Not answere just need point srry
6 pies.
If 8 teachers finish one whole pie, and they need to feed 47, then they need 6 pies with 8 slices each aka 48 slices total, there will be one slice leftover for the principal :D

has characteristic equation

which has roots at

. The negative root has multiplicity 2. So the general solution is
So 5,10,15,20,25,30,35,40,45 so Aylson needs 1 more bead. Because 45 beads are already used!
Answer:
The solution is 
Step-by-step explanation:
The equation

can be rewritten as

and can be further simplified to
.
Now, taking the inverse sine of both sides we get:


The value of the right side on the interval
is
,
which makes the equation (2)

solving for
gives

which is our solution.