Does the function f(x) = x^3-4x^2+2x-6/x-3 have a slant asymptote? If so, find an equation of the slant asymptote. If not, explain

Does The Function F(x) = X^3-4x^2+2x-6/x-3 Have A Slant Asymptote? If So, Find An Equation Of The Slant

Answers

Answer 1

Answer:

No slant asymptote.

Step-by-step explanation:

No it hasn't .

If we do the division we find the quotient is a trinomial in x^2 so not a straight line, so there is no slant asymptote.

The one asymptote is the vertical line x = 3, because when x = 3 the denominator becomes 0.

Answer 2

Final answer:

To find the slant asymptote for the given function f(x), perform long division of the numerator by the denominator. The result is a quadratic function, which is the equation of the slant asymptote, specifically y = x^2 - x - 3.

Explanation:

The function f(x) = (x^3 - 4x^2 + 2x - 6)/(x - 3) does indeed have a slant asymptote, since the degree of the numerator is exactly one more than the degree of the denominator. To find the equation of the slant asymptote, you may perform polynomial long division or synthetic division. You would divide x^3 - 4x^2 + 2x - 6 by x - 3 to obtain the quotient which will be the equation of the slant asymptote.

When you do that, you'll find that the quotient is x^2 - x - 3. Since there's no remainder, or the remainder is of lesser degree than the denominator, the function approaches the line y = x^2 - x - 3 as x approaches infinity or negative infinity. This quadratic function is the slant asymptote for f(x).


Related Questions

An Ice Hockey rink is a rectangle with a perimeter of 174 meters. The length is 9 meters more than twice the width. What equation describes this problem? (Remember that the perimeter is twice the length plus twice the width)

Answers

Answer:

Let width be x metres

so, length is "9 metres more than twice the width" --> 9+2x

So, perimeter is x + x + (9+2x) + (9+2x) = 174

6x + 18 = 174

6x = 156

 

x = 156/6

x = 26m

width = 26m

length is therefore 9+2(26) --> 9+52 --> 61m

Step-by-step explanation:

The temperature fell from 0 Degrees Fahrenheit to 15 and one-half Degrees Fahrenheit below 0 in 5 and three-fourths hours. Wen tried to find the change in temperature per hour. Her work is shown below. Negative 15 and one-half divided by 5 and three-fourths = negative StartFraction 31 over 2 EndFraction divided by StartFraction 23 over 4 EndFraction = negative StartFraction 31 over 2 EndFraction times StartFraction 23 over 4 EndFraction = Negative StartFraction 713 over 8 EndFraction When she checked the answer by estimating, it did not make sense. What error did Wen make? Wen incorrectly converted a mixed number to an improper fraction. Wen added the numerators and denominators instead of multiplying. Wen did not take the reciprocal of the divisor. Wen did not change the division problem to multiplication.

Answers

Answer:

C. Wen did not take the reciprocal of the divisor.

Find the circumference of a circle with a diameter of 5inches

Answers

Answer:

15.7

Step-by-step explanation:

5 times 3.14 will give you circumference of a circle

Answer:

15.7 in

Step-by-step explanation:

Circumference = pi × d

3.14 × 5

15.7 inches

PLEASE HELP!
put the following fractions in order from smallest to biggest

1/2, 3/4, 3/8, 5/8, 5/16, 7/16, 9/16 and 11/16 inches

Answers

5/16
3/8
7/16
1/2
9/16
5/8
11/16
3/4

:)

what is 4^4 . 4^44 please help​

Answers

Answer:

4^48

Step-by-step explanation:

you add the exponents

Answer:

[tex]4^{48}[/tex]

Step-by-step explanation:

[tex]4^{4} *4^{44} =4^{48}[/tex]

You can just calculate this if you'd like and it'd still be the same answer...

Determine the area of a triangle with m

Answers

You could add ALOT more to your question

Answer:

I'm guessing they're asking about trig functions, topic test. Answer: B) 10 units^2

Step-by-step explanation:

just took the topic test on edge2021

90 is 45% of what number

Answers

Answer:

200

Step-by-step explanation:

90=.45x (x being the number)

(multiply by 100/45)

90(100/45)

9000/45=

x=200

Answer is 200

Since if 50% would mean 100, double it to get the 100%, which is 200

Ileana buys a large circular pizza that is divided
into eight equal slices. She measures along the
outer edge of the crust from one piece and finds it
to be 5 1/2 inches. What is the diameter of the pizza
to the nearest inch?

