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3 years ago

What is the square root of -1

Mathematics

1 answer:

patriot [66]3 years ago

6 0

Answer:

Step-by-step explanation:

This is the answer you get when you square and you get a negative number.

You might be interested in

If a number x is chosen at random from the numbers -2,-1, 0, 1,2.what is the probability that x2<2.

Katyanochek1 [597]

Answer:

Do you mean 2x<2 or

X <2 or do you mean x²<2

Step-by-step explanation:

If your question is X²<2

Then

Total outcomes=5

Possible outcomes=3(-1,0,1)

Probability of x²<2=3/5

If your question means probability of2x<2

Then

Total outcomes=5

Possible outcomes=3 (-2,-1,0)

Probability of 2x<2=3/5

If your question means x< 2

Then

Total outcomes=5

Possible outcomes=4 (-2,-1,0,1)

Probability of x <2 =4/5

If I have not answered your question

then you can comment and ask me if you have any doubts

Hope this helps

8 0

4 years ago

Write the roster from of<br> { x:x is a factor of 42 }

Brrunno [24]

Answer:

the correct answer is

{2,3,6,7,14,21,}

3 0

3 years ago

What is the x-Intercept of the line?

Burka [1]

Answer:

<h2>x-intercept: x = 12 → (12, 0)</h2>

Step-by-step explanation:

We must find the equation of a line.

The point-slope form of an equation of a line:

$y-y_1=m(x-x_1)$

m - slope

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points from the table (22, 36) and (27, 54). Substitute:

$m=\dfrac{54-36}{27-22}=\dfrac{18}{5}\\\\y-36=\dfrac{18}{5}(x-22)$

The x-intercept is for y = 0. Susbtitute:

$0-36=\dfrac{18}{5}(x-22)$ <em> multiply both sides by 5</em>

$-180=18(x-22)$ <em>divide both sides by 18</em>

$-10=x-22$ <em>add 22 to both sides</em>

$12=x$

4 0

3 years ago

(a) Suppose anxn has finite radius of convergence R and an ≥ 0 for all n. Show that if the series converges at R, then it also c

valina [46]

Answer:

a) See the proof below.

b) $\sum \frac{(-x)^n}{n}$

Step-by-step explanation:

Part a

For this case we assume that we have the following series $\sum a)n x^n$ and this series has a finite radius of convergence $R$ and we assume that $a_n \geq 0$ for all n, this information is given by the problem.

We assume that the series converges at the point $x= R$ since w eknwo that converges, and since converges we can conclude that:

$\sum a)n R^n < \infty$

For this case we need to show that converges also for $x=-R$

So we need to proof that $\sum a_n (-R)^n < \infty$

We can do some algebra and we can rewrite the following expression like this:

$\sum a_n (-R)^n = \sum (-1)^n a)n R^n$ and we see that the last series is alternating.

Since we know that $\sum a_n x^n$ converges then the sequence { $a_n R^n$ } must be positive and we need to have $lim_{n\to \infty} a^n R^n = 0$

And then by the alternating series test we can conclude that $\sum a_n (-R)^n$ also converges. And then we conclude that the power series $a_n x^n$ converges for $x=-R$ ,and that complete the proof.

Part b

For this case we need to provide a series whose interval of convergence is exactly (-1,1]

And the best function for this $\frac{(-x)^n}{n}$

Because the series $\sum \frac{(-x)^n}{n}$ converges to $-ln(1+x)$ when $|x|$ using the root test.

But by the properties of the natural log the series diverges at $x=-1$ because $\sum \frac{1}{n} =\infty$ and for $x=1$ we know that converges since $\sum \frac{-1}{n}$ is an alternating series that converges because the expression tends to 0.

6 0

3 years ago

How do you turn 68 out of 80 in a fraction percent decimal?

serg [7]

$As \ a \ fraction: \frac{17}{20}
 \\ As \ a \ percent:0.85
 \\ As \ a \ decimal:0.0085
 \\$

8 0

4 years ago