The museum's show for july features 30 oil painting by diferent artist. all artists show the same number of paintings and each artist shows more than 1 painting. how many artists could be featured in the show ? type of art : oil painting 30,photographs 24, sketches 21.

Since the function is not a reflection over the x-axis we know that the maximum of 20 reached is due to a translation up and not an increase in amplitude.

Basic form of a sinusoidal function: F(t) = A Cos(bt - c) + d

|A| = amplitude, distance from max/min to center of the graph.
b = frequency
2π/b = period
c = phase shift, shifts graph left/right
d = vertical shift

Given information:
max = 20 ; min = 0 so the amplitude is 20/2 , A = 10
Center of the graph is then shifted up 10 units. d = 10
period is 4 = 2π/b
b = π/2

* insert the values..
F(t) = 10 Cos(πt/2) + 10

 should look something like that. Maybe has a phase shift, c value or sine instead of cosine would still be a valid solution.