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# minimum distance

Best Answer Yoruichi-san, 29 June 2014 - 09:07 PM

The height of point P, i.e. the distance between P and D.

Spoiler for Now that I have more time...
Go to the full post

13 replies to this topic

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Posted 25 June 2014 - 11:22 PM

A point P needs to be located somewhere on the line AD so that the total length L of cables linking P to the points A, B, and C is minimized. What is the minimum value of L?

My image won't upload so you can see it here:

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Posted 26 June 2014 - 12:12 AM

For those who can't access this image:

There is a triangle BPC where on one line segment BC there is a point D such that BD=2 and DC=3. Extending through P is a line segment going from some point A to D which is a distance of 5 and perpendicular to BC. Find the minimum total distance of all the "cables" by placing p in an optimal place.

Edited by BMAD, 26 June 2014 - 12:13 AM.

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Posted 28 June 2014 - 05:19 PM

hint: pythagoras is a straightforward approach

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### #4 plasmid

plasmid

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Posted 28 June 2014 - 07:40 PM

Would anyone who's able to access the image be able to attach it as a figure?
From the description, I'm not sure what the cables are whose distance needs to be minimized.
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### #5 kukupai

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Posted 28 June 2014 - 08:41 PM

#### Attached Images

Edited by kukupai, 28 June 2014 - 08:43 PM.

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### #6 bonanova

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Posted 28 June 2014 - 10:42 PM

I got the same figure.

But, with plasmid, I don't know where the cables are.

Assumption (from post 1): We are to minimize PA + PB + PC.

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Vidi vici veni.

### #7 Yoruichi-san

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Posted 29 June 2014 - 12:12 AM

Spoiler for I get...

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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

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### #8 plasmid

plasmid

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Posted 29 June 2014 - 03:12 AM

Thanks, kukupai.

I haven't fully worked out the equations, but I don't think that's it.

Spoiler for counterexample

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### #9 Yoruichi-san

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Posted 29 June 2014 - 04:07 AM

Spoiler for Corrected using mathematica

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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

Chromatic Witch links now on my 'About Me' page! Episode 3 is finally here!

When life hands me lemons, I make invisible ink.

### #10 bonanova

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Posted 29 June 2014 - 07:02 AM

Spoiler for Using iterative method

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Vidi vici veni.

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