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inna [77]
11 months ago
7

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

le and simpson's rule to a first-year student majoring in math? what do these rules solve? what are the error limits of each method? under what circumstances would you use one method instead of the other?
Mathematics
1 answer:
harkovskaia [24]11 months ago
3 0

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

brainly.com/question/16996659

#SPJ4

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At his favorite restaurant, Dylan orders a soda with his dinner. The ice in his drink has a mass of 6 g and a volume of 20 cm3.
frez [133]

Answer:

0.3

Step-by-step explanation

The formula to find density is m/v=p

m=mass

v=volume

p=density

<h3>---------------------------</h3>

All we have to do is plug in 6g and 20cm^3

This will give us 6/20 which simplifies to 3/10

With this you can easily figure out that the decimal for 3/10 is 0.3

So the density of the ice is <u>0.3</u>

<u>Hope this helped!</u>

5 0
2 years ago
Which is the zero of the function f(x)=(x+3) (2x-1)(x+2) ?
Scrat [10]

Answer:

x= -3     x = 1/2     x=-2

Step-by-step explanation:

f(x)=(x+3) (2x-1)(x+2)

Set equal to zero

0 =(x+3) (2x-1)(x+2)

Using the zero product property

x+3 =0   2x-1 =0    x+2 =0

x= -3    2x =1       x = -2

x= -3     x = 1/2     x=-2

6 0
3 years ago
Somebody help me !!!! HELPP please!!!
stellarik [79]
Step 1: Read and understand the problem statement.

You are given (time, depth) pairs of (20 s, 8 cm) and (40 s, 0 cm) and asked to write an equation that describes the relationship of depth (y) to time (x).

The rate of change is (0 cm -8 cm)/(40 s -20 s) = -8 cm/(20 s) = -2/5 cm/s. Then in point-slope form using the second point, the linear function rule is
  y = (-2/5)(x -40) +0
You can expand this to
  y = (-2/5)x +16
  y = -0.4x +16 . . . . . . using a decimal number for the slope

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If the bathtubs in your "draining race" start with the same level, the one with the steepest slope (-0.5 cm/s) will win.

8 0
3 years ago
What is gcf of 24, 60, and 36
maxonik [38]

Answer:

12

Step-by-step explanation:

3 0
3 years ago
Determine whether the point (2, 2) is a solution to the system of equations. Explain your reasoning in complete sentences. Prove
goblinko [34]

Answer:

(0,2) is the solution of the given functions.

Step-by-step explanation:

We have been given two functions  f(x)=|x-1|+1  and g(x)=3x+2

To find the solution of the two functions mathematically, we will equate the given functions:

3x+2=|x-1|+1

3x+1=|x-1|

When we will open the modulus function we will have two values +, -

In positive case:

3x+1 =x-1

2x=-2

x=-1

Now, substitute x=-1 in g(x)=3x+2 we get

g(-1)=3(-1)+2=-1

Hence, (-1,-1) is the solution of the given functions.

In negative case:

Now, 3x+1=-(x-1)

3x+1=-x+1

4x=0

x=0

Now, put x=0 in g(x)=3x+2 we get

g(0)=3(0)+2=2

We have another solution: (0,2)

The point (2,2) is not the solution.

And graphically, the solution of two functions is their intersection point which is (0,2)

Hence, (0,2) is the solution of the function.


6 0
3 years ago
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