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3 years ago

What is the horizontal asymptote of the rational function f(x) = 3x / (2x - 1)?

Mathematics

2 answers:

-BARSIC- [3]3 years ago

6 0

Answer:

Step-by-step explain

Find the horizontal asymptote for f(x)=(3x^2-1)/(2x-1) :

A rational function will have a horizontal asymptote of y=0 if the degree of the numerator is less than the degree of the denominator. It will have a horizontal asymptote of y=a_n/b_n if the degree of the numerator is the same as the degree of the denominator (where a_n,b_n are the leading coefficients of the numerator and denominator respectively when both are in standard form.)

If a rational function has a numerator of greater degree than the denominator, there will be no horizontal asymptote. However, if the degrees are 1 apart, there will be an oblique (slant) asymptote.

For the given function, there is no horizontal asymptote.

We can find the slant asymptote by using long division:

(3x^2-1)/(2x-1)=(2x-1)(3/2x+3/4-(1/4)/(2x-1))

The slant asymptote is y=3/2x+3/4

butalik [34]3 years ago

6 0

Answer:

y = 3/2.

Step-by-step explanation:

This is the ratio of the coefficients of the terms in x of highest degree of the function:

y = 3/2.

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A car dealership pays a wholesome price of $12,000 to purchase a vehicle. The car dealership wants to make a 32% profit. The car

cestrela7 [59]

Answer:

$102.96

Step-by-step explanation:

Lets take this one part at a time.

the dealership pays 12000 for the car, so they start at -12000 for how much money they have.

The dealership wants to make a 32% profit. This means they want to make back the 12000 plus 32% of that. what is 32% of 12000? just multiply 12000 bty .32 In the end it works out that the price they sell it for is 15840

I do want to mention that there is a chance the 32% might also be accounting the bonus. So in other words the dealership spent 12000 for the car then however much in paying the bonus, and they want to make a 32% profit on both of these combined. I do not think that is what it is asking for, but I wanted to mention it.

Anyway, with a sales price of $15,840 it says the bonus is 6.5% of that. to find that just do the multiplication .065 * 15840 = 1029.60. So this is the bonus normally.

Now the question says the salesperson offers a 10 percent discount. This changes the sales price (by 10%) and the bonus they earn. let's calculate both.

First 10% discount of the sales price is .9*15840 = 14,256

Then 6.5% of that is .065*14256 = 926.64 So this is the new bonus.

The question wants the difference of the two bonuses, and difference is subtraction. so 1029.60 - 926.64 = 102.96 So if the salesperson offers a 10% discount they lose $102.96

5 0

3 years ago

I need help with this question please.

garri49 [273]

Answer:

Yes, the ratio stays 2:3

Step-by-step explanation:

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2 years ago

Explain how you would answer 3 - (-5)

Margarita [4]

Answer:

3- (-5) + -2.

Step-by-step explanation:

Anything plus a negative number will either make that negative number go closer to zero, or turn into a positive number.

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2 years ago

Surface area of 8in,4in,14in

andriy [413]

Answer:

160 in^2.

Step-by-step explanation:

I guess this is a prism with 6 faces so the surface area is:

2 * 8 * 4 + 2 * 8*4 + 2*4*4

= 64 + 64 + 32

= 160 in^2.

7 0

3 years ago

I am thinking of a number, let's call it x . If I increase twice my number by 5, the result is the same as if I triple my number

Mrrafil [7]

Answer: 6

Step-by-step explanation:

Let the number be x

If I increase twice my number by 5, the result is the same as if I triple my number and subtract 1. This can be formed into an equation as:

(2 × x) + 5 = (3 × x) - 1

2x + 5 = 3x - 1

5 + 1 = 3x - 2x

x = 6

The number you are thinking of is 6

4 0

3 years ago