Hi all - my homework is kicking my butt this week. Normally I do ok, but some questions have me stumped.
1.A rancher wants to fence in an area of 1500000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?
Note: the answer is to be the length of fence which is a minimum, not the length of a side which achieves that minimum.
2.Let Q = (0,5) and R = (10,6) be given points in the plane. We want to find the point P = (x,0) on the x axis such that the sum of distances PQ+PR is as small as possible.
To solve this problem, we need to minimize the following function of x: f(x) = ?
over the closed interval [A,B] where A = ? and B = ?
3.Find the length of the shortest line from the origin to the line y = 1-5x
4.A racer can cycle around a circular loop at the rate of 3 revolutions per hour. Another cyclist can cycle the same loop at the rate of 5 revolutions per hour. If they start at the same time (t=0), at what first time are they farthest apart?
5.Two men are at opposite corners of a square block which is 500 feet on a side. They start to walk at the same time; one man walking east at the rate of 3 feet per second, and the other walks west at the rate of 2 feet per second. At what time are they closest?
6.A rectangle is to be drawn in the first quadrant with one leg on the y-axis, and the other on the x-axis, and a vertex on the curve y = 1-.22x^2 Find the coordinates of that vertex which form the rectangle of greatest area.
How do I figure this stuff out???