Need help on calculus problem

[2slow2go]

Hi guys i need help on a problem that we have to do for class at the end of the week.

Here is the problem.

There is two towns that are apart from each other. We must build a road from each town to the existing road. On this problem, you do not have exact values to work with so you need to assign letters to the distances you need for the problems: distance from one town to the road;distance from the other town to the road, and distance on the road that they are from each other( Constants A,B,C). That means we can make the roads to the existing road anyway we like as long as it a linear line.

Find the shortest distance connecting the two towns via the existing road.
First find a function for total amount of road to be built.

Possible ways i thought of solving this problem is pythagoreum theorum.

You can also have the two roads from the towns meet together at the existing road.

A hint from the teacher was using a optimization approach

here is a general picture.
http://i9.photobucket.com/albums/a72/vi3tst4/untitled.jpg

[MikeisNissan]

I wish i knew. I hate math.

[RiversideS13]

just fold the paper, than you will have shortest distance yay

[blasting_speed]

You lost me at "Hey guys i need....'' sorry. I say you go for the classic '' my dog ate my homework''. NEVER FAILS :o

[bbejj123]

sorry i took calculus two years ago and dont remember much of it...and dont need any more math for my career =)

[Impact Drift]

uhhhhhhhhhh false?

[s14sx]

I wish I could help you,but I didnt get the problem. may be just draw two lines somewhere on the existing road to find the shortest way?

[2slow2go]

the line can be drawn anyway as long as it is linear,

your sopose to find a function i guess? that shows the shortest distance

[240sx_sr20det]

I'm in Calculus, but its 12:45 and I was at a UNH party last night til 6:30 this morning, so as far as thinking goes...

I'm...

no..

help..


I'll check back in the morning.

[Dirty Dee]

The only thing i can think of off the top of my head is:
La= length of road from A to C
Lb= length of road from B to C
Lc= length of road C between roads A and B
Xa= x-component of road A
Xb= x-component of road B Xb>=Xa
La= sqrt[(A^2)+(Xa^2)]
Lb= sqrt{(B^2)+[(C-Xb)^2]}
Lc= Xb-Xa

Total road length= La+Lb+Lc

Is this a low or high lvl calc class?

Test boundary conditions ie: Xa=0, Xb=C, Xa=Xb=0 or Xa=Xb!=0 and plug in some values for A,B, and C to see which is shorter

[Helghast]

42.

The answer is ALWAYS 42.

[ZenkiCam]

OMG dirty D you hurt my brain... Math Money management FTW y0!

[2slow2go]

well im in high school but im taking the calculus class (math 124) at a college.

it basically a equation for total lenght of road to be built.

i guess you use derivitives of each road to see it minimum(shortest possible road) and do that for all three of them and somehow combine them together?

and the teacher said USE OPTIMIZATION in which i havent done hw for 1 chapter now so ima learn it tonite...

[powersteeringless180sx]

The only thing i can think of off the top of my head is:
La= length of road from A to C
Lb= length of road from B to C
Lc= length of road C between roads A and B
Xa= x-component of road A
Xb= x-component of road C Xb>=Xa
La= sqrt[(A^2)+(Xa^2)]
Lb= sqrt{(B^2)+[(C-Xb)^2]}
Lc= Xb-Xa

Total road length= La+Lb+Lc

Is this a low or high lvl calc class?

Test boundary conditions ie: Xa=0, Xb=C, Xa=Xb=0 or Xa=Xb!=0 and plug in some values for A,B, and C to see which is shorter


everything looks correct on the lengths but where does the x component come from?

[240sx_sr20det]

I'd said I'd help, but I can't. I have court, ahhhh.

Dirty Dee has most of it though. Good luck!

[Dirty Dee]

everything looks correct on the lengths but where does the x component come from?


the X components are the projections of the roads A and B on C

ie: if road A started at the origin and went 5 miles up and 3 miles right to point (3,5) Xa would be 3

and i accidentally labeled Xb as Xc, but corrected my first post

[2slow2go]

so you used pythareom theorum for road a and b? i still really dont get what you did with the x components(xb and xa). is it similar to if u have c-x for one side of the triangle when figuring out road a or b? or is it just 2 seperate variables for one side lenght of the triangle to calculate lenght of road a or b?

can you demonstrate it on the picture that i drew?

from all that i got?

lenght of road=sqrt[(A^2)+(Xa^2)]+sqrt{(B^2)+[(C-Xb)^2]}+Xb-Xa then?

sorrry for the trouble but thanks alot so far dirty dee

[Dirty Dee]

Here's the pic:
http://i110.photobucket.com/albums/n103/cg350z/calc.jpg

Now that i think about it, use the equation for the whole length of the road

the first derivative will give you the rate of increase of the road, i think.

the second derivative will give you max and minimum points( positive value will be min, negative will be max), and comparing the first and second derivative, you can see which point will be the shortest and which will be longest. When testing this, set either Xa as a constant with varying Xb, vice versa, or Xa=Xb

[exitspeed]

psssht. Easy.

It's 4.

Yea, just 4.

JK.

That's my stand-by answer to any type of math problem I can't figure out.

[g6civcx]

This is actually a challenging problem. Is the existing road longer than C?

[-=RS13=-]

Here's the pic:
http://i110.photobucket.com/albums/n103/cg350z/calc.jpg

Now that i think about it, use the equation for the whole length of the road

the first derivative will give you the rate of increase of the road, i think.

the second derivative will give you max and minimum points( positive value will be min, negative will be max), and comparing the first and second derivative, you can see which point will be the shortest and which will be longest. When testing this, set either Xa as a constant with varying Xb, vice versa, or Xa=Xb

use this approach. I had this on my Math 100 midterm back in the day. Let me see if i cand find it. It's a common problem that there are just tons of variations of