Question 626697
Using Torrecelli's Principle, it can be shown that the depth d of a liquid
 in a bottle with a hole of area 0.5 cm^2 in its side can be approximated by
 d=0.0034t^2-0.52518t + 20, 
where t is the time since a stopper was removed from the hole.
 When will the depth be 10cm? Round to the nearest tenth of a second.
:
d = 10 cm find t
0.0034t^2-0.52518t + 20 = 10
:
0.0034t^2-0.52518t + 20 - 10 = 0
a quadratic equation
0.0034t^2-0.52518t + 10 = 0
use the quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
in this equation: x=t; a=.0034; b=-.52518; c=10
:
After a lot of tedious math, two solutions t=22.2 sec, t=132.2 sec