Find the inverse of the equation f(x)=ln(x/x-2)

Step-by-step explanation:

∫ 9 arctan(1/x) dx

If u = 9 arctan(1/x), then:

du = 9 / (1 + (1/x)²) (-1/x²) dx

du = -9 dx (1/x²) / (1 + (1/x²))

du = -9 dx / (x² + 1)

If dv = dx, then v = x.

∫ u dv = uv − ∫ v du

= 9x arctan(1/x) − ∫ -9x dx / (x² + 1)

= 9x arctan(1/x) + 9/2 ∫ 2x dx / (x² + 1)

= 9x arctan(1/x) + 9/2 ln(x² + 1)

Evaluate from x=1 to x=√3.

[9√3 arctan(1/√3) + 9/2 ln(3 + 1)] − [9 arctan(1) + 9/2 ln(1 + 1)]

[9√3 (π/6) + 9/2 ln(4)] − [9 (π/4) + 9/2 ln(2)]

(3π√3)/2 + 9/2 ln(4) − (9π/4) − 9/2 ln(2)

(6π√3)/4 + 9 ln(2) − (9π/4) − 9/2 ln(2)

(6π√3 − 9π)/4 + 9/2 ln(2)

Answer:

[tex]9\left(\frac{1}{2}\ln \left(2\right)-\frac{\pi }{4}+\frac{\pi }{2\sqrt{3}}\right)[/tex]

Step-by-step explanation:

We are given the integral 9 arctan(1/x)dx on the interval x[ from 1 to √3 ].

Now let's say that u = arctan(1/x). The value of 'du' would be as follows:

du = - x / (1 + x²) * dx

If we apply integration by parts, v = 1, and of course u = arctan(1/x):

=> 9x arctan(1/x) − ∫ -9x dx / (x² + 1)

=> 9[x arctan(1/x) - ∫ - x / (1 + x²) * dx] on the interval x[ from 1 to √3 ]

Let's now simplify the expression ' ∫ - x / (1 + x²) * dx':

=> (Take the constant out, in this case constant = - 1), - ∫ x / (1 + x²) * dx

=> (Apply u-substitution, where u = 1 + x²), - ∫ 1/2u * du

=> (Take constant out again, in this case 1/2), - 1/2 ∫ 1/u * du

=> (Remember that 1/u * du = In( |u| )), - 1/2In( |u| )

=> (Substitute back 'u = 1 + x²), - 1/2In| 1 + x² |

So now we have the expression '9[x arctan(1/x) + 1/2In| 1 + x² |]' on the interval x[ from 1 to √3 ]. Let's further simplify this expression;

[tex]9\left[x\arctan \left(\frac{1}{x}\right)+\frac{1}{2}\ln \left|1+x^2\right|\right]^{\sqrt{3}}_1\\\\=> 9\left[\frac{1}{2}\left(2x\arctan \left(\frac{1}{x}\right)+\ln \left|1+x^2\right|\right)\right]^{\sqrt{3}}_1[/tex]

Now computing the boundaries we have the following answer:

[tex]9\left(\frac{1}{2}\ln \left(2\right)-\frac{\pi }{4}+\frac{\pi }{2\sqrt{3}}\right)[/tex]

Answer:

1/49

Step-by-step explanation:

7^-2

1/49

7^2 is usually 49 for negative exponents just flip it

Answer:

(7)^-2

Step-by-step explanation:

hope this helps

Answer: 46

Step-by-step explanation:

10 (3 +1) + 6

30 + 10 + 6

46

Answer:

D. Multiply/divide both sides by the same non-zero constant

A. Yes

Just Did It On Khan Academy

Step-by-step explanation:

This question is incomplete, the complete question is;

A basketball player has a 60% accuracy rate for making free throws. During practice, this player fails to make a free throw three times in a row, but is finally successful on the fourth attempt.

