Answer:
The solution to the differential equation
y' = 1 + y²
is
y = tan x
Step-by-step explanation:
Given the differential equation
y' = 1 + y²
This can be written as
dy/dx = 1 + y²
Separate the variables
dy/(1 + y²) = dx
Integrate both sides
tan^(-1)y = x + c
y = tan(x+c)
Using the initial condition
y(0) = 0
0 = tan(0 + c)
tan c = 0
c = tan^(-1) 0 = 0
y = tan x
Answer:

Step-by-step explanation:
Recall that the formula for the length of an arc of circumference is given by the formula:

where
is the radian form of central angle subtended , and R is the radius of the circumference. What is important is to have the angle given in radians for this formula to be valid.
In our case, the angle (
) is already in radians, so we can apply the formula directly:

Terminating, because it ends. If it was repeating it would go in infinitely, like Pi.
Answer:
45595
Step-by-step explanation:
plug in 7 for n and solve
This is the population 7 years after 2002(2009)