Help I Dont understand

Answer:

Step-by-step explanation:

Let

[tex]I(a) = \displaystyle \int_0^\infty \frac{\sqrt x \arctan(ax)}{1+x^2} \, dx[/tex]

Differentiate with respect to a :

[tex]I'(a) = \displaystyle a \int_0^\infty \frac{x^{\frac32}}{(1+x^2)(1+a^2x^2)} \, dx[/tex]

Substitute y = √x :

[tex]I'(a) = \displaystyle 2a \int_0^\infty \frac{y^4}{(1+y)(1+a^2y)} \, dy[/tex]

Polynomial division yields

[tex]\dfrac{y^4}{(1+y)(1+a^2y)} \\\\ = \dfrac1{a^2}y^2 - \left(\dfrac1{a^2} + \dfrac1{a^4}\right)y + \dfrac1{a^2} + \dfrac1{a^4} + \dfrac1{a^6} - \dfrac{\left(1+\frac1{a^2} + \frac1{a^4} + \frac1{a^6}\right)y + \frac1{a^2} + \frac1{a^4} + \frac1{a^6}}{(1+y)(1+a^2y)}[/tex]

Computing I'(a) isn't so difficult from here. You'd find (assuming a ≥ 0)

[tex]I'(a) = \displaystyle \frac\pi{\sqrt2\left(\sqrt a + a + a^{\frac32} + a^2\right)}[/tex]

Integrate both sides with respect to a. On the right side, substituting b = √a yields

[tex]\displaystyle \int \frac{da}{\sqrt a + a + a^{\frac32} + a^2} = \int \frac{2b}{b + b^2 + b^3 + b^4} \, db \\\\ = 2 \int \frac{db}{1 + b + b^2 + b^3} \\\\ = 2 \int \frac{db}{(1+b)(1+b^2)} \\\\ = \int \left(\frac1{1+b} + \frac{1-b}{(1+b^2)}\right) \, db \\\\ = \frac14 \left(2 \arctan(b) + 2 \ln(1 + b) - \ln(1 + b^2)\right) + C \\\\ = \frac14 \left(2 \arctan(\sqrt a) + 2 \ln(1 + \sqrt a) - \ln(1 + a)\right) + C[/tex]

Noting that a = 0 makes the integral I(a) vanish, we have

[tex]0 = \dfrac14 \left(2 \arctan(\sqrt0) + 2\ln(1 + \sqrt0) - \ln(1 + 0)\right) + C \implies C = 0[/tex]

and so

[tex]\displaystyle I(a) = \frac\pi{4\sqrt2} \left(2 \arctan(\sqrt a) + 2 \ln(1 + \sqrt a) - \ln(1 + a)\right)[/tex]

We recover the integral we want with a = 1, which gives a value of

[tex]\displaystyle \int_0^\infty \frac{\sqrt x \arctan(x)}{1 + x^2} \, dx = \boxed{\frac{\pi^2 + 2\pi\ln(2)}{4\sqrt2}}[/tex]

Answer:

5/6

Step-by-step explanation:

Answer:

5/6

Step-by-step explanation:

All of the answers either increase or reduce to 8/10 except 5/6

Hope this helps! Please mark as brainliest answer if correct.

Stay safe, God bless, and happy studying!

Answer:

alternate angled

Step-by-step explanation:

add up to 180

========================================================

Explanation:

Going from the first term to the second, we add on -2

Then going from the second term to the third, we add on +2

This inconsistency (-2 vs +2) means we don't have a common difference, and therefore the sequence is not arithmetic.

------------

Now let's divide each term by their previous term

term2/term1 = 0/2 = 0

term3/term2 = 2/0 = undefined

We can stop here and conclude that we don't have a common ratio either, so this sequence is not geometric.

------------

Side note: The subsequence 0,2,4,6,... is arithmetic with common difference d = 2 because we add 2 to each term. It's that first 2 in the original sequence that breaks everything.

Answer:

12

Step-by-step explanation:

Given :-

Two numbers => 48 and 60

To Find :-

HCF of 48 and 60

Solving :-

Prime factorize the numbers.

48 = 2⁴ x 3

60 = 2² x 3 x 5

Solution :-

HCF (48, 60) = 2² x 3 = 12

Answer: 119/50 in decimal form 2.38000

Step-by-step explanation: 4.9 can be made to 49/10

 Find the Least Common Multiple

     The left denominator is :       25  

     The right denominator is :       10

Least Common Multiple:

     50

Answer:

x less than or equal to -2

Answer:

what are you trying to solve?

Answer:

3

Step-by-step explanation:

Answer:

down

Step-by-step explanation:

c) 6 and 8

a) 7 and 1

b) 5 and 4

Answer:

x = 31 1/2

Step-by-step explanation:

If y = 42, that means the original y = 28 was multiplied by 1.5, so we have to multiply x = 21 by 1.5 to find the answer.

21 * 1.5 = 31.5 A.K.A 31 1/2

Answer:

persent i think

Step-by-step explanation:

9514 1404 393

Answer:

  congruent

Step-by-step explanation:

Angles supplementary to the same angle are congruent.

