Answer:
Vertical asymptotes are at
.
Step-by-step explanation:
The rational function is given as:
![y=\frac{4x^2+1}{x^2-1}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B4x%5E2%2B1%7D%7Bx%5E2-1%7D)
Vertical asymptotes are those values of
for which the function is undefined or the graph moves towards infinity.
For a rational function, the vertical asymptotes can be determined by equating the denominator equal to zero and finding the values of
.
Here, the denominator is ![x^2-1](https://tex.z-dn.net/?f=x%5E2-1)
Setting the denominator equal to zero, we get
![x^2-1=0\\x^2=1\\x=\pm \sqrt{1}\\ x= -1\ and\ x = 1](https://tex.z-dn.net/?f=x%5E2-1%3D0%5C%5Cx%5E2%3D1%5C%5Cx%3D%5Cpm%20%5Csqrt%7B1%7D%5C%5C%20x%3D%20-1%5C%20and%5C%20x%20%3D%201)
Therefore, the vertical asymptotes occur at
.
-x² + 8x - 6 = 0
x = <u>-(8) +/- √((8)² - 4(-1)(-6))</u>
2(-1)
x = <u>-8 +/- √(64 - 20)</u>
-2
x = <u>-8 +/- √(44)
</u> -2<u>
</u>x = <u>-8 +/- 2√(11)
</u> -2
x = <u>-8 + 2√(11)</u> x = <u>-8 - 2√(11)
</u> -2 -2<u>
</u>x = 4 - √(11) x = -8 + √(11)
The answer is subtract 5
Hope this helps
X = 11π / 6 = 330 °
To find the reference angle for angle in Quadrant IV the formula is:
α = 360° - x
α = 360° - 330° = 30°
Answer:
The reference angle is 30° or π/6.