Answer:
y=4 sin(4x)
Step-by-step explanation:
So you are given y(0)=0. This means when x=0, y=0.
So plug this in:
0=c1 cos(4*0)+c2 sin(4*0)
0=c1 cos(0) +c2 sin(0)
0=c1 (1) +c2 (0)
0=c1 +0
0=c1
So our solution looks like this after applying the first boundary condition:
y=c2 sin(4x).
Now we also have y(pi/8)=4. This means when x=pi/8, y=4.
So plug this in:
4=c2 sin(4*pi/8)
4=c2 sin(pi/2)
4=c2 (1)
4=c2
So the solution with the given conditions applies is y=4 sin(4x) .
Testing:
y'=16 cos(4x)
y''=-64 sin(4x).
y''+16y=0
-64 sin(4x)+16(4 sin(4x))
-64 sin(4x)+64 sin(4x)
0
So the solution still works.
I got -441 hope this helps you
Answer:
d
Step-by-step explanation:
11.85 which rounds to 12, 12 should be the correct answer
110