- 4 inches
- 7 inches
- 8 inches
- 14 inches

Answers

Answer:

14

Step-by-step explanation:

the edge of one slice of pizza is 5.5 and there are eight slices so i multiplied 5.5 by eight to get the circumference

the circumference is 44 so i divided that by pi to get the diameter which was 14 after you round

if your more of a numbers/formula person this might be more helpful:

circumference: 5.5 x 8 = 44

formula for diameter is  [tex]d=\frac{C}{\pi }[/tex]

so, [tex]d=\frac{44}{\pi }[/tex]

     [tex]d=14[/tex]

The diameter of the pizza is 14 inches.

Given that the pizza is divided into 8 equal slices and one of the outer edges measures 5 1/2 inches.

When need to find the diameter of the pizza.

What is the formula to find the circumference of the circle?

The formula to find the circumference of the circle is 2πr.

Since a pizza is divided into 8 equal parts.

So, the circumference of 1 part=2πr/8=πr/4

πr/4=5.5 inches.

⇒πr=22

⇒r=7 inches.

Then, diameter=14 inches.

Therefore, the diameter of the pizza is 14 inches.

To learn more about the circumference of a circle visit:

https://brainly.com/question/27177006.

#SPJ5

DNA TAC ACC TTG GCG ACG ACT Write the mRNA strand then the Amino Acid sequence.

Answers

AUG UGG AAC CGC UGC AGU

Which ordered pair must be removed to make the relation a function. {(1, −5), (2, −4), (3, 4), (4, 3), ( 3, -4)}

Answers

Answer:

I actually have no idea

Step-by-step explanation:

Answer:

either the ordered pair (3 , 4) or (3 , -4)

Step-by-step explanation:

a function is where there is only one x to each y value

each x value must not be the same

What is the value of x?
Enter your answer in the box.

Answers

Answer:

x=4

Step-by-step explanation:

to find RT, you would do the 60-60-90 rule and you would get 4, x and RT are the same value because of the 45-45-90 rule, so x=4

Find the value of x in the following diagram.

Answers

Answer:

x = 3.5

Step-by-step explanation:

diameter = radius × radius

d= ( 3x + 1 ) + ( x + 8 )

3x + 1 = x + 8

subtract 1 and x

2x = 7

divide by 2

x = 3.5

In his living room rashad has a window shaped liked a rectangle . It is 7.2 feet high and 8.7 feet wide. What is the area of the window

Answers

Answer:62.64

Step-by-step explanation:

You have to multiply them

HURRY PLEASEEEEE!!!!

Use r = 2 and r = 5 to determine if the two expressions are equivalent.
r + 4(2 + r) – 12    8 + 2r – 6

Complete the statements.
1.When r = 2, the first expression is ?.
2.When r = 2, the second expression is 6.
3.When r = 5, the first expression is 21.
4.When r = 5, the second expression is .?
5.The expressions are not equivalent.

Answers

The two expressions are not equivalent to each other at r =2 and r = 5.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Use r = 2 and r = 5 to determine if the two expressions are equivalent.

r + 4(2 + r) – 12    8 + 2r – 6

First put r = 2 in both the expressions:-

E1 = 2 + 4 ( 2 + 2 ) -12

E1 =6

E2 = 8 + ( 2 x 2 ) - 6

E2 = 6

Secondly, put r = 5 in both the expressions.

E1 = 2 + 4 ( 2 + 5 ) - 12

E1 = 30

E2 = 8 + ( 2 x 5 ) -6

E2 = 12

The two expressions are not equivalent at r = 2 and r =5.

To know more about Expression follow

https://brainly.com/question/723406

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Answer: 6, 12

Step-by-step explanation:

proof :)

Choose the correct answer

Answers

Answer:

Option D

Step-by-step explanation:

Assuming you're referring to slope, the rule is rise/run or "rise over run" so as i look at this line i see it rises 1 unit and then runs back or negatively 4 units, therefor the answer is D 1/-4

Please mark as brainliest :)

explain how the formula for the volume of a cone is derived

Answers

Answer:

The volume of a cone is 1 3 π r 2 h \frac { 1 } { 3 } \pi r ^{ 2 } h 31πr2h, where r denotes the radius of the base of the cone, and h denotes the height of the cone.

Step-by-step explanation:

(happy to help)

Final answer:

The volume of a cone is derived using the principle of integrating infinitesimally thin discs along the height of the cone, given by the formula V = ⅓πr²h.

Explanation:

The formula for the volume of a cone is derived using calculus and geometric principles. Consider a cone generated by rotating a line around one of the coordinate axes. If we know the formula for the area A of a circle, it can be extended to find the volume of a cone. The area A of a circle is πr², where r is its radius. The formula for the volume V of a cone is ⅓ × base area × height, which can be expressed as V = ⅓πr²h, with h being the cone's height.

Using integral calculus, the cone's volume is found by stacking infinitesimally thin discs (each with volume πr²dx, where dx is the disc's thickness) along the cone's height. The radius r changes linearly from the base to the apex, following the relationship r = (h - x)tan(a), where a is the semivertical angle of the cone. Thus, you integrate from the apex (0) to the base (h) to find the entire volume of the cone.

A salesperson earns a 2​% commission rate on sales of camera equipment. Yesterday she earned ​$60 in commission. What were her sales that​ day?

Answers

Answer:
Her sales were $3,000 worth

Explanation:

To find the salesperson's total sales, we use the formula Commission = Sales x Commission Rate, where $60 is the commission earned at a 2% rate. Dividing $60 by 0.02 gives us the total sales of $3000 for that day.

The student has asked about calculating the total sales based on a commission earned by a salesperson. To find out the total sales we can use the formula: Commission = Sales * Commission Rate. Given that the salesperson earned a $60 commission at a 2% commission rate, we set up the equation: 60 = Sales * 0.02. To solve for Sales, we divide both sides by 0.02, which gives us Sales = 60 / 0.02. Thus, the total sales for that day were $3000.

Find the slope of a line which goes through the points (2,5) and (−4,3)

Answers

Answer:

slope (m) = 0.75

Step-by-step explanation:

Slope (m) =

ΔY

ΔX

=

1

3

= 0.33333333333333

θ =

arctan( ΔY ) + 180°

ΔX

= 198.43494882292°

ΔX = -4 – 2 = -6

ΔY = 3 – 5 = -2

Distance (d) = √ΔX2 + ΔY2 = √40 = 6.3245553203368

Equation of the line:

y = 0.33333333333333x + 4.3333333333333

or

y =  

1 x

3

+  13

3

When x=0, y = 4.3333333333333

When y=0, x = -13

please mark brainliest

A leading dental journal has claimed that 64% of young adults do not brush their teeth
regularly. A dental hygienist wants to conduct a survey to verify this with her young adult patients and wants to do so with a margin of error of +/-5%. What minimum sample size,
rounded to the nearest whole person, would the hygienist need to use?

Answers

Answer:

About 30%

Step-by-step explanation:

Well, um...

If 64% did not, then 36% of them do.

So, about 30% Do.

Select the measurements that are equivalent to one hundred grams.
1,000 mg
10,000 cg
0.1 kg
10 hg

Answers

Answer:

100 grams is = to 0.1 kg

Step-by-step explanation:

100 grams is = to 10,000 mg which is incorrect. I am not sure what the other answer choices are, but C is your correct answer.

Final answer:

The measurements equivalent to one hundred grams are 10,000 centigrams (cg) and 0.1 kilograms (kg). The other options provided do not equal 100 grams.

Explanation:

To determine which measurements are equivalent to one hundred grams, we need to understand the relationship between different units of mass. In the metric system, mass is commonly measured in kilograms (kg), grams (g), and milligrams (mg), among others. Here is a reference based on the information you provided:

1 kilogram (kg) = 1000 grams (g)

1 gram (g) = 1000 milligrams (mg)

Now, let's evaluate each option provided in the question:

1,000 mg = 1 g (not 100 g)

10,000 cg = 100 g (since 1 g = 100 centigrams (cg))

0.1 kg = 100 g (since 1 kg = 1000 g)

10 hg = 1000 g (since 1 hectogram (hg) = 100 g)

Therefore, the measurements equivalent to one hundred grams are 10,000 cg and 0.1 kg.


Which best describes the data for June, July, and August?

A.a cluster
B. a gap
C. low frequency
D. Symmetric


Pls I need this really quick

Answers

Answer: A cluster.

Step-by-step explanation:

A cluster has ups and downs and one peak.

Answer:

A: a cluster

Step-by-step explanation:


There are 8 baseball players in the dugout for practice. Each player shakes hands with each of the other player ONLY ONCE.
How many handshakes are there?

Answers

Answer: 28

Explanation:

There are 8 players. For each player, there are 7 people to shake hands with. So we have 8*7 = 56 handshakes so far; however, we double count since the sequence AB is the same as BA (where A and B are player names). Order does not matter when it comes to shaking hands. So we have to divide by 2 to fix the double count. We go from 56 to 56/2 = 28. There are 28 different combinations.

You can use the formula [tex]_nC_r = \frac{n!}{r!(n-r)!}[/tex] with n = 8 and r = 2, but the formula is a bit confusing to be honest if you aren't familiar with it. The exclamation marks indicate factorials.

Extra info: The value 28 can be found in Pascals triangle. Look at the row that starts with 1, 8, ... then note how 28 is in the third slot. Keep in mind that you start at r = 0 and count up by 1. So r = 2 corresponds to the third slot.

Answer:

8  players in total

Step-by-step explanation:

what is the surface area of a storage box that measures 21 centimeters by 18 centimeters by 16 centimeters

Answers

Answer:

2004 cm²

Step-by-step explanation:

To solve this problem, you just need to plug your values into the rectangular prism formula: A=2(wl+hl+hw)

Assuming that the length is 21 cm, the width is 18 cm, and the height is 16 cm, your problem would look like this:

A=2((18x21)+(16x21)+(16x18))=2(378+336+288)=2x1002=2004 cm²

A certain shampoo is available in two sizes. A 23.7-ounce bottle costs $4.97 . A 33.8 -ounce bottle costs $7.48 . Find the unit price for each size. Then state which size is the better buy based on the unit price. Round your answers to the nearest cent.
Unit price for the 23.7 Price per ounce
33.8 Price per ounce

Answers

Answer:

23.7 ounce = 20 cents per ounce

33.8 ounce = 22 cents per ounce

The 23.7 ounce bottle is a better deal because it is only 20 cents per ounce, rather than 22 cents per ounce.

If the spinner is spun 40 times, predict the number of times the spinner would land on Section B

Answers

Answer:

11

Step-by-step explanation:

bkbkbk

What is the A ⋃ B for the venn diagram

Answers

11,12,13,14,15,16,17

Answer:

The elements contain in A U B is {11,12,13,14,15,16,17} .

There are 7 elements in A U B.

Find the slope of a line passing though the given points (1,4) (3,2)

Answers

i believe the slope is -1

What is the perimeter of a triangle with side lengths of 8 cm, 8 cm, and 3 cm?

Plz help

Answers

Answer:

19

Step-by-step explanation:

8+8+3 = 19

The perimeter of the triangle would be 19

Lin says that the inequalities h>150 and h<160 describe her height in centimeters. what do the inequalities tell us about her height?

Answers

Answer:

Her height is in between 150 and 160

Step-by-step explanation:

Given

h > 150

h < 160

Required

What do these represent?

First, the inequalities need to be combined.

If h < 160, then this means that 160 > h.

So, h > 150 and 160 > h can be combined to form an inequality in the following form;

160 > h > 150

This.meeans 160 is greater than h and h is greater than 150.

If this is related to her height, it means 160 is greater than her height and her height is greater than 150;

In other words, her height is in between 150 and 160

Jan conducts an experiment and tosses a coin 40 times. She gets heads 30 times instead of the expected 20. What could be a reason for this difference?
A) She miscounted.
B) She needs more trials.
C) She needs a different coin.
D) She got 30 and that is close enough.

Answers

the answer is B. hope i helped

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