Answer:
y-incercepts:
sinh(x):0, cosh(x)=1
Limits:
positive infinity: sinh(x): infinity, cosh(x): infinity
negative infinity: sinh(x): - infinity, cosh(x): infinity
Step-by-step explanation:
We are given that
To find out the y-incerpt of a function, we just need to replace x by 0. Recall that . Then,
For the end behavior, recall the following:
Using the properties of limits, we have that
Answer:
a) City Suburbs city 0.98 0.02 , Suburbs 0.01 0.99
b) 0.333 , 0.667
c ) Using the steady-state probabilities, There will be an increase in the Suburb population and a decrease in City population
Step-by-step explanation:
2% living within the city limits move to suburbs
1% living within the suburbs move to the city
a) Matrix of transition probabilities
City Suburbs city 0.98 0.02 , Suburbs 0.01 0.99
<u>b) Steady -state probabilities </u>
attached below
steady state probabilities = 0.333 , 0.667
<u>c) Determine the population changes the steady-state probabilities </u>
Using the steady-state probabilities, There will be an increase in the Suburb population and a decrease in City population i.e. a decrease from 40% to 33%
Answer:
Lots of connections!
Step-by-step explanation:
I attached some images to make it more clear.
Visual and verbal discussion:
A good starting point is the circle. One can think of a circle as the set of points that are equidistant to a certain point. In that sense, one can define a circle using the distance. At the same time, given a point in the plane, we can connect the point with the origin of the coordinates system forming a rectangle triangle! (See 2nd image)
Algebraic discussion:
1. The distance Formula:
Given two points in the plane and
we can find the distance between both points with the distance formula:
2. Equation of a circle centered at a point
3. The Pythagorean Theorem:
Given a triangle of sides and hypotenuse
we have that
Only by writing this equations we can already see the similarities between all three.
In fact, the most amazing thing about all three is that they are equivalents. That is, we can obtain every single one of them as an immediate result of another.
For instance, as I said before, one can think of a circle as the set of points equidistant to a certain origin or center point. So we could use the distance formula for each point on the circumference and we would obtain always the same value hence obtaining the equation of a circle.
Also as we discussed, any point on the plane form a rectangle triangle with its coordinates and calculating the distance of said point to the origin of the coordinate system would give us no other thing than the hypotenuse of said triangle!
