# Question #4c1d5

Mar 7, 2017

(Approximately) $91.3$ km/h

#### Explanation:

We are told
$\textcolor{w h i t e}{\text{XXX}} 80 = 0.0081 {s}^{2} + 0.137 s$

written in standard parabolic form:
$\textcolor{w h i t e}{\text{XXX}} 0.0081 {s}^{2} + 0.137 s - 80 = 0$

using the quadratic formula for solutions:
$\textcolor{w h i t e}{\text{XXX}} s = \frac{- 0.137 \pm \sqrt{{0.137}^{2} - 4 \times 0.0081 \times \left(- 80\right)}}{2 \times 0.137}$

with the help of a spreadsheet to do the calculations:
$\textcolor{w h i t e}{\text{XXX")s=91.28317433color(white)("XX")orcolor(white)("XX}} s = - 108.1967546$
and we can ignore the negative result as extraneous.