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vredina [299]
2 years ago
7

How do you do these 2 questions?

Mathematics
1 answer:
zavuch27 [327]2 years ago
5 0

Answer:

0 ≤ an ≤ bn

The series ∑₁°° bn converges

The series ∑₁°° an converges by comparison to ∑₁°° bn.

0 ≤ an ≤ bn

The series ∑₁°° bn diverges

The comparison test is inconclusive for our choice of bn.

Step-by-step explanation:

an = 1 / (n² + n + 3) and bn = 1 / n²

The numerators are the same, and the denominator of an is greater than the denominator of bn.  So 0 ≤ an ≤ bn.

bn is a p series with p > 1, so it converges.

Since the larger function converges, the smaller function also converges.

an = (3n − 1) / (6n² + 2n + 1) and bn = 1 / (2n)

If we rewrite bn as bn = (3n − 1) / (6n² − 2n), we can tell that when the numerators are equal, the denominator of an is greater than the denominator of bn.  So 0 ≤ an ≤ bn.

bn is a p series with p = 1, so it diverges.

The larger function diverges.  We cannot conclude whether the smaller function converges or diverges.

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On a trip to Griffith Observatory, Dave rode his bicycle six more than twice as many miles in the afternoon as in the morning. I
podryga [215]

Answer:

Dave rode his bicycle 17 miles in the morning

Dave rode his bicycle 40 miles in the afternoon

Step-by-step explanation:

* Lets study the information to solve the question

- Dave rod his bicycle in the morning and again in the afternoon

- Six more than twice as many miles in the afternoon as in the morning

  means the distance in the afternoon is 6 more than twice the distance

  in the morning

- The entire trip was 57 miles means the total distance in the morning

  and in the afternoon was 75

* To solve the question let the distance in the morning is x miles

∵ The distance in the morning = x miles

∵ The distance in the afternoon is 6 more than twice the distance

  in the morning

∴ The distance in the afternoon = 2x + 6 miles

∵ The distance in entire trip = 57 miles

- The distance in the morning and the distance in the afternoon = 57 miles

∴ x + (2x + 6) = 57 ⇒ simplify

∴ 3x + 6 = 57 ⇒ subtract 6 from both sides

∴ 3x = 51 ⇒ divide both sides by 3

∴ x = 17 miles

∵ The distance in the morning is x miles

∴ Dave rode his bicycle 17 miles in the morning

∵ The distance in the afternoon = 2x + 6 miles

- Substitute the value of x

∴ The distance in the afternoon = 2(17) + 6 = 34 + 6 = 40 miles

∴ Dave rode his bicycle 40 miles in the afternoon

4 0
3 years ago
5x-2<8 i need to solve this question
svetlana [45]
I did this excat problem in school but my teacher just gave us the answer which is X<2
7 0
3 years ago
Read 2 more answers
-11 - 5x = 6(5x + 4)
gavmur [86]

Answer:

x=-1

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
The senior classes at High School A and High School B planned separate trips to Lake Compounce. The senior class at High School
storchak [24]

Answer:

Number of students in vans =15 and bus =46

Step-by-step explanation:

use variables for the vans and buses

let x= vans and y=buses

Now solve the 2 equations simultaneously

<em><u>remember</u></em><em><u> </u></em><em><u>to</u></em><em><u> </u></em><em><u>number</u></em><em><u> </u></em><em><u>your</u></em><em><u> </u></em><em><u>equations</u></em>

6x+7y=412..........1

6x+9y=504.........2

make x the subject of one equation

and label it equation 3

6x=412—7y

x =  \frac{206}{3}  -  \frac{7y}{6} .............3

subs 3 into 2

6( \frac{206}{3}  -  \frac{7y}{6} ) + 9y = 504

412 - 7y + 9y = 504

- 7y + 9y = 504 - 412

2y = 92

y = 46...................4

subs 4 into 1

6x + 7(46) = 412

6x + 322 = 412

6x = 412 - 322

6x = 90

x = 15

Therefore there are 15 students in each van and 46 students in each bus.

3 0
2 years ago
We used these functions to represent the two sides of the equation:
katrin [286]

The solution to the system of equation graphed is (-1, -3)

<h3>Solution to system of equation</h3>

Given the system of equations graphed on the plane expressed as:

f(x) = 3x

g(x) = 4x + 1

Equate

f(x) = g(x)

3x = 4x + 1

3x - 4x = 1

-x = 1

x = -1

Determine the value of y

y = 3x

y = 3(-1)

y = -3

Hence the solution to the system of equation graphed is (-1, -3)

Learn more on system of equation here: brainly.com/question/847634

#SPJ1

4 0
2 years ago
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