Answer:
Step-by-step explanation:
Given that,
y' = 17y ( 1-y^7)
Let y=1
Then, y' = 0 for all t
Then show that it is the only stable equilibrium point so that as y→1, t→∞ with any initial value.
So, the graph solution will be
y(0) = 1 and this will be an horizontal line
If, y(0) > 1 then, y' < 0 by inspecting the first equation, so the graph is has decreasing solution.
Likewise, if y(0) < 1 then, y' > 0 and the graph is increasing.
So no matter the initial condition, graph of the solution will be asymptotic to the horizontal line above.
This make the limit be 1.
This shows that x = 1 is a stable equilibrium.
Answer:
The equation of the new function is 
Step-by-step explanation:
Suppose we have a function f(x).
a*f(x), a > 1, is vertically stretching f(x) a units. Otherwise, if a < 1, we are vertically compressing f(x) by a units.
f(x - a) is shifting f(x) a units to the right.
f(x + a) is shifting f(x) a units to the left
In this question:
Vertically compressing by 1/2:
This is the same as multiplying the function by 1/2. So
The equation of the new function is
The slope is rise over run
3/5
Answer:
$560
Step-by-step explanation:
Given that :
Principal, P= $500
Interest rate, r = 12% per year
Amount in account after 1 year
Time = 1 year
Using the relation :
A = P(1 + rt)
A = final amount in account
A = $500(1 + 0.12(1))
A = $500(1 + 0.12)
A = $500(1.12)
A = $560
Answer:
8ab
Step-by-step explanation:
