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
Gennadij [26K]
3 years ago
10

Question 16 (5 points)

Mathematics
1 answer:
Aloiza [94]3 years ago
6 0

Answer:

i think its b

???

Step-by-step explanation:

im sorry if im wrong im not very confident on my answer :(

You might be interested in
Сalculus2<br> Please explain in detail if possible
Tom [10]

Looks like n_t is the number of subintervals you have to use with the trapezoidal rule, and n_s for Simpson's rule. In the attachments, I take both numbers to be 4 to make drawing simpler.

  • For both rules:

Split up the integration interval [1, 8] into <em>n</em> subintervals. Each subinterval then has length (8 - 1)/<em>n</em> = 7/<em>n</em>. This gives us the partition

[1, 1 + 7/<em>n</em>], [1 + 7/<em>n</em>, 1 + 14/<em>n</em>], [1 + 14/<em>n</em>, 1 + 21/<em>n</em>], ..., [1 + 7(<em>n</em> - 1)/<em>n</em>), 8]

The left endpoint of the ith interval is given by the arithmetic sequence,

\ell_i=1+\dfrac{7(i-1)}n

and the right endpoint is

r_i=1+\dfrac{7i}n

both with 1\le i\le n.

For Simpson's rule, we'll also need to find the midpoints of each subinterval; these are

m_i=\dfrac{\ell_i+r_i}2=1+\dfrac{7(2i-1)}{2n}

  • Trapezoidal rule:

The area under the curve is approximated by the area of 12 trapezoids. The partition is (roughly)

[1, 1.58], [1.58, 2.17], [2.17, 2.75], [2.75, 3.33], ..., [7.42, 8]

The area A_i of the ith trapezoid is equal to

A_i=\dfrac{f(r_i)+f(\ell_i)}2(r_i-\ell_i)

Then the area under the curve is approximately

\displaystyle\int_1^8f(x)\,\mathrm dx\approx\sum_{i=1}^{12}A_i=\frac7{24}\sum_{i=1}^{12}f(\ell_i)+f(r_i)

You first need to use the graph to estimate each value of f(\ell_i) and f(r_i).

For example, f(1)\approx2.1 and f(1.58)\approx2.2. So the first subinterval contributes an area of

A_1=\dfrac{f(1.58)+f(1)}2(1.58-1)=1.25417

For all 12 subintervals, you should get an approximate total area of about 15.9542.

  • Simpson's rule:

Over each subinterval, we interpolate f(x) by a quadratic polynomial that passes through the corresponding endpoints \ell_i and r_i as well as the midpoint m_i. With n=24, we use the (rough) partition

[1, 1.29], [1.29, 1.58], [1.58, 1.88], [1.88, 2.17], ..., [7.71, 8]

On the ith subinterval, we approximate f(x) by

L_i(x)=f(\ell_i)\dfrac{(x-m_i)(x-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+f(m_i)\dfrac{(x-\ell_i)(x-r_i)}{(m_i-\ell_i)(m_i-r_i)}+f(r_i)\dfrac{(x-\ell_i)(x-m_i)}{(r_i-\ell_i)(r_i-m_i)}

(This is known as the Lagrange interpolation formula.)

Then the area over the ith subinterval is approximately

\displaystyle\int_{\ell_i}^{r_i}f(x)\,\mathrm dx\approx\int_{\ell_i}^{r_i}L_i(x)\,\mathrm dx=\frac{r_i-\ell_i}6\left(f(\ell_i)+4f(m_i)+f(r_i)\right)

As an example, on the first subinterval we have f(1)\approx2.1 and f(1.29)\approx1.9. The midpoint is roughly m_1=1.15, and f(1.15)\approx2. Then

\displaystyle\int_{\ell_1}^{r_1}f(x)\,\mathrm dx\approx\frac{1.29-1}6(2.1+4\cdot2+1.9)=0.58

Do the same thing for each subinterval, then get the total. I don't have the inclination to figure out the 60+ sampling points' values, so I'll leave that to you. (24 subintervals is a bit excessive)

For part 2, the average rate of change of f(x) between the points D and F is roughly

\dfrac{f(5.1)-f(2.7)}{5.1-2.7}\approx\dfrac{1.3-2.6}{5.1-2.7}\approx-0.54

where 5.1 and 2.7 are the x-coordinates of the points F and D, respectively. I'm not entirely sure what the rest of the question is asking for, however...

8 0
3 years ago
FOR 40 POINTS<br> The is used to measure volume.<br> choices:<br> meter<br> gram<br> liter
Pachacha [2.7K]

Answer:

liter

Step-by-step explanation:

4 0
3 years ago
Find the value of "x".
Gnoma [55]

Answer:

49 . hope you found it helpful

3 0
3 years ago
If you wanted to find the difference of 6/25 - 4/5 what common denominator schould you choose? Why
goldfiish [28.3K]
6/25 - 4/5.......u should choose the lowest common denominator which is 25.
6/25 - 20/25 = - 14/25

however, even if u didn't pick the lowest....lets say u picked 50
6/25 - 4/5 = 12/50 - 40/50 = - 28/50 reduces to - 14/25...u will still get the same answer...u will just have to reduce

the reason u want to pick the lowest common denominator is because it is easier....if u do not pick the lowest, u will have to reduce....so picking the lowest just saves you time. also u can round up or down if u wanna be more smart
5 0
3 years ago
Read 2 more answers
How much is half of 2.893
borishaifa [10]
2.893/2 = 1.4465 Pretty much it
5 0
3 years ago
Other questions:
  • A triangle on a coordinate plane is translated according to the rule T-8,4(x, y). Which is another way to write this rule?
    6·1 answer
  • Factor: 15c^2 +37c +20
    13·1 answer
  • What is the mean number of cakes jenny bakes in a month
    9·2 answers
  • What is the solution to the equation 2(4-8x)+5(2x-3)=20-5x
    9·2 answers
  • 5.00a+1.50c=917 how do you do it?
    7·1 answer
  • F(x)=71(0.93)^2x growth or decay
    8·1 answer
  • Think about the numbers -10 and 10. How could you describe these numbers? What is the same and what is different about these num
    13·1 answer
  • 1. The area of a square tile is 36 square centimeters. What is the length of the tile?
    5·1 answer
  • -2(3x-3)=4x x= Would you please help me Solve the equation for x
    11·2 answers
  • Select the correct answer:
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!