A more detailed version of Theorem I says that, if the function f (x, y) is continuous near the point (a, b), then at least one solution of the differential equation y' = f(x, y) exist on some open interval I containing the point x = a and moreover, that if in addition the partial derivative partial differential f/partial differential y is continuous near (a, b), then this solution is unique on some (perhaps smaller) interval J. In Problems 11 through 20, determine whether existence of at least one solution of the given initial value problem is thereby guaranteed and, if so, whether uniqueness of that solution is guaranteed. dy/dx = 2x^2y^2: y(1) = -1
dy/dx = x ln y: y(1) = 1
dy/dx = cubicroot y: y(0) = 1
dy/dx = cubicroot y: y(0) = 0
dy/dx = Squareroot x- y: y(1) = 2
dy/dx = Squareroot x - y: y(2) = 2
dy/dx = Squareroot x - y: y(2) = 1
y dy/dx = x - 1: y(0) = 1
y dy/dx = x - 1: y(1) = 0
dy/dx = ln(1 + y^2): y(0) = 0
dy/dx = x^2 - y^2: y(0) = 1

step-by-step explanation:

answer:

step-by-step explanation:

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 ☺