1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Bogdan [553]
3 years ago
10

State the horizontal asymptote of the rational function.f(x) = quantity x squared plus six x minus eight divided by quantity x m

inus eight
Mathematics
2 answers:
padilas [110]3 years ago
4 0
F(x)=(x²+6x-8)/(x-8) has a vertical asymptote at x=8. When x is large f(x) approaches x which is a 45 degree line (gradient 1). There is no horizontal asymptote.
Alexus [3.1K]3 years ago
3 0

Answer:

There is no horizontal asymptote for the function f(x).

Step-by-step explanation:

We have the function f(x) = \frac{x^2+6x-8}{x-8}. Notice that if x=8 the function is not defined, because the denominator of the fractions equals zero, and the numerator don't. This fact is equivalent to the existence of a vertical asymptote at x=8. In mathematical language:

\lim_{x\rightarrow 8^+} \frac{x^2+6x-8}{x-8} = +\infty

and

\lim_{x\rightarrow 8^-} \frac{x^2+6x-8}{x-8} = -\infty.

Now, in case that f(x) has an horizontal asymptote the following must hold:

\lim_{x\rightarrow +\infty} \frac{x^2+6x-8}{x-8} = L\in\mathbb{R}

But, actually

\lim_{x\rightarrow \infty} \frac{x^2+6x-8}{x-8} = \infty.

Hence, there is no horizontal asymptote.

Anyway, f(x) has an asymptote, but no horizontal. In order to obtain the slope of the asymptote, we need to find the following limit:

\lim_{x\rightarrow +\infty} = \frac{f(x)}{x} = \lim_{x\rightarrow +\infty} \frac{x^2+6x-8}{x(x-8)} = \frac{x^2+6x-8}{x^2-8x} = 1.

Then asymptote has equation y=x+n. To find n we calculate the limit

\lim_{x\rightarrow +\infty} (f(x)-mx) = \lim_{x\rightarrow +\infty} \frac{x^2+6x-8}{x-8} -x = \lim_{x\rightarrow +\infty} \frac{14x-8}{x-8} = 14

Hence, the asymptote at +\infty is y = x+14.

You might be interested in
ANSWER QUICKLY FOR BRAINLIEST!! <br><br><br> What is the volume of the triangular prism?
Anton [14]
156


4x6=24
24/2=12
12x13=156
8 0
2 years ago
Steve is buying apples for the fifth grade.each bag holds 12 apples.if there are 75 students total,how many bags of apples will
kirill115 [55]
72 divided by 12 equals 6 apples each student
7 0
3 years ago
Read 2 more answers
Find the mass and center of mass of the lamina that occupies the region D and has the given density function rho. D is the trian
Alla [95]

Answer: mass (m) = 4 kg

              center of mass coordinate: (15.75,4.5)

Step-by-step explanation: As a surface, a lamina has 2 dimensions (x,y) and a density function.

The region D is shown in the attachment.

From the image of the triangle, lamina is limited at x-axis: 0≤x≤2

At y-axis, it is limited by the lines formed between (0,0) and (2,1) and (2,1) and (0.3):

<u>Points (0,0) and (2,1):</u>

y = \frac{1-0}{2-0}(x-0)

y = \frac{x}{2}

<u>Points (2,1) and (0,3):</u>

y = \frac{3-1}{0-2}(x-0) + 3

y = -x + 3

Now, find total mass, which is given by the formula:

m = \int\limits^a_b {\int\limits^a_b {\rho(x,y)} \, dA }

Calculating for the limits above:

m = \int\limits^2_0 {\int\limits^a_\frac{x}{2}  {2(x+y)} \, dy \, dx  }

where a = -x+3

m = 2.\int\limits^2_0 {\int\limits^a_\frac{x}{2}  {(xy+\frac{y^{2}}{2} )} \, dx  }

m = 2.\int\limits^2_0 {(-x^{2}-\frac{x^{2}}{2}+3x )} \, dx  }

m = 2.\int\limits^2_0 {(\frac{-3x^{2}}{2}+3x)} \, dx  }

m = 2.(\frac{-3.2^{2}}{2}+3.2-0)

m = 2(-4+6)

m = 4

<u>Mass of the lamina that occupies region D is 4.</u>

<u />

Center of mass is the point of gravity of an object if it is in an uniform gravitational field. For the lamina, or any other 2 dimensional object, center of mass is calculated by:

M_{x} = \int\limits^a_b {\int\limits^a_b {y.\rho(x,y)} \, dA }

M_{y} = \int\limits^a_b {\int\limits^a_b {x.\rho(x,y)} \, dA }

M_{x} and M_{y} are moments of the lamina about x-axis and y-axis, respectively.

