Prove that y = arcsinx on the root of 1 x squared satisfies the equality (1 - x squared)y' - xy = 1

Answers

Answer 1

Answer:

Step-by-step explanation:

The first part is a computation, combining the chain and quotient rules. We know that the derivative of f(x)=arcsin(x) is 1/sqrt(1-x2), and we need to differentiate the denominator. We use the chain rule: let u=1-x^2, and v=sqrt(u). Then du/dx=-2x, and dv/du = 1/(2 sqrt(u)). Combining, dv/dx=-x/sqrt(1-x2). Now, we put everything together using the quotient rules: y' = (f'v-v'f)/v2. Multiplying by (1-x2)=v2, we obtain (1-x2)y'= sqrt(1-x2)/sqrt(1-x2) +xarcsin(x)/sqrt(1-x2), which we can rewrite as 1+xy, as desired. Let's call this equation ().

We prove the second part by induction on n. To do this, we need two things: a base case, that is, proving the case n=0, and an inductive step, where we prove case n+1 from case n. To do the base case, we differentiate both sides of equation (*) that we proved above: d/dx ((1-x2 )y') = d/dx (xy+1 ). On the left-hand side, we get -2xy'+(1-x2 )y'', using the product rule, and on the right-hand side, we get xy'+y, similarly. Rearranging, we've proven the case n=0 of the desired statement. The inductive step is similar: we differentiate the equation from case n using the chain rule. Each of the first two terms splits into two: respectively, -2xy(n+2)+(1-x2)y(n+3), and (2n+3)y(n+1)+(2n+3)xy(n+2). If we combine the terms with the same numbers of derivatives on y, we get (1-x2)y(n+3)-(2n+5)xy(n+2)-((n+1)2+2n+3)y(n+1)=0 -which is what we wanted to prove, since ((n+1)2+2n+3) simplifies to (n+2)2.


Related Questions

Evaluate.

2 1/4 + 2/5 / (-1/2)-1/4

Enter your answer as a mixed number in simplest form in the box.

Answers

Answer:

[tex]1\frac{1}{5}[/tex]

Step-by-step explanation:

2 1/4 + 2/5 / (-1/2)-1/4

order of operation states you do division before subtraction or addition

2 1/4 -4/5 -1/4....divide 2/5 by -1/2

2 - 4/5.................combine like terms

6/5........................subtract

1 1/5.......................simplify

Please help me please!!!!!!!!!

Answers

Step-by-step explanation:

the radius is diameter divided by 2

7/2/2 =1 .75

circumference of a circle is 2πr

2*22/7*1.75=11

3.14*11 =34.54

X+y=6 x-y=-2 solve by elimination

Answers

Step-by-step explanation:

x + y = 6

+ x - y = -2

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

2x + 0 = 4

x = 2

2 + y = 6

y = 4

please help with this

Answers

Answer:

2,4,6,

6,12,18

10,20,30

what is a degree 3 polynomial with integer coefficients with zeros 3, -4, 5

Answers

4 would it or maybe 12

6d + 20b ≤ 150

Solve for D and B

The help is highly appreciated and the best answer will get brainliest
thank you

Answers

Answer:

solving for b is b ≤ 15/2 - 3d/10

solving for d is d ≤ 25 - 10b/3

let f be the function given by f(x)=sin x + e^-x +3x. which of the following statements is true for y=f(x).

Answers

Applying derivatives, it is found that the correct options are:

A. [tex]y^{\prime\prime}(x) = -\sin{x} + e^{-x}[/tex]

D. [tex]y - y^{\prime\prime\prime\prime}(x) = 3x[/tex]

The function given is:

[tex]f(x) = \sin{x} + e^{-x} + 3x[/tex]

It's first four derivatives are:

[tex]y^{\prime}(x) = \cos{x} - e^{-x} + 3[/tex]

[tex]y^{\prime\prime}(x) = -\sin{x} + e^{-x}[/tex]

Hence, option A is correct.

[tex]y^{\prime\prime\prime}(x) = -cos{x} - e^{-x}[/tex]

[tex]y^{\prime\prime\prime}(x) \neq y^{\prime}(x)[/tex], hence, option B is incorrect.

[tex]y^{\prime\prime\prime\prime}(x) = sin{x} + e^{-x}[/tex]

It is not the multiplication of the first and of the third derivative, hence option C is incorrect.

[tex]y - y^{\prime\prime\prime\prime}(x) = 3x[/tex]

[tex]\sin{x} + e^{-x} + 3x - \sin{x} - e^{-x} = 3x[/tex]

[tex]3x = 3x[/tex]

Hence, option D is correct.

A similar problem is given at https://brainly.com/question/17042788

find the degree of the polynomial 5ab^3-7a^5c^2-5

Answers

Answer:

7

Step-by-step explanation:

as -7a^5c^2 term has two cofficient a and b and each have power.by adding power of one term we get 7

The graph below represents the function f(x) and the translated function g(x).
AVA
2x
/g(x)
a
If f(x) = x, which of the following functions could be an algebraic representation of g(x)?

Answers

I think it could be A

Keith’s Florists has 15 delivery trucks, used mainly to deliver flowers and flower arrangements
in the Greenville, South Carolina, area. Of these 15 trucks, 6 have brake problems. A sample
of 5 trucks is randomly selected.
a. What is the probability that 2 of those tested have defective brakes? (5 marks)
b. Is this a discrete or continuous distribution? Explain.

Answers

Answer:

= 0.419

Step-by-step explanation:

in pic  

(Hope this helps can I please have brainlist (crown)☺️)

Write the equation of the line in fully simplified slope-intercept form.

Answers

Answer:

Where is the problem?

Step-by-step explanation:

what is the area of the rectangle below?

Answers

120, you get the area by multiplying the width and length

Answer:

B. 120sq. units

Step-by-step explanation:

The area A of a rectangle is given by the formula, A=lw , where l is the length and w is the width.

so

8 * 15 = 120sq. units

They estimate that their current fridge (older) which they got for free cost them $19 a month in electricity charges to operate

Answers

Answer:

That's an expensive a ss refrigerator It's time to choose an energy star refrigerator that's only going to cost them about $2.90 per month. in about 32 months paying $19 a month they would have paid for an energy star refrigerator. if they keep that same refrigerator they would be buying a brand new refrigerator every 32 months. spending the 600 dollars now for a new refrigerator would save them $16.10 per month. The savings would pay for that same refrigerator in about 38 months.

Help!!!!! I will give out brainiest to best answer!!!

Answers

Answer:

see below

Step-by-step explanation:

a = 4

b = -2

c = -8

d = -11

Answer:

a=4, b=-2, c=-8, and d=-11

Step-by-step explanation:

its pretty easy

what is the measure of angle x

Answers

Answer:

180

Step-by-step explanation:

Find the value of X in triangles by subtracting known angle measurements from 180 degrees. Since the value of all angles within a triangle must equal 180 degrees, if you know at least two angles, you can subtract them from 180 to find the missing third angle.

The length of the
hypotenuse of a right-
angled triangle is 7.8 cm,
correct to 1 decimal place.
One of the shorter side
lengths is 2.1 cm, correct
to 1 decimal place. Estimate
the length of the remaining
side, rounding your answer
to 1 decimal place.

Answers

Answer:

7.5 cm

Step-by-step explanation:

Since it's a right triangle, apply pythegorean theorem

Let the missing side be x

[tex] {7.8}^{2} = 2.1 { }^{2} + x {}^{2} [/tex]

[tex]60.84 = 4.41 + {x}^{2} [/tex]

[tex] {x}^{2} = 60.84 - 4.41[/tex]

[tex] {x}^{2} = 56.43[/tex]

[tex] \sqrt{ {x}^{2} } = \sqrt{56.43} [/tex]

[tex]x = 7.5[/tex]

Therefore, the length of the missing side is 7.5 cm


Four candy stores are competing with each other. Which
store offers the best buy for candy?
A.) Sweet Store: 12 pack for $3.00
B.) Delicious Treats: 22 pack for $4.62
C.) Sugar Factory: 18 pack for $5.40
D.) Chocolate Shop: 36 pack for $7.20

Answers

Answer: The Chocolate shop

Step-by-step explanation:

We should get the cost per one pack for each store.

For the Sweet Store we divide 3.00 by twelve for the cost of one which is:

3 divided by 12 = 0.25

One pack at a sweet store is $0.25

Now do the same for the other stores:

4.67 divided by 22 = 0.21 (Rounded to 2 decimal points)

5.40 divided by 18 = 0.3

7.20 divided by 36 = 0.2

Sweet Store: one pack is $0.25

Delicious Treats: one pack is $0.21

Sugar Factory: one pack is $0.30

Chocolate Shop: one pack is $0.20

Therefore the Chocolate shop is giving you the best deal since each pack is cheaper.

