Answer:
Option: C is correct.
![x=\ln\sqrt{\dfrac{t+1}{1-t}}](https://tex.z-dn.net/?f=x%3D%5Cln%5Csqrt%7B%5Cdfrac%7Bt%2B1%7D%7B1-t%7D%7D)
Step-by-step explanation:
We are asked to solve for 'x' such that we are given a equation as:
![\dfrac{e^x-e^{-x}}{e^x+e^{-x}}=t](https://tex.z-dn.net/?f=%5Cdfrac%7Be%5Ex-e%5E%7B-x%7D%7D%7Be%5Ex%2Be%5E%7B-x%7D%7D%3Dt)
This equation could also be written as:
![e^x-e^{-x}=t(e^x+e^{-x})\\\\e^x-e^{-x}=te^x+te^{-x}\\\\e^x-te^x=te^{-x}+e^{-x}\\\\(1-t)e^x=(t+1)e^{-x}\\\\e^{2x}=\dfrac{t+1}{1-t}](https://tex.z-dn.net/?f=e%5Ex-e%5E%7B-x%7D%3Dt%28e%5Ex%2Be%5E%7B-x%7D%29%5C%5C%5C%5Ce%5Ex-e%5E%7B-x%7D%3Dte%5Ex%2Bte%5E%7B-x%7D%5C%5C%5C%5Ce%5Ex-te%5Ex%3Dte%5E%7B-x%7D%2Be%5E%7B-x%7D%5C%5C%5C%5C%281-t%29e%5Ex%3D%28t%2B1%29e%5E%7B-x%7D%5C%5C%5C%5Ce%5E%7B2x%7D%3D%5Cdfrac%7Bt%2B1%7D%7B1-t%7D)
on taking logarithmic function on both the sides we have:
![2x=\ln (\dfrac{t+1}{1-t})](https://tex.z-dn.net/?f=2x%3D%5Cln%20%28%5Cdfrac%7Bt%2B1%7D%7B1-t%7D%29)
(since
)
as we know ![\dfrac{1}{2}\times \ln b = \ln (b^\frac{1}{2})](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%20%5Cln%20b%20%3D%20%5Cln%20%28b%5E%5Cfrac%7B1%7D%7B2%7D%29)
Hence, we have: ![x=\ln\sqrt{\dfrac{t+1}{1-t}}](https://tex.z-dn.net/?f=x%3D%5Cln%5Csqrt%7B%5Cdfrac%7Bt%2B1%7D%7B1-t%7D%7D)
Hence, option C is correct.
Answer:
the square root of 91 lies between 9 and 10
Arrange the numbers in ascending order:
8 , 9 , 9 , 9, 10 , 10 , 10 ,10
Median = 10
Answer: 10
Answer:
30303
Step-by-step explanation:
math bro
Let the number be x ,,, 2x-4=x-10x=-6