The discontinuity occurs at x = 0, since that is the only "problem" place in the graph that makes the function undefined. A vertical asymptote exists there. It is nonremoveable.

4 0

3 years ago

Whats the answer to that question?

gavmur [86]

Answer:

-0.9090... can be written as $\frac{10}{11}$ .

Explanation:

Any <em>repeating </em>decimal can be written as a fraction by dividing the section of the pattern to be repeated <em>by </em>9's.

We can start by listing out

0.909090... = 9/10 + 0/100 + 9/1000 + 0/10000 + 9/100000 + 0/1000000 + ...

Now. we let this series be equal to x, that is

$x$ = 9/10 + 0/100 + 9/1000 + 0/10000 + 9/100000 + 0/1000000 + ...

Now, we'll multiply both sides by 100 .

$100x$ = 90 + 0 + 9/10 + 0/100 + 9/1000 + 0/10000 + ...

Then, subtract the 1st equation from the second like so:

$100x$ = 90 + 0 + 9/10 + 0/100 + 9/1000 + 0/10000 + 9/100000 + 0/1000000 + ...

$-x$ = - 9/10 - 0/100 - 9/1000 - 0/10000 - 9/100000 - 0/1000000 - ...

And we end up with this:

$99x=90$

Finally, we divide both sides by 99 in order to isolate x and get the fraction we're looking for.

$x=\frac{90}{99}$

Which can be reduced and simplified to

$x=\frac{10}{11}$

Hope this helps!

4 0

3 years ago

Every two out of three kids sang at the talent show. What percent of the kids did not sing at the talent show? (round)

kvv77 [185]

66.7 %
convert to decimal the multiply by 100

5 0

3 years ago