Answer:
Step-by-step explanation:
1/6 + 1/6 + 1/3 + 1/3 + 1/3 + 1/2 + 2/3 + 2/3 + 2/3 + 5/6 = 14/3
(14/3)/11 = 14/33
Hope this helps!
(Please mark Brainliest)
How can 4.17 be written as a whole number with a fraction?
1 answer:
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Answer:
The rule that represents the function is therefore the function is
Step-by-step explanation:
We have 5 ordered pairs in the plane xy. This means that <em>every pair has the form (x, y).</em>
Then, we have 5 values of x, which will give us 5 values of y, using the rule that represents the function.
<u>The easy evaluation is that when x=0, the value of y is y=1,</u> and then we can evaluate the rule for x=-1, and x=1, <em>the value of y is the same, y=2</em>. We can see here that we have a parabolic function, that is not centered in the origin of coordinates because when x=0, y=1.
So <u>we propose the rule </u><u> which is correct for the first 3 values of x.</u>
Now, <em>we evaluate the proposed rule when x=2, and when x=3</em>. This evaluations can be written as
Therefore, the rule is correct, and the function is
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
for -∞ <
< ∞
We can say let = f(y) =
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 = 0
This means = 0
For this to be possible = 1
which means that =
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)
