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
Mrac [35]
3 years ago
12

100 points , please help. I am not sure if I did this correct if anyone can double-check me thanks!

Mathematics
1 answer:
Nookie1986 [14]3 years ago
8 0

Step-by-step explanation:

\lim_{n \to \infty} \sum\limits_{k=1}^{n}f(x_{k}) \Delta x = \int\limits^a_b {f(x)} \, dx \\where\ \Delta x = \frac{b-a}{n} \ and\ x_{k}=a+\Delta x \times k

In this case we have:

Δx = 3/n

b − a = 3

a = 1

b = 4

So the integral is:

∫₁⁴ √x dx

To evaluate the integral, we write the radical as an exponent.

∫₁⁴ x^½ dx

= ⅔ x^³/₂ + C |₁⁴

= (⅔ 4^³/₂ + C) − (⅔ 1^³/₂ + C)

= ⅔ (8) + C − ⅔ − C

= 14/3

If ∫₁⁴ f(x) dx = e⁴ − e, then:

∫₁⁴ (2f(x) − 1) dx

= 2 ∫₁⁴ f(x) dx − ∫₁⁴ dx

= 2 (e⁴ − e) − (x + C) |₁⁴

= 2e⁴ − 2e − 3

∫ sec²(x/k) dx

k ∫ 1/k sec²(x/k) dx

k tan(x/k) + C

Evaluating between x=0 and x=π/2:

k tan(π/(2k)) + C − (k tan(0) + C)

k tan(π/(2k))

Setting this equal to k:

k tan(π/(2k)) = k

tan(π/(2k)) = 1

π/(2k) = π/4

1/(2k) = 1/4

2k = 4

k = 2

You might be interested in
The measures of ∠1, ∠2, and ∠3 are 40%, 12.5%, and 25% of the sum of the angle measures of the quadrilateral. Find the value of
sweet [91]

The value of x is 81

Step-by-step explanation:

The sum of the interior angles of any quadrilateral is 360°

  • The measure of ∠1 is 40% of the sum of the angle measures of the quadrilateral
  • The measure of ∠2 is 12.5% of the sum of the angle measures of the quadrilateral
  • The measure of ∠3 is 25% of the sum of the angle measures of the quadrilateral
  • We need to find the value of x

∵ The figure have 4 sides

∴ The figure is a quadrilateral

∵ The sum of the measures of the interior angles of a

    quadrilateral is 360°

- Add the four angles and equate the sum by 360

∴ m∠1 + m∠2 + m∠3 + x = 360

∵ m∠1 = 40% of the sum of the angle measures of the quadrilateral

∴ m∠1 = 40% × 360 = \frac{40}{100} × 360 = 144°

∵ m∠2 = 12.5% of the sum of the angle measures of the quadrilateral

∴ m∠2 = 12.5% × 360 = \frac{12.5}{100} × 360 = 45°

∵ m∠3 = 25% of the sum of the angle measures of the quadrilateral

∴ m∠3 = 25% × 360 = \frac{25}{100} × 360 = 90°

- Substitute these values in the equation above

∴ 144 + 45 + 90 + x = 360

- Add the like terms in the left hand side

∴ 279 + x = 360

- Subtract 279 from both sides

∴ x = 81°

The value of x is 81

Learn more:

You can learn more about the polygons in brainly.com/question/6281564

#LearnwithBrainly

5 0
3 years ago
Please help! posted picture of question
Dvinal [7]
Since the graph of the given functions is a straight line, the graph belongs to a linear function, as all linear functions have their graphs as a straight line. For a non-linear function the graph is not a straight line. 

For a relation (non-function), the line passes through same value of x for more than one points. 

Hence the correct answer is "Linear Function"
8 0
2 years ago
The accompanying table shows the number of bacteria present in a certain culture over a 6 hour period, where x is the time, in h
madam [21]

The number of bacteria present after 15 hours is 18928

<h3>How to determine the exponential equation?</h3>

An exponential equation is represented as;

y = ab^x

Where

a = y, when x = 0

From the table, we have:

y = 1796 when x = 0

So, we have:

y = 1796b^x

Also, we have the point (1, 2097)

This gives

2097 = 1796b^1

Divide by 1796

b = 1.17

Substitute b = 1.17 in y = 1796b^x

y = 1796(1.17)^x

This means that the exponential equation is y = 1796(1.17)^x

After 15 hours, we have:

y = 1796(1.17)^15

Evaluate

y = 18928

Hence, the number of bacteria present after 15 hours is 18928

Read more about exponential equation at:

brainly.com/question/23729449

#SPJ1

7 0
1 year ago
DUE TODAY!!!! I WILL MARK BRAINLIST
11Alexandr11 [23.1K]
Median: 3
mode: 3
range: 9
interquartile range: 2

the outliers are 9 and 5. there is a cluster between 2 and 3.
5 0
3 years ago
Which of the following numbers is irrational?
Nastasia [14]

The believe the answer would be D.

7 0
2 years ago
Other questions:
  • The Saginaw Bay tides vary between two feet and eight feet. The tide is at its lowest point when time (t) is 0 and completes a f
    14·2 answers
  • 25+5 Times blank equals 35
    13·1 answer
  • Three consecutive even integers such that 12 less than three times the largest is equal to 96 more than the sum of the first and
    5·1 answer
  • Please help and explain! will mark brainliest!
    15·2 answers
  • Plz plz huty The chart below shows Mrs. Thompson's grocery bill. What is the average amount Mrs. Thompson spent on groceries?
    11·2 answers
  • X + 4 = -14 im frustraded i need an answer haha hewpppp
    6·1 answer
  • What is the slope of the line that passes through the points (1,-1) and (3,-7)? Group of answer choices
    11·1 answer
  • Which rule is correct for translation 2 units right and 6 units down
    5·2 answers
  • 3. A savings account is started with an initial deposit of $500. The account earns 1.5% interest compounded annually. (a) Write
    8·1 answer
  • Which of the following statements are true regarding functions?<br><br> Check all that apply.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!