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Alexeev081 [22]
2 years ago
5

Answer each question by finding the slope or y-intercept of each linear relationship.

Mathematics
1 answer:
jarptica [38.1K]2 years ago
8 0
A. y=0.5x
B y=-2x
C y=6x
D y=12
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Consider the following equation of the form dy/dt = f(y)dy/dt = ey − 1, −[infinity] < y0 < [infinity](a) Sketch the graph
kotegsom [21]

Complete Question:

The complete question is shown on the first uploaded image

Answer:

a) The graph of  f(y) versus y. is shown on the second uploaded image

b) The critical point is at y = 0  and the solution is asymptotically unstable.

c)The phase line is shown on the third uploaded image

d) The sketch for the several graphs of solution in the ty-plane  is shown on the fourth uploaded image

Step-by-step explanation:

Step One: Sketch The Graph of  f(y) versus y

Looking at the given differential equation

       \frac{dy}{dt} = e^{y} - 1 for -∞ < y_{o} < ∞

 We can say let \frac{dy}{dt} = f(y) =e^{y} - 1

Now the dependent value is f(y) and the independent value is y so to sketch is graph we can assume a scale in this case i cm on the graph is equal to 2 unit for both f(y) and y and the match the coordinates and after that join the point to form the graph as shown on the uploaded image.

Step Two : Determine the critical point

   To fin the critical point we have to set   \frac{dy}{dt} = 0

       This means e^{y} - 1 = 0

                          For this to be possible e^{y} = 1

                          which means that  e^{y} = e^{0}

                          which implies that y = 0

Hence the critical point occurs at y = 0

meaning that the equilibrium solution is y = 0

As t → ∞, our curve is going to move away from y = 0  hence it is asymptotically unstable.

Step Three : Draw the Phase lines

A phase line can be defined as an image that shows or represents the way an ODE(ordinary differential equation ) that does not explicitly depend on the independent variable behaves in a single variable. To draw this phase line , draw the y-axis as a vertical line and mark on it the equilibrium, i.e. where  f(y) = 0.

In each of the intervals bounded  by the equilibrium draw an upward

pointing arrow if f(y) > 0 and a downward pointing arrow if f(y) < 0.

      This phase line would solely depend on y does not matter what t is

On the positive x axis it would get steeper very quickly as you move up (looking at the part A graph).

For  below the x-axis which stable (looking at the part a graph) we are still going to have negative slope but they are going to be close to 0 and they would take a little bit longer to get steeper  

Step Four : Draw a Solution Curve

A solution curve is a curve that shows the solution of a DE (deferential equation)

Here the solution curve would be drawn on the ty-plane

So the t-axis(x-axis) is its the equilibrium  that is it is the solution

If we are above the x-axis it is going to increase faster and if we are below it is going to decrease but it would be slower (looking at part A graph)

5 0
3 years ago
Can someone please help me with these questions.
Juli2301 [7.4K]

Answer:

Question 1 - 81.74 Pound sterling

Question 2 - 20.28 Pound sterling

Question 3 - 21.72 United States Dollar

Question 4 - 429.38 New Zealand Dollar

Question 5 - 451.28 Euro

Question 6 - 2,936.88 Chinese Yuan

(That's all I got.)

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3 years ago
Find the volume for the regular pyramid.<br><br><br><br> V =
Paul [167]

Answer:

What do you mean by that?

4 0
2 years ago
He table shows the number of grade 7 and grade 8 students on the student council at Jeremy’s school.
Artyom0805 [142]

Answer:

Im pretty sure the answer is B, forgive me if I am wrong.

Step-by-step explanation:

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3 years ago
The area of a square is 81 square centimeters. What is the perimeter of the square?
loris [4]

Answer:

p = 36cm

Step-by-step explanation:

p = 4a

4 × 9 = 36

<em>good luck, i hope this helps :) </em>

<em />

3 0
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