Find the vertical and horizontal asymptote if they exist

Hello!

Vertical asymptotes are determined by setting the denominator of a rational function to zero and then by solving for x.

Horizontal asymptotes are determined by:

1. If the degree of the numerator < degree of denominator, then the line, y = 0 is the horizontal asymptote.

2. If the degree of the numerator = degree of denominator, then y = leading coefficient of numerator / leading coefficient of denominator is the horizontal asymptote.

3. If degree of numerator > degree of denominator, then there is an oblique asymptote, but no horizontal asymptote.

To find the vertical asymptote:

2x² - 10 = 0

2(x² - 5) = 0

(x - √5)(x + √5) = 0

x = √5 and x = -√5

Graphing the equation, we realize that x = -√5 is not a vertical asymptote, so therefore, the only vertical asymptote is x = √5.

To find the horizontal asymptote:

If the degree of the numerator < degree of denominator, then the line, y = 0 is the horizontal asymptote.

Therefore, the horizontal asymptote of this function is y = 0.

Short Vertical asymptote: x = √5 and horizontal asymptote: y = 0

a)(x-2)^2+(y-1)^2=9

step-by-step explanation:

(picture explains)

d 25 pi/6

step-by-step explanation:

the diameter is 10 inches

the radius is 1/2 of the diameter or 5 inches

the area of the circle is

a = pi r^2

  = pi 5^2

  = 25 pi

the slice is 60 degrees of the entire circle.

60 degrees out of 360   60/360 = 1/6

the area of the slice is 1/6 of the circle

a slice = 1/6 a circle

a slice = 1/6 * 25 pi