To determine the stopping distance [tex]\( W \)[/tex] on a wet road when a car is traveling at [tex]\( x = 60 \)[/tex] miles per hour, you'll use the given equation:
[tex]\[ W(x) = 0.02 x^2 + 0.5 x \][/tex]
Here, we need to substitute [tex]\( x = 60 \)[/tex] into the equation.
Let's break down the steps:
1. Substitute [tex]\( x = 60 \)[/tex] into [tex]\( W(x) \)[/tex]:
[tex]\[ W(60) = 0.02 \cdot 60^2 + 0.5 \cdot 60 \][/tex]
2. Calculate [tex]\( 60^2 \)[/tex]:
[tex]\[ 60^2 = 3600 \][/tex]
3. Multiply [tex]\( 0.02 \)[/tex] by [tex]\( 3600 \)[/tex]:
[tex]\[ 0.02 \cdot 3600 = 72 \][/tex]
4. Multiply [tex]\( 0.5 \)[/tex] by [tex]\( 60 \)[/tex]:
[tex]\[ 0.5 \cdot 60 = 30 \][/tex]
5. Add the results from steps 3 and 4 to find [tex]\( W(60) \)[/tex]:
[tex]\[ 72 + 30 = 102 \][/tex]
Thus, the stopping distance when the car is traveling at 60 miles per hour on a wet road is [tex]\( 102 \)[/tex] feet.
Therefore, the final answer is:
[tex]\[ W(60) = 102 \text{ feet} \][/tex]
