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Veseljchak [2.6K]
2 years ago
15

Determine if the given pair of lines is parallel, perpendicular, or neither. y=-3x+5 and y=-3x-15

Mathematics
1 answer:
a_sh-v [17]2 years ago
8 0

Answer: parallel

Step-by-step explanation: look at the slopes: since both are -3x (the same slope) the lines are parallel

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fredd [130]

\dfrac{\partial\left(2xy^4+\frac1{x+y^2}\right)}{\partial y}=8xy^3-\dfrac{2y}{(x+y^2)^2}

\dfrac{\partial\left(4x^2y^3+\frac{2y}{x+y^2}\right)}{\partial x}=8xy^3-\dfrac{2y}{(x+y^2)^2}

so the ODE is indeed exact and there is a solution of the form F(x,y)=C. We have

\dfrac{\partial F}{\partial x}=2xy^4+\dfrac1{x+y^2}\implies F(x,y)=x^2y^4+\ln(x+y^2)+f(y)

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f'(y)=0\implies f(y)=C

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8+\ln9=C

so

\boxed{x^2y^3+\ln(x+y^2)=8+\ln9}

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Answer:

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