Answer:
(B) a = 41%, b = 3%
Step-by-step explanation:
The result from the survey is given below:
The second table is given as:
Now, from the first table
Total Number of Respondents =116
Therefore:
Therefore:
a=41%
b=3%
The correct option is B.
Fill in the missing decimal number. To decrease by 14% multiply by...
1 answer:
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Answer:
Take the square root of the constant (number w/o the variable) and then multiply that by 2.
Step-by-step explanation:
A perfect square trinomial is something like this: If I have 6x, and I want to find the last term I would take half a six and then square it to get 9.
SO.... To get the middle term of a perfect square trinomial, you would need to do the reverse.. So...
1) Take the square root of the constant...
2) Multiply that by 2
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)
