Need major Help with a few Calculus questions....

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???

Quote:

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Originally Posted by derekjonathon

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???

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Do you understand the idea between optimization? You always set up an equation and take the derivative in an effort to maximize or minimize, so the real challenge with these problems is normally setting up the equation(s)

For the 3rd problem you can be clever. You should know that the shortest distance between a point and a line is the distance of a new line, from your point perpindicular to the given line. This means that instead of using calculus, you can find the perpindicular line that goes through your point, find the intersection and use the distance formula. Or, use calculus

Please don't post more than three questions in a thread. Otherwise the thread can get convoluted and difficult to follow. Start new threads as necessary for remaining questions. eg. If you have five questions, post three of them in one thread and start a new thread for the remaining two etc.

And if the question has more than two parts to it, it is best to post only that question and its parts in the thread and start a new thread for other questions.

Please start new threads. Thread closed.