Given the differential equation x′=−(x+3)(x+1)3(x−1)2(x−2.5). list the constant (i. e. equilibrium) solutions to this differential equation in increasing order and indicate whether or not these solutions are stable, semi-stable, or unstable.

=-3       Stable

=-1       Instable

=1        Semistable

=2.5    Instable

Step-by-step explanation:

Equilibrium constant solutions (or critical points) occur whenever x′ = f(x) = 0

x′=−(x+3)(x+1)3(x−1)2(x−2.5)=0

=-3

=-1

=1

=2.5

we can see the plot of x′ = f(x) in the figure annexed. In order to analyse the stability of the constant solutions, we must see how the function changes around the constant solutions X's:

(i.) If f(x) < 0 on the left of X, and f(y) > 0 on the right of

X, then the equilibrium solution is unstable.

(ii.) If f(X) > 0 on the left of X, and f(y) < 0 on the right of

X, then the equilibrium solution y = c is stable.

(iii.) If f(x) > 0 on both sides of X, or f(x) < 0 on both

sides of c, then the equilibrium solution y = X is

semistable.

Then:

=-3       Stable

=-1       Instable

=1        Semistable

=2.5    Instable

the answer is 510

step-by-step explanation:

15 • 13 = 195

15 • 12 = 180

15 • 5 = 75

12 • 5 = 60

195 + 180 = 375

375 + 75 = 450

450 + 60 = 510

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