All categories

3 years ago

Find the horizontal asymptote

Mathematics

1 answer:

eimsori [14]3 years ago

5 0

Answer:

Correct answer: h = 3/5 or y = 3/5

Step-by-step explanation:

Given:

h(x) = (3x² - 9x - 4) / (5x² - 4x + 8)

h = lim x -> ∞ (3x² - 9x - 4) / (5x² - 4x + 8) the numerator and denominator will be divided by x² and get

h = lim x -> ∞ (3 - 9(1/x) - 4 (1/x²)) / (5 - 4(1/x) + 8 (1/x²)

The terms 1/x and 1/x² when x strives ∞ they strives 0

x -> ∞ ⇒ 1/x -> 0 and x -> ∞ ⇒ 1/x² -> 0

h = (3 - 0 - 0) / (5 - 0 + 0)

Horizontal asymptote is h = 3/5 or y = 3/5

God is with you!!!

You might be interested in

Graph triangle RST with vertices R3, 7), S(-5, -2), and T(3, -5) and its image after a reflection over 3

Alja [10]

Skis dhdjaknsjdkjshdjdkbsjfkdnbskdksndjrjdbndje

6 0

2 years ago

What is the vertex of the graph of the function below?

balandron [24]

I think it is A
Aaaaaaaaaaaaaaaaa

7 0

1 year ago

Find the area of the polygon.

Anastaziya [24]

Answer:

to find the area of a polygon

formula: area = 1/2 x perimeter x apothem

Step-by-step explanation:

Here is what it means: Perimeter = the sum of the lengths of all the sides. Apothem = a segment that joins the polygon's center to the midpoint of any side that is perpendicular to that side.

5 0

2 years ago

Find the smallest positive $n$ such that \begin{align*} n &\equiv 3 \pmod{4}, \\ n &\equiv 2 \pmod{5}, \\ n &\equiv

Alex777 [14]

4, 5, and 7 are mutually coprime, so you can use the Chinese remainder theorem right away.

We construct a number $x$ such that taking it mod 4, 5, and 7 leaves the desired remainders:

$x=3\cdot5\cdot7+4\cdot2\cdot7+4\cdot5\cdot6$

Taken mod 4, the last two terms vanish and we have

$x\equiv3\cdot5\cdot7\equiv105\equiv1\pmod4$

so we multiply the first term by 3.

Taken mod 5, the first and last terms vanish and we have

$x\equiv4\cdot2\cdot7\equiv51\equiv1\pmod5$

so we multiply the second term by 2.

Taken mod 7, the first two terms vanish and we have

$x\equiv4\cdot5\cdot6\equiv120\equiv1\pmod7$

so we multiply the last term by 7.

Now,

$x=3^2\cdot5\cdot7+4\cdot2^2\cdot7+4\cdot5\cdot6^2=1147$

By the CRT, the system of congruences has a general solution

$n\equiv1147\pmod{4\cdot5\cdot7}\implies\boxed{n\equiv27\pmod{140}}$

or all integers $27+140k$ , $k\in\mathbb Z$ , the least (and positive) of which is 27.

3 0

3 years ago

At Oliver's Hats, there are 18 baseball caps and 2 other hats. What percentage of the hats are baseball caps?

Kisachek [45]

Answer:

90%

Step-by-step explanation:

18+2=20

18/20=.9

.9*100=90

6 0

2 years ago