A cosine is just a sine shifted to the left by π/2. A cosine of 4x is shifted to the left by only π/8 because of the factor 4. Sketch them.
The region we're looking for is this sausage-shaped part between the cos and the sin.
The x intercepts are at π/8 for the cosine and π/4 for the sine. The midpoint between them is at (π/8 + π/4)/2 = 3/16π.
The region is point symmetric around the x axis, so the y coordinate of the centroid is 0.
So the centroid is at (3/16π, 0)
The value per share is 50 per share.
In order to find this, you take the total value of the stock and then divide by the number of shares.
200,000/4,000 = 50.
Therefore, it is 50 per share.
43
30
45
10
47
These are the answers in order
