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]
3 years ago
8

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

Mathematics
2 answers:
Natalka [10]3 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]3 years ago
4 0

Answer:

its d on edge ;)

Step-by-step explanation:

You might be interested in
Jack spent $40 on new shoes then he spent half of what he had left on clothes finally he gave five dollars to his brother now he
aleksandrvk [35]
This is a working backwards problem.  You know he has $35 at the end.  Before he gave his brother $5, he would have $40, which is half of what he had before he bought the clothes, so he would have had $80.  Before he spent the $40 on shoes, he would have had $120, so the answer is $120.
4 0
3 years ago
6 9/10 x 20/21<br> Simplify your answer completely and change to a mixed number.
Sidana [21]

Answer:

6\frac{4}{7}

Step-by-step explanation:

Hello,

I am going to start with to change to a improper fraction:

1. I will convert 6 and 9/10 into a improper fraction:

69/10

2. Now that I have converted the mixed fraction into a improper I can multiply the numerator and the denominator.

69 * 20 / 21 * 10 = 1380/210

3. Now I can simplify this value and convert it into a mixed fraction

46/7

After further simplifying I can convert this into an mixed number

6\frac{4}{7}

5 0
2 years ago
Simply<br> (2k-9)^2+(k+2)^2=(2k+1)^2+(k-8)^2
vova2212 [387]

The square of a binomial expands as follows:

(a+b)^2=a^2+2ab+b^2

Expanding all the binomials, we have

4k^2-36k+81+k^2+4k+4=4k^2+4k+1+k^2-16k+64

Sum like terms:

5k^2-32k+85=5k^2-12k+65

Simplify terms appearing on both sides:

-32k+85=-12k+65

Move all terms involving k to the left and all numbers to the right:

-20k=-20

Divide both sides by -20:

k=1

6 0
3 years ago
I need help with all of it ...
erastovalidia [21]
1)
36/3 x 42/3 = 12yd x 14yd

12×14=168

you will need 168 square yards to recarpet the kindergarten.


2)
168×24.99=4198.32

it will cost $4198.32 to recarpet the kindergarten.


3)
3.5 is 35% of 10

4198.32÷3.5=1198.52

they will need to sell 1199 coupon books to completely pay for the the recarpeting.
6 0
3 years ago
Jessica is 5 years older than her sister Jenna. Jenna tells her sister that in 5 years, she will be as old as Jessica was 5 year
vlabodo [156]

Answer:

x + 5 = (x + 5) - 5, which has no solution ⇒ answer C

Step-by-step explanation:

* Lets study the situation in the problem

- Jessica is 5 years older than her sister Jenna

- After five years Jenna's age will be as old as Jessica was five years ago

- Jenna's age now is x

* Lets change all information above to equation

∵ Janna's age now is x

∵ Jessica is 5 years old than Janna

∴ The age of Jessica now is x + 5

- After 5 years Janna's age will be add by 5 years

∵ Her age now is x

∴ Her age after 5 years will be x + 5

- From 5 years ago Jessica's age was her age now mins 5 years

∵ Her age now is x + 5

∴ Her age from 5 years ago is (x + 5) - 5

∵ Janna's age after 5 years = Jessica age from 5 years ago

∴ x + 5 = (x + 5) - 5

- Lets solve the equation to know how many solution

∵ x + 5 = x + 5 - 5 ⇒ add the like terms

∴ x + 5 = x ⇒ subtract x from both sides

∴ 5 = 0

- But 5 ≠ 0, the two sides of the equation not equal each other

∴ There is no solution for this equation

* The equation is x + 5 = (x + 5) - 5, which has no solution

8 0
3 years ago
Read 2 more answers
Other questions:
  • Whats the answer, can someone plz help me????
    9·1 answer
  • Please help I can’t figure this out
    14·1 answer
  • Which of the following is the most precise definition of a line segment based on the notions of "point" and "line"? A. A line se
    11·1 answer
  • Runelle collected river water for an experiment. She poured it into 8 jars. Each jar had the mixed number two and three fourths
    9·1 answer
  • Find the absolute extrema of the function over the region R. (In each case, R contains the boundaries.) Use a computer algebra s
    10·1 answer
  • Function A is a linear function with an x-intercept of -3 and a y-intercept of -9. Which of the following functions has the same
    8·1 answer
  • David begins the summer with a savings of $54.00 more than Fatima. David's job pays $8.25 per hour. Fatima's job pays $9.75. If
    7·1 answer
  • ΔABC has the following angle measures: A = 40 degrees, B = 60 degrees, and C = 80 degrees. The triangle is reflected across the
    9·1 answer
  • If the mine winch drum diameter is 4,5 calculate how far the counterweight will lift for each single rotation of the drum use th
    5·1 answer
  • Solve similar triangles (advanced)<br><br> Solve for x<br><br> A, 3, B^2, x, D, 13, E, C
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!