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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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Which is the best description of an extraneous solution?

Degger [83]

Answer:

A solution that results in a false statement when substituted back into the original equation.

Step-by-step explanation:

An extraneous solution is one that arises in a solution of equations, but which on closer inspection is not a solution to the original equation. Therefore, they imply an error in the development of the solution of the equation, so they cannot be taken as a valid solution since, when replacing the result with the missing variable, the equation does not obtain the desired result.

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2 years ago

Write in slope-intercept form an equation of the line that passes through the given points. (2, 4), (3, 6) y=

GrogVix [38]

Answer:

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2 years ago

in a random sample of 28 people, the mean commute time to work was 31.2 minutes and the standard deviation was 7.3 minutes. assu

antoniya [11.8K]

Answer:

The margin of error of u is of 3.8.

The 99% confidence interval for the population mean u is between 27.4 minutes and 35 minutes.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 28 - 1 = 27

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 27 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.99}{2} = 0.995$ . So we have T = 2.7707

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 2.7707\frac{7.3}{\sqrt{28}} = 3.8$

In which s is the standard deviation of the sample and n is the size of the sample.

The margin of error of u is of 3.8.

The lower end of the interval is the sample mean subtracted by M. So it is 31.2 - 3.8 = 27.4 minutes

The upper end of the interval is the sample mean added to M. So it is 31.2 + 3.8 = 35 minutes

The 99% confidence interval for the population mean u is between 27.4 minutes and 35 minutes.

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Answer:

Step-by-step explanation:

the total cost for this question is $12.10.

let me know if this helped.

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2 years ago

"A grain silo is shown below.

Phantasy [73]

V = r² π h + 1/2 · 4/3 r³ π
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2 years ago