Question 4 (10 points)

respond to the following in a minimum of 175 of your own words: how would you explain the differences between the trapezoidal ru

harkovskaia [24]

The differences between the trapezoidal rule and simpson's rule is -

The trapezoidal rule and Simpson's method, the latter a set of formulas of varying complexity, are both Newton-Cotes formulas, that are used to examine and model complex curves.

<h3>What is trapezoidal rule?</h3>

The trapezoidal rule is just an integration rule that divides a curve into small trapezoids to calculate the area under it. A area under the curve is calculated by adding the areas of all the small trapezoids.

Follow the steps below to use the trapezoidal rule to determine the area under given curve, y = f. (x).

Step 1: Write down the total number of sub-intervals, "n," as well as the intervals "a" and "b."
Step 2: Use the formula to determine the width of the sub-interval, h (or) x = (b - a)/n.
Step 3: Use the obtained values to calculate this same approximate area of a given curve, ba f(x)dx Tn = (x/2) [f(x0) + 2 f(x1) + 2 f(x2) +....+ 2 f(n-1) + f(n)], where xi = a + ix

<h3>What is Simpson's method?</h3>

Simpson's rule is used to approximate the area beneath the graph of the function f to determine the value of the a definite integral (such that, of the form b∫ₐ f(x) dx.

Simpson's 1/3 rule provides a more precise approximation. Here are the steps for using Simpson's rule to approximate the integral ba f(x) dx.

Step 1: Figure out the values of 'a' & 'b' from interval [a, b], as well as the value of 'n,' which represents the number of subintervals.
Step 2: Determine the width of every subinterval using the formula h = (b - a)/n.
Step 3: Using the interval width 'h,' divide this same interval [a, b] [x₀, x₁], [x₁, x₂], [x₂, x₃], ..., [xn-2, xn-1], [xn-1, xn] into 'n' subintervals.
Step 4: In Simpson's rule formula, substitute all of these values and simplify. b∫ₐ f(x) dx ≈ (h/3) [f(x0)+4 f(x1)+2 f(x2)+ ... +2 f(xn-2)+4 f(xn-1)+f(xn)].

Thus, sometimes we cannot solve an integral using any integration technique, and other times we don't have a particular function to integrate. Simpson's rule aids in approximating the significance of the definite integral in such cases.

To know more about the Simpson's method and trapezoidal rule, here

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3 0

10 months ago

choose three numbers from 2 to 5 write the numbers as addends in addition sentence show two ways to find the sum

slava [35]

3 4 3.5 are ur number

3+ 4+ 3.5=10.5

7 0

3 years ago

The first two terms in an arithmetic progression are 57 and 46. The last term is -207. Find the sum of all the terms in this pro

statuscvo [17]

Answer:

-1875

Step-by-step explanation:

An arithmetic sequence has a common difference as a sequence. Here the common differnece is -11.

So our sequence so far looks like,

(57,46,35,24....). We know the last term of the sequence is -207 and we need to find the nth term of that series so we use arithmetic sequence

$a _{1} + (n - 1)d$

where a1 is the inital value,

d is the common differnece and n is the nth term.

We need to find the nth term so

$57 + (n - 1)( - 11) = - 207$

$(n - 1)( - 11) = - 264$

$n - 1 = 24$

$n = 25$

So the 25th term of a arithmetic sequence is last term, now we can use the sum of arithmetic sequence

which is

$\frac{a _{1} + a _{n} }{2} n$

$\frac{57 + ( - 207)}{2} (25) =$

$\frac{ - 150}{2} (25)$

$- 75(25) = - 1875$

6 0

2 years ago

Read 2 more answers

Following are the published weights (in pounds) of all of the team members of Football Team A from a previous year.178; 203; 212

mylen [45]

Answer:

a. 241; b. 206.0; c. 272.0; d. 174 to 232; other answers (see below).

Step-by-step explanation:

First, at all, we need to organize the data from the smallest to the largest value:

174 178 178 184 185 185 185 185 188 190 200 203 205 206 210 212 212 212 212 215 215 220 223 228 230 232 241 241 242 245 247 250 250 259 260 260 265 265 270 272 273 275 276 278 280 280 285 285 286 290 290 295 302

This step is important to find the median, the first quartile, and the third quartile. There are numerous methods to find the median and the other quartiles, but in this case, we are going to use a method described by Tukey, and it does not need calculators or software to estimate it.

