49*56= ? also here is a pic !!

What are all values of x for which the series shown converges?

adoni [48]

Answer:

One convergence criteria that is useful here is that, if aₙ is the n-th term of this sequence, then we must have:

Iaₙ₊₁I < IaₙI

This means that the absolute value of the terms must decrease as n increases.

Then we must have:

$\frac{(x -2)^n}{n*3^n} > \frac{(x -2 )^{n+1}}{(n + 1)*3^{n+1}}$

We can write this as:

$\frac{(x -2)^n}{n*3^n} > \frac{(x -2 )^{n+1}}{(n + 1)*3^{n+1}} = \frac{(x -2)^n}{(n + 1)*3^n} * \frac{(x - 2)}{3}$

If we assume that n is a really big number, then:

n + 1 ≈ 1

And we can write:

$\frac{(x -2)^n}{n*3^n} > \frac{(x -2)^n}{(n)*3^n} * \frac{(x - 2)}{3}$

Then we have the inequality

$1 > (x - 2)/3$

And remember that this must be in absolute value, then we will have that:

-1 < (x - 2)/3 < 1

-3 < x - 2 < 3

-3 + 2 < x < 3 + 2

-1 < x < 5

The first option looks like this, but it uses the symbols ≤≥, so it is not the same as this, then the correct option will be the second.

5 0

2 years ago

Mark spends $36 at a basketball game. He buys a T-shirt for $22. He then buys a bottle of water for $4 and 2 tacos. How much is

Arturiano [62]

Answer:

each taco is $7.

Step-by-step explanation:

In total he spent $36. He bought a shirt for $22 and a bottle of water for $4.

22+4= 26

36-22= 14

14 divided by 2= 7

5 0

3 years ago

Read 2 more answers

PLEASE HELP I WILL GIVE BRAINLEST

nadya68 [22]

OK. All the work is in the attached drawing.

Please spend enough time with it to understand what was done and how, so that you can do the next problem like this one completely on your own.

Good luck !

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Here's a picky pickypoint to think about concerning the "cost". I'm not quite sure what to do about this:

The initial, one-time $55 is a "deposit". If she doesn't smash the bike or steal it, she gets the $55 back when she returns the bike.

So if she eventually gets the $55 back, is it a cost ? ? I don't know how to think about it.

She does need to give them the $55 at the beginning, just to take the bike out. So she has to have it with her and give it to them temporarily, even though she'll get it back, and she'll still have it when she returns home.

So here's the story:

-- While she HAS the bike, the graph correctly shows all the money she needs, in order to get the bike, and keep it for however long she keeps it.

-- Finally, at the end of the week, after she returns the bike and gets her $55 back, the line and everything on the graph will shift down by $55. The line will start at zero, and the little red ordered pairs will also shift straight down and still be on the line.

To put it one more way:

-- While Jen has the bike, the y-intercept of the graph is $55.

-- After she returns the bike in good condition, the y-intercept is zero.