Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing

This Question is Closed

baldymcgee6 Group TitleBest ResponseYou've already chosen the best response.0
@LolWolf, @AccessDenied, @lgbasallote
 one year ago

baldymcgee6 Group TitleBest ResponseYou've already chosen the best response.0
wait, thats wrong
 one year ago

baldymcgee6 Group TitleBest ResponseYou've already chosen the best response.0
sinh(3t)/sinh(t)=1+2cosh(2t) for t≠0
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.0
they aren't equal...try again
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.0
ok finally
 one year ago

baldymcgee6 Group TitleBest ResponseYou've already chosen the best response.0
@Algebraic! do you know how to do it?
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.2
\[ \text{sinh} \; x = \frac{e^x  e^{x}}{2} \] We can rewrite the lefthand side to match the righthand side. \[ \frac{e^{3x}  e^{3x}}{2} \div \frac{e^x  e^{x}}{2} \\ \frac{e^{3x}  e^{3x}}{\cancel{2}} \times \frac{\cancel{2}}{e^x  e^{x}}\\ \frac{e^{3x}  e^{3x}}{e^x  e^{x}} \\ \frac{(e^x)^3  (e^{x})^3}{e^x  e^{x}} \] If we consider the numerator as a difference of cubes, we can factor it like this: \( a^3  b^3 = (a  b)(a^2 + ab + b^2)\). Notice that this creates a factor in the denominator that is also in the numerator.
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.2
When the factors cancel, this remains: \[ \frac{\cancel{(e^x  e^{x})}((e^x)^2 + e^x e^{x} + (e^{x})^2)}{\cancel{e^x  e^{x}}} \\ = e^{2x} + 1 + e^{2x} \] Which starts to look a lot like 2cosh 2x + 1, it should be simple manipulation to justify that from there.
 one year ago

baldymcgee6 Group TitleBest ResponseYou've already chosen the best response.0
@AccessDenied YOU ROCK, thanks so much!!
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.2
I should note that I am using x instead of t. My bad. :P
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.2
and, I'm glad to help! :)
 one year ago

baldymcgee6 Group TitleBest ResponseYou've already chosen the best response.0
thanks so much again
 one year ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.0
don't forget, you can redeem your medals for cash prizes at the end of every month.
 one year ago

LolWolf Group TitleBest ResponseYou've already chosen the best response.1
So we know: \[ \sinh x=\frac{e^xe^{x}}{2} \]Therefore: \[ \sinh 3x=\frac{e^{3x}e^{3x}}{2} \]So: \[ \frac{\sinh(3t)}{\sinh(t)}=\frac{2}{e^xe^{x}}\cdot\frac{e^{3x}e^{3x}}{2}=\frac{2e^x}{e^{2x}1}\cdot\frac{e^{6x}1}{2e^{3x}}=\\ \frac{2e^x}{e^{2x}1}\cdot\frac{e^{6x}1}{2e^{3x}}=\frac{(e^{2x}1)(e^{4x}+e^{2x}+1)}{e^{2x}(e^{2x}1)}=\\ \frac{e^{4x}+e^{2x}+1}{e^{2x}}=e^{2x}+1+e^{2x}=1+2\cosh x \]Ahh, this takes forever... and I mad a mistake halfway through, so I had to restart... anyways, +1 internets to @AccessDenied
 one year ago

baldymcgee6 Group TitleBest ResponseYou've already chosen the best response.0
lol, thanks for you valiant effort @LolWolf
 one year ago

LolWolf Group TitleBest ResponseYou've already chosen the best response.1
Valiantly late, haha, but, yes
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.