duskystarlight
New member
- Joined
- Feb 25, 2006
- Messages
- 3
I apologize if this is in the wrong category-- it'll just prove that I -really- don't know what I am doing. So, I'm taking IMP III [unfortunately] and if I do not hand in the redo of my Problem of the Weeks in on Monday, I will recieve NO CREDIT. