Need help understanding two questions.

S

Student 26608

New member
Joined
Feb 4, 2006
Messages
3
Hi, I need some assistance understanding the following two questions:

---------------------------

Kim is in a boat 3 km from the nearest point O to a straight beach. Her destination, D, is 6 km along the beach from O. Kim knows that she can row at 4 km/h and walk at 5 km/h.

a), b) and c) have been completed (if you need those, I can type them up).

d) By using the length of variable x as shown in the diagram below, determine a mathematical relationship which will allow Kim to calculate the total time for any route of this type. Use your graphic calculator to sketch this graph over the domain [0,6], and provide a copy of this in your report. Describe and discuss key features of this graph.

e) Find and describe the route for which her travelling time will be the least, and compare this with the 2 routes you have already investigated.

traveltime8bz.jpg


---------------------------

I have no idea what a mathematical relationship is, or what a domain is. Any help would be appreciated.

Thanks in advance

- Student 26608
 
Mathematical relationship: an equation relating your two variables (x and a distance along the beach, presumably), probably involving Pythagoras here, which you can use to write an equation for total time in terms of just one variable, and then graph.

A domain of [0, 6] on your calculator means to set the x-axis from 0 to 6.
 
I forgot to include the diagram, I don't know if it makes any difference to what you said now. Sorry.

Mathematical relationship: an equation relating your two variables (x and a distance along the beach, presumably), probably involving Pythagoras here, which you can use to write an equation for total time in terms of just one variable, and then graph.
Click to expand...
I've been using
Code: 
        distance
time = ----------
         speed
to calculate how long it would take. I'm not sure how I could incorporate Pythagoras here or even how to graph it (all that I get with the above formula is a straight line) :?
 
The total time to reach point D from B is (time from B to C)+(time from C to D)

=\(\displaystyle \frac{6-x}{r_{w}}+\frac{sqrt{x^{2}+9}}{r_{r}}\)

where \(\displaystyle r_{w}\) and \(\displaystyle r_{r}\)= the respective rates for walking and

rowing.

So, we have:

t=\(\displaystyle \frac{6-x}{5}+\frac{sqrt{x^{2}+9}}{4}\)

Now, differentiate, set to 0, and solve for x to find e(the minimal time).
 
You must log in or register to reply here.
Top