Calculating moments:

For moment about x-axis:

M_{x} = \int\limits^a_b {\int\limits^a_b {y.\rho(x,y)} \, dA }

M_{x} = \int\limits^2_0 {\int\limits^a_\frac{x}{2}  {2.y.(x+y)} \, dy\, dx }

M_{x} = 2\int\limits^2_0 {\int\limits^a_\frac{x}{2}  {y.x+y^{2}} \, dy\, dx }

M_{x} = 2\int\limits^2_0 { ({\frac{y^{2}x}{2}+\frac{y^{3}}{3})}\, dx }

M_{x} = 2\int\limits^2_0 { ({\frac{x(-x+3)^{2}}{2}+\frac{(-x+3)^{3}}{3} -\frac{x^{3}}{8}-\frac{x^{3}}{24}  )}\, dx }

M_{x} = 2.(\frac{-9.x^{2}}{4}+9x)

M_{x} = 2.(\frac{-9.2^{2}}{4}+9.2)

M_{x} = 18

Now to find the x-coordinate:

x = \frac{M_{y}}{m}

x = \frac{63}{4}

x = 15.75

For moment about the y-axis:

M_{y} = \int\limits^2_0 {\int\limits^a_\frac{x}{2}  {2x.(x+y))} \, dy\,dx }

M_{y} = 2.\int\limits^2_0 {\int\limits^a_\frac{x}{2}  {x^{2}+yx} \, dy\,dx }

M_{y} = 2.\int\limits^2_0 {y.x^{2}+x.{\frac{y^{2}}{2} } } \,dx }

M_{y} = 2.\int\limits^2_0 {x^{2}.(-x+3)+\frac{x.(-x+3)^{2}}{2} - {\frac{x^{3}}{2}-\frac{x^{3}}{8}  } } \,dx }

M_{y} = 2.\int\limits^2_0 {\frac{-9x^3}{8}+\frac{9x}{2}   } \,dx }

M_{y} = 2.({\frac{-9x^4}{32}+9x^{2})

M_{y} = 2.({\frac{-9.2^4}{32}+9.2^{2}-0)

M{y} = 63

To find y-coordinate:

y = \frac{M_{x}}{m}

y = \frac{18}{4}

y = 4.5

<u>Center mass coordinates for the lamina are (15.75,4.5)</u>

3 0
3 years ago
Kaylee has 2 gallons each of red and blue paint, and 1 gallon each of orange and green paint. She paints her bedroom with these
Aleks04 [339]

Answer:

3( 73/84 )left over

Step-by-step explanation:

She had 6 gallons in total

2/3+1/4+1/2+5/7=179/84   =  2 ( 11/84)

6/1-179/84 = 325/84    =  3(73/84)

She used  179/84

She have left 325/84

179/84   +  325/84 = 6

   With mixed numbers:

2  11/84  

3  73/84

 2+3=5                11/84+73/84= 84/84 =1

5+1=6

 

8 0
3 years ago
What does 49.39 round to.
Verizon [17]
If you want to round 49.39 to the nearest tenths place you will have to look at your tenths digit. The digit is 3, right? Look at the next number after 3. It is the number 9 for the hundredths place. If the number is bigger than 5 you round it. If it is smaller, you keep it the same. 9 is bigger than 5 so you make the 3 into a 4. Then, you're answer is 49.4 or 49.40 (Which are basically the same answer) It also works the same with the other digits. Simple, right? :)
4 0
3 years ago
Other questions:
  • Please Help
    15·1 answer
  • Carlos calculated the missing side length of one of these triangles using the Pythagorean Theorem. Which triangle is it?
    11·2 answers
  • I need help with this ;-; can someone help me how to get the answer as well?
    10·2 answers
  • Answer! The amount of time it takes to complete a reading assignment might be a function of which of the folowing ?
    9·2 answers
  • Don’t know how to start this problem can someone show me the steps to this problem!?
    8·1 answer
  • Someone please help with this
    13·1 answer
  • Which situation would best be represented by positive 6 ?
    14·2 answers
  • Gordon types 3,724 words in 49 minutes. Find the unit rate. Gordon types words per minute. ​
    10·1 answer
  • Consider the line y equals 2 over 5 x plus 4.
    15·1 answer
  • A girl get n cedis pocket money money each week. she saves her money for five weeks and buys a present for her mother which cost
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!