The answer to this problem “12 = 15(z-1/5) is : Z = 1
now, if the denominator turns to 0, the fraction becomes undefined, and you get a "vertical asymptote" when that happens, so let's check when is that
![\bf sin\left(x-\frac{2\pi }{3} \right)=0\implies sin^{-1}\left[ sin\left(x-\frac{2\pi }{3} \right) \right]=sin^{-1}(0) \\\\\\ x-\frac{2\pi }{3}= \begin{cases} 0\\ \pi \end{cases}\implies \measuredangle x= \begin{cases} \frac{2\pi }{3}\\ \frac{5\pi }{3} \end{cases}](https://tex.z-dn.net/?f=%5Cbf%20sin%5Cleft%28x-%5Cfrac%7B2%5Cpi%20%7D%7B3%7D%20%20%5Cright%29%3D0%5Cimplies%20sin%5E%7B-1%7D%5Cleft%5B%20sin%5Cleft%28x-%5Cfrac%7B2%5Cpi%20%7D%7B3%7D%20%20%5Cright%29%20%5Cright%5D%3Dsin%5E%7B-1%7D%280%29%0A%5C%5C%5C%5C%5C%5C%0Ax-%5Cfrac%7B2%5Cpi%20%7D%7B3%7D%3D%0A%5Cbegin%7Bcases%7D%0A0%5C%5C%0A%5Cpi%20%0A%5Cend%7Bcases%7D%5Cimplies%20%5Cmeasuredangle%20x%3D%0A%5Cbegin%7Bcases%7D%0A%5Cfrac%7B2%5Cpi%20%7D%7B3%7D%5C%5C%0A%5Cfrac%7B5%5Cpi%20%7D%7B3%7D%0A%5Cend%7Bcases%7D)
now, at those angles, the function is asymptotic, check the picture below
9514 1404 393
Answer:
1 < x < 29
Step-by-step explanation:
The triangle inequality requires the sum of the two shortest sides exceed the longest side.
<u>When x and 14 are the shortest</u>:
x + 14 > 15
x > 1
<u>When 14 and 15 are the shortest</u>:
14 +15 > x
29 > x
Then the requirement for the length of x is ...
1 < x < 29
_____
<em>Additional comment</em>
The length of the third side of a triangle can be between the difference and sum of the two given sides.
