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Arisa [49]
3 years ago
12

Use the Midpoint Rule and the given data to estimate the value of the integral I. (Give the answer to two decimal places.)

Mathematics
1 answer:
svlad2 [7]3 years ago
5 0

Answer:

a) integral = 24.72

b) |Error| ≤ 0.4267

Step-by-step explanation:

a)

The integral:

\int_{0}^{3.2} f(x) dx

can be  approximated with the midpoint rule, as follows:

6.7*(0.8 - 0.0) + 8.9*(1.6 - 0.8) + 6.9*(2.4-1.6) + 8.4*(3.2 - 2.4) = 24.72

(that is, all the intervals are 0.8 units length and f(x) is evaluated in the midpoint of the interval)

b)The error bound for the midpoint rule with <em>n</em> points is:

|Error| ≤ K*(b - a)^3/(24*n^2)

where <em>b</em> and are the limits of integration of the integral and K = max |f''(x)|

Given that -5 ≤ f''(x) ≤ 1, then K = 5.  Replacing into the equation:

|Error| ≤ 5*(3.2 - 0)^3/(24*4^2) = 0.4267

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ExtremeBDS [4]
Answer: 4

find the largest number (5) and take away the smallest (1)

5-1=4
6 0
3 years ago
Lakima has a spinner divided into 5 equal sections that are labeled 1 though 5. She wants to compare the theoretical probability
Scrat [10]

Using probability concepts, it is found that:

  • The theoretical probability of spinning an odd number is equal to 3/5 = 0.6.
  • The experimental probability of spinning an odd number is equal to 1/2 = 0.5.
  • Therefore, the theoretical probability of spinning an odd number is greater than the experimental probability of spinning an odd number.

<h3>What is a probability?</h3>

A probability is given by the <u>number of desired outcomes divided by the number of total outcomes</u>.

A theoretical probability is calculated without considering experiments, and we have that 3 out of the 5 numbers(1,3,5) and are odd, hence the theoretical probability is given by:

pT = 3/5 = 0.6.

For an experimental probability, we consider the experiments. Of the 6 spins, 3 resulted in an odd number, hence the experimental probability is given by:

p = 3/6 = 1/2 = 0.5.

Therefore, the theoretical probability of spinning an odd number is greater than the experimental probability of spinning an odd number.

More can be learned about probabilities at brainly.com/question/14398287

#SPJ1

3 0
2 years ago
HELP I need help.<br> The winner will have 3035 points but for now, 100 points.
OLga [1]

Answer:

$6960

Step-by-step explanation:

p is not the principle. It is the principal.

I = prt

p = $6000

r = 8% = 0.08

t = 2

I = ($6000)(0.08)(2)

I = $960

Total amount after 2 years = principal + interest

Total amount = $6000 + $960

Total amount = $6960

8 0
2 years ago
Read 2 more answers
What is the value of x?
SSSSS [86.1K]
All angles in a triangle add up to 180

180 = 9 + 15 + 2x - 1 + 3x

180 = 24 - 1 + 2x + 3x

180 = 23 + 5x

180 - 23 = 5x

157 = 5x

Divide both sides by 5

X = 31.4 or 157/5
3 0
3 years ago
Solve number 8 please
beks73 [17]

Answer:

see explanation

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k )² = r²

where (h, k ) are the coordinates of the centre and r is the radius

given

x² + y² - 8x + 8y + 23 = 0

collect the x and y terms together and subtract 23 from both sides

x² - 8x + y² + 8y = - 23

using the method of completing the square

add ( half the coefficient of the x / y terms )² to both sides

x² + 2(- 4)x + 16 + y² + 2(4)y + 16 = - 23 + 16 + 16

(x - 4)² + (y + 4)² = 9 ← in standard form

with centre = (4, - 4 ) and r = \sqrt{9} = 3

this is shown in graph b

7 0
2 years ago
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