Find the value of x 63° (2x + 3)°

Answer:

[tex]\displaystyle \int {x^{-11}(1 + x^4)^\Big{- \frac{1}{2}}} \, dx = \boxed{ - \frac{\sqrt{x^4 + 1} (8x^8 - 4x^4 + 3)}{30x^{10}} + C }[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Rule [Basic Power Rule]:

Integration

Integration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:
[tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Integration Methods: U-Substitution, U-Solve, Trigonometric Substitution

Step-by-step explanation:

*Note:

The problem is too big to fit all work. I will assume that you know how to do basic calculus.

Step 1: Define

Identify given.

[tex]\displaystyle \int {x^{-11}(1 + x^4)^\Big{- \frac{1}{2}}} \, dx[/tex]

Step 2: Integrate Pt. 1

Step 3: Integrate Pt. 2

Identify variables for u-substitution/u-solve.

Step 4: Integrate Pt. 3

Start solving the integral using u-solve:

[tex]\displaystyle \begin{aligned}\int {x^{-11}(1 + x^4)^\Big{- \frac{1}{2}}} \, dx & = \int {\frac{1}{x^{11}\sqrt{x^4 + 1}}} \, dx \\& = \int {\frac{1}{2u^6 \sqrt{u^2 + 1}}} \, du \\& = \frac{1}{2} \int {\frac{1}{u^6 \sqrt{u^2 + 1}}} \, du \\\end{aligned}[/tex]

Step 5: Integrate Pt. 4

Identify variables for trigonometric substitution.

Step 6: Integrate Pt. 5

Let's focus on just the integral itself. Apply the Trigonometric Substitution Integration Method and other basic integration techniques listed under "Calculus":

[tex]\displaystyle \begin{aligned}\int {\frac{1}{u^6 \sqrt{u^2 + 1} }} \, du & = \int {\frac{\sec^2 v}{\tan^6 v \sqrt{\tan^2 v + 1} }} \, dv \\& = \int {\frac{\sec v}{\tan^6 v}} \, dv \\& = \int {\cot v \csc v (\csc^2 v - 1)^2} \, dv \\\end{aligned}[/tex]

Step 7: Integrate Pt. 6

Identify variables for u-substitution/u-solve again.

Use another variable besides u to avoid confusion with earlier substitutions:

Step 8: Integrate Pt. 7

Reduce the integral using the U-Solve Integration Method and other basic integration techniques listed under "Calculus":

[tex]\displaystyle \begin{aligned}\int {\frac{1}{u^6 \sqrt{u^2 + 1} }} \, du & = \int {\frac{\sec^2 v}{\tan^6 v \sqrt{\tan^2 v + 1} }} \, dv \\& = \int {\frac{\sec v}{\tan^6 v}} \, dv \\& = \int {\cot v \csc v (\csc^2 v - 1)^2} \, dv \\& = \int {-(w^2 - 1)^2} \, dw \\& = - \int {(w^2 - 1)^2} \, dw \\& = - \int {\bigg( w^4 - 2w^2 + 1 \bigg)} \, dw \\\end{aligned}[/tex]

Step 9: Integrate Pt. 8

Solve the integral using basic integration techniques listed under "Calculus":

[tex]\displaystyle\begin{aligned}- \int {\bigg( w^4 - 2w^2 + 1 \bigg)} \, dw & = - \Bigg[ \int {w^4} \, dx - \int {2w^2} \, dx + \int {} \, dx \Bigg] \\& = - \Bigg[ \int {w^4} \, dx - 2 \int {w^2} \, dx + \int {} \, dx \Bigg] \\& = - \Bigg[ \frac{w^5}{5} - \frac{2w^3}{3} + w + C \Bigg] \\& = - \frac{w^5}{5} + \frac{2w^3}{3} - w + C \\& = - \frac{\csc^5 v}{5} + \frac{2\csc^3 v}{3} - \csc v + C \\\end{aligned}[/tex]

[tex]\displaystyle\begin{aligned}- \int {\bigg( w^4 - 2w^2 + 1 \bigg)} \, dw & = - \frac{(u^2 + 1)^\Big{\frac{5}{2}}}{5u^5} + \frac{2(u^2 + 1)^\Big{\frac{3}{2}}}{3u^3} - \frac{\sqrt{u^2 + 1}}{u} + C \\\end{aligned}[/tex]

Step 10: Integrate Pt. 9

Let's substitute our integral value into our integral from "Step 4":

[tex]\displaystyle\begin{aligned}\frac{1}{2} \int {\frac{1}{u^6 \sqrt{u^2 + 1}}} \, du & = - \frac{(u^2 + 1)^\Big{\frac{5}{2}}}{10u^5} + \frac{(u^2 + 1)^\Big{\frac{3}{2}}}{3u^3} - \frac{\sqrt{u^2 + 1}}{2u} + C \\& = - \frac{(x^4 + 1)^\Big{\frac{5}{2}}}{10x^{10}} + \frac{(x^4 + 1)^\Big{\frac{3}{2}}}{3x^6} - \frac{\sqrt{x^4 + 1}}{2x^2} + C \\& = \boxed{ - \frac{\sqrt{x^4 + 1}(8x^8 - 4x^4 + 3)}{30x^{10}} + C } \\\end{aligned}[/tex]

∴ we have found the indefinite integral.

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Topic: Calculus

Number line equality to -5< =< -1

Answer:

B. light

Step-by-step explanation:

When specific frequencies of light are absorbed by a material, it forms an absorption spectrum.

Answer:

∠ AOC = 124°

Step-by-step explanation:

the 3 angles lie on a straight line and sum to 180°

sum the 3 angles and equate to 180

3x + 94 + x + 30 + 2x - 4 = 180

6x + 120 = 180 ( subtract 120 from both sides )

6x = 60 ( divide both sides by 6 )

x = 10

Then

∠ AOC = 3x + 94 = 3(10) + 94 = 30 + 94 = 124°

Answer:

7840 ft^3

Step-by-step explanation:

give brainliest please!

(10*14*40) + (14*40*8)1/2

Answer:

a and b I know for sure, im not sure about the others sorry

Answer:

17.2 is 17.2 units to the right of zero on the number line.

Step-by-step explanation:

On a number line positive numbers are on the right of 0 and negative numbers are one the left of 0.

Please mark brainliest :)

Answer: Right

Step-by-step explanation:

    All positive numbers are to the right of zero on the number line.

   All negative numbers are to the left of zero on the number line.

        17.2 is a positive number, so;

17.2 is 17.2 units to the (right/left) of zero on the number line.

Answer:

B I just got that question it was B

Answer:

y = (1/5)x - 12/5

Step-by-step explanation:

First, you need to find the slope (m). This can be done by using the given points and the following equation.

y₁ - y₂ = m(x₁ - x₂)

-3 - (-2) = m(-3 - 2)

-1 = -5m

1/5 = m

Next, you need to find the y-intercept (b). You can do this by using the slope and the values of a point in the following equation.

y = mx + b

-2 = (1/5)(2) + b

-2 = 2/5 + b

-2.4 = b

-12/5 = b

Putting the information together, you are left with your final equation.

y = (1/5)x - 12/5

Answer:

  C = 25°, b = 62.3, c = 32.1

Step-by-step explanation:

The Law of Sines can be used to solve a triangle when two angles and a side opposite one of them is given.

__

The angle sum theorem can be used to find the third angle.

  C = 180° -A -B = 180° -30° -125° = 25°

__

The Law of Sines tells you ...

  a/sin(A) = b/sin(B) = c/sin(C)

  b = a(sin(B)/sin(A)) = 38·sin(125°)/sin(30°) ≈ 62.3

  c = a(sin(C)/sin(A)) = 38·sin(25°)/sin(30°) ≈ 32.1

The solution is ...

  C = 25°, b = 62.3, c = 32.1

Using translation concepts, it is found that the parent function graphed in this problem is [tex]y = \sqrt{x}[/tex].

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, we have only one graph, which has the format of the square root of x, hence the function is:

[tex]y = \sqrt{x}[/tex]

More can be learned about translation concepts at https://brainly.com/question/4521517

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Answer: 12

Step By Step Explanation:

Answer:

Step-by-step explanation:

Given :

f(x) = x − 3

g(x) = x² − x

Note : (f+g)(x) = f(x) + g(x)

then

(f+g)(2) = f(2) + g(2)

           = (2 - 3) + (2² - 2)

           = -1  +  2

           = 1

another method:

(f+g)(x) = f(x) + g(x) =  x − 3 + x² − x = x² - 3

then

(f+g)(2) = 2² - 3 = 4 - 3 = 1

Answer:

32

Step-by-step explanation:

4 ÷ 1/8

make 4 into a fraction

4/1 ÷ 1/8

when dividing a fraction you change the divide into multiply and you flip the second fraction:

4/1 × 8/1 = 32

Answer:

32

Step-by-step explanation:

1/8 = 1 / 8 = 0.125        4 / 0.125 = 32

mad skillz gl cheating on your I-ready test

Answer:f^8

Step-by-step explanation:

F^7 multiplied by F^1 =f (7+6+1)= f^8F

The area of the walkway that is painted with the 12 arrows will be 840 cm². Then the correct option is C.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

This figure represents an arrow painted on a walkway 12 times.

The figure is given below.

The figure is the combination of a triangle and a rectangle. Then the area of the figure will be

Area = 1/2 x 8 x 5 + 10 x 5

Area = 20 + 50

Area = 70 cm²

Then the area of the walkway that is painted with the 12 arrows will be

Area of the walkway = 70 x 12

Area of the walkway = 840 cm²

More about the geometry link is given below.

https://brainly.com/question/7558603

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Answer:

90°

Step-by-step explanation:

This is important to remember, the three interior angles will always have a sun of 180.

knowing this it’s pretty basic math

a + b + c = 180

33 + 57 + c = 180

90 + c = 180

[subtract 90 from each side (90 cancels out)]
c = 90°

…

Check
- > 33 + 57 + 90 = 180

33 + 147 + = 180

180 = 180

Check!

Answer:

First Number=9

Second number=18

Third Number=72

Step-by-step explanation:

let's take the first number as X

X+(9+X)+[4(9+X)]=99

X+9+X+36+4=99

6X=99-45

X=54/6

X=9

Answer:

3:2.

Step-by-step explanation:

They have 15 - 6 = 9 problems to do, so it is:

9:6

= 3:2.

Answer:

9/15

Step-by-step explanation:

15 - 6 = 9 as a fraction would be 9 meaning what is left and 15 as meaning how much they started with so it is 9/15 also called 9 over 15

Hope This Helped

Answer:

x = 67 *272    = 364.48 = 364 (rounded as requested).  

Step-by-step explanation:

Use the proportion

   50 = 272  

    67      x

Then the two solutions of the quadratic equation are 4/5 and 3.

Here we want to solve the quadratic equation:

(-5x + 4)*(x - 3) = 0

The two solutions are the values of x for which each parenthesis becomes equal to zero, so the two solutions are given by:

-5x + 4 = 0

x - 3 = 0

If we solve these two equations we get:

x = -4/-5 = 4/5

x = 3

Then the two solutions are 4/5 and 3.

If you want to learn more about quadratic equations:

https://brainly.com/question/1214333

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3.9x+0.8y is the answer to your question.

Answer:

18.4 years

Step-by-step explanation:

The compound interest formula:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

For this problem we have

[tex]P= 2000\\r= 0.06\\n= 4\\A= 2000(3)= 6000[/tex]

We plug our numbers...

[tex]6,000= 2,000(1+\frac{0.06}{4} )^{4t} \\[/tex]

Then divide

[tex]6,000/2,000=3[/tex]

[tex]3= (1.015)^{4t}[/tex]

Apply log both sides

[tex]3log=(1.015) 4tlog[/tex]

Solve for t

[tex]t= \frac{3log}{(4log(1.015))} =18.4 years[/tex]

Answer:

42 sq ft.

Step-by-step explanation:

[tex]A=w *l[/tex]

[tex]A=14 *3=42[/tex]

=42 sq ft

(note: i dont think it matters how you put the numbers, they still mulitply up to 42)

Hope this helped

~rere