1->dương vô cùng 1/x*(9+lnx^2)dx

Answers

Answer 1

It looks like you are trying to compute the improper integral,

[tex]I = \displaystyle\int_1^\infty \dfrac{\mathrm dx}{x(9+\ln^2(x))}[/tex]

or some flavor of this. If this interpretation is correct, substitute u = ln(x) and du = dx/x. Then

[tex]I = \displaystyle\int_0^\infty \dfrac{\mathrm du}{9+u^2} \\\\ = \frac13\arctan\left(\frac u3\right)\bigg|_{u=0}^{u\to\infty} \\\\ = \frac13\lim_{u\to\infty}\arctan\left(\frac u3\right) \\\\ = \frac13\times\frac\pi2 = \boxed{\frac\pi6}[/tex]


Related Questions

Find the length of the hypotenuse.Round to the nearest 10th if necessary.(40pts)

Answers

Answer:

5 is our hypotenuse

Step-by-step explanation:

[tex]a^{2} + b^{2} = c^{2}[/tex]

c is our hypotenuse

[tex]3^{2} + 4^{2} = c^2[/tex]

[tex]9 + 16 = 25[/tex]

[tex]25 = c^{2}[/tex]

c = 5

5 is our hypotenuse

Answer:

x = 5

Step-by-step explanation:

[tex]c=\sqrt{a^2+b^2} \\a= \sqrt{3^2+4^2} \\c=\sqrt{9+16} \\c= \sqrt{25} \\c= 5[/tex]

help please thank you

Answers

Answer:

150*2/3=100

take school size then multiply it by the ratio to get the amount of student who prefer such toothpaste.

Step-by-step explanation:

write me 2 equivalent fractions of 1/3=_=_

Answers

1/3 = 2/6 = 4/12

Multiply both sides by 2 to get 2/6 and both sides by 4 to get 4/12

Pls help!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

See below:

Step-by-step explanation:

First fill in:

180* . Every triangle has interior measurments of 180* total

Second fill in: Reason is definition of sum of triangle's interior angles

Third fill in: 2x. Everything in this equation is asking for the angles. First angle is 28, second angle is 2x, and third angle is x-4.

Fourth fill in: x=52

I found this by doing the following:

First, 180-28, so we can see how many degree we are left with.

152.

Now, make an equation:

152=2x+x-4

Simplify

152=3x-4

Add 4 to both sides to cancel out the -4.

156=3x

divide 156/3=52.

Now we know that x=52.

Although the question doesn't ask for this, you would now substitue 52 back into each of the equations to find that degree. For example, 2x=2(52), or 104*.

Answer:

See image

Step-by-step explanation:

All the angles of a triangle add up to 180°

The given diagram shows all the measures: 28°, x - 4° , and 2x

So add them up, set equal to 180 and solve for x. Combine like terms and subtract 24 from both sides of the equation. Divide both sides by 3. x = 52

ements
Question 8
1 pts
(08.02 MC)
Rewrite x2 - 2x - 3-0 in the form (x -a)? - b, where a and b are integers, to determine the a and b
values.
Oa-4 and b3
O a-3 and b 2
Oa-2 and b 1
Oa - 1 and b 4
Question 9
1 pts

Answers

Step-by-step explanation:

Given,

x² - 2x - 3 = 0

x² - (3x - x) - 3 = 0

x² - 3x + x - 3 = 0

x(x - 3) + 1(x - 3) = 0

(x - 3)(x + 1) = 0

x = 3 & -1

Now,

a and b are integers

So

a = 3 & b = -1 or

a = -1 & b = 3

Answer:

a = 3 , b = -1          or            a = -1 , b = 3

Step-by-step explanation:

x² - 2x - 3 = 0

x² - 3x + 1x - 3 = 0

x ( x - 3 ) +1 ( x - 3 ) = 0

( x - 3 ) ( x + 1 ) = 0

So,

x - 3 = 0                   or                x + 1 = 0

x = 0 + 3                                      x = 0 - 1

x = 3                                            x = -1

Therefore,

( x - a) ( x - b )

As a and b are integers

It can be,

a = 3 , b = -1          or            a = -1 , b = 3

Hope this helps you.

Let me know if you have any other questions :-)

​what is y=2x+3 y=−3x+3 ​

Answers

Step-by-step explanation:

equate the two equations

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Use the quadratic formula to solve the equation.

X^2 - 7x – 6 = 0

Answers

Step-by-step explanation:

[tex]x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

a=1.

b=-7

c=-6

x=

[tex] \frac{ - ( - 7) + \sqrt{ (- 7)^{2} - 4(1)( - 6)} }{2(1)} [/tex]

OR

[tex] \frac{ - ( - 7) - \sqrt{ (- 7) ^{2} - 4(1)( - 6)} }{2(1)} [/tex]

Therefore x= 7,772

OR

x=-0,772

Hello help please please I need help help help

Answers

Answer:

45

Step-by-step explanation:

They are both the same length-

2. When 3 is added to the difference between seven times a number and 8, the result is greater than 13
added to 6 times the number. Write an inequality to match the given situation.
A. 7x + 8-3 < 6x + 13
B. 6x + 13 > (7x - 8) + 3
C. (7x-8) + 3 > 6x + 13
D. 6x + 13 < 7x + 8-3

Answers

Answer:

C

Step-by-step explanation:

HELP 40 POINTS!!!!!!!!!​

Answers

y - 5 = -1.75(x + 3)
this may be the answer. I’m not completely sure though. X=4y-41/7 or x equals four y minus 41 over 7 :)))

Express as a single power.

Answers

a) 1

b) -5

c) [tex]\frac{6^3.6^5}{6^2.6^4} = \frac{6^{3+5} }{6^{2+4} } = \frac{6^8}{6^6} = 6^{8-6}=6^2[/tex]

Find NMC triangle's perimeter if BO:BK=1:3 and ABC triangle's perimeter is 96

Answers

Answer:

  80

Step-by-step explanation:

If we assume the triangles are similar and are isosceles, and that BK is an altitude, then we can work the problem.

Triangle OKN will be similar to triangle BKA, so ...

  AN : AK = BO : BK = 1 : 3

Then ...

  AN : AK : KC = 1 : 3 : 3

In terms of ratio units, ...

  AN = 1

  AC = 3+3 = 6

  NC = 6-1 = 5

This means NC : AC = 5 : 6. The triangle perimeters will have the same ratio.

  perimeter(NMC) = 5/6·perimeter(ABC) = 5/6·96

  perimeter(NMC) = 80

Estimate the quotient. 2,506 / 2

Answers

Answer:

1253

Step-by-step explanation:

2500/2 is 1250.

so 2506/2 will be a bit above.

1253 is an estimate

f(x)=x+1/x-2
find the inverse

Answers

X=1/2
Could be your answer

The population of New York state can be modeled by: 19.71 P(t) =
1 + 61.22e-0.03513tP is the population in millions
and t is the number of years since 1800
What was the population in 2020?
P(220) = [?] million
Round your answer to the nearest thousandth.

Answers

Answer:

  19.193 million

Step-by-step explanation:

Put the given value in the formula and do the arithmetic.

  P(220) = 19.71/(1 +61.22e^(-0.03513·220))

  P(220) = 19.71/(1 +61.22e^-7.7286) = 19.71/(1 +0.02694046)

  P(220) ≈ 19.193 . . . million

19.19293355

Nearest thousandth is 19.193

Find all perfect squares between 100 and 300.

Answers

Answer: The answer in the first image.

Explanation: The explanation is in the second image.

the line passes through the point (6,1) and has a slope of -1/2 what is the point slope form and slope intercept form ​

Answers

This is the answer ur looking for
Hope I helped!

Hi there! :)

We are given the slope of the line and a point that it passes through.

Using this information, we can write the equation in point-slope form:

y-y1=m(-x1)

y-1=-1/2(x-6)

y-1=-1/2x+3

Now, move -1 to the right, using the opposite operation:

y=-1/2x+3+1

y=-1/2x+4

And that's our equation. Hope it helps.

*Graceful Dreamer here to help

Good luck.

5) Solve 5 - 2x < 7.
A) x < -1
B) x>-1
0x<-12
D) X > -12

Answers

Answer:

i think B. x>-1 is answer

Step-by-step explanation:

good luck

What is the inverse of y=5x-5

Answers

Answer:the answer is in the picture below

Step-by-step explanation:plz give brainlist

One weekend Bill earned 3 times as much as Jim. Tom earned $5 more than Jim. In all, they earned $60. How much did each earn?

Answers

Answer:

Step-by-step explanation:

J

B = 3J

T = J + 5

J + 3J + J + 5 = 60

5J = 55

J = $11

B = $33

T = $16

The amount earned by Jim, Bill and Tom is equal to [tex]\boldsymbol{\$ 11},\boldsymbol{\$ 33},\boldsymbol{\$ 16}[/tex].

"Important information"

Let .

The amount earned by Jim be [tex]\boldsymbol{x}[/tex].

Amount earned by Bill [tex]=\boldsymbol{3x}[/tex]

Amount earned by Tom [tex]=\boldsymbol{x+5}[/tex]

Total amount earned by all [tex]=\boldsymbol{\$ 60}[/tex][tex]x+3x+x+5=60\\5x=55\\x=11[/tex]

So,

Amount earned by Jim [tex]=\boldsymbol{\$ 11}[/tex]

Amount earned by Bill [tex]=3(11)[/tex] [tex]=\boldsymbol{\$ 33}[/tex]

Amount earned by Tom [tex]=11+5[/tex] [tex]=\boldsymbol{\$ 16}[/tex]

Find out more information about money here:

https://brainly.com/question/2696748?referrer=searchResults

Eight people met in a public park for a nature walk. Before they set off to look for birds, they all introduce themselves and each person shook hands with each of the other people. How many handshake were exchanged?

Answers

Answer:

56 handshakes

Step-by-step explanation:

one person shakes seven hands

eight people shook seven hands each

8×7=56

In the gift shop of the History of Flight museum, Elisa bought a kit to make a model of a jet airplane. The actual plane is 27 feet long with a wingspan of 18 feet. If the finished model will be 13.5 inches long, what will the wingspan be?

Answers

The length of the wingspan of the finished model based on the dimensions of the kit is 0.75 feet

Given:

Kit

Plane = 27 feet

wingspan = 18 feet

Model:

Plane = 13.5 inches

Wingspan = x feet

convert 13.5 inches to feet

1 feet = 12 inches

13.5 inches = 1.125 feet

So,

equate Ratio of plane to wingspan

27 : 18 = 1.125 : x

27/18 = 1.125 / x

cross product

27 × x = 18 × 1.125

27x = 20.25

x = 20.25/27

x = 0.75 feet

Therefore, the length of the wingspan of the finished model based on the dimensions of the kit is 0.75 feet

Learn more about ratio:

https://brainly.com/question/1781657

Can someone help me with this

Answers

Answer:

10 square inches

Step-by-step explanation:

[tex]area \: formula \: = \frac{1}{2} bh[/tex]

h= 5 inches

b= 4 inches

[tex] \frac{1}{2} \times 4 \times 5 = 10[/tex]

Hi, I already answered this question on your other post (seems like you posted this question twice): https://brainly.com/question/26075347 (check that link out)

How can multistep linear equations be written to represent different
scenarios?

Answers

Answer:

Linear equations use one or more variables where one variable is dependent on the other. Almost any situation where there is an unknown quantity can be represented by a linear equation, like figuring out income over time, calculating mileage rates, or predicting profit

Pls help I’ll brainlest ASAP

Answers

Answer:

Slope: -1/4x

y-int: 2

Step-by-step explanation:

Witch equation can be simplified to find the inverse of y=5x^2+10

Answers

Answer:

[tex]\huge\boxed{y=\sqrt{\dfrac{x-10}{2}}\ \text{for}\ x\geq10}[/tex]

Step-by-step explanation:

[tex]y=5x^2+10\\\\\text{exchange x to y and vice versa}\\\\x=5y^2+10\qquad|\text{subtract 10 from both sides}\\\\x-10=5y^2\qquad|\text{divide both sides by 5}\\\\\dfrac{x-10}{5}=y^2\\\\y^2=\dfrac{x-10}{5}\to y=\sqrt{\dfrac{x-10}{2}}[/tex]

What is the correct unit rate?And what is Jessie's likely error?​

Answers

Answer:

4

Step-by-step explanation:

1[tex]\frac{1}{2} / \frac{1}{8} = \frac{1}{2} * \frac{8}{1} = \frac{8}{2} = 4[/tex]

she forget that fraction will reverse if it move below or up side, I think

How to test a function graphically​

Answers

Answer:

Step-by-step explanation:

Inspect the graph to see if any vertical line drawn would intersect the curve more than once. If there is any such line, the graph does not represent a function. If no vertical line can intersect the curve more than once, the graph does represent a function.

that is known as the vertical line test

Answer:

Inspect the graph to see if any vertical line drawn would intersect the curve more than once. If there is any such line, the graph does no represent a function. If no vertical line can intersect the curve more than once, the graph does represent a function.

Step-by-step explanation:

NEED NOW PLEASE.....

Answers

Answer:

2+(-6)

Step-by-step explanation:

hope this helps

What is the solution to 12x=4x2+9? x=23

Answers

Answer:

x = 17/12

Step-by-step explanation:

12x = 4 x 2 +9

12x = 8 +9

12x = 17

x = 17/12 After divided

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