Question

question 6 of 10
the finishing time for a runner completing the 200-meter dash is affected by
the tail-wind speed, s. the change, t, in a runners performance is modeled by
the function shown below:

t = 0.0119s² - 0.308s - 0.0003

predict the change in a runners finishing time with a wind speed of 3
meters/second. note: a negative answer means the runner finishes with a
lower time.

round to the nearest hundredth.

Explanation:

Step1: Substitute \( s = 3 \) into the function

We have the function \( t = 0.0119s^{2}-0.308s - 0.0003 \). Substitute \( s = 3 \) into it:
\( t=0.0119\times(3)^{2}-0.308\times(3)-0.0003 \)

Step2: Calculate each term

First, calculate \( 0.0119\times(3)^{2} \):
\( 3^{2}=9 \), so \( 0.0119\times9 = 0.1071 \)
Then, calculate \( 0.308\times3=0.924 \)

Step3: Combine the terms

Now, substitute these values back into the expression for \( t \):
\( t = 0.1071- 0.924-0.0003 \)
First, \( 0.1071 - 0.924=- 0.8169 \)
Then, \( -0.8169-0.0003=-0.8172 \)

Step4: Round to the nearest hundredth

Rounding \( - 0.8172 \) to the nearest hundredth, we look at the thousandth place, which is 7. Since \( 7\geq5 \), we round up the hundredth place. So \( - 0.8172\approx - 0.82 \)

Answer:

\(-0.82\)