All categories

3 years ago

What does infinite=/mean

Mathematics

1 answer:

givi [52]3 years ago

5 0

Answer:

Infinite describes things that are endless

Step-by-step explanation:

You might be interested in

Y=squareroot y+6 <br> Answer

Ivanshal [37]

Square root 6 is the answe

5 0

3 years ago

Read 2 more answers

What is 4x - 6 = 22 equal?<br><img src="https://tex.z-dn.net/?f=8008" id="TexFormula1" title="8008" alt="8008" align="absmiddle"

sineoko [7]

The answer is 4.

22 - 6 = 16
16 divided by 4 = 4

6 0

3 years ago

Read 2 more answers

Lodi solves the equation 3+ x/2=10 and justified each step as shown. Identify Lodi’s error and fix his mistake. Remember the jus

ad-work [718]

3+ x/2 = 10 Given

x/2 = 7 Subtraction property of equality

x = 14 Multiplication property of equality

8 0

3 years ago

Question on laplace transform... number 7

irinina [24]

Recall a few known results involving the Laplace transform. Given a function $f(t)$ , if the transform exists, then denote it by $F(s)$ . We have

$\mathcal L_s\left\{e^{ct}f(t)\right\}=\mathcal L_{s-c}\left\{f(t)\right\}=F(s-c)$

$\mathcal L_s\left\{\displaystyle\int_0^t f(u)\,\mathrm du\right\}=\dfrac{F(s)}s$

$\mathcal L_s\left\{f'(t)\right\}=sF(s)-f(0)$

Let's put all this together by taking the transform of both sides of the ODE:

$y'(t)+2e^{-2t}\displaystyle\int_0^te^{2u}y(u)\,\mathrm du=e^{-t}\sin t$

$\implies \bigg(sY(s)-y(0)\bigg)+2\mathcal L_s\left\{e^{-2t}\displaystyle\int_0^te^{2u}y(u)\,\mathrm du\right\}=\dfrac1{(s+1)^2+1}$

Here we use the third fact and immediately compute the transform of the right hand side (I'll leave that up to you).

Now we invoke the first listed fact:

$\mathcal L_s\left\{e^{-2t}\displaystyle\int_0^te^{2u}y(u)\,\mathrm du\right\}=\mathcal L_{s+2}\left\{\displaystyle\int_0^te^{2u}y(u)\,\mathrm du\right\}$

Let $g(u)=e^{2u}y(u)$ . From the second fact, we get

$\mathcal L_s\left\{\displaystyle\int_0^tg(u)\,\mathrm du\right\}=\dfrac{G(s)}s\implies\mathcal L_{s+2}\left\{\displaystyle\int_0^tg(u)\,\mathrm du\right\}=\dfrac{G(s+2)}{s+2}$

From the first fact, we get

$G(s)=\mathcal L_s\left\{e^{2u}y(u)\right\}=Y(s-2)$

so we're left with

$\dfrac{G(s+2)}{s+2}=\dfrac{Y((s+2)-2)}{s+2}=\dfrac{Y(s)}{s+2}$

To summarize, taking the Laplace transform of both sides of the ODE yields

$sY(s)+\dfrac{2Y(s)}{s+2}=\dfrac1{(s+1)^2+1}$

Isolating $Y(s)$ gives

$Y(s)=\dfrac1{\left(s+\frac2{s+2}\right)\left((s+1)^2+1\right)}$
$Y(s)=\dfrac{s+2}{\left((s+1)^2+1\right)^2}$

All that's left is to take the inverse transform. I'll leave that to you as well. You should end up with something resembling

$y(t)=\dfrac12(t\cos t-(t+1)\sin t)(\sinh t-\cosh t)$

4 0

3 years ago

Trying to find percent of change

Contact [7]

Move the decimals two places to the right

3 0

3 years ago

Read 2 more answers