Integrate:–
[tex]\Huge{{\large{∫} \frac{dx}{ \sqrt{x \sqrt{x} - x {}^{2} } }}}[/tex]

Answers

Answer 1

9514 1404 393

Answer:

  4arcsin(x^(1/4)) +C

Step-by-step explanation:

Let x = z^4. Then dx = 4z^3·dz, and the given expression is ...

  [tex]\displaystyle\frac{dx}{\sqrt{x\sqrt{x}-x^2}}=\frac{4z^3\,dz}{\sqrt{z^4z^2-z^8}}=4\cdot\frac{dz}{\sqrt{1-z^2}}[/tex]

and its integral is ...

  [tex]\displaystyle\int{\frac{4\,dz}{\sqrt{1-z^2}}}=4\arcsin{(z)}+C=\boxed{4\arcsin{\sqrt[4]{x}}+C}[/tex]

__

Note that the original integrand is only defined on the interval (0, 1).


Related Questions

y=x^2-3, what is your y value when x=4​

Answers

Answer:

13

Step-by-step explanation:

4^2 is 16

16-3=13

that's all that you have to do you replace the x with 4 and do a normal equation

Answer: y=13

Y=(4)^2-3

y=16-3

y=13

If 50 grams of sweats cost $2.10,find the cost of 380 of sweats,giving your answer correct to the nearest 5 cent

Answers

Answer:

$15.95

Step-by-step explanation:

cost of 1 gram of sweet = $2.10 / 50 = 0.042

Cost of 380 g = 380 x 0.042 = $15.96

to the nearest 5 cent = 15.95

!!!!!!!!!PLEASE HELP!!!!!!!!

Answers

Answer:

A

Step-by-step explanation:

This answer is A hope I help

What is one thing that you want to accomplish next year in math? State your goal for math (in a complete sentence):

Answers

Answer:

I want to take better notes that include examples and definitions.

Step-by-step explanation:

Answer:

My goal in math that I would like to accomplish next year is to be a hard-working student who is self-managed and can work under pressure. ( switch it up a little if it doesn't match you)

Step-by-step explanation:

use two multipliers to convert 81 square feet to square yards

Answers

9 square yards..........

The graph of a linear function is shown.

A coordinate plane with a straight line passing through (negative 4, 2), (0, 0), and (4, negative 2).
Which word describes the slope of the line?

positive
negative
zero
undefined

Answers

Zeros can be observed graphically or solved for algebraically. A linear function can have none, one, or infinitely many zeros. If the function is a horizontal line ( slope = [latex]0[/latex]), it will have no zeros unless its equation is [latex]y=0[/latex], in which case it will have infinitely many.

Answer:

answer is negative

Step-by-step explanation:

2021 edge :)

What is the greatest
common factor (GCF)
of 25 and 75?

Answers

Answer:

25

Step-by-step explanation:

Answer:

GCF is 25

Step-by-step explanation:

Here's a great calculator for this! glad i could help.

https://www.mathsisfun.com/greatest-common-factor-tool.html

What is the rate of change or slope of 2y + 3x = 1

Answers

Answer:

I dont have a clue

Step-by-step explanation:

i am doing this for points

Y=(3x-1)/-2 is the equation

Casey polled 50 seventh grade students. He asked who they planned to vote for as class president. Thirty students said they would vote for Lynne. Twenty said they would vote for Marcus.
Use this probability to predict how many seventh graders in their class of 450 students will vote for Lynne

Answers

Answer:

270 students

Step-by-step explanation:

First, you need to do a ratio.

30          x

-------  = --------

50           450

In order to solve this, you need to multiply 450 times 30 and that equals 13500. 13500 divided by 50 is 270. That means that about 270 students will vote for Lynn.

Solve the volume of the cylinder 3m 10m

Answers

272.74 if 3 is the radius and the height is 10

Answer:

If π=22/7

volume of cylinder =282.857m³

Name a point that is not contained in any of the 3 lines a, b, or c​

Answers

I would say W because he’s just all alone chillin in the corner not touching a, b or c lines.

There is a bag of tiles where 8 are red, 5 are blue, 4 are orange, and 3 are green. If one is picked at random, replaced, and another marble is picked, what is the probability that they are both orange? in a percent or fraction

Answers

Answer:

There would be 1/25 chance (4%).

Step-by-step explanation:

So there's 4 orange marbles and there's 20 total marbles since:

8 Red + 5 Blue + 4 Orange + 3 Green

With this, the chance of drawing an orange marble is 4/20, or 1/5. Because the marble is replaced back after being picked, the same chance would occur for the second picking.

To combine these chances, multiply them together for the answer.

1/5 * 1/5 = 1/25 (4%)

8+5+4+3=20
(1/20)*(1/20)=1/40

What is 1/2 off of 3.48

Answers

Answer:

2.98

Step-by-step explanation:

1/2 as a decimal is 0.5 so 3.48 - 0.5 is 2.98

Help ASAP please !! No scam I really need this ! Trigonometry coordinates !

Answers

Answer:

A' (0,2)

B (-6,12)

C' (6,0)

How many glasses like the one shown can be filled three quarters full from a pitcher holding 150 cubic in ches of water.

Answers

Answer:

6

Step-by-step explanation:

I had this question

Which is the equation of the line that passes through the point (-3,-9) and has an undefined slope?

Answers

Answer:

Step-by-step explanation:

i dont know

Enter the rate as a fraction. Then find the unit rate. Sara drove 39 miles on 3 gallons of gas.

Answers

Answer:

The unit rate: 13 mi/gallon. Fraction 39/3

Step-by-step explanation:

39 miles/3 gallons. Simplify. 13 miles/1 mile=13 mi/gallon

Please mark brainliest!

Msm555 can you please help?!

Answers

Answer:

Solution given:

Sin C=21/29Sin C=30/50Cos C=36/39Cos 8/17

Help please gotta pass

Answers

Answer:

(59,93)

Step-by-step explanation:

Find K please and thank you

Answers

Answer:

k=48 degree(given in the diagram)

Step-by-step explanation:

Answer:

your answer is 45 degrees

Step-by-step explanation:

Can someone help me out on all three questions I’d appreciate ittt

Answers

Answerilll help ya so it's a

Step-by-step explanation:

Answer:

use desmos graphing calculator

Priya, variable "p", jumped 3 inches more than Xeno, “x”, in a high jump contest. Mai, “m”, jumped three times as many inches higher than Priya. If Mai jumped 14 inches, how many inches did Xeno reach? (You can use a tape diagram or hanger diagram to help solve this problem). ***EXPLAIN how you found your answer below:

Answers

Answer:

Xeno jumped 1 2/3 in

Step-by-step explanation:

if Mai jumped 3 times higher than Priya dividing Mai's 14 by 3 would get Priya's height. Then by subtracting 3 from Priya's height, which is 4 2/3, you get Xeno's height which is 1 2/3 in

The value of k is represented by the equation

Answers

option 3 ) the value of k is represented by the equation

If someone saved $0.85 every day for 40 years how much money do they have today?(365 days a year.)

Answers

12,410 i think lol but i’m not great at math

Answer:

12,410

Step-by-step explanation:

.85 x 365 = 310.25

310.25 x 40 = 12,410

Jess says that two of the three points below are on a line through the origin.
(3.8), (6, 21), and (9, 24)
Part A
Which two points could lie on the same line through the origin? Explain why. Explain why
the third point could not.
* I will give brainliest*

Answers

Answer:

(3, 8) and (9, 24) lie on the same line through the origin.

because (9, 24) is the result of dilatation of (3, 8) with scale factor 3.

(6, 21) is not the result, because 21 ≠ 2×8, even 6 = 2×3

Write the equation of the line in slope-intercept form that has a slope of -1/2 and goes through the point (2,3)

Answers

ANSWER : y=-1/2x+4
Y=mx+c
Gradient = y2-y1/x2-x1
Gradient = -1/2 as mentioned
y=-1/2x+c
Pick (2,3) 2 as x variable and 3 as y
3=-1/2(2)+c
3=-1+c
3+1=c
4=c
Equation y=-1/2x+4

Find the 8th term 50,20,8

Answers

Answer:

0

Step-by-step explanation:

Answer:

0.08192

Step-by-step explanation:

Given 50, 20, 8, ...

The sequence is geometric in nature

The nth term of the geometric sequence is exoressed as;

Tn = ar^{n-1}

a is the first term = 50

r is the common ratio = 20/50 = 8/20 = 2/5

n is the number of term = 8 (since we need the 8th term)

Substitute

T8 = 50(2/5)^{8-1}

T8 = 50(2/5)^7

T8 = 50(128/78,125)

T8 = 0.08192

Hence the 8th term is 0.08192.

The total number of cars produced by TESLA each year is y = 200000(1.25)x , where x represents the number of years after 2020. how many cars will be produced in year 2025 (five years later)?

Answers

Answer:

y=1250000

Step-by-step explanation:

Multiply 200000 by 1.25.

y = 250000 ⋅5

Multiply 250000 by 5.

y=1250000

Answer:

Step-by-step explanation:

ijaciiudui uchi icbdicj

Solve the system of linear equations.
2x + 3y = 5
X+ y = 5

Answers

X=4,y=1........!!!!!! Hope this helps

Answer:

Step-by-step explanation:

(10,-5)

Solve for x.
2x + 24
3x - 26
x = [?]

Answers

Answer:

set them equal to eachother, i gotta look at my notes tho

Step-by-step explanation:

I think it's like this

3x-26=2x+24

We simpilfy the equation to the form which is simple to understand.

3x-26=2x+24

We move allterms containing X to the left and all others terms to the right

+3x-2x=+24+26

We simplfiy left and right sideof the eqution.

+1x=+50

We divide both sides of the equation by 1 to get x.

x=50

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