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3 years ago

Evaluate C(7,3) A.) 4 B.) 35 C.) 70

Mathematics

2 answers:

Sedbober [7]3 years ago

7 0

Answer:

35, is your answer my friend

butalik [34]3 years ago

6 0

Answer:

math

way

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Step-by-step explanation:

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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:

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

We have:

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

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

2 years ago

7 copies 0f 1 fourth what does it equal

kvasek [131]

7 copies I assume means multiplication. 7 x 1/4=7/4. When multiplying fractions, the numerator is multiplied.

8 0

2 years ago

How do you find the holes, vertical, and horizontal asymptote of an equation?

AfilCa [17]

This is a great question, but it's also a very broad one. Please find and post one or two actual rational expressions, so we can get started on specifics of how to find vertical and horiz. asymptotes.

In the case of vert. asy.: Set the denom. = to 0 and solve for x. Any real x values that result indicate the location(s) of vertical asymptotes.

4 0

2 years ago

Find the difference quotient for the function f(x)=−5x−3f(x)=−5x−3. simplify your answer as much as possible.

tino4ka555 [31]

Difference quotient = [f(x+h) - f(x)]/h

[-5(x+h) -3 - (-5x -3)]/h
[-5x -5h -3 + 5x +3]/h
[-5h]/h
-5

6 0

2 years ago

Solve for the missing x coordinate above

Cloud [144]

The unknown vertex is on the perpendicular bisector of the opposite side. So the x coordinate is the same as that of the midpoint, x=(18+52)/2=35.

7 0

3 years ago