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ziro4ka [17]
3 years ago
8

Simplify: square root 8i^2

Mathematics
1 answer:
Vesna [10]3 years ago
8 0

Answer: The answer would be to simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

2i√2

So according to me the answer should be 2i√2 .

* Hopefully this helps: )

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Please, I need help in this ??
nignag [31]

Answer:

\int\frac{x^{4}}{x^{4} -1}dx = x + \frac{1}{4} ln(x-1) - \frac{1}{4} ln(x+1)-\frac{1}{2} arctanx + c

Step-by-step explanation:

\int\frac{x^{4}}{x^{4} -1}dx

Adding and Subtracting 1 to the Numerator

\int\frac{x^{4} - 1 + 1}{x^{4} -1}dx

Dividing Numerator seperately by x^{4} - 1

\int 1 + \frac{1}{x^{4}-1 }\, dx

Here integral of 1 is x +c1 (where c1 is constant of integration

x + c1 + \int\frac{1}{(x-1)(x+1)(x^{2}+1)}\, dx----------------------------------(1)

We apply method of partial fractions to perform the integral

\frac{1}{(x-1)(x+1)(x^{2}+1)} = \frac{A}{x-1} + \frac{B}{x+1} + \frac{C}{x^{2} + 1}------------------------------------------(2)

\frac{1}{(x-1)(x+1)(x^{2}+1)} = \frac{A(x+1)(x^{2} +1) + B(x-1)(x^{2} +1) + C(x-1)(x+1)}{(x-1)(x+1)(x^{2} +1)}

1 = A(x+1)(x^{2} +1) + B(x-1)(x^{2} +1) + C(x-1)(x+1)-------------------------(3)

Substitute x= 1 , -1 , i in equation (3)

1 = A(1+1)(1+1)

A = \frac{1}{4}

1 = B(-1-1)(1+1)

B = -\frac{1}{4}

1 = C(i-1)(i+1)

C = -\frac{1}{2}

Substituting A, B, C in equation (2)

\int\frac{x^{4}}{x^{4} -1}dx = \int\frac{1}{4(x-1)} - \frac{1}{4(x+1)} -\frac{1}{2(x^{2}+1) }

On integration

Here \int \frac{1}{x}dx = lnx and \int\frac{1}{x^{2}+1 } dx = arctanx

\int\frac{x^{4}}{x^{4} -1}dx = \frac{1}{4} ln(x-1) - \frac{1}{4} ln(x+1) - \frac{1}{2} arctanx + c2---------------------------------------(4)

Substitute equation (4) back in equation (1) we get

x + c1 + \frac{1}{4} ln(x-1) - \frac{1}{4} ln(x+1) - \frac{1}{2} arctanx + c2

Here c1 + c2 can be added to another and written as c

Therefore,

\int\frac{x^{4}}{x^{4} -1}dx = x + \frac{1}{4} ln(x-1) - \frac{1}{4} ln(x+1)-\frac{1}{2} arctanx + c

4 0
3 years ago
Two non-simultaneous events have an equal likelihood of occurring (50%). If the events are independent of each other, what is th
BARSIC [14]
There are 4 possibilities:

1) No event happens
2) event A happens, not event B
3) event B happens, not event A
4) both events happen

seeing as there is a 50% chance of either event happening, I would assume that all 4 possibilities have an equal chance of happening

so if there are 4 events, then each one is 25% likely.

So the probability if them both occurring is 25%

I think
7 0
3 years ago
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Gnesinka [82]
He's a silly goober and he likes to joke around
6 0
3 years ago
An account earns simple interest.<br> $1675 at 4.6% for 4 years
Paul [167]

Answer:

$308.20

Step-by-step explanation:

The simple interest formula i = p·r·t applies here:

($1675)(0.046)(4) = $308.20

5 0
3 years ago
A fair dice is rolled
iren2701 [21]

Answer:

1/6

Step-by-step explanation:

8 0
3 years ago
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