A Rubber Band Problem?

Question

The ends of a relaxed rubber band are held above the 1-inch and 10-inch marks on a 12-inch ruler. The band is then stretched so that its ends line up with the ends of the ruler. Find all points of the band, if any, that end up where they started.

Nick · Accepted Answer

Step 1: Fix right end of band at 10'' and stretch 1'' to the left (scale points factor 10/9).
................ ......... |------ (10/9)(10 - x) --------------|
|<------- | ------------ | ------- | ------------------------------ X| -------------|
0 ...... 1 ........... y ....... x ............... ............... 10 ........... 12

Step 2: Fix left end of the band at 0'' and stretch 2'' to the right (scale points factor 12/10).
|-------- (12/10)y -----------|
|X --------------------- | ------- | ------------------------------ | ------------->|
0 ...................... y ........ x ............... ............. 10 .......... 12

Then we require

(12/10)y = x
(12/10)(10 - (10/9)(10 - x)) = x
12(x - 1)/9 = x
12x - 12 = 9x
3x = 12
x = 4''

? · Answer

Sqdancefan,

For some reason, Yahoo! won't let me respond to your email about the equation editor that I use. 
I use MathType by Design Science http://www.dessci.com/en/products/mathtype/

It came free when I bought a copy of Microsoft Office more than 10 years ago!

A Rubber Band Problem?

2 個解答