Use the equation to answer the following question y=(x-3(x+2)/(x+4)(x-4)(x+2)

Mathematics

1 answer:

givi [52]3 years ago

8 0

Answer:

See below

Step-by-step explanation:

The given rational function is;

$y=\frac{(x-3)(x+2)}{(x+4)(x-4)(x+2)}$

The given function is not continuous where the denominator is equal to zero.

$(x+4)(x-4)(x+2)=0$

The function is discontinuous at $x=-4,x=4,x=-2$

b) The point at x=-2 is a removable discontinuity(hole) because (x+2) is common to both the numerator and the denominator.

The point at x=-4 and x=4 are non-removable discontinuities(vertical asymptotes)

c) The equation of the vertical asymptotes are x=-4 and x=4

To find the equation of the horizontal asymptote, we take limit to infinity.

$\lim_{x\to \infty}\frac{(x-3)(x+2)}{(x+4)(x-4)(x+2)}=0$

The horizontal asymptote is y=0

You might be interested in

9% tax on a $59.99 purchase what is the sales tax?

lianna [129]

5.99
Is the sales tax

4 0

3 years ago

Joey and Armando live on the same st as the park. The park is 9/10 mile from Joey's home. Joey leaves home and walks to Armando'

AleksandrR [38]

Let's start by assuming Armando's house is between Joey's and the park.

Let $x$ be the distance Joey walked to Armando's house.

<span>The park is 9/10 mile from Joey's home. Joey leaves home and walks to Armando's home. Then Joey and Armando walk 3/5 mile to the park.

</span> $\dfrac{9}{10} = x + \dfrac{3}{5}$

$x = \dfrac{9}{10} - \dfrac{3}{5} = \dfrac{9}{10} -\dfrac{6}{10} = \dfrac{3}{10}$

That's probably the answer they're looking for. But what if the park is between Joey and Armando's houses or Joey is between the park and Armando? (The latter isn't really possible with the given distances.)

Let $a, b, c$ be the distances between three collinear points like we have here. Our equation is really a few equations in one, something like

$\pm a \pm b = \pm c$

Let's get rid of the plus/minuses. Squaring,

$a^2 + b^2\pm 2ab = c^2$

$\pm 2ab = c^2-a^2-b^2$

$4a^2b^2 = (c^2-a^2-b^2)^2$

For us, that's a quadratic equation for $c^2$

$4(9/10)^2(3/5)^2= (c^2-(9/10)^2 - (3/5)^2)^2$

I'll skip right to the solutions,

$c^2=\dfrac{9}{100} \textrm{ or } c^2=\dfrac{9}{4}$

$c=\dfrac{3}{10} \textrm{ or } c=\dfrac{3}{2}$

We could have gotten the 3/2 just by adding 9/10+3/5 but this was more fun.

6 0

3 years ago

How to divide this? WITH SOLUTION i need the answer plss

Olin [163]

Answer:

Step-by-step explanation:Please mark me as the brainlyest