Find the distance between two points in the simplest radical form

Answers

Answer:

The answer will be 5.

Step-by-step explanation:

using the formula d=/(x2-x1)2 +(y2-y1)

Complete the sentences to make true statements

6 is 100 times ____.
0.06 is 10 times ____.
60 is 1/100 of ____.

Answers

Answer:

6 is 100 times 0.06  

0.06 is 10 times 0.006  

60 is 1/100 of 6,000

Step-by-step explanation:

Since 6/100 is equal to 0.06, we can say that 6 is the result of multiplying 0.06 by one hundred (0.06 x 100 = 6).  

On the other hand, since 0.06 / 10 is equal to 0.006, it is correct to say that 0.006 x 10 is equal to 0.06 (0.006 x 10 = 0.06).  

Finally, 60 is one hundredth of 6000, since multiplying 60 x 100 the result is 6,000 (6,000 / 100 = 60).

hope this really helped!!

mark me brainliest :D

The complete sentences are:

6 is 100 times 0.06 .

0.06 is 10 times 0.006.

60 is 1/100 of 6,000.

"6 is 100 times greater than 0.06":

This means that if you multiply 0.06 by 100, you get 6.

So, 6 is indeed 100 times larger than 0.06.

"0.06 is 10 times greater than 0.006":

In this case, if you multiply 0.006 by 10, you get 0.06.

Thus, 0.06 is 10 times larger than 0.006.

"60 is 1/100 of 6,000":

This means that if you divide 6,000 by 100, you get 60.

So, 60 is a hundredth (1/100) of 6,000.

Hence, 6 is 100 times 0.06  

0.06 is 10 times 0.006  

60 is 1/100 of 6,000

To learn more on Number system click:

https://brainly.com/question/1763119

#SPJ3

Aldo earns 51 dollars a week working at the bookstore he makes one dollar more for each book that he sells . the amount , A (in dollars )that Aldo earns a week of he sales b books is given by the following function
A(b)=51+b​

Answers

Answer:

False.

Step-by-step explanation:

A x b does not equal to A + b. Addition and mutiplication is different.

Ivan was the 31st person in line. His position in line was just behind 5/9 of the total number of people in line. How many people were in line? HELP PLEASE WILL MARK BRAINLIEST

Answers

31=1-(5/9)x

30=-(5/9)x

x=54

The answer is 54 people.

hope this helps :)

7.
"iş, oluş, durum bildiren köklere fiil kökü denir. Fill
kökleri -mek / -mak mastar eki ile anlamlı şekilde
söylenir."
Açıklamaya göre verilen sözcüklerden hangisi-
nin kökü fiil değildir?
A) evim
B) seçim
C) giyim
D) verim

Answers

Answer:

ABWJRIRISBDBDBHSHS

Step-by-step explanation:

Hatdog HWHWHWHSHSHSQIWIW

If F=(-3)
Find: F(x)=4x^2-5

Answers:
-41
31
29
None of the Above ​

Answers

Answer:

31

Step-by-step explanation:

as we put the value of X in the function it gives 3

PLEASE HELP.
Directions: find x so that L || M. state the converse used

Answers

Answer:

  8. x=6; supplementary consecutive interior angles

  10. x = 4; no applicable theorem

Step-by-step explanation:

8.

The marked angles are "consecutive interior" angles. When their sum is 180°, the lines l and m will be parallel.

  (7x -15) +(24x +9) = 180

  31x = 186

  x = 6

Consecutive interior angles being supplementary will make the lines parallel.

__

10.

The sum of the remote interior angles of a triangle is equal to the exterior angle:

  28x = 48 +16x

  12x = 48

  x = 4

The above relation holds regardless of whether line l is parallel to line m. There is no applicable theorem or converse.

_____

Additional comment

Adding the marking shown in the attachment would make the converse of the alternate interior angles theorem applicable to problem 10.

Consider the following data to determine whether there is a significant difference between the values of Group 1 and Group 2. Let the significance level be 5%. Group 1: 15, 17, 26, 11, 18, 21, 13, 29 Group 2: 23, 14, 24, 13, 22, 23, 18, 21 What rank will be given to the value 15

Answers

Using the t-distribution, it is found that since the p-value of the test is 0.72 > 0.05, there is not significant difference between the values of each group.

