A curve asymptote is a line where the distance between the curve and the line approaches 0. The function is undefined for the value of x=(5/2). Thus, x=(5/2) is an asymptote.
<h3>What are asymptotes?</h3>
A curve asymptote is a line where the distance between the curve and the line approaches 0 when one or both of the x or y coordinates approaches infinity.
The asymptotes are the values for which the function is not defined. The asymptotes of a fractional function are found by equating its denominator's factors against zero. Therefore, the value of the asymptotes is,
![(2x-5)=0\\\\2x=5\\\\x=\dfrac52](https://tex.z-dn.net/?f=%282x-5%29%3D0%5C%5C%5C%5C2x%3D5%5C%5C%5C%5Cx%3D%5Cdfrac52)
![x-5=0\\\\x=5](https://tex.z-dn.net/?f=x-5%3D0%5C%5C%5C%5Cx%3D5)
Now, substitute the value of x as (5/2) and 5, to know if the function is defined or not.
![f(x) = \dfrac{(7x-1)(x-5)}{(2x-5)(x-5)}\\\\\\f(5) = \dfrac{[7(5)-1](5-5)}{[2(5)-5](5-5)}\\\\\\f(5) = \dfrac{(35-1)(0)}{(10-5)(0)} = 0](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cdfrac%7B%287x-1%29%28x-5%29%7D%7B%282x-5%29%28x-5%29%7D%5C%5C%5C%5C%5C%5Cf%285%29%20%3D%20%5Cdfrac%7B%5B7%285%29-1%5D%285-5%29%7D%7B%5B2%285%29-5%5D%285-5%29%7D%5C%5C%5C%5C%5C%5Cf%285%29%20%3D%20%5Cdfrac%7B%2835-1%29%280%29%7D%7B%2810-5%29%280%29%7D%20%3D%200)
Since for the value of x=5, the function is defined and returns the value as 0. Thus, x=5 is not an asymptote.
![f(x) = \dfrac{(7x-1)(x-5)}{(2x-5)(x-5)}\\\\\\f(\frac52) = \dfrac{[7(\frac52)-1](\frac52-5)}{[2(\frac52)-5](\frac52-5)}\\\\\\f(\frac52) = \dfrac{(16.5)(-2.5)}{(0)(-2.5)} = \dfrac{\infty}{0}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cdfrac%7B%287x-1%29%28x-5%29%7D%7B%282x-5%29%28x-5%29%7D%5C%5C%5C%5C%5C%5Cf%28%5Cfrac52%29%20%3D%20%5Cdfrac%7B%5B7%28%5Cfrac52%29-1%5D%28%5Cfrac52-5%29%7D%7B%5B2%28%5Cfrac52%29-5%5D%28%5Cfrac52-5%29%7D%5C%5C%5C%5C%5C%5Cf%28%5Cfrac52%29%20%3D%20%5Cdfrac%7B%2816.5%29%28-2.5%29%7D%7B%280%29%28-2.5%29%7D%20%3D%20%5Cdfrac%7B%5Cinfty%7D%7B0%7D)
Since the function is undefined for the value of x=(5/2). Thus, x=(5/2) is an asymptote.
Learn more about Asymptotes:
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Answer:
Geometric Sequence
Step-by-step explanation:
Since we are multiplying each successive term by common ratio <em>r</em> of -2, we have our sequence:
![a_n = 2.4(2)^{n-1}](https://tex.z-dn.net/?f=a_n%20%3D%202.4%282%29%5E%7Bn-1%7D)
To solve this problem, we make use of the z statistic.
What we have to do here is to find for the z score using the given data and
from the standard probability tables for z, we locate the proportion of the
fish longer than 12 inches.
The formula for calculating the z score is:
z = (x – μ) / σ
where,
x = the sample value = 12 inches
μ = the sample mean = 11 inches
σ = 2 inches
so,
z = (12 – 11) / 2
z = 1 / 2
z = 0.5
Since we are looking for the values greater than 12, so
this is a right tailed test. Using the tables, the value of p at this value of
z is:
p (z = 0.5) = 0.3085
Therefore there is a 30.85% probability that the fish is
longer than 12 inches.