p(x=k) = p^k (1-p)^k-1

Using the geometric distribution formula, what is the probability of this player successfully making a free throw on the fourth attempt? Each attempt is independent of each other and answer choices are rounded to the hundredths place.

a.) 0.04

b.) 0.60

c.) 0.40

d.) 0.10

Answer: a.) 0.04

Step-by-step explanation:

Given that;

The basketball player has 60% accuracy of  free throws

Now the probability of the player successfully making a free throw on the fourth attempt.

probability of success p = 0.60

number of failure k = 3

the given p.d.f of geometric distribution p(x=k) = p^k (1-p)^k-1

{ 0 <p<= 1 , k=0,1,2,3... }

we substitute our given data

p(x=3) = 0.60^3 (1-0.6)^3-1

= (0.60)^3 (0.40)^2

= 0.216 * 0.16

= 0.035 = 0.04 ( OPTION A)

Answer:

[tex]d = \frac{C}{\pi}[/tex]

Step-by-step explanation:

[tex]C= \pi d\\[/tex]

Isolate d ; Divide both sides of the equation by [tex]\pi[/tex]

[tex]\frac{C}{\pi} = \frac{\pi d}{\pi }[/tex]

Simplify

[tex]\frac{C}{\pi} = d\\\\d = \frac{C}{\pi}[/tex]

Note; Another formula for d(diameter) =

[tex]2\times radius[/tex]

Answer:

+1 is the distanse of the following point

Answer:

58

Step-by-step explanation:

Prime Numbers = 2+3+5+7+11+13+17

= 58

Answer:

2401 is your answer hope this helps

Answer:

I think it would be angles A and B.

Hope this helps!

Answer:

2

Step-by-step explanation:

You'll need to find the reciprocal of m. -1/4 is your is your m and when you find the reciprocal you flip the number to 4/1 or 4 and change the negative to a positive. Then graph (4,11), you don't need to worry about your y intercept, b, or -1. On your graph go down 4 and over one to the left because it's positive the line should be going like " / "  <-- that. Keep going down until your y is three and whatever your x is, is your answer. Ex: (4,11) (3,7) (2,3). Hopefully, you understand :)

Complete Question

Given two independent random samples with the following results:

[tex]n_2=13\ , \= x_2=171\ s_1=23[/tex]  

Use this data to find the 90% confidence interval for the true difference between the population means. Assume that the population variances are equal and that the two populations are normally distributed.

Step 1 of 3: Find the point estimate that should be used in constructing the confidence interval.

Step 2 of 3: Find the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.

Step 3 of 3: Construct the 90% confidence interval. Round your answers to the nearest whole number.

Answer:

Step 1 of 3:

    [tex]\= x_p  =  15[/tex]

Step 2 of 3:

    [tex]E =7.79[/tex]

Step 3 of 3:

   [tex] 7.21 < \mu_1 - \mu_2 < 22.79[/tex]

Step-by-step explanation:

Now considering the Step 1 of 3, the  point estimate that should be used in constructing the confidence interval  is mathematically represented as  

        [tex]\= x_p = \= x_1 - \= x_2[/tex]

=>     [tex]\= x_p = 186 - 171[/tex]

=>     [tex]\= x_p = 15[/tex]

Now considering the Step 2 of 3

Given that the confidence level is  90% then the level of significance is mathematically represented as

     [tex]\alpha = (100-90)\%[/tex]

=>    [tex]\alpha = 0.10[/tex]

Generally the degree of freedom is mathematically represented as

        [tex]df = n_1 + n_2 - 2[/tex]

=>    [tex]df = 13 + 13 - 2[/tex]

=>   [tex]df = 24[/tex]

From the student t-distribution table the critical value of  [tex]\frac{\alpha }{2}[/tex] at a degree of freedom of  [tex]df = 24 \ is \ \ t_{\frac{\alpha }{2} ,df} = 1.711[/tex]

