Anyone care to help me with these?

1. A man lives on an island 1 km from the mainland. The library is 3 km along the shore from the point on the shore closest to the island. The man can paddle his canoe at 3 km/h and jog at 5 km/h. Where should he land on the shore in order to get to the library in the shortest possible time?

2. A straight section of railroad track crosses two highways at points 400m and 600m respectively, from an intersection. Determine the largest rectangle lot that can be laid in the triangle formed by the railroad and the highways.

3. Determine the maximum volume of a box that can be constructed with 3000 cm(squared) of material such that the box has a square base and no top.


I'll need em by wednesday. Thanks

..Aight..

..I'll try to get bacc to you by the end of my lunch break today..

~1ne

..I still have a few hours until I take my lunch. Too much crap to finish. I figured I'll do one in the meantime while I worked..

3) X = 31.62; Y = 15.81; Volume = 15,810

..If you need the work written out, I can try to scan the sheet I scribbled on. I'm pretty sure that it's correct, though I don't have a graphing calculator with me, because I checked it by pluggin' in the numbers into the surface area equation..

..I'll try to get to the other two when I can. If for some reason I can't, I apologize..


~1ne

good, that's the answer I got for that one. It's already been handed in but I appreciate it man. Thanks!

I got the same x and y dimensions but a different volume... looks like you mixed up which dimension was which when you plugged em back into the volume equation. 15.81 is the length & width, 31.62 the height... I get volume = 7904cm^3

First question:

He should land 2.25km from the library along the shore

Second:

I assume the highways intersect at a right angle? If not I can't think how to do it... you'd have too many variables to get a straight numeric answer... anyway, assuming it IS a right angle I get the max area of the rectangle to be 79600m^2 ... not as sure about this one as the other two though...

I'd be interested to know what the answers were if you got them?

^yahoo