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
zhannawk [14.2K]
2 years ago
5

Please help me answer this question

Mathematics
1 answer:
ratelena [41]2 years ago
6 0

By the definition of the hyperbolic function tanh x, we have proven that \frac{1-tanh \ x}{1 + tanh \ x}=e^{-2x}

<h3>Hyperbolic functions & Proof of identities </h3>

By definition

tanh \ x=\frac{e^{x} -e^{-x}}{e^{x} +e^{-x}}

Then,

\frac{1-tanh \ x}{1 + tanh \ x}=\frac{1-\frac{e^{x} -e^{-x}}{e^{x} +e^{-x}} }{1+ \frac{e^{x} -e^{-x}}{e^{x} +e^{-x}} }

=1-\frac{e^{x} -e^{-x}}{e^{x} +e^{-x}} \div (1+ \frac{e^{x} -e^{-x}}{e^{x} +e^{-x}} })

=\frac{e^{x} +e^{-x}-(e^{x} -e^{-x})}{e^{x} +e^{-x}} \div (\frac{e^{x} +e^{-x}+e^{x} -e^{-x}}{e^{x} +e^{-x}} })

=\frac{e^{x} +e^{-x}-e^{x} +e^{-x}}{e^{x} +e^{-x}} \div \frac{e^{x} +e^{-x}+e^{x} -e^{-x}}{e^{x} +e^{-x}} }

=\frac{e^{-x}+e^{-x}}{e^{x} +e^{-x}} \div \frac{e^{x} +e^{x} }{e^{x} +e^{-x}} }

=\frac{2e^{-x}}{e^{x} +e^{-x}} \div \frac{2e^{x} }{e^{x} +e^{-x}} }

=\frac{2e^{-x}}{e^{x} +e^{-x}} \times \frac{e^{x} +e^{-x}}{2e^{x}}

=\frac{2e^{-x}}{1} \times \frac{1}{2e^{x}}

=\frac{2e^{-x}}{2e^{x}}

=\frac{e^{-x}}{e^{x}}
=e^{-x} \times \frac{1}{e^{x}}

= e^{-x} \times e^{-x}

= e^{-x+-x}

= e^{-x-x}

= e^{-2x}

Hence, we have proven that \frac{1-tanh \ x}{1 + tanh \ x}=e^{-2x}

Learn more on Proof of Identities here: brainly.com/question/2561079

#SPJ1

You might be interested in
What is 34827 x 7 =<br><br> Jasper over here..
kirill [66]

Answer:

243789

Step-by-step explanation:

(34827) 7 = 243789

Hope this helps!

3 0
2 years ago
Read 2 more answers
What is the product of 3/5 x 4/9 written in simplest form?
frosja888 [35]
Mmm... I think it is 5/8... I think.
3 0
3 years ago
Read 2 more answers
Which measure of center would you use to describe a data set with no extreme values and no big gaps?
xxTIMURxx [149]

Answer:

The median

Step-by-step explanation:

The median always exists. The median does not have to be one of the data

3 0
3 years ago
Read 2 more answers
The function C(x) = 25x + 50 represents the labor cost (in dollars) for Certified Remodeling to build a deck, where x is
Whitepunk [10]

Answer:

  • Master Remodeling

Step-by-step explanation:

<em>Original question is attached</em>

<h3>Option 1</h3>
  • C(x) = 25x + 50
  • C(8) = 25*8 + 50 = $250
<h3>Option 2</h3>
  • As per table, the rate of change is $30 per 2 hours.
  • So 8 hours will cost
  • $190 + $30 = $220

As we see the second option is cheaper so we should hire the Master Remodeling

5 0
3 years ago
Jawad has seven rocks ​
Neporo4naja [7]

Answer:

What’s the question?

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Other questions:
  • Solve the following system of equations:
    12·2 answers
  • Most __________ signs are rectangular, with the longer dimension vertical, and have a white background.
    9·1 answer
  • Hi, so i have a question and i'm giving away free points so here's the question! If you answer ill put out another question and
    8·1 answer
  • Write the equation of the line that passes through the points (1,-7)(1,−7) and (-6,-9)(−6,−9). Put your answer in fully reduced
    9·2 answers
  • Ms. Sperlak bakes 3 1/2 pies in 20 minutes. At this rate how many pies can she bake in 1 hour? 2 hours? (This is math)
    9·1 answer
  • If AB is 12, what is the length of A'B'?
    15·1 answer
  • 15/32 × 8/15??<br>please answer quick​
    8·1 answer
  • In a school, 50% of students are younger of students younger than 10, 1/2 are 10 years old and 1/10 are older than 10 but younge
    9·1 answer
  • Jenny received a $30.50 gift card for a photo center. She used it to buy prints that cost 20 cents each. The remaining balance,
    5·1 answer
  • What's the distance between (0,2) and (0,8)?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!