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tia_tia [17]
3 years ago
7

Paula Purchaser borrowed $500 at 12 percent for one year. She paid a $25 processing fee. The interest paid will be $ . Thus, the

total finance charge (the interest plus the processing fee) will be $ Therefore, the APR = total finance charge ÷ amount borrowed = %.
Mathematics
1 answer:
kiruha [24]3 years ago
4 0
Interest = $500*0.12=$60
Processing fee = $25
Total finance charge = $(60+25)=$85.

APR=(total finance charge)/amount borrowed 
=85/500
=17%
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1. Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.
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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

                 <u>                                         </u>

                                            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;

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Now; the integral is:

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

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