3 years ago

HURRY ILL GIVE BRAINLIEST!!!

Mathematics

1 answer:

Free_Kalibri [48]3 years ago

3 0

ANSWER

D) (a + 1, b + m)

EXPLANATION

The given line passes through (a,b) and has slope m.

The equation is:

$y - b = m(x - a)$

When x=a+1, we obtain

$y - b = m(a + 1 - a)$

This

$y = m( 1 ) + b$

$y = m + b$

Therefore,(a + 1, b + m) must also lie on this line.

The correct answer is D.

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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

$W(f(t),g(t))=e^{2t}g'(t)-2e^{2t}g(t)=3e^{4t}$
$\implies e^{-2t}g'(t)-2e^{-2t}g(t)=3$
$\implies\dfrac{\mathrm d}{\mathrm dt}[e^{-2t}g(t)]=3$
$\implies e^{-2t}g(t)=\displaystyle\int3\,\mathrm dt$
$\implies e^{-2t}g(t)=3t+C$
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where $C$ is any arbitrary constant.