2 years ago

What is -3/4x + 1/2y - 9/4x - 11/2y in simplest form?

Mathematics

1 answer:

Allushta [10]2 years ago

7 0

Answer: -3x-5y

Step-by-step explanation:

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If thewronskian w of f and g is 3e4t,and if f(t) = e2t,find g(t).

ehidna [41]

$W(f(x),g(x))=\begin{vmatrix}f(x)&g(x)\\f'(x)&g'(x)\end{vmatrix}=f(x)g'(x)-g(x)f'(x)$

We have $f(t)=e^{2t}\implies f'(t)=2e^{2t}$ , so

$W(f(t),g(t))=e^{2t}g'(t)-2e^{2t}g(t)=3e^{4t}$
$\implies e^{-2t}g'(t)-2e^{-2t}g(t)=3$
$\implies\dfrac{\mathrm d}{\mathrm dt}[e^{-2t}g(t)]=3$
$\implies e^{-2t}g(t)=\displaystyle\int3\,\mathrm dt$
$\implies e^{-2t}g(t)=3t+C$
$\implies g(t)=3te^{2t}+Ce^{2t}$

where $C$ is any arbitrary constant.