A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing

This Question is Closed

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1\[\begin{align*} \\\text{(b)}&&g(t)=t^2\sinh(3t)\\ \\&&G(p)=\mathcal L\{t^2\sinh(3t)\}\\ \\&&=\int\limits_0^\infty t^2\sinh(3t)e^{pt}\text dt\\ \\&&=\int\limits_0^\infty t^2\left(\frac{e^{3t}e^{3t}}{2}\right)e^{pt}\text dt\\ \\&&=\frac12\int\limits_0^\infty t^2\left(e^{3t}e^{3t}\right)e^{pt}\text dt\\ \\&&=\frac12\left[\int\limits_0^\infty t^2e^{(p3)}\text dx\int\limits_0^\infty t^2e^{(p+3)}\text dt\right]\\ \\&&=\frac12\left[\frac{2!}{(p3)^3}\frac{2!}{(p+3)^3}\right]\\ \\&&=\frac{1}{(p3)^3}\frac{1}{(p+3)^3}\\ \\&&=\frac{(p+3)^3(p3)^3}{(p3)^3(p+3)^3}\\ \\&&=\frac{(p+3)(p^2+6p+9)(p3)(p^26p9)}{\left((p3)(p+3)\right)^3}\\ \\&&=\frac{(p^3+6p^2+9p+3p^2+18p+27)(p^36p^29p3p^2+18p+27)}{\left(p^29\right)^3}\\ \\&&=\frac{18p^2+18p}{\left(p^29\right)^3}\\ \\&&=\frac{18p(p+1)}{\left(p^29\right)^3}\\ \end{align*}\]

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1or should i leave my solution as \[G(p)=\frac{1}{(p3)^3}\frac{1}{(p+3)^3}\]

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.0Your work is cut off pretty badly

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3don't leave that answer the difference form, what simplification u have done was required, i think...

Miyuru
 2 years ago
Best ResponseYou've already chosen the best response.0I can't see the rest of the steps @UnkleRhaukus how can i see that. ?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3\(\begin{align*} \\\text{(b)} &g(t)=t^2\sinh(3t)\\ \\ &G(p)=\mathcal L\{t^2\sinh(3t)\}\\ \\ &=\int\limits_0^\infty t^2\sinh(3t)e^{pt}\text dt\\ \\ &=\int\limits_0^\infty t^2\left(\frac{e^{3t}e^{3t}}{2}\right)e^{pt}\text dt\\ \\ &=\frac12\int\limits_0^\infty t^2\left(e^{3t}e^{3t}\right)e^{pt}\text dt\\ \\ &=\frac12\left[\int\limits_0^\infty t^2e^{(p3)}\text dx\int\limits_0^\infty t^2e^{(p+3)}\text dt\right]\\ \\ &=\frac12\left[\frac{2!}{(p3)^3}\frac{2!}{(p+3)^3}\right]\\ \\ &=\frac{1}{(p3)^3}\frac{1}{(p+3)^3}\\ \\ &=\frac{(p+3)^3(p3)^3}{(p3)^3(p+3)^3}\\ \\ &=\frac{(p+3)(p^2+6p+9)(p3)(p^26p9)}{\left((p3)(p+3)\right)^3}\\ \\ &=\frac{(p^3+6p^2+9p+3p^2+18p+27)(p^36p^29p3p^2+18p+27)}{\left(p^29\right)^3}\\ \\ &=\frac{18p^2+18p}{\left(p^29\right)^3}\\ \\ &=\frac{18p(p+1)}{\left(p^29\right)^3}\\ \end{align*}\)

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1now what can we do

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3thst the final answer, what u got

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3though i may suggest another way to \((p+3)^3(p3)^3\) using a^3b^3 formula would simplify it easier..... rather than (a+b)^3 twice..but not much difference

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1what formula do you mean \[a^3b^3=(ab)(a^2+ab+b^2)\]?

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1apply that to the denominator ,?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3you entire answer is fine

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3i just suggested another way to simplify the numerator from \( (p+3)^3(p3)^3\)

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1i not sure where you mean

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3\((p+3)^3(p3)^3 \\ (p+3p+3)(p^2+6p+9+p^29+p^26p+9) \\ (6)(3p^2+9)\) did i make any error ?

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1oh you mean like that

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3@UnkleRhaukus how di u get\( 18p^2+18p\) i am getting 18p^2+54

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1your probably right

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3\((p+3)^3 = (p+3)(p^23p+9)\)

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3\((p3)^3=(p3)(p^2+3p+9)\)

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3rest of the solution is correct welcome ^_^
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
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.