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3 years ago

How do you do this question?

Mathematics

1 answer:

IRINA_888 [86]3 years ago

5 0

Answer:

∑ (-1)ⁿ⁺³ 1 / (n^½)

∑ (-1)³ⁿ 1 / (8 + n)

Step-by-step explanation:

If ∑ an is convergent and ∑│an│is divergent, then the series is conditionally convergent.

Option A: (-1)²ⁿ is always +1. So an =│an│and both series converge (absolutely convergent).

Option B: bn = 1 / (n^⁹/₈) is a p series with p > 1, so both an and │an│converge (absolutely convergent).

Option C: an = 1 / n³ isn't an alternating series. So an =│an│and both series converge (p series with p > 1). This is absolutely convergent.

Option D: bn = 1 / (n^½) is a p series with p = ½, so this is a diverging series. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.

Option E: (-1)³ⁿ = (-1)²ⁿ (-1)ⁿ = (-1)ⁿ, so this is an alternating series. bn = 1 / (8 + n), which diverges. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.

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I'd really appreciate some help on these questions, I'm really struggling

nikklg [1K]

We can use linear combinations of the equations to eliminate variables.

3x - 4y = 1
-2x + 3y = 1

To eliminate y we'll make the linear combination of 3 times the first equation minus four times the second.

9x - 12y = 3
-8x + 12y = 4

Adding,
x = 7

We could solve for y directly but let's use another linear combination, twice the first plus three times the second:

2(3x - 4y) + 3(-2x + 3y)= 2(1)+3(1)

y = 5

Check: 3(7)-4(5)=1 good. -2(7)+3(5)=1 good.

Q18 Answer: (7,5)

y = -3x + 5
5x - 4y = -3

4y +1(5x - 4y) = 4(-3x + 5) + 1(-3)

5x = -12x + 20 -3

17 x = 17

x = 1
y = -3(1) + 5 = 2
Check: 5(1) - 4(2) = -3 good

Q19 Answer (1,2)

6x + 5y = 25
x = 2y + 24
6x = 12y + 144
5y = 25 - 12y - 144
17y = -119
y = -119/17= -7
x = 2y+24= 10
Check: 6(10)+5(-7)=25 good 2y+24=2(-7)+24=10=x good

Q20 Answer (10,-7)

3x + y = 18
-7x + 3y = -10
9x + 3y = 54
9x - -7x = 54 - -10
16x = 64
x=4
y = 18 -3x = 18-12=6

Check: 3(4)+6=18 good, -7(4)+3(6)=-10 good

Q21 Answer: (4,6)

6 0

3 years ago

Vector question, please help

77julia77 [94]

Answer:

yes.

Step-by-step explanation:

3 0

2 years ago

A bicycle rider increases his speed from 5 m/s to 15 m/s in 10 seconds

valentina_108 [34]

To find the acceleration of the bicycle rider, we are going to use the acceleration formula: $a= \frac{v_{f}-v_{i}}{t}$
where
$a$ is the acceleration
$v_{i}$ is the initial speed
$v_{f}$ is the final speed
$t$ is the time

We know from our problem that increases his speed from 5 m/s to 15 m/s in 10 seconds, so his initial speed is 5 m/s and his final speed is 15 m/s; therefore, $v_{i}=5$ , $v_{f}=15$ , and $t=10$ . Lets replace those values in our formula:
$a= \frac{v_{f}-v_{i}}{t}$
$a= \frac{15-5}{10}$
$a= \frac{10}{10}$
$a=1$

We can conclude that the acceleration of the bicycle rider 1 m/s^2

4 0

3 years ago

3(x-1)=2x+9. Solve equation

Anna11 [10]

Hello.

In order to solve this equation, we need to isolate the variable (in this case, the variable is x)

The first step is to use the Distributive Property and distribute 3:

$\mathrm{3(x-1)=2x+9}$

$\mathrm{3x-3=2x+9}$

Now, add 3 to both sides:

$\mathrm{3x-3+3=2x+9+3}$

$\mathrm{3x=2x+9+3}$

$\mathrm{3x=2x+12}$

Now, subtract 2x from both sides:

$\mathrm{3x-2x=2x-2x+12}\\\mathrm{3x-2x=12}$

$\mathrm{x=12}$

Therefore, the answer is

$\mathrm{x=12}$

I hope it helps.

Have a nice day.

$\boxed{imperturbability}$

5 0

2 years ago

Read 2 more answers

A university warehouse has received a shipment of 25 printers, of which 10 are laser printers and 15 are inkjet models. If 6 of

Tanya [424]

Answer:

The probability is 0.31

Step-by-step explanation:

To find the probability, we will consider the following approach. Given a particular outcome, and considering that each outcome is equally likely, we can calculate the probability by simply counting the number of ways we get the desired outcome and divide it by the total number of outcomes.

In this case, the event of interest is choosing 3 laser printers and 3 inkjets. At first, we have a total of 25 printers and we will be choosing 6 printers at random. The total number of ways in which we can choose 6 elements out of 25 is $\binom{25}{6}$ , where $\binom{n}{k} = \frac{n!}{(n-k)!k!}$ . We have that $\binom{25}{6} = 177100$

Now, we will calculate the number of ways to which we obtain the desired event. We will be choosing 3 laser printers and 3 inkjets. So the total number of ways this can happen is the multiplication of the number of ways we can choose 3 printers out of 10 (for the laser printers) times the number of ways of choosing 3 printers out of 15 (for the inkjets). So, in this case, the event can be obtained in $\binom{10}{3}\cdot \binom{15}{3} = 54600$

So the probability of having 3 laser printers and 3 inkjets is given by

$\frac{54600}{177100} = \frac{78}{253} = 0.31$

4 0

3 years ago