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ira [324]
3 years ago
10

What is the constant of variation if y varies inversely as x and y = 3 when x = 6? PLZ HELP ME I DONT UNDERSTAND

Mathematics
1 answer:
mojhsa [17]3 years ago
7 0

Answer:

k = 18

Step-by-step explanation:

Given that y varies inversely as x then the equation relating them is

y = \frac{k}{x} ← k is the constant of variation

To find k use the condition y = 3 when x = 6, that is

3 = \frac{k}{6} ( multiply both sides by 6 )

18 = k

The constant of variation is k = 18

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(X^2+y^2+x)dx+xydy=0<br> Solve for general solution
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Check if the equation is exact, which happens for ODEs of the form

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M(x,y)=x^2+y^2+x\implies\dfrac{\partial M}{\partial y}=2y

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so the ODE is not quite exact, but we can find an integrating factor \mu(x,y) so that

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\dfrac{\partial(\mu M)}{\partial y}=\dfrac{\partial(\mu N)}{\partial x}\implies \dfrac{\partial\mu}{\partial y}M+\mu\dfrac{\partial M}{\partial y}=\dfrac{\partial\mu}{\partial x}N+\mu\dfrac{\partial N}{\partial x}

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\dfrac{\partial(x^3+xy^2+x^2)}{\partial y}=2xy

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Now we look for a solution of the form F(x,y)=C, with differential

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