All categories

3 years ago

Please give me the correct answer

Mathematics

1 answer:

Ksenya-84 [330]3 years ago

7 0

Answer:

ten billion

Step-by-step explanation:

You might be interested in

Evaluate the integral of the quantity x divided by the quantity x to the fourth plus sixteen, dx . (2 points) one eighth times t

Anika [276]

Answer:

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c$

Step-by-step explanation:

Given

$\int\limits {\frac{x}{x^4 + 16}} \, dx$

Required

Solve

Let

$u = \frac{x^2}{4}$

Differentiate

$du = 2 * \frac{x^{2-1}}{4}\ dx$

$du = 2 * \frac{x}{4}\ dx$

$du = \frac{x}{2}\ dx$

Make dx the subject

$dx = \frac{2}{x}\ du$

The given integral becomes:

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{x}{x^4 + 16}} \, * \frac{2}{x}\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{1}{x^4 + 16}} \, * \frac{2}{1}\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du$

Recall that: $u = \frac{x^2}{4}$

Make $x^2$ the subject

$x^2= 4u$

Square both sides

$x^4= (4u)^2$

$x^4= 16u^2$

Substitute $16u^2$ for $x^4$ in $\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16u^2 + 16}} \,\ du$

Simplify

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16}* \frac{1}{8u^2 + 8}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{2}{16}\int\limits {\frac{1}{u^2 + 1}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du$

In standard integration

$\int\limits {\frac{1}{u^2 + 1}} \,\ du = arctan(u)$

So, the expression becomes:

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(u)$

Recall that: $u = \frac{x^2}{4}$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c$

4 0

3 years ago

What would be the exponent if you wrote 2,670 in scientific notation? Just write the number for your answer.

just olya [345]

Answer:

2.67 x 10^3

Step-by-step explanation

The exponent is equal to how many numbers are after the decimal point. So, since there are 3 numbers after the decimal point, the exponent would be 3. Hope this helps :)

4 0

3 years ago

Alice is riding the train to her job in Paris, France. She accidentally purchased a ticket for zone 4, but she is

stepan [7]

Answer:

3005 euro is the answer

7 0

2 years ago

Whats (14-7) multiplied by (40-32) plz gib right answer!

jenyasd209 [6]

Answer:

Step-by-step explanation:

(14-7) x (40-32) = 7 x 8

= 56

Hope you understood :)

6 0

3 years ago

Read 2 more answers

(Math Help Quick Lots of points please thanks)

Elden [556K]

Answer:

E = {0, 1, 2, 3)

Step-by-step explanation:

<u>Integer</u>: a number with no decimal or fractional part, from the set of negative and positive numbers, including zero
< means less than
> means more than

E = {0, 1, 2, 3)

8 0

3 years ago

Read 2 more answers

Please give me the correct answer ​

Please give me the correct answer