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4 years ago

What is the y-coordinate of the point that divides the directed

Mathematics

1 answer:

Rus_ich [418]4 years ago

3 0

Answer: C) 0

Step-by-step explanation: Just took the test on edge

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What is the surface area of a sphere with the radius of 3?

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A≈113.1

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Ao se olhar para a história da Álgebra, desde os primórdios quando o objeto de estudo eram equações algébricas específicas até o

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3 years ago

For every 20 penguins at the North Pole there are 9 polar bears. If you encountered 27 polar bears, how many penguins would you

cluponka [151]

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Solve for the indicated variable.<br> a -c=d-r. for a<br> a=

sveticcg [70]

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a= d-r +c

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3 years ago

Sketch the equilibrium solutions for the following DE and use them to determine the behavior of the solutions.

GREYUIT [131]

Answer:

$y=\dfrac{1}{1-Ke^{-t}}$

Step-by-step explanation:

Given

The given equation is a differential equation

$\dfrac{dy}{dt}=y-y^2$

$\dfrac{dy}{dt}=-(y^2-y)$

By separating variable

⇒ $\dfrac{dy}{(y^2-y)}=-t$

$\left(\dfrac{1}{y-1}-\dfrac{1}{y}\right)dy=-dt$

Now by taking integration both side

$\int\left(\dfrac{1}{y-1}-\dfrac{1}{y}\right)dy=-\int dt$

⇒ $\ln (y-1)-\ln y=-t+C$

Where C is the constant

$\ln \dfrac{y-1}{y}=-t+C$

$\dfrac{y-1}{y}=e^{-t+c}$

$\dfrac{y-1}{y}=Ke^{-t}$

$y=\dfrac{1}{1-Ke^{-t}}$

from above equation we can say that

When t will increases in positive direction then $e^{-t}$ will decreases it means that ${1-Ke^{-t}}$ will increases, so y will decreases. Similarly in the case of negative t.

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3 years ago