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4 years ago

What is the oblique asymptote of the function f(x) = the quantity x squared minus 5x plus 6 over the quantity x minus 4?

Mathematics

1 answer:

Paraphin [41]4 years ago

4 0

Answer:

x - 1

Step-by-step explanation:

We know that, a slant or oblique asymptote of a rational function is the asymptote that helps in determining the direction of the function.

It occurs when the polynomial in the numerator is a higher degree than the polynomial in the denominator.

Now, we divide the numerator by denominator using long division method and the first two terms in the quotient ( forming a linear function ) is the equation of the oblique asymptote.

We are given the rational function, $f(x) = \frac{x^{2}-5x+6}{x-4}$ .

After dividing we get that, the quotient is x - 1.

Hence, the equation of the oblique asymptote is x-1.

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3 years ago

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3 years ago

Read 2 more answers

The circumference of the ellipse approximate. Which equation is the result of solving the formula of the circumference for b?

Serhud [2]

Answer:

$b = \sqrt{\frac{C^{2} }{2(\pi )^{2} } - a^{2}}$

Step-by-step explanation:

Given - The circumference of the ellipse approximated by $C = 2\pi \sqrt{\frac{a^{2} + b^{2} }{2} }$ where 2a and 2b are the lengths of 2 the axes of the ellipse.

To find - Which equation is the result of solving the formula of the circumference for b ?

Solution -

$C = 2\pi \sqrt{\frac{a^{2} + b^{2} }{2} }\\\frac{C}{2\pi } = \sqrt{\frac{a^{2} + b^{2} }{2} }$

Squaring Both sides, we get

$[\frac{C}{2\pi }]^{2} = [\sqrt{\frac{a^{2} + b^{2} }{2} }]^{2} \\\frac{C^{2} }{(2\pi)^{2} } = {\frac{a^{2} + b^{2} }{2} }\\2\frac{C^{2} }{4(\pi)^{2} } = {{a^{2} + b^{2} }$

$\frac{C^{2} }{2(\pi )^{2} } = a^{2} + b^{2} \\\frac{C^{2} }{2(\pi )^{2} } - a^{2} = b^{2} \\\sqrt{\frac{C^{2} }{2(\pi )^{2} } - a^{2}} = b$

∴ we get

$b = \sqrt{\frac{C^{2} }{2(\pi )^{2} } - a^{2}}$

8 0

3 years ago

Classify the following into monomials, binomial and trinomials.

Degger [83]

A monomial is an expression containing a single term.
A binomial is an expression having two terms.
A trinomial is an expression having three terms.

Here -6 is a monomial having a single term -6.
-5 + x is a binomial containing two terms -5 and x.
32x - y is a binomial having two terms 32x and -y.
6x² + 5x - 3 is a trinomial having three terms 6x², 5x and -3.
z² +2 is a binomial having two terms z² and 2.

Answers

monomial
binomial
binomial
trinomial
binomial

Hope you could understand.

If you have any query, feel free to ask.

5 0

2 years ago