<u>Question Completion</u>
PIE CHART NUMBERS:
Answer:
0.000063
Step-by-step explanation:
Number of Respondents, n=1400
Probability that they would rate their financial shape as excellent = 0.09
Number of Those who would rate their financial shape as excellent
=0.09 X 1400
=126
Therefore:
The probability that 4 people chosen at random would rate their financial shape as excellent
Answer:
Option b. Two solutions
Step-by-step explanation:
In order to find how many real number solutions the equation has we have to solve it
Given equation: -4x² + 10x + 6 = 0
taking 2 common from the equation
2(-2x² + 5x + 3) = 0
-2x² + 5x + 3 = 0
taking minus sign common from the above equation
2x² - 5x - 3 = 0
We will solve this equation by factorization in such a way that the sum of two factors is equal to -5x and the product is -6x²
2x² - 6x + x - 3 = 0
taking common above
2x(x-3) + 1(x-3) = 0
taking (x-3) common
(2x+1)(x-3) = 0
2x + 1 = 0
2x = -1
x =
x - 3 = 0; x = 3
the solutions are
Both values are real numbers, therefore correct option is b
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)
