3 years ago

Please help me!!!!!!!!!!!!!!

Mathematics

1 answer:

bezimeni [28]3 years ago

3 0

The answer is C, 15b4√2b

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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.

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4 years ago

The sum of 28 consecutive odd positive integers is a perfect cube. Determine the smallest possible set? What is the first and la

aleksandrvk [35]

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Step-by-step explanation:

The smallest set starts at 71. The last term is 125.

The total is 2,744, which is $14^{3}$ .

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3 years ago

Oxana [17]

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An unknown number decreased by six

FinnZ [79.3K]

It would be a variable minus 6 so for example n-6

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3 years ago

Please help me!!!!!!!!!!!!!!​

Please help me!!!!!!!!!!!!!!