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aksik [14]
3 years ago
12

What is the answer to 125÷3​

Mathematics
2 answers:
Sunny_sXe [5.5K]3 years ago
5 0

Answer:

41.6666667?? I didnt know if you needed is simplified .-.

labwork [276]3 years ago
4 0

Answer:

41.6 repeating .

Step-by-step explanation:

125 divided by 3 is 41.6 with the 6 repeating .

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Por favor ayuda con estw problema de la transformada de ls derivada<br> Y''-6y+9y=t y(0)=0 y' (0)=1
Hunter-Best [27]

Parece que refieres a la transformada de Laplace. Aplica la transformada a los lados ambos de la ecuación diferencial:

\mathcal L_s\{y''(t)-6y'(t)+9y(t)\}=\mathcal L_s\{t\}

Denota por Y(s)=\mathcal L_s\{y(t)\} la transformada de y(t). En el lado izquierdo obtenemos

\mathcal L_s\{y''(t)-6y'(t)+9y(t)\}=\mathcal L_s\{y''(t)\}-6\mathcal L_s\{y'(t)+9\mathcal L_s\{y(t)\}

\mathcal L_s\{y''(t)-6y'(t)+9y(t)\}=(s^2Y(s)-sy(0)-y'(0))-6(sY(s)-y(0))+9Y(s)

\mathcal L_s\{y''(t)-6y'(t)+9y(t)\}=(s^2-6s+9)Y(s)-1

\mathcal L_s\{y''(t)-6y'(t)+9y(t)\}=(s-3)^2Y(s)-1

y a la derecha,

\mathcal L_s\{t\}=\dfrac1{s^2}

Ahora resuelve para Y(s):

(s-3)^2Y(s)-1=\dfrac1{s^2}

(s-3)^2Y(s)=1+\dfrac1{s^2}

Y(s)=\dfrac{s^2+1}{s^2(s-3)^2}

Expande la fracción por la derecha en fracciones parciales; busque a,b,c,d tal que

\dfrac{s^2+1}{s^2(s-3)^2}=\dfrac as+\dfrac b{s^2}+\dfrac c{s-3}+\dfrac d{(s-3)^2}

s^2+1=as(s-3)^2+b(s-3)^2+cs^2(s-3)+ds^2

s^2+1=(a+c)s^3+(-6a+b-3c+d)s^2+(9a-6b)s+9b

Emparejando los términos con igual grado da el sistema con soluciones

\begin{cases}a+c=0\\-6a+b-3c+d=1\\9a-6b=0\\9b=1\end{cases}\implies a=\dfrac2{27},b=\dfrac19,c=-\dfrac2{27},d=\dfrac{10}9

Pues

Y(s)=\dfrac2{27}\dfrac1s+\dfrac19\dfrac1{s^2}-\dfrac2{27}\dfrac1{s-3}+\dfrac{10}9\dfrac1{(s-3)^2}

y tomar la transformada inversa es trivial. Obtenemos

\mathcal L^{-1}_t\{Y(s)\}=\dfrac2{27}\mathcal L^{-1}_t\left\{\dfrac1s\right\}+\dfrac19\mathcal L^{-1}_t\left\{\dfrac1{s^2}\right\}-\dfrac2{27}\mathcal L^{-1}_t\left\{\dfrac1{s-3}\right\}+\dfrac{10}9\mathcal L^{-1}_t\left\{\dfrac1{(s-3)^2}\right\}

\boxed{y(t)=\dfrac2{27}+\dfrac t9-\dfrac2{27}e^{3t}+\dfrac{10}9te^{3t}}

8 0
3 years ago
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