Thread: parametrics!

this is a true/false question, and i know i can use a graphing calculator, but i dont quite remember how to do it, or what signifies this to be true or false. help please!

two runners are 100 ft. apart. On a signal, they run to a flag on the ground midway between them. The faster runner hesitates for 0.1 sec. The following parametric equations model the race to the flag:

x1=10(t-.1)
y1=3

x2=100-9t
y2=3

Use your graphing calculator to simulate the race. Based on this simulation, runner x1/y1 wins the race.

Assuming that you have a TI-83/84...

Hit MODE, then change "FUNC" to "PAR", and "SEQUENTIAL" to "SIMUL".

Hit Y=, and then enter in your equations.

Hit WINDOW, then change the viewing dimensions to the following (these are my suggestions):
Xmin=0
Xmax=100
Xscl=10
Ymin=2
Ymax=4
Yscl=1
(I didn't mention the t-values; it's possible that you won't need to change them.)

Then hit GRAPH. Hopefully, you'll get a simulation.

I don't know if X1/Y1 wins the race or not, because on my calculator the graphs were rendered rather quickly. It might help if you figure out a set of parametric equations that will put a single, short line segment in the middle (at x = 50) to indicate the flag.

Don't forget to change the settings back in MODE when you're done.