Answer:
3.856 seconds
Step-by-step explanation:
Set d=10 and solve for t.
10 = -12t^2 -3t +200
12t^2 +3t -190 = 0 . . . . . . subtract the expression on the right to put into standard form
This is a quadratic equation, so the quadratic formula can be used to find solutions. That formula tells you the solution to ...
ax^2 +bx +c = 0
is
x = (-b ±√(b² -4ac))/(2a)
__
We have a=12, b=3, and c=-190. The variable in our equation is t, not x. Putting these values into the formula, we find ...
t = (-3 ±√(3² -4(12)(-190)))/(2·12)
t = (-3 ±√9129)/24
t = (-3 ±95.546)/24 = -4.106, +3.856
The coconut will be about 10 ft off the ground after 3.856 seconds.
