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valentinak56 [21]
2 years ago
10

Show all work to identify the asymptotes and state the end behavior of the function f(x)=5x/x-25

Mathematics
1 answer:
Nina [5.8K]2 years ago
6 0

Using the asymptote concept, it is found that:

  • The vertical asymptote is of x = 25.
  • The horizontal asymptote is of y = 5.
  • Considering the horizontal asymptote, it is found that the end behavior of the function is that it tends to y = 5 to the left and to the right of the graph.

<h3>What are the asymptotes of a function f(x)?</h3>

  • The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
  • The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.

In this problem, the function is:

f(x) = \frac{5x}{x - 25}

Considering the denominator, the vertical asymptote is:

x - 25 = 0 -> x = 25.

The horizontal asymptote is found as follows:

y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{5x}{x - 25} = \lim_{x \rightarrow \infty} \frac{5x}{x} = \lim_{x \rightarrow \infty} 5 = 5

Hence the end behavior of the function is that it tends to y = 5 to the left and to the right of the graph.

More can be learned about asymptotes and end behavior at brainly.com/question/28037814

#SPJ1

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The Reunion Tower in Dallas, Texas, is topped by a spherical dome that has a surface area of approximately 13,924 \pi square fee
Salsk061 [2.6K]

The volume of the spherical dome will be 12.9π cubic feet when the surface area of the dome is 13.924π.

<h3>What is the volume of the sphere?</h3>

The volume of the cone is the amount of quantity, which is obtained in the 3-dimensional space. The dome is the shape of a semi-sphere the volume of the dome will be half of the volume of the sphere.

Given that the Reunion Tower in Dallas, Texas, is topped by a spherical dome that has a surface area of approximately 13,924π square feet.

The volume of the dome will be calculated as below:-

SA = 13.924π

2πr² = 13.92π

r = √6.96

r = 2.63 feet

Volume = 2 / 3 πr³

Volume = ( 2 / 3 ) π ( 2.63)³

Volume = 12.24π cubic feet

Therefore, the volume of the spherical dome will be 12.9π cubic feet.

To know more about volume follow

brainly.com/question/24247548

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7 0
1 year ago
Find the 4th term in the following sequence (n = 4)
lisabon 2012 [21]

this formula, doesn't rely on a product, relies on a "sum", or is namely an arithmetic sequence, aₙ₋₁ -3 is another way of saying, the value of the previous term minus 3, so it relies on the ordinal value of a term, so is an recursive formula, well, let's get it when n = 4.

\begin{array}{ccll} order&term&value\\ \cline{1-3} 1&a_1&8\\ 2&a_2&a_{2-1}-3\\ &&a_1-3\\ &&8-3\\ &&5\\ 3&a_3&a_{3-1}-3\\ &&a_2-3\\ &&2\\ 4&a_4&a_{4-1}-3\\ &&a_3-3\\ &&2-3\\ &&-1 \end{array}

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2 years ago
Subtract -2k3 + k2 - 9 from 5k3 - 3k + 7.
tankabanditka [31]
5k3-3k+7-(-2k3+k2-9)
basically rewrite with simple algebra principles
15k-3k+7-(-6k+2k-9)
split up the parenthesis
15k-3k+7+6k-2k+9
sort them
15k-3k+6k-3k+7+9
short down by adding up the similar factors
answer: 18k+18
factorise
18(k+1)
both forms are right
8 0
3 years ago
Read 2 more answers
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