Answer:
15.5 cm
Step-by-step explanation:
You want the difference between the values of x that make y=0. Solving for those values, we get ...
0 = -0.1(x -1)^2 +6
0 = (x -1)^2 -60 . . . . . . . . . multiply by -10
60 = (x -1)^2 . . . . . . . . . . . add 60
±√60 = x -1 . . . . . . . . . . . . take the square root
At this point, it should be obvious that the difference between the two solutions will be 2√60 = 4√15. If it is not, we can find the two solutions and take their difference:
x1 = 1 +√60
x2 = 1 -√60
Then the difference is ...
x1 -x2 = (1 +√60) -(1 -√60) = 2√60
60 has a square factor (4), so we can simplify this radical to ...
x1 -x2 = 4√15 ≈ 15.4919 ≈ 15.5
The ends of the rainbow are about 15.5 cm apart.
