2 years ago

What is the slope of the line that is perpendicular to the line whose equation is 2x+y=4??

Mathematics

1 answer:

zmey [24]2 years ago

6 0

Answer:

The slope would be 1/2

Step-by-step explanation:

y= mx +b

m= slope

perpendicular lines have slopes that are multiplied in order to get -1

these are important

2x + y = 4

subtract 2x

y=-2x +4

your slope is -2

-2 * ? = -1

? = -1/-2

? = 1/2

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Solve the differential equation dy/dx+4xy=x

Irina-Kira [14]

$\dfrac{\mathrm dy}{\mathrm dx}+4xy=x$
$\dfrac{\mathrm dy}{\mathrm dx}=x(1-4y)$

This ODE is separable, so you can write

$\dfrac{\mathrm dy}{1-4y}=x\,\mathrm dx$

Integrating both sides gives

$-\dfrac14\ln|1-4y|=\dfrac12x^2+C$
$\ln|1-4y|=-2x^2+C$
$1-4y=e^{-2x^2+C}$
$1-4y=Ce^{-2x^2}$
$y=\dfrac{1-Ce^{-2x^2}}4$