Please help me with this.
The finishing time for a runner completing the 200-meter dash is affected by the tail-wind speed, s. The change, t, in a runner's performance is modeled by the function shown below:
t= 0.0119s^2 - 0.308s - 0.0003
Predict the change in a runner's 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.
Thank you, Damon. Now I can do my other problems on my own :)
Ah, the ever-fascinating world of running and wind speeds! Let's find out how the wind affects a runner's finishing time, shall we?
According to the function you provided, the change in a runner's performance, labeled as "t," can be calculated using the formula t = 0.0119s^2 - 0.308s - 0.0003. And you want to know what happens when the wind speed, "s," is 3 meters per second. Fascinating!
So, let's plug in that wind speed value of 3 into our function and see what happens. Mathematically, that would look like this:
t = 0.0119(3)^2 - 0.308(3) - 0.0003
Now, let's do some mathemagic:
t = 0.0119(9) - 0.924 - 0.0003
t = 0.1071 - 0.924 - 0.0003
t = -0.8162
So, based on the calculations, with a wind speed of 3 meters per second, the change in the runner's finishing time is -0.8162 (rounded to the nearest hundredth).
In simpler terms, it means the runner's finishing time is estimated to be about 0.82 seconds faster with that particular tailwind. Remember, a negative value implies a decrease in time. Hopefully, that doesn't blow your mind too much!
To predict the change in a runner's finishing time with a wind speed of 3 meters/second, we need to substitute the value of s (wind speed) into the given function and evaluate it.
The function is:
t = 0.0119s^2 - 0.308s - 0.0003
Substituting s = 3 into the function:
t = 0.0119(3)^2 - 0.308(3) - 0.0003
Simplifying the equation:
t = 0.0119(9) - 0.924 - 0.0003
t = 0.1071 - 0.924 - 0.0003
t ≈ -0.8162
Since the problem specifically states that a negative answer means the runner finishes with a lower time, we can interpret this result as the runner's finishing time will be approximately 0.8162 seconds lower with a wind speed of 3 meters/second.
Remember to round your answer to the nearest hundredth, so the predicted change in the runner's finishing time with a wind speed of 3 meters/second is -0.82 seconds.
That is interesting, a little tailwind helps but a lot hurts. also zero has an effect? why?
anyway
if s = 3
t = .0119 *9 - .308 *3 - .0003
t = +.1071 - .924 - .0003
t = -.8172 seconds (wow, a lot)
= -.82 rounded