is not a head.

Since the first flip is not a head, we need to start over and obtain a new run of n consecutive heads.

Therefore, the expectation of Xn-1 conditioned on Xn-1 > 1 is equal to E(Xn).

Putting it all together, we have:

E(X) = E(H) + E(Xn-1)

    = 1/p + E(Xn)

Simplifying further, we get:

E(X) = 1/p + E(Xn)

Now, notice that E(X) is equal to E(Xn) when n = 1.

Therefore, we can write:

E(X) = 1/p + E(X)  (since E(X1) = E(X))

Solving for E(X), we find:

E(X) = 1/p

Finally, let's substitute k = n-1 into the expression:

E(Xn) = 1/p

Since k = n-1, we have:

E(Xn) = 1/p = Ek=p-k

Therefore, we have shown that E(Xn) = Ek=p-k.

Learn more about probability at https://brainly.com/question/13604758

#SPJ4

8. The probability that a mature hen will lay an egg on a given day is 0.80. Hannah has 6 hens. Using the table, what is the probability that at
least 2 of the hens will lay eggs on a given day?
4
Number of Eggs
Probability
0
0.000064
1
0.002
2.
0.015
3
0.082
5
0.393
6
?
0.246

Answers

The answer is A hope that helps

Find 0. Round to the nearest degree.
A. 20°
B. 69°
C. 21°
D. 70°​

Answers

Answer:

21

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Hope this helped, and please mark as brainliest! <3

Ben weighs 41.9 kg. His older brother weighs 57.6 kg. How much more does his older brother weigh?

Answers

Step-by-step explanation:

[tex]57.6 - 41.9 = 5.7[/tex]

Find the value of x.

Answers

hello i know its wrong but lol. i tried to help.

PLZ ANSWER THIS CORRECTLY FOR 100 POINTS AND BRANLIEST :DD

Answers

#x

2x+30+62=1802x+92=1802x=88x=44

Angle 1

2(44)+3088+30118°

Angle 2

62°(Opposite angles)

Answer:

A)  x = 44

B)  m∠1 = 118°

    m∠2 = 62°

Step-by-step explanation:

Part A

Angles on a straight line sum to 180°

⇒ (2x + 30) + 62 = 180

⇒ 2x + 30 + 62 = 180

⇒ 2x + 92 = 180

⇒ 2x = 88

⇒ x = 44

Part B

Vertical Angle Theorem:  The opposite vertical angles of two straight intersecting lines are congruent.

⇒ m∠1 = (2x + 30)

Substituting the found value of x:

⇒ m∠1 = 2(44) + 30

⇒ m∠1 = 88 + 30

⇒ m∠1 = 118°

Using the Vertical Angle Theorem:

⇒ m∠2 = 62°

The area of a rectangular garden in square feet can be represented by 22 - 102 +21. The length is 2 - 7 feet. You have been hired to fertilize the
garden. Recall that the area of the garden is 22 - 10z +21. If 2 = 20 and the fertilizer costs $0.27 per square foot, how much it cost to fertilize
the garden?

Answers

The area of a rectangular garden in square feet can be represented by z² - 10z +21. The length is z - 7 feet. You have been hired to fertilize the

garden. Recall that the area of the garden is z² - 10z +21. If z = 20 and the fertilizer costs $0.27 per square foot, how much it cost to fertilize

the garden?

Answer:

$ 59.67

Step-by-step explanation:

The area of a rectangular garden in square feet can be represented by z² - 10z +21 square feet

If z = 20

Therefore:

The area of the rectangular garden is:

20² - 10 × 20 + 21

400 - 200 + 21

= 221 square feet

The fertilizer costs $0.27 per square foot, how much it cost to fertilize

the garden?

The cost of fertilize the garden is calculated as:

1 square feet = $0.27

221 square feet = x

Cross Multiply

221 square feet × $0.27

=$ 59.67

Please help me :(((((((

Answers

Answer:

The answer is B

Step-by-step explanation:

Each smaller rectangle is being multiplied by a so 2a + 3a + 4a would give you the total area of the entire large rectangle.

What is the sum of the interior angles of a regular dodecagon (12 sided polygon)? Round to
the nearest thousandth.