At the null hypothesis, we test if the groups have the same values, that is, the subtraction of their means is 0:

[tex]H_0: \mu_2 - \mu_1 = 0[/tex]

At the alternative hypothesis, we test if the groups have different values, that is, the subtraction of their means is different of 0:

[tex]H_1: \mu_2 - \mu_1 \neq 0[/tex]

First, we have to find the mean and the standard deviation for both samples, hence, using a calculator:

[tex]\mu_1 = 18.75, \sigma_1 = 6.2507, \mu_2 = 19.75, \sigma_2 = 4.2678[/tex]

The standard errors are:

[tex]s_1 = \frac{\sigma_1}{\sqrt{n_1}} = \frac{6.2507}{\sqrt{8}} = 2.21[/tex]

[tex]s_2 = \frac{\sigma_2}{\sqrt{n_2}} = \frac{4.2678}{\sqrt{8}} = 1.5089[/tex]

For the distribution of differences, we have that:

[tex]\overline{x} = \mu_2 - \mu_1 = 19.75 - 18.75 = 1[/tex]

[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{2.21^2 + 1.5089^2} = 2.676[/tex]

We have the standard deviation for the samples, hence, the t-distribution is used. The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu[/tex] is the value tested at the null hypothesis, which is 0 for this problem. Hence, the value of the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

[tex]t = \frac{1 - 0}{2.676}[/tex]

[tex]t = 0.37[/tex]

To find the p-value, we have a two-tailed test, as we test if the means are different from a value, with t = 0.37 and 8 + 8 - 2 = 14 df.

Using a t-distribution calculator, this p-value is of 0.72.

Since the p-value of the test is 0.72 > 0.05, there is not significant difference between the values of each group.

A similar problem is given at https://brainly.com/question/15682365

Addison plays 6 songs in of an hr. How many
songs can she play for 4 hours?

Answers

Answer:

24

Step-by-step explanation:

4x6=12or 2x6=12so then 12+12=24

Answer:

6 songs per hour, so multiply that with the number asked which is four

so four times six is24

so she can play 24 songs in four hours!

~ ...

~ !

~ !

a
2. During one month, a homeowner used 400 units of electricity and 120 units of gas for a total cost
of $73.60. The next month, 350 units of electricity and 200 units of gas were used for a total cost of
$72. Find the cost of a unit of gas.
Define variables:
Equation:
Equation:
Solution:

Answers

Answer:

Step-by-step explanation:

120G + 400E  = 73.60

            400E = 73.60 - 120G

                   E = 0.184 - 0.3G

                   200G + 350E = 72.00

200G + 350(0.184 - 0.3G) = 72.00

         200G + 64.4 - 105G = 72.00

                                   95G = 7.60

                                        G = $0.08/unit

What's 9 + 10?


Whoever gets it right get's the crown!

Answers

Answer:

jokes aside it is 19

Step-by-step explanation:

but if it is jokes then 21

Answer:

Step-by-step explanation:

the answer would be 21

Please Help me Solve this question

Answers

Answer:

Step-by-step explanation:

Correct Answer: C

We can rely on the guess and check method to easily solve this problem. Let’s first pick arbitrary values of x and y to eliminate some answer choices.

Let’s consider the case where |x| and let x = 3 and y = -10.

Because x/y = -3/10 < 1, answer choice A is incorrect.

Because |x|2 = (3)2 = 9 and |-10| = 10, we have that |x|2 < y, so answer choice B is also incorrect.

Because x2 + 1= (3)2 + 1 = 10 and y2 + 1 = (10)2 + 1 = 101, we have that x2 + 1 < y2 + 1, so answer choice D is also incorrect.

Now, let’s consider the case where |x|>|y| and let x = 3 and y = -2.

Then, x-2 = 1/x2 = 1/9 and y-2 = 1/y2 = 1/4. This means that x-2 < y-2 , so answer choice E is also incorrect.

This means that answer choice C is correct. We can manipulate the inequality to see why this is true: (x/3 – 5) > (y/3 – 5)

We add 5 to both sides: x/3 > y/3

We multiply both sides by 3: x > y.

We know this is true since we are given that x > 1 > -1 > y, which simplifies to x > y.

Please view the image above for the question ^^​

Answers

Answer:

2

Step-by-step explanation:

After reflecting ABC over the y-axis and translating that image down, ABC will map onto DEF.

Answer:

(2)

Step-by-step explanation:

If you reflect ABC across the y axis it would look like DEF but above the x axis; translate it down and you get DEF.

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