# Math Help - Distance between two bugs

1. ## Distance between two bugs

Here the question is:
Two bugs are walking along lines in 3-space. At time t bug 1 is at the point (x; y; z) on the line
x = 4 - t; y = 1 - t; z = 2 + t
and at the same time t bug 2 is at the point (x, y, z) on the line
x = t; y = 1 + t; z = 1 + 2t
Assume that the distance is in centimeters and that the time is in minutes.
(a) Find the distance between the bugs at time t = 0.
(b) Use a graphing utility to graph the distance between the bugs as a function of time from t = 0 to t = 5.
Please print out a copy of your graph. [You may use an online graphing program, or you can also use
the virtual TI on your computer, and save the image of your plot by right clicking on the graph and
choosing Take Screenshot and choosing LCD only, black/white (BMP)]
(c) What does the graph tell you about the distance between the bugs?
(d) How close do the bugs get? (Please be exact.)

My problem was i stucking at this question part c and d.
The answer for question part a and b,

a)When t=0
Distance between the bugs = 4.123 cm

b) when t= 1, Distance=2.236cm
when t=2, distance = 2.236cm
when t=3, distance = 4.123cm
when t=4, distance = 6.403cm
when t=5, distance = 8.775cm

2. Originally Posted by wkn0524
Here the question is:
Two bugs are walking along lines in 3-space. At time t bug 1 is at the point (x; y; z) on the line
x = 4 - t; y = 1 - t; z = 2 + t
and at the same time t bug 2 is at the point (x, y, z) on the line
x = t; y = 1 + t; z = 1 + 2t
Assume that the distance is in centimeters and that the time is in minutes.
(a) Find the distance between the bugs at time t = 0.
(b) Use a graphing utility to graph the distance between the bugs as a function of time from t = 0 to t = 5.
Please print out a copy of your graph. [You may use an online graphing program, or you can also use
the virtual TI on your computer, and save the image of your plot by right clicking on the graph and
choosing Take Screenshot and choosing LCD only, black/white (BMP)]
(c) What does the graph tell you about the distance between the bugs?
(d) How close do the bugs get? (Please be exact.)

My problem was i stucking at this question part c and d.
The answer for question part a and b,

a)When t=0
Distance between the bugs = 4.123 cm

b) when t= 1, Distance=2.236cm
when t=2, distance = 2.236cm <<<<<<
when t=3, distance = 4.123cm <<<<<< typo: The distances should be shifted one step up
when t=4, distance = 6.403cm <<<<<<
when t=5, distance = 8.775cm
1. From the graph of the distance function you see that the bugs come first closer to each other and afterwards the distance increases.

2. Obviously the distance is shortest around t = 1. To get the exact value you have to differentiate the distance function

$d(t)=\sqrt{9t^2-18t+17}$

wrt t and solve the equation d'(t) = 0 for t. You'll get t = 1 and thus the minimum distance is $d_{min} = d(1) = \sqrt{8}$

3. c) The distance will be increase
d) Closest distance will be when time = 1.5

4. Thanks for helping. But i think i will using hand drawing and not using Ti calculator to draw. Because im till do not know how to using that function yet.