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Akimi4 [234]
3 years ago
13

What does the mode of this set of data represent?

Mathematics
1 answer:
Sidana [21]3 years ago
3 0
It should be D because the mode is the value that occurs the most often. 
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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
I need help with this pls!!
SSSSS [86.1K]
Answer : (12,4)
that is the max point
8 0
3 years ago
What are the zeros of this function?
BabaBlast [244]

Answer:

x = 0 and x = 6

Step-by-step explanation:

See the graph attached to this question.

It is clear from the graph that the curve touches x-axis i.e. y becomes zero at points x = 0 and x = 6

Therefore, the give parabola has zeros at x = 0 and x = 6. (Answer)

Zeros of a function y = f(x) are determined from the equation f(x) = 0 and solving it we will get the x-values which are the zeros of the function.

3 0
3 years ago
Which expresses 1050 : 2000 in decimal form
MatroZZZ [7]

Answer: 10.5 : 20.2

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
4. What is the unit rate for a pound of seed? Circle the correct answer choice.
Vladimir79 [104]
<h3>Answer:  B) $1.75</h3>

===================================================

Explanation:

To get the unit cost, we divide the total cost over the number of pounds.

We can do this for any row

  • row one: ($17.50)/(10) = $1.75
  • row two: ($35.00)/(20) = $1.75
  • row three: ($52.50)/(30) = $1.75
  • row four: ($70.00)/(40) = $1.75

You don't need to show all four row calculations. You can simply pick one row.

This tells us that each pound costs $1.75

Put another way: the price is $1.75 per pound

3 0
3 years ago
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