Alan

I would call that standard form! If you mean scientific form it is 1.55*10^4

Ok, an internet search suggests that standard form is another way of saying scientific form!

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Turn these upside down to get the X on top

x/sin(32) = 16/sin(98)

Now multiply both sides by sin(32)

x = 16*sin(32)/sin(98)

Now use a calculator.

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They stick to the wet posts and the wet glass (and themselves) via surface tension.

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Your last line is correct.  

However, your 2nd line should start with a 36, not just a 3; and your third line should say y^2 = 81/36 (you take the square root in the next line).

Your fourth line should say y = ±9/6 as 9 is the square root of 81 and 6 is the square root of 36

Now 9/6 = 3*3/(2*3) 

So y = ±3/2  (or ±1.5)

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Here's a photo of the soap film solution:

Thanks, but I can't really take credit for it - it's a well-known optimisation problem, I've come across various versions of it dozens of times before.

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Because you are Anonymous we can't see your images (I recommend that you register).  However, I think the minimum road length configuration will probably look something like the following:

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Thanks all.

Melody, I hope that's not meant to be me blowing my own trumpet!

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