Decompose

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July 6th 2006, 08:22 PM
Lane

1 math question

Identify the form of the partial fraction decomposition. Do not solve for the constants. 8x2+7x
(x+5)3

A: A + Bx + Cx2
X+5 (x+5)2 (x+5)3

B: A + B + C
X+5 (x+5)2 (x+5)3

C: Ax2 + Bx + C
(x+5)3

D: A + Bx+C
X+5 (x+5)2

Identify the conic section with the given equation.
5x2-6y2-9x+2y+3=0

p.s. all the two and threes after the par. and x's are supposed to be raised to that power!
July 7th 2006, 05:03 AM
Soroban

Hello, Lane!

Quote:

Identify the form of the partial fraction decomposition for: . $\frac{8x^2+7x}{(x+5)^3}$

$A\!:\;\frac{A}{x+5} + \frac{Bx}{(x+5)^2} + \frac{Cx^2}{(x+5)^3} <br />$ . . . $B\!:\;\;\frac{A}{x+5} + \frac{B}{(x+5)^2} + \frac{C}{(x+5)^3}$

. . . $C\!:\;\;\frac{Ax^2 + Bx + C}{(x+5)^2}$ . . . . . $D\!:\;\;\frac{A}{x+5} + \frac{Bx+C}{(x+5)^2}$

With repeated linear factors,
. . we need a linear fraction for "each power".

Since $x+5$ is cubed, the denominators must be: . $x+5,\;(x+5)^2,\;(x+5)^3$

The answer is choice $B.$
July 7th 2006, 06:40 AM
Soroban

Hello, Lane!

We can "eyeball" the second one . . .

Quote:

Identify the conic section: . $5x^2-6y^2-9x+2y+3\:=\:0$

Since the $x^2$ -term and the $y^2$ -term have opposite signs,

. . the conic is a $\text{hyperbola.}$

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