Answers

Answer:

1800°

Step-by-step explanation:

(12-2)x180 = 1800

Jamal uses the line of best fit y = 700x + 38,000 to predict his annual salary, y, after x years.

What is the y-intercept of the line of best fit and what is the meaning of the y-intercept?

Answers

The y intercept should be 38,000

y=mx+b

B, the last variable is the y-intercept.

The y-intercept is n intercept is a point on the y-axis, through which the slope of the line passes and the y-intercept of the given equation is 38,000.

What is a y-intercept?

In Maths, an intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.

The given equation is y=700x+38,000 to predict his annual salary, y, after x years.

In the given equation, y-intercept is 38,000.

Therefore, the y-intercept is n intercept is a point on the y-axis, through which the slope of the line passes and the y-intercept of the given equation is 38,000.

To learn more about the y-intercept visit:

brainly.com/question/14180189.

#SPJ2

The lines below are parallel. If the slope of the green line is -3, what is the
slope of the red line?
m =

Answers

Answer:

-3

Step-by-step explanation:

parallel lines are congruent which means that they equal the same thing

find the value of x... assume segments that appear tangent are tangent.

Answers

Answer:

x=12

Step-by-step explanation:

a^2 + b^2 = c^2

5^2 + b^2 = 13^2

25 + b^2 = 169

b^2= 144

b=12 Therefore,

x=12

Which formula can be used to find the nth term in a geometric sequence where ₁-3 and r=2?
Oa-3+2(n-1)
O a-3(n-1)+2
O a-3-1-2
Oa-3-2-1

Answers

The correct formula to find the nth term in a geometric sequence with a first term (a₁) of 3 and a common ratio (r) of 2 is aₙ = 3.2^(n-1).The correct answer is option D.

In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio. In this case, the first term (a₁) is 3, and the common ratio (r) is 2.

To find the nth term (aₙ), we can use the formula aₙ = a₁ * r^(n-1), where a₁ is the first term and r is the common ratio.

Plugging in the given values, we get aₙ = 3 * 2^(n-1), which simplifies to aₙ = 3.2^(n-1). Therefore, option D is the correct formula.

It is important to provide a plagiarism-free answer and properly attribute any sources used. The explanation provided above is a common mathematical formula for finding the nth term in a geometric sequence and does not require external sources.

For more such questions on geometric,click on

https://brainly.com/question/19241268

#SPJ8  

The probable question may be:

Which formula can be used to find the nth term in a geometric sequence where a_{1} = 3 and r=2?

A. a_{n} - 3 + 2(n - 1)

B. a_{2} - 3(n - 1) + 2

C. a_{3} = 3 ^ (n - 1) * 0.2

D. a_{n} = 3.2 ^ (n - 1)

Amad collected 42 plates in February for a project he plans to make. He had collected a total of 91 plates by the end of March. Which equation can be used to find the number of plates Amad collected in March? A. 42 * p = 91 b. P - 91 = 42 c. 91 / p = 42 d. P + 42 = 91

Answers

Answer:

Option D: P + 42 = 91

Step-by-step explanation:

Plates collected in February = 42

Total Plates collected = 91

Plates in February + Plates in March = total plates

42 + P = 91 or

P + 42 = 91

What is the constant of proportionality in the table below?

Answers

Answer:

12

Step-by-step explanation:

y = kx where 'k' is the constant of proportionality

24 = 2 x 12

36 = 3 x 12

48 = 4 x 12

60 = 5 x 12

Clara visits the aquarium while on vacation. The aquarium is 2 1/2 from her hotel. She walks 1/4 mile to the bus stop, take the bus for 1 3/4 miles, and walks the rest of the way to the aquarium.

Answers

Answer:

1/2

Step-by-step explanation:

Three coins are tossed. Draw a Tree-diagram to show the possible outcomes. What is the sample space for this event? Also, find the probability of getting:

a) no heads

b) exactly 2 tails

c) at least 2 heads

d) at most 2 tails

Answers

There are 6 possible outcomes:P(HHH) + P(HHT) + P(HTH) + P(THH) + P(HTT) + P(THT) = 7/8

a) No heads: 0.125

b) Exactly 2 tails: 0.375

c) At least 2 heads: 0.5

d) At most 2 tails: 0.875.