<h3>Part a: Median</h3>

In this case, we have 53 values (an odd number of values), the median is the value that has the same number of values below and above it, so what is the value that has 26 values below and above it? Well, in the organized data above this value is the 27th value, because it has 26 values above and below it:

174 178 178 184 185 185 185 185 188 190 200 203 205 206 210 212 212 212 212 215 215 220 223 228 230 232 241 241 242 245 247 250 250 259 260 260 265 265 270 272 273 275 276 278 280 280 285 285 286 290 290 295 302

The median is 241.

<h3>Part b: First Quartile</h3>

For the first quartile, we need to calculate the median for the lower half of the values from the median previously obtained. Since we have an odd number of values (53), we have to include the median in this calculation. We have 27 values (including the median), so the "median" for these values is the value with 13 values below and above it.

174 178 178 184 185 185 185 185 188 190 200 203 205 206 210 212 212 212 212 215 215 220 223 228 230 232 <em>241</em>

Since we are asking to round the answer to one decimal place, the first quartile is 206.0

<h3>Part c: Third Quartile</h3>

We use the same procedure used to find the first quartile, but in this case, using the upper half of the values.

<em>241</em> 241 242 245 247 250 250 259 260 260 265 265 270 272 273 275 276 278 280 280 285 285 286 290 290 295 302

So, the third quartile is 272.0

<h3>Part d: The middle 50% </h3>

The second quartile is the median and "50% of the data lies below this point" (Quartile (2020), in Wikipedia). Having this information into account, 50% of the weights lies below the median 241.

Thus, the middle 50% of the weights are from 174 to 232.

174 178 178 184 185 185 185 185 188 190 200 203 205 206 210 212 212 212 212 215 215 220 223 228 230 232 <em>241</em>

<h3>Part e: Sample or Population 1</h3>

If the population were all professional football players, the right option is:

<em>The above data would be a sample of weights because they represent a subset of the population of all football players. </em>

It represents a sample. Supposing Football Team A are all professional, they can be considered a sample from all professional football players.

<h3>Part f: Sample or Population 2</h3>

If the population were Football Team A, the right option is:

<em>The data would be a population of weights because they represent all of the players on Football Team A. </em>

<h3>Part g: population mean and more</h3><h3>Part i</h3>

The mean for the population of weights of Football Team A is the sum of all weights (12529 pounds) divided by the number of cases (53).

$\\ \mu = \frac{12529}{53} = 236.39622641509433$

$\\ \mu = \frac{12529}{53} = 236.40$

The standard deviation for the population is:

$\\ \sigma = \sqrt(\frac{(x_{1}-\mu)^2 + (x_{2}-\mu)^2 + ... + (x_{n}-\mu)^2}{n})$

In words, we need to take either value, subtract it from the population mean, square the resulting value, sum all the values for the 53 cases (in this case, the value is 74332.67924), divide the value by 53 (1402.50338) and take the square root of it (37.45001).

Then, the population standard deviation is 37.45.

The weight that is 3 standard deviations below the mean can be obtained using the following formula:

$\\ z = \frac{x - \mu}{\sigma}$

$\\ \mu= 236.40\;and\;\sigma=37.45$

Then, in the case of three standard deviations below the mean, z = -3.

$\\ -3 = \frac{x - 236.40}{37.45}$

$\\ x = -3*37.45 + 236.40$

$\\ x = 124.05$

For the player that weights 209 pounds:

$\\ z = \frac{x - \mu}{\sigma}$

$\\ z = \frac{229 - 236.40}{37.45}$

$\\ z = -0.19$

<h3>Part h: Comparing Weights of Team A and Team B</h3>

For Team B, we have a <em>mean</em> and a <em>standard deviation</em> of:

$\\ \mu=240.08\;and\;\sigma=44.38$

And Player B weighed 229 pounds.

$\\ z = \frac{x - \mu}{\sigma}$

$\\ z = \frac{229 - 240.08}{44.38}$

$\\ z = -0.70$

This value says that Player B is lighter with respect to his team than Player A, because his weight is 0.70 below the mean of Football Team B, whereas Player A has a weight that is closer to the mean of his team. So, the answer is:

<em>Player B, because he is more standard deviations away from his team's mean weight.</em>

<h3 />

4 0

3 years ago

Emma throws an object upward from a hill that is 64 feet high. The object has an initial velocity of 48 feet per second. The fun

sveta [45]

Well, i know that a non linear function always has a number power greater than 1, and a linear function only has a number power 1 or less.

Hope this helps

8 0

3 years ago

Read 2 more answers