Question 1115545


{{{D(t) = 17t^2 - 100t}}} gives the distance a car going a certain speed will skid in {{{t }}}seconds. 

Find the time it would take for the car to skid {{{D(t) =190}}} feet.

{{{D(t) = 17t^2 - 100t}}}...substitute {{{D(t)}}}

{{{190 = 17t^2 - 100t}}}

{{{17t^2 - 100t-190=0}}}...use quadratic formula


{{{t = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

{{{t = (-(-100) +- sqrt( (-100)^2-4*17*(-190) ))/(2*17) }}}

{{{t = (100 +- sqrt( 10000+12920 ))/34 }}}

{{{t = (100 +- sqrt( 22920 ))/34 }}}

{{{t = (100 +- 151.39)/34 }}}...use positive value

{{{t = (100 + 151.39)/34 }}}

{{{t = 251.39/34 }}}

{{{t =7.39 }}} seconds