Mathematics, 17.03.2020 23:40 vbucks72

Let .

Find the hole in the graph of y = r(x).

Answers: 3

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Answer from: bluexorsit7603

x=8

Step-by-step explanation:

Discontinuity of a Function

We can find some functions whose graphs cannot be plotted in one stroke. It can be a hole or a vertical asymptote or a jump. To find a possible hole in a rational function, we must set both numerator and denominator to 0 independently. If a common point is found, it's a candidate for a hole if the function could eventually be redefined as continuous.

Let's find the zeros of the numerator

8x-x^2=0

Factoring

x(8-x)=0

We find two solutions: x=0, x=8

Let's find the zeros of the denominator

x^4-64x^2=0

Factoring

x^2(x-8)(x+8)=0

We find three roots: x=0, x=8, x=-8

There are two common points where the function can have holes, those are

$x=0,\ x=8$

We are not sure if those values are holes or not until we find the limits

$\displaystyle \lim\limits_{x \rightarrow 8}\frac{x(8-x)}{x^2(x-8)(x+8)}$

Simplifying

$\displaystyle =\lim\limits_{x \rightarrow 8}-\frac{1}{x(x+8)}$

$\displaystyle =-\frac{1}{128}$

Since the limit exists, the function can be redefined to cover up the hole. Now let's find the limit in x=0

$\displaystyle \lim\limits_{x \rightarrow 0}\frac{x(8-x)}{x^2(x-8)(x+8)}$

Simplifying

$\displaystyle =\lim\limits_{x \rightarrow 0}-\frac{1}{x(x+8)}$

$\displaystyle =-\frac{1}{0}=-\infty$

The limit does not exist and goes to infinity, it's not a hole, thus the only hole occurs when x=8

Answer from: Quest

there has been genes found in the x chromosome of males that have been linked to [homo/hetero]sexuality. in addition to the reign of the x chromosome, a section of chromosome 8 has also been link to, "alot of ppl are so " these facts were proven true after a 2014 study of a gay male and his strait brother. according to newscientist.com,"chromosome 14 and is mainly active in the thyroid, but also the brain. called tshr, it makes a type of receptor protein that recognises and binds to a hormone that stimulates the thyroid. in this way, the gene plays an important role in controlling thyroid function. the fact that tshr seems to be involved in sexual orientation fits with evidence that thyroid function seems to be linked to sexuality."

in conclusion, "ppl are so gay" due to their genetics.

Answer from: Quest

{x = -1/2 , y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer: {x = -1/2 , y = -1

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