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2 years ago

11

consider the line y=-5/2×+9 What is the slope of a line parallel to this line? What is the slope of line perpendicular to this l

ine ?

1 answer:

MatroZZZ [7]2 years ago

3 0

Answer:

Slope of the parallel line = -5/2

Slope of the perpendicular line = 2/5

Explanations:

The given equation of the line is:

$y\text{ = }\frac{-5}{2}x\text{ + 9}$

The slope-intercept form of the equation of a line is:

y = mx + c

where m is the slope of the line

and c is the y-intercept

Comparing this to the given equation

m = -5/2

c = 9

Note:

When two equations are parallel, they have equal slope

When two equations are perpendicular, the product of their slopes equals -1, that is slope of the perpendicular line = -1/m

The slope of the parallel line = -5/2

The slope of the perpendicular line = -1 ÷ (-5/2)

The slope of the perpendicular line = -1 x (-2/5)

The slope of the perpendicular line = 2 / 5

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3 years ago

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8 0

2 years ago

Please help with these partial fractions!!!

VARVARA [1.3K]

a. Factorize the denominator:

$\dfrac{x+14}{x^2-2x-8}=\dfrac{x+14}{(x-4)(x+2)}$

Then we're looking for $a,b$ such that

$\dfrac{x+14}{x^2-2x-8}=\dfrac a{x-4}+\dfrac b{x+2}$

$\implies x+14=a(x+2)+b(x-4)$

If $x=4$ , then $18=6a\implies a=3$ ; if $x=-2$ , then $12=-6b\implies b=-2$ . So we have

$\dfrac{x+14}{x^2-2x-8}=\dfrac3{x-4}-\dfrac2{x+2}$

as required.

b. Same setup as in (a):

$\dfrac{-3x^2+5x+6}{x^3+x^2}=\dfrac{-3x^2+5x+6}{x^2(x+1)}$

We want to find $a,b,c$ such that

$\dfrac{-3x^2+5x+6}{x^2(x+1)}=\dfrac ax+\dfrac b{x^2}+\dfrac c{x+1}$

Quick aside: for the second term, since the denominator has degree 2, we should be looking for another constant $b'$ such that the numerator of the second term is $b'x+b$ . We always want the polynomial in the numerator to have degree 1 less than the degree of the denominator. But we would end up determining $b'=0$ anyway.

$\implies-3x^2+5x+6=ax(x+1)+b(x+1)+cx^2$

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which tells us $a-2=-3$ and $a+6=5$ ; in both cases, we get $a=-1$ . Then

$\dfrac{-3x^2+5x+6}{x^2(x+1)}=-\dfrac1x+\dfrac6{x^2}-\dfrac2{x+1}$

as required.

5 0

4 years ago