__

Here, angles 1 and 3 are both supplementary to angle 2, so ...

  angle 1 and angle 3 are congruent

Answer: The correct equation should be 0.2+5.8=6

Step-by-step explanation: First of all let's look at the equation without the decimal ".8". So, it would be 2+5 which equals 7. Since the sum is greater, adding a decimal will make the sum larger than 6. 2+5.8=7.8, therefore the correct equation being 0.2+5.8=6. Hopes this makes sense and helps!

The profit that Jude made during the party was £3700.

Profit is the difference between revenue and cost. It is given by:

Profit = Revenue - Cost

From the question:

The total cost = 300 + 2500 + 500 + (1 * 400 people) = £3700

Revenue = 400 ticket * £16 = £6400

Profit = Revenue - Cost = £6400 - £3700

The profit that Jude made during the party was £3700.

Find out more on profit at: https://brainly.com/question/23103804

Divide both systems:

y=4(4)^x

y=4^x+1

Answer:

The answer is True.

Step-by-step explanation:

The earliest civilizations developed between 4000 and 3000 BCE, when the rise of agriculture and trade allowed people to have surplus food and economic stability.

Hope this helps you!

[tex]\frac{m}{4.2} =7\\m = 4.2 * 7 = 29.4[/tex]

Hope that helps!

Answer:

m = 29.4

Step-by-step explanation:

[tex]\frac{m}{4.2}=7[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}4.2[/tex]

[tex]\frac{4.2m}{4.2}=7\cdot \:4.2[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]m=29.4[/tex]

Check Answer;

[tex]\frac{29.4}{4.2}[/tex]

[tex]\mathrm{Multiply\:the\:numerator\:and\:denominator\:by:}\:10[/tex]

[tex]\frac{294}{42}[/tex]

[tex]\mathrm{Write\:the\:problem\:in\:long\:division\:format}[/tex]

[tex]42\overline{|\smallspace294}[/tex]

[tex]\begin{matrix}\:\:\:\:\:\:\:\:\:\:\emptyspace7\:\:\:\:\:\:\:\:\:\:\:\:\\ 42\overline{|\smallspace294}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\underline{\emptyspace2\emptyspace9\emptyspace4}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}[/tex]

Hence, m = 29.4

~learn with Lenvy~

Answer:

A

Step-by-step explanation:

Since cosine is positive and sine is negative that puts θ in Quad IV.

From right triangles we know:

Cos θ = adjacent/hypotenuse = 5/13

sin θ = opposite/hypotenuse = ?/13

To find the opposite side across from θ use the pythagorean theorem.

5² + y² = 13²

25 + y² = 169

y² = 144

y = 12

we are given  that sin is < 0 so sinθ = -12/13

Answer:

A

Step-by-step explanation:

[tex]\cos(\theta)=\dfrac{\textsf{adjacent side}}{\textsf{hypotenuse}}=\dfrac{5}{13}[/tex]

[tex]\textsf{As }\cos(\theta) > 0 \textsf{ the angle is in quadrant I or IV}[/tex]

Using Pythagoras' Theorem a² + b² = c² to find the side opposite the angle:

⇒ 5² + b² = 13²

⇒ b² = 144

⇒ b = 12

⇒ opposite side = 12

[tex]\implies \sin(\theta)=\dfrac{\textsf{opposite side}}{\textsf{hypotenuse}}=\dfrac{12}{13}[/tex]

[tex]\textsf{As }\sin(\theta) < 0 \textsf{ then }\sin(\theta)=-\dfrac{12}{13} \textsf{ and the angle is in either quadrant III or quadrant IV}[/tex]

Therefore, the common quadrant is quadrant IV and

[tex]\sin(\theta)=-\dfrac{12}{13}[/tex]

Answer:

(b) NO

Step-by-step explanation:

It must have the square to to be a right angle

Answer:

A: It is obtuse

B: It is a right angle

Step-by-step explanation:

A: Angle RST equals 110*, if it is greater than 90*, it is obtuse

B: Right Angles are 90*, so this is simple, you subtract RST by UST, so 110-20=90

9514 1404 393

Answer:

Step-by-step explanation:

The point-slope form of the equation for a line with slope m through point (h, k) is ...

  y -k = m(x -h)

Comparing this to the equation you have, you see that you have a "point-slope form" equation with m=7 and (h, k) = (4, 2).

__

The standard form of an equation for a line is ...

  ax +by = c

where a, b, c are mutually prime integers and a > 0.

Putting your equation into standard form would make it look like ...

  7x - y = 26

Your equation is not in correct standard form.

_____

see https://brainly.com/question/18537811 for more information

Answer:

4/5

Step-by-step explanation:

There are 10 tiles total, and E and I are vowels. This makes 2/10 of the tiles tiles. The other 8/10 are not vowels.

8/10 can be simplified down to 4/5.

There is a 4/5 probability of picking a letter that is not a vowel.

A function is a relation in which there is only one y-value for every x-value.

If we given an input of 3 for x, for example, we would only get one output for y, like 1, for example.

If we look at the table, we can see that the x-value of 3 gives us two outputs: 7 and 9.

Therefore, this relation is not a function.

Answer:

It's multiply both by thesame number

Step-by-step explanation:

For example:

If we want to change this fraction to a simplest form:

5/25

We simply multiply both sides by 5,which will give us:

5/5

And if you want simplify it further, the answer will be 1

Thanks.

Answer:

Uh how to use segmant tool

Step-by-step explanation:

not there