Answer:

Step-by-step explanation:
S = Arc Lenth
θ = Radians
R = Radius
S = θR
So, now that we understand the formula, we will convert 72° into radians by introducing the equation
, x = 72
S = 
given that R = 10
S = 
S = 
We simplify 720 as 180 goes into 720 4 times and we get
S = 
Hope this helps
Take the homogeneous part and find the roots to the characteristic equation:

This means the characteristic solution is

.
Since the characteristic solution already contains both functions on the RHS of the ODE, you could try finding a solution via the method of undetermined coefficients of the form

. Finding the second derivative involves quite a few applications of the product rule, so I'll resort to a different method via variation of parameters.
With

and

, you're looking for a particular solution of the form

. The functions

satisfy


where

is the Wronskian determinant of the two characteristic solutions.

So you have




So you end up with a solution

but since

is already accounted for in the characteristic solution, the particular solution is then

so that the general solution is
22/4 cups. 1/2 times 2 is 1 cup. 11/4 times 2 is 22/4