Zweed From Netherlands, joined Apr 2004, 455 posts, RR: 0 Posted (9 years 10 months 9 hours ago) and read 1998 times:

It's sunday afternoon and my girlfriend is taking some math classes, she asked for my help and as I said, its sunday afternoon and I my total lack of math skills is even larger than they would be without this hang over,

A parking lot has the area of 900 sq. metres, it has be rectangular
A fence is going to be built around this lot.
What dimension will give us the least amount of money spent on the fence?

Backfire From Germany, joined Oct 2006, 0 posts, RR: 0
Reply 9, posted (9 years 10 months 7 hours ago) and read 1917 times:

Assume the parking lot is a rectangle with length x.

Its width must therefore be 900/x

Therefore the perimeter is twice the longer side plus twice the shorter side.

Perimeter P = 2x + 2(900/x)

Therefore P = 2x + 1800/x

From this equation it can be seen that, if x is small, P becomes very high because of the second term. Similarly if x is large, P also becomes high because of the first term. In between there is a value of x for which P becomes a minimum (minimum P, of course, means the shortest fence and the least cost).

To find the minimum of the P-x curve, you have to differentiate P with respect to x:

P = 2x + 1800/x

so: dP/dx = 2 - 1800/(x^2)

The minimum of the P-x curve is the point at which the slope (dP/dx) is zero.

Thus: 2 - 1800/(x^2) = 0

1800 = 2(x^2)

(x^2) = 900

and therefore x = 30

So the length is 30 and the width is (900/x) ... also 30.

It is indeed a square, but since a square is, by definition, rectangular, the problem is solved.

Kalakaua From United States of America, joined Jan 2004, 1516 posts, RR: 5
Reply 11, posted (9 years 9 months 4 weeks 1 day 19 hours ago) and read 1804 times:

Backfire has it... or at least has the jist of it. Other than that, everyone else is wrong!!!

Gravity explains the motions of the planets, but it cannot explain who set the planets in motion.