Mathematics: If dy/dt=-2y and if y=1 when t=0, what is the value of t for which y=1/2

If dy/dt=-2y and if y=1 when t=0, what is the value

Ответ:

tashanicole

06.01.2022

$\bf \displaystyle \int -2t\cdot dt\implies -2\int t\cdot dt\implies -2\cdot \cfrac{t^2}{2}+C
\\\\\\
-t^2+C=f(x)\qquad 
\begin{cases}
f(x)=y=1\\
t=0
\end{cases}\implies -0^2+C=1\implies C=1
\\\\\\
-t^2+1=f(x)\\\\
-----------------------------\\\\
-t^2+1=f(x)\qquad f(x)=\cfrac{1}{2}\implies -t^2+1=\cfrac{1}{2}
\\\\\\
1-\cfrac{1}{2}=t^2\implies \pm \sqrt{\cfrac{1}{2}}=t\implies \cfrac{1}{\pm \sqrt{2}}=t
\\\\\\
\pm \cfrac{\sqrt{2}}{2}=t\impliedby \textit{with a rationalized denominator}$

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Ответ:

Brucechavez3334

29.07.2022

Mathematics

96 units^2

Step-by-step explanation:

Base: 6 × 6 = 36

Faces: 5 × 6 = 30 (×2 = 60)

Add: 36 + 60 = 96

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If dy/dt=-2y and if y=1 when t=0, what is the value of t for which y=1/2

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