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3 years ago

10

Solve 3/10 n-3 1/5 = -1 1/5

1 answer:

steposvetlana [31]3 years ago

5 0

3/10 n-3 1/5=-1 1/5
convert mixed numbers to a improper fractions:3 1/5=16/5
$\frac{3}{10}n- \frac{16}{5}=-1* \frac{1}{5}$
convert mixed numbers to a improper fractions:1 1/5=6/5
$\frac{3}{10}n- \frac{16}{5}=- \frac{6}{5}$
add 16/5 to both sides
$\frac{3}{10}- \frac{16}{5}+ \frac{16}{5}=- \frac{6}{5}+ \frac{16}{5}$
simplify
3/10 n=2
multiply both sides by 10
$10* \frac{3}{10}n=2*10$
simplify
3n=20
divide both sides by 3
$\frac{3n}{5}= \frac{20}{3}$
simplify
$n= \frac{20}{3}$
Hope this helps

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Separate the left side into partial fractions. We want coefficients a and b such that

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$\implies \dfrac1{(y+1)(y-2)} = \dfrac{a(y-2)+b(y+1)}{(y+1)(y-2)}$

$\implies 1 = a(y-2)+b(y+1)$

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Integrating both sides yields

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With the initial condition y(0) = 1, we find

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so that the particular solution is

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It's not too hard to solve explicitly for y; notice that

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Then

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$\dfrac3{y+1} = 1 + \dfrac12 e^{3x}$

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$y+1 = \dfrac6{2+e^{3x}}$

$y = \dfrac6{2+e^{3x}} - 1$

$\boxed{y = \dfrac{4-e^{3x}}{2+e^{3x}}}$

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