Given that three coins are tossed, we need to draw a Tree-diagram to show the possible outcomes and then find the sample space for this event.

Afterward, we need to find the probability of getting:

a) no heads

b) exactly 2 tails

c) at least 2 heads

d) at most 2 tails

Tree-diagram:

It is a tree diagram representing the tossing of three coins to show all possible outcomes.Sample space:

It is the set of all possible outcomes.

The sample space for this event is: {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

a) No heads are (TTT) and the probability of getting no head is:

P(TTT) = 1/8

= 0.125

b) Exactly two tails are (HHT, HTH, THH) and the probability of getting exactly 2 tails is:

P(HHT) + P(HTH) + P(THH) = 3/8

= 0.375

c) At least 2 heads means getting 2 heads or 3 heads. There are 4 possible outcomes:P(HHH) + P(HHT) + P(HTH) + P(THH) = 1/2 = 0.5d)

At most 2 tails mean getting 0 tails or 1 tail.

There are 6 possible outcomes:P(HHH) + P(HHT) + P(HTH) + P(THH) + P(HTT) + P(THT) = 7/8

= 0.875

Hence, the answers are:

a) No heads: 0.125

b) Exactly 2 tails: 0.375

c) At least 2 heads: 0.5

d) At most 2 tails: 0.875.

To know more about probability , visit ;

https://brainly.com/question/13604758

#SPJ11

What Is 21+21,000 Please tell me what the answer

Answers

Answer:

21021

Step-by-step explanation:

You flip a coin. What is P(not tails)? 50%

Answers

Heads I think I’m not really sure what your asking.

The cone below has a radius of 1 inch and height of 4 inches. What is the slant height in inches?

a. √-5

b. √−−17

c. 15

d. 17

Answers

Answer:

Step-by-step explanation:

Answer pls it's due

Answers

wanna b my bestie :plead:

someone help, what’s 1+1?

Answers

It's 2 sir/ Maam Your Welcome

consider the following time series. t 1 2 3 4 5 yt 6 11 9 14 15

Answers

The given time series data is represented by the pairs (t, y(t)): (1, 6), (2, 11), (3, 9), (4, 14), and (5, 15).

The time series data provided consists of values of the dependent variable y at different time points t. In this case, we have the values of y at time points 1, 2, 3, 4, and 5. The corresponding values of y are 6, 11, 9, 14, and 15, respectively.

Time series data is commonly used in various fields, such as economics, finance, and engineering, to analyze patterns and trends over time. By examining the values in the given time series, one can identify any trends, seasonality, or other patterns that may be present in the data.

To know more about time series click here: brainly.com/question/29818565

#SPJ11


what’s the measure of angle B?

Answers

Answer:

60°

Step-by-step explanation:

∠B=(240-120)/2=120/2=60°

Jayden is trying to pick out an outfit for the first day of school. He can choose from 2
pairs of pants, 3 t-shirts, and 6 pairs of shoes. How many different outfits does
Jayden have to choose from?

Answers

Answer:

36

Step-by-step explanation:

Use the counting principle.

2 * 3 * 6 = 36

Answer: 36

Answer: 30 outfits

Step-by-step explanation:

2 x 5 x 3 =30

Other Questions
which idea does this poster promote? a. women should get paid the same as men. b. women can do some jobs better than men. c. women can do the same jobs as men. d. women are harder workers than men. The analysis of cost and perfect competition and measuring a nation income and the goods of market and the measuring the cost of living and unemployment for ksa on year 2020 the answer should include grahp make economeic analysis for cost of living unemployment perfect competition nation income for year 2020 Two 2.40cm X 2.40cm plates that form a parallel-plate capacitor are charged to +/- 0.708nC A. What is potential difference across the capacitor if the spacing between the plates is 1.30mm ? B. What is the electric field strength inside the capacitor if the spacing between the plates is 2.60mm? c. What is the potential difference across the capacitor if the spacing between the plates is 2.60mm? I = P x A x T model can be used to calculate which of the following?a) level of urbanization b) people overpopulation c) rate of industrialization through collaborative negotiations both side work together to maximize the outcome or create a win-win result Which of the following null hypotheses is appropriate for an independent-measures t test?H: < 4H: 0H: = 0H: 0 for any data set, which measures of central location have only one value? which of the following is not one of the so-called ""three ds of economic cycle analysis?"" (a) dispersion; (b) drive (or momentum); (c) depth; (d) duration. The following items and amounts are taken from the 2021 financial records of Labrador Co. All amounts are U.S. dollars. Supplies expense... $32,000 Salaries payable.. $5,000 Equipment.. 72,000 Common stock.. 50,000Salaries expense.... 150,000 Cash.... 12,000 Utilities expense... 8,200 Retained earnings, Jan. 1, 2021...... 47,000Dividends.... 1,000 Insurance expense...... 12,000 Accounts payable.......... 6,000 Repair expense.. 14,000Accounts receivable........ 26,800 Service revenue.. 220,000a) Prepare an income statement for the year ending December 31, 2021. b) Prepare a statement of stockholders' equity for the year ending December 31, 2021. c) Prepare a balance sheet as of December 31, 2021. Make sure each statement is in proper form with a complete heading (name of company, name of report, date or time period as appropriate). Oslo Company prepared the following contribution format income statement based on a sales volume of 1,000 units (the relevant range of production is 500 units to 1,500 units): Sales $ 45,000 Variable expenses 31,500 Contribution margin 13,500 Fixed expenses 8,640 Net operating income $ 4,860.1. If sales increase to 1,001 units, what would be the increase in net operating income?2. If sales decline to 900 units, what would be the net operating income?3. If the selling price increases by $2 per unit and the sales volume decreases by 100 units, what would be the net operating income?4. If the variable cost per unit increases by $1, spending on advertising increases by $1,350, and unit sales increase by 170 units, what would be the net operating income?5.What is the break-even point in dollar sales? The acceptable risk of incorrect acceptance is most related to:A) audit efficiency.B) audit results.C) audit effectiveness.D) audit estimation. (Sovereign Default Model) Let it be a risk free rate on the T-Bills. Let Dt be the amount of debt. When the government issues the amount of debt Dt and defaults on it, the household consumption with any given ne (0, 1) in the next period is given by C = (1-n)Y (Default)When the government does not default, the household consumption in the next period is given by C=Y1 Dt (No- Default)Finally, the income shock in the next period Yt+1 is uniformly distributed from 0.5 to 1.5. That is, the probability density function for Yt+1 is given by f(y)=1 if 0.5 Yt 1.5 (3) (4) f(y) = 0, otherwise a) An investor bought the bond issued by the government at the price of P. What is the return on this bond when the government defaults (i.e., compute id)? b) Let i = 0 and n = 0.4, and the investors are risk-neutral. (i) Find a range of Dt such that the bond price for this debt is the same as that for the T-Bills. (ii) Find a range of Dt such that the bond price is zero. (Note that D 0). (iii) Find a range of D, such that no investors would buy this bond in the government bond auction market. c) Let it = 0 and n = 0.4, Dt = 0.4, and the investors are risk-neutral. What is the probability of default on this debt, pa ? What is the sovereign spread on this debt when the government issues D = 0.4 amount of debt in the government bond auction market? how is a "learning relationship" different from many customer intelligence activities that companies have historically executed (e.g., marketing research, focus groups, etc.)? URGENT PLEASE HELP WITH TWENTY-FIVE POINTS:5. Write a short paragraph that explains the central idea of the article. Use at least two details from the article to support your response. conscious marketing values suggest that a company's rules should include a code of ethics and a system for defining what? . _____ contracts involve payment to the supplier for direct and indirect actual costs and often include fees.a. Firm-fixed-price b. Lump sumc. Cost-reimbursable d. Fixed-price incentive fee the epa is responsible for setting and enforcing regulation related to _______.a.workplace environmentc.traffic and roadwaysd.workplace efficiency Formulate a new strategy for University of Manchester considering the key elements of Strategy Formulation. In a certain college, 55% of the students are women. Suppose we take a sample of two students. Use a probability tree to find the probability(a) thatbothchosenstudentsarewomen.(b) thatatleastoneofthetwostudentsisawoman. michael porter is of the conviction that strategy is the outcome of deliberate, rational analysis. a different perspective put forth by henry mintzberg says