1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
nignag [31]
3 years ago
15

Determine whether the following statements are true and give an explanation or a counter example. a. The Trapezoid Rule is exact

when used to approximate the definite integral of a linear function. b. If the number of subintervals used in the Midpoint Rule is increased by a factor of​ 3, the error is expected to decrease by a factor of 8. c. If the number of subintervals used in the Trapezoid Rule is increased by a factor of​ 4, the error is expected to decrease by a factor of 16.
Mathematics
1 answer:
Norma-Jean [14]3 years ago
3 0

Answer:

statement is TRUE  

statement is FALSE  

statement is TRUE  

Step-by-step explanation:

(a)  

By using the Trapezoidal Rule, the definite integral can be computed by applying linear interpolating formula on each sub interval, and then sum-up them, to get the value of the integral  

So, in computing a definite integral of a linear function, the approximated value occurred by using Trapezoidal Rule is same as the area of the region.  Thus, the value of the definite integral of a linear function is exact, by using the Trapezoidal Rule.  

Therefore, the statement is TRUE  

(b) Recollect that for each rule of both the midpoint and trapezoidal rules, the number of sub-internals, n increases by a factor of a. then the error decreases by a factor of a^2.  

So, for the midpoint rule, the number of sub-intervals, n is increased by a factor of 3, then the error is decreased by a factor of 32 = 9, not 8. Therefore, the statement is FALSE  

(c) Recollect that for each rule of both the midpoint and trapezoidal rules, the number of sub-internals, n increases by a factor of a. then the error decreases by a factor of a^2.  

So, for the trapezoidal rule, the number of sub-internals, n is increased by a factor of 4. then the error is decreased by a factor of 42 = 16  

Therefore, the statement is TRUE  

You might be interested in
Which of the following is equivalent to 140 centiliters?
Norma-Jean [14]
The answer is C) because one litre=100 centiliters, and one kilolitre=one litre which means that one kilolitre =100000 centiliters
So 140 centiliters are 140 divided by 100000 kiloliters=0.00140 kiloliters
6 0
3 years ago
Read 2 more answers
Webwork Homework Help; If you but that link that leads to a virus i'm reporting your account!
Darya [45]

9514 1404 393

Answer:

  f(x) = sin(0.62832(x +1))

Step-by-step explanation:

The period of the function is the difference between x=4 and x=-6, which is 10 units. Then the horizontal scaling needs to be such that when x changes by 10, the argument of the sine function changes by 2π. That scaling will make it ...

  f(x) = sin(2π(x/10)) = sin(πx/5)

The upward zero-crossing is seen to be at -1, so this function has been shifted left 1 unit. This requires we replace x with x+1:

  f(x) = sin(π/5(x +1))

If we use the given numerical value for pi, this becomes ...

  f(x) = sin(0.62832(x +1))

8 0
2 years ago
How to put 50,000,000 in standard form?
SVEN [57.7K]

Answer:

50,000,000 is in standard form.

Step-by-step explanation:

This is because standard form would be a written number. So, the non-standard form of 50,000,000 would be fifty million.

6 0
3 years ago
Find the area of the circle. round your answer to the nearest hundredths. the diameter is 2cm​
masha68 [24]

Answer:

3.14 cm squared

Step-by-step explanation:

First, identify the formula necessary to calculate the area of the circle.

Area of a circle = pi x r^2

Remember, the radius is just half of the diameter! Then to square a number, is to multiply it by itself once.

pi x 1^2 =?

pi x 1

Pi

The circumference of your circle is approximately 3.14 cm squared.

6 0
3 years ago
A = 2bh+6<br>make b subject algebraic expression ​
Sindrei [870]

Answer:

b = (a - 6)/2h

Step-by-step explanation:

a = 2bh + 6 (subtract 6 from both sides)

a - 6 = 2bh (divide both sides by 2)

(a - 6)/2 = bh (divide both sides by h)

(a - 6)/2h = b

Brainliest, please :)

6 0
1 year ago
Other questions:
  • What is the answer ?
    9·1 answer
  • What is the solution to the system of equations? 3x + 10y = -47 5x- 7y = 40<br>Please and thank u
    8·2 answers
  • Compare 8.25 and 8.250
    12·1 answer
  • 1 7/11 X 2 5/6 find the product
    8·2 answers
  • W(x)=-3x-4 find w (7)
    12·2 answers
  • PLEASE ANSWER ASAP
    8·2 answers
  • Factor 9s^2 - 36s + 35
    8·1 answer
  • Jamie wants at least 40 roses to bloom in her garden. She noticed that 12 roses have already bloomed. Which inequality could be
    15·1 answer
  • Find the missing side lengths
    10·1 answer
  • Help ASAP!!! Will Mark Brainliest!!! Don't Know, Don't Answer!!!
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!