1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Harlamova29_29 [7]
4 years ago
8

Solve for x. (e^x-e^-x)/((e^x+e^-x)=t

Mathematics
2 answers:
Natalka [10]4 years ago
6 0

\dfrac{e^x-e^{-x}}{e^x+e^{-x}}=t\\\\\dfrac{e^x-e^{-x}}{e^x+e^{-x}}=(e^x-e^{-x}):(e^x+e^{-x})=\left(e^x-\dfrac{1}{e^x}\right):\left(e^x+\dfrac{1}{e^x}\right)\\\\=\left(\dfrac{(e^x)^2}{e^x}-\dfrac{1}{e^x}\right):\left(\dfrac{(e^x)^2}{e^x}+\dfrac{1}{e^x}\right)=\dfrac{e^{2x}-1}{e^x}:\dfrac{e^{2x}+1}{e^x}\\\\=\dfrac{e^{2x}-1}{e^x}\cdot\dfrac{e^x}{e^{2x}+1}=\dfrac{e^{2x}-1}{e^{2x}+1}\\\\\text{substitute}\ e^{2x}=s


\text{therefore}\\\\\dfrac{e^x-e^{-x}}{e^x+e^{-x}}=t\to\dfrac{s-1}{s+1}=t\ \ \ \ |\cdot(s+1)\\\\s-1=t(s+1)\\\\s-1=ts+t\ \ \ \ |+1\\\\s=ts+t+1\ \ \ |-ts\\\\s-ts=t+1\\\\s(1-t)=t+1\ \ \ \ |:(1-t)\neq0\\\\s=\dfrac{t+1}{1-t}\to e^{2x}=\dfrac{t+1}{1-t}\ \ \ \ |\ln\\\\\ln e^{2x}=\ln\left(\dfrac{t+1}{1-t}\right)\\\\2x\ln e=\ln\left(\dfrac{t+1}{1-t}\right)\\\\2x=\ln\left(\dfrac{t+1}{1-t}\right)\ \ \ \ |:2\\\\\boxed{x=\dfrac{1}{2}\ln\left(\dfrac{t+1}{1-t}\right)}\\\\\text{The domain:}\\\\t\in(-1;\ 1)


\text{Used:}\\\\a^{-n}=\dfrac{1}{a^n}\\\\(a^n)^m=a^{nm}\\\\\log_ab^n=n\cdot\log_ab\\\\\log_aa=1

SIZIF [17.4K]4 years ago
4 0

Answer:

its d on edge ;)

Step-by-step explanation:

You might be interested in
Question 1 of 10
Jet001 [13]
The answer should be true
4 0
3 years ago
Read 2 more answers
Which of the following statements is false?
Vaselesa [24]

Answer: A

Step-by-step explanation:

A is false. Not all reals numbers are rational numbers. Some real numbers can contain irrational numbers, like \sqrt{2}. This is a real number, but isn't rational since it cannot be represented as a ratio.

6 0
2 years ago
Read 2 more answers
Josephina is four years younger than Cameron and the sum of their ages is 88. write an equation and solve it to figure out their
slavikrds [6]
Josephina is 42 and Cameron is 46. The equation is 42 plus 46 = 88.
3 0
3 years ago
Read 2 more answers
What is the answer of question 26 please is for my brother
777dan777 [17]

Answer: the answer is D

Step-by-step explanation:

4 0
3 years ago
How many pounds are in 6 tons, 200 pounds
asambeis [7]

Answer:

there are 12000 pounds in 6 tons

5 0
3 years ago
Read 2 more answers
Other questions:
  • Would you most likely measure a leaf using ounces ,pounds o tons? explain
    7·2 answers
  • Use the substitution method to solve the system of equations.<br><br>8x + 5y = 9 <br>y = x + 7
    8·1 answer
  • A pair of in-line skates is on sale for $90. If this price represents a 9% discount from the original price, what is the origina
    12·1 answer
  • Determine the contrapositive of the conditional statement: If My Mom has to work, then I babysit my little sister.
    5·1 answer
  • A portion of the graph of f(x) = −x2 − 10x − 21 is shown. Which of the following describes all solutions for f(x)?
    12·1 answer
  • Yo can someone help me out
    8·2 answers
  • Which of the following pairs, show the terms?​
    15·2 answers
  • No pic/link to answer pls. NEED TODAY
    8·2 answers
  • HELP IM DESPERATE QUICK NO LINKS!!! DONT PUT LINKS
    7·1 answer
  • The perimeter of a triangle is 26 feet. One side of the triangle is 3 times the second side. The third side is 6 feet longer tha
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!