The length of a car's skid mark in feet is given by L=0.046s2−0.199s+0.264,where sis the car's speed in miles per hour. If the length of a skid mark is 100feet, find the speed in miles per hour the car was traveling.

Question

anonymous · Answer

@aum

anonymous · Answer

@Jared25

anonymous · Answer

@1DEA

anonymous · Answer

$$L=0.046s ^{2}-0.199s+2.264$$ correct?

aum · Answer

Solve for s:  $$100 =  0.046s^2−0.199s+0.264$$

anonymous · Answer

yes, that is correct, but I am not sure how to solve it

anonymous · Answer

@aum @jared25

aum · Answer

$$
100 =  0.046s^2−0.199s+0.264 \
\text{Subtract 100:}\
0 = 0.046s^2−0.199s-99.736 \
0.046s^2−0.199s-99.736 = 0 \
\text{Divide by 0.046:}\
s^2 - 4.3261s - 2168.17 = 0 \
s = \frac{4.3261 \pm \sqrt{(-4.3261)^2 -4*1*(-2168.17)}}{2*1}  = 
 \frac{4.3261 \pm 93.2277}{2}  = 48.8, - 44.5 \
s = 48.8 \text{ miles / hour}$$