Generally the pooled variance is mathematically represented as    

  [tex]s_p^2 = \frac{ (13 -1 ) 33^2 + (13 -1 ) 23^2 }{(13 - 1 )(13 - 1)}[/tex]

         [tex]s_p^2 = 134.83 [/tex]

Generally the margin of error is mathematically represented as

  [tex]E = t_{\frac{\alpha }{2} ,df } * \sqrt{\frac{s_p^2}{n_1} +\frac{s_p^2}{n_2} }[/tex]

=>     [tex]E = 1.711* \sqrt{\frac{134.83}{13} +\frac{134.83}{13}}[/tex]

=>     [tex]E =7.79[/tex]

Now considering the Step 3 of 3

Generally the 90% confidence interval is mathematically represented as

              [tex]\= x_p -E < \mu_1 - \mu_2 < \= x_p +E[/tex]

=>  [tex] 15 -7.79 < \mu_1 - \mu_2 < 15 +7.79[/tex]

=>  [tex] 7.21 < \mu_1 - \mu_2 < 22.79[/tex]

Answer:

A) f(n) = 12 + 2(n-1)

Step-by-step explanation:

Arithmetic Sequence Formula:

a(n) = a(1) + (n-1)d

d = 2

a(1) = 12

a(n) = 12 + 2(n-1)

Answer:

Step-by-step explanation:

A) f(n) = 12 + 2(n-1)

Answer:

Answer:

Javon is incorrect

Step-by-step explanation:

You have to subtract 5 both sides to move it to the other side:

5 -2x -1/3 = 4

5 - 5 - 2x - 1/3 = 4 -5

-2x - 1/3 = -1

Answer:

Javon is incorrect because he didnt subtract 5 from both sides, or add -5

Step-by-step explanation:

I had this question

Answer:

16

Step-by-step explanation:

did the calculation

Answer:

Therefore the highest common factor of 80 and 16 = 8

Answer:

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

Step-by-step explanation:

Answer:

2.1544

Step-by-step explanation:

[tex]\sqrt[3]{10}[/tex] = 2.1544

check: 2.1544^3

Answer:

10

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

all sides are equal

Answer:

Step-by-step explanation:

We can see that the scale factor is 2

Corresponding sides have length of:

Therefore corresponding angles, opposite to corresponding sides are:

Correct answer option:

Answer:

His answer is correct!

Step-by-step explanation:

Got it right

Answer:

$6/ book

Step-by-step explanation:

Unit price = Total cost/ total number of items

                = 90/15

                =$6 per book

Answer:

12

Step-by-step explanation:

40/100*30

=12

Answer:

12..

Step-by-step explanation:

off topic but broski i think we're in the same school program?

Answer:

-2x cos x + 2 sin x + C

Step-by-step explanation:

∫ (2x sin x) dx

If u = 2x, then du = 2 dx.

If dv = sin dx, then v = -cos x.

∫ u dv = uv − ∫ v du

= 2x (-cos x) − ∫ (-cos x) (2 dx)

= -2x cos x + 2 ∫ cos x dx

= -2x cos x + 2 sin x + C

Answer:

[tex]\displaystyle \large{2 \sin x - 2x \cos x + C}[/tex]

Step-by-step explanation:

We are given the indefinite integral:

[tex]\displaystyle \large{\int {2x \sin x} \ dx }[/tex]

Using by-part method, we have to substitute u-term and dv appropriately.

By-part is an integration of product rules, when integrated the product rules of differentiation, we’ll obtain:

[tex]\displaystyle \large{\int {u} \ dv = uv - \int {v} \ du}[/tex]

Above is by-part method/formula.

Where 4 terms are presented:

Our main terms to substitute are u and dv which mean u-term has to be a function that’s differentiatable and dv has to be a function that’s integratable.

The main concept of by-part is to understand how to substitute appropriately which you can simply follow below:

LIATE

Stands for Logarithm, Inverse (Trigonometry), Algebraic, Trigonometric and Exponential.

These are in orders from first to last on what to let u-term first. That means logarithm functions must be the first to substitute themselves as u-term, so if you encounter a logarithmic function and a polynomial function, you must let u = logarithmic function while dv = polynomial.

In this case, we have 2x which is polynomial and sin(x) which is trigonometric. According to LIATE, we have to let Algebraic or Polynomial 2x be first to substitute as u-term, that means our dv is trigonometric sin(x).

Therefore, we have:

Now, substitute these terms in accordingly to formula of by-part.

[tex]\displaystyle \large{\int {2x \sin x} \ dx = 2x \cdot (-\cos x) - \int {-\cos x \cdot 2 \ dx}}\\ \displaystyle \large{\int {2x \sin x} \ dx = -2x \cos x + \int {2 \cos x \ dx}}\\ \displaystyle \large{\int {2x \sin x} \ dx = -2x \cos x + 2 \int {\cos x \ dx}}\\ \displaystyle \large{\int {2x \sin x} \ dx = -2x \cos x + 2 \cdot \sin x + C}\\ \displaystyle \large{\int {2x \sin x} \ dx = -2x \cos x + 2 \sin x + C}[/tex]

__________________________________________________

Summary

  Property

[tex]\displaystyle \large{ \int {k f(x)} \ dx = k \int{f(x)} \ dx \ \ \ \ \tt{(k \ \ \ is \ \ \ a \ \ \ constant.)}\\[/tex]

Only shown in explanation.

  By-Part

[tex]\displaystyle \large{\int u \ dv = uv- \int v \ du}[/tex]

  LIATE

The functions in order that should be u-term from first to last.

These functions above do not have integration formula by default.

  Indefinite Integral

Make sure to always add + C after evaluating the integral, regardless what multiplies or attempts to affect + C, we must always add + C.

__________________________________________________

The reciprocal of 15 1/4 is 4/61

Step-by-step explanation:

15 1/4 multiply 15 by 4 and then add 1 it will give you 61/4 then you change into reciprocal which will be 4/61

Answer:

-20 - 10 = -30

Answer: -30

Step-by-step explanation: basically -20 + -10 = -30

Answer:

B. (8, 1)

Step-by-step explanation:

Given M(6, 5) as midpoint of PQ, and P(4, 9),

let [tex] P(4, 9) = (x_2, y_2) [/tex]

[tex] Q(?, ?) = (x_1, y_1) [/tex]

[tex] M(6, 5) = (\frac{x_1 + 4}{2}, \frac{y_1 + 9}{2}) [/tex]

Rewrite the equation to find the coordinates of Q (x1, y1):

[tex] 6 = \frac{x_1 + 4}{2} [/tex] and [tex] 5 = \frac{y_1 + 9}{2} [/tex]

Solve for each:

[tex] 6 = \frac{x_1 + 4}{2} [/tex]

Multiply both sides by 2

[tex] 6*2 = \frac{x_1 + 4}{2}*2 [/tex]

[tex] 12 = x_1 + 4 [/tex]

Subtract 4 from both sides

[tex] 12 - 4 = x_1 + 4 - 4 [/tex]

[tex] 8 = x_1 [/tex]

[tex] x_1 = 8 [/tex]

[tex] 5 = \frac{y_1 + 9}{2} [/tex]

Multiply both sides by 2

[tex] 5*2 = \frac{y_1 + 9}{2}*2 [/tex]

[tex] 10 = y_1 + 9 [/tex]

Subtract 9 from both sides

[tex] 10 - 9 = y_1 + 9 - 9 [/tex]

[tex] 1 = y_1 [/tex]

[tex] y_1 = 1 [/tex]

Coordinates of Q is (8, 1)

Answer:

21:00 AST

Step-by-step explanation:

10:00 uk time

Australia time is 11 hours ahead of UK time then

10:00 + 11 hours

21:00 AUSTRALIA TIME

OR 9:00 PM Australia time