Is this an arithmetic sequence? (#17)

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.

4 0

3 years ago

What is the equation of the line that passes through (–2, –3) and is perpendicular to 2x – 3y = 6?

lyudmila [28]

An equation that would be perpendicular is opposite the reciprocal.

6 0

3 years ago

Peyton is a sprinter who can run the 40-yard dash in 4.5 seconds. he converts his speed into miles per hour, as shown below.

oksano4ka [1.4K]

The correct question is
Peyton is a sprinter who can run the 40-yard dash in 4.5 seconds. He converts his speed into miles per hour, as shown below
Which ratio is incorrectly written to convert his speed?

the picture in the attached figure

we know that
The term (5280 ft/1 mi) is incorrect
"Feet" needs to be on the bottom to cancel with the previous term.
"Mile" needs to be on top in the numerator so that the answer can be expressed in "miles per hour"

the correct term is (1 mi/5280 ft)

5 0

3 years ago

Wendy is paid $12 per hour and plans to work between 30 and 35 hours per week. Identify the independent and dependent quantity i

UNO [17]

The independent quantity is her pay and the dependent quantity is the hours she works in a week.
I believe the range would be 30 to 35 hours and the domain would be $360 to $450.

4 0

3 years ago

Read 2 more answers

If line A contains the points (3, -4) and (6, -2), and line B contains the points (-1, 5) and (1, 2), prove that the lines are p

vivado [14]

Answer:

Correct answer: sa · sb = 2/3 · (- 3/2) = - 1

Step-by-step explanation:

Given:

line A - (x₁, y₁) = (3, -4) and (x₂, y₂) = (6, -2)

line B - (x₁, y₁) = (-1, 5) and (x₂, y₂) = (1, 2)

The slope is calculated using the following formula:

s = (y₂ - y₁) / (x₂ - x₁)

sa = (-2 - (-4)) / (6 - 3) = (-2 + 4) / 3 = 2 / 3

sa = 2 / 3

sb = (2 - 5) / (1 - (-1)) = -3 / 2

when lines are perpendicular to each other then the slopes are in the next relationship:

sa · sb = - 1

we will check:

sa · sb = 2/3 · (- 3/2) = - 1

God is with you!!!

7 0

3 years ago