ant problem

[taifast]

at time 0, an ant is moving at a constant speed in a straight line is at (0,-5,-3). At time 10, the ant is at the point (-4,-1,-1). all units are in inches and minutes.

1) what is the peed of the ant?
2) write a parametric equation that describes where the ant is after t minutes.
3) where is the ant after 1 minutes and 20 seconds?

 

[pka]

at time 0, an ant is moving at a constant speed in a straight line is at (0,-5,-3). At time 10, the ant is at the point (-4,-1,-1). all units are in inches and minutes.
1) what is the peed of the ant?
2) write a parametric equation that describes where the ant is after t minutes.
3) where is the ant after 1 minutes and 20 seconds?

Tell us what you have done so far on this problem.
How far did the ant move in ten minutes?

 

[taifast]

1) d=6 in so speed=6/10=.6in/min

2) vector from (0,-5,-3) to (-4,-1,-1) is (-4,4,2)

that is how i have gone

 

[pka]

\(\displaystyle \left\{ \begin{array}{l} x = \frac{{ - 4t}}{{10}} \\
y = - 5 + \frac{{4t}}{{10}} \\
z = - 3 + \frac{{2t}}{{10}} \\
\end{array} \right.\)

 

[taifast]

could you show me how you did that?

 

[pka]

could you show me how you did that?

Do you see that \(\displaystyle t=0\text{ gives }(0.-5,-3)\) and \(\displaystyle t=10\text{ gives }(-4.-1,-1)~?\)

Do you see where I used the vector \(\displaystyle <-4,4,2>~?\)

Why divide by 10?

 

[taifast]

yes, i see it now. thank you so much, i really appreciate it. are you a math teacher?

 

[taifast]

geometry problem

dear pka, could you please help me with this one too?

The triangle ABC has medians AD, BE, and CF, and centroid G. Medians AD and BE are perpendicular.


a)[FONT=&quot] [/FONT]1)What is the relationship of the length BC to the length GD?

b)[FONT=&quot] [/FONT]2)Prove that AG=BC

I solve the first problem, GD is 1/6 of BC. But there is no way that AG=BC, from what I can see, AG=2GD=2x1/6BC=1/3BC. What am I doing wrong?