Find the general solution to the differential equation modeling how a person learns: Dy/dt=100-y. Then find the particular solutions with the following initial conditions:
y(0)=35: y=
y(0)= 125: y=
Plot the slope field of this differential equation and sketch the solutions with y(0) = 35 and y(0) = 125. Which of these two particular solutions could represent how a person learns?
A. y(0) =35
B. y(0) = 125.
C. either of these
D. none of the above

y=mx+b

step-by-step explanation:

m is slope, b is y-intercept

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation:

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: