Please do these thank you!!!!!!!!ASAP this is 7th grade math

1. Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.

german

Answer:

Step-by-step explanation:

1.

To write the form of the partial fraction decomposition of the rational expression:

We have:

$\mathbf{\dfrac{8x-4}{x(x^2+1)^2}= \dfrac{A}{x}+\dfrac{Bx+C}{x^2+1}+\dfrac{Dx+E}{(x^2+1)^2}}$

2.

Using partial fraction decomposition to find the definite integral of:

$\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}dx$

By using the long division method; we have:

$x^2-8x-20 | \dfrac{2x}{2x^3-16x^2-39x+20 }$

$- 2x^3 -16x^2-40x$

$x+ 20$

So;

$\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}= 2x+\dfrac{x+20}{x^2-8x-20}$

By using partial fraction decomposition:

$\dfrac{x+20}{(x-10)(x+2)}= \dfrac{A}{x-10}+\dfrac{B}{x+2}$

$= \dfrac{A(x+2)+B(x-10)}{(x-10)(x+2)}$

x + 20 = A(x + 2) + B(x - 10)

x + 20 = (A + B)x + (2A - 10B)

Now; we have to relate like terms on both sides; we have:

A + B = 1 ; 2A - 10 B = 20

By solvong the expressions above; we have:

$A = \dfrac{5}{2}$ $B = \dfrac{3}{2}$

Now;

$\dfrac{x+20}{(x-10)(x+2)} = \dfrac{5}{2(x-10)} + \dfrac{3}{2(x+2)}$

Thus;

$\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}= 2x + \dfrac{5}{2(x-10)}+ \dfrac{3}{2(x+2)}$

Now; the integral is:

$\int \dfrac{2x^3-16x^2-39x+20}{x^2-8x-20} \ dx = \int \begin {bmatrix} 2x + \dfrac{5}{2(x-10)}+ \dfrac{3}{2(x+2)} \end {bmatrix} \ dx$

$\mathbf{\int \dfrac{2x^3-16x^2-39x+20}{x^2-8x-20} \ dx = x^2 + \dfrac{5}{2}In | x-10|\dfrac{3}{2} In |x+2|+C}$

3. Due to the fact that the maximum words this text box can contain are 5000 words, we decided to write the solution for question 3 and upload it in an image format.

Please check to the attached image below for the solution to question number 3.

4 0

3 years ago

How to solve the equation (x+k) = (x+k-1)(x+k)?

Brilliant_brown [7]

This solution might become quite complex.
Please try to keep up with me, and I'll go slowly:

You said       (x + k)   = (x + k - 1) (x + k)

Divide each side by (x+k):    1     = (x + k - 1)

Add 1 to each side: 2       = (x + k )

Subtract 'k' from each side:    2 - k = x

3 0

3 years ago

Read 2 more answers

2. Solve each given equation and show your work. Tell whether each equation has one solution, an infinite number of solutions, o

Brut [27]

Hello!

To solve algebraic equations, we need to use SADMEP. SADMEP is an acronym used only solve for x in algebraic equations. SADMEP is expanded to be: subtraction, addition, division, multiplication, exponents, and parentheses.

(a) 4 + 2(-1) = 10 + 2 (multiply)

4 + -2 = 10 + 2 (add)

2 = 12

This equation has no solutions because 2 is never equal to 12.

(b) 30 = 10 - (6 + 10) (simplify the parentheses)

30 = 10 + -1(16) (multiply)

30 = 10 - 16 (simplify)

30 = -6

This equation has no solutions because 30 and -6 is never equal to each other.

(c) 8x = 4x + 4x + 10(x - x)

8x = 4x + 4x + 10(x - x) (simplify [add and subtract])

8x = 8x + 10(0) (multiply)

8x = 8x

This equation has an infinite number of solutions because if you substitute any value into the original equation, both sides of the equation will be always equal.

7 0

3 years ago

What is the value of x ?

valina [46]

Answer:

The value of x = 9

Step-by-step explanation:

∵ The figure has right angle and a line ⊥ from the right angle to the hypotenuse

∴ There is a relation between the ⊥ line and the two parts of the hypotenuse

∴ (⊥)² = multiplication of the two parts of the hypotenuse

∴ (6)²= 4 × x

∴ 36 = 4 × x

∴ x = 36/4 = 9

4 0

3 years ago

When producing hydrogen iodide, the energy of the reactants is 581 kJ/mol, and the energy of the products is 590 kJ/mol. The equ

dimaraw [331]

The energy of the reaction is 9 kJ/mol and the reaction is endothermic.

<h3>What is the total energy of the reaction?</h3>

We know that in a reaction, there could be loss or gain of energy. If there is a loss of energy in a reaction, it means that the reaction is exothermic and heat is given out. If heat is gained in the reaction, it means that the reaction is endothermic and heat is absorbed.

Given that;

Energy of the products = 590 kJ/mol

Energy of the reactants = 581 kJ/mol

Using;

Energy of products - Energy of reactants

= 590 kJ/mol - 581 kJ/mol

= 9 kJ/mol

Learn more about energy of reaction:brainly.com/question/2223923

#SPJ1

5 0

1 year ago