To predict the change in a runner's finishing time with a wind speed of 4 meters/second, we'll use the given function:
[tex]\[ t = 0.0119s^2 - 0.308s - 0.0003 \][/tex]
Given that [tex]\( s = 4 \)[/tex] meters/second, we substitute [tex]\( s \)[/tex] with 4 in the function to find [tex]\( t \)[/tex]:
1. Substitute [tex]\( s = 4 \)[/tex] into the equation:
[tex]\[ t = 0.0119(4)^2 - 0.308(4) - 0.0003 \][/tex]
2. Calculate the square term:
[tex]\[ 4^2 = 16 \][/tex]
3. Multiply by the coefficient [tex]\( 0.0119 \)[/tex]:
[tex]\[ 0.0119 \times 16 = 0.1904 \][/tex]
4. Multiply [tex]\( 4 \)[/tex] by the coefficient [tex]\( -0.308 \)[/tex]:
[tex]\[ -0.308 \times 4 = -1.232 \][/tex]
5. Combine all the terms:
[tex]\[ t = 0.1904 - 1.232 - 0.0003 \][/tex]
6. Perform the calculations:
[tex]\[ t = 0.1904 - 1.232 = -1.0416 \][/tex]
[tex]\[ -1.0416 - 0.0003 = -1.0419 \][/tex]
So, the change in the runner's performance is approximately [tex]\( -1.0419 \)[/tex] seconds.
To round this result to the nearest hundredth, we observe the third decimal place to determine if we need to round up or down. Here, the third decimal place is 1, which means we round down:
Therefore, [tex]\( t \)[/tex] rounded to the nearest hundredth is:
[tex]\[ -1.04 \][/tex]
So, the predicted change in the runner's finishing time with a wind speed of 4 meters/second is:
[tex]\[ t \approx -1.04 \][/tex]
This means the runner finishes approximately 1.04 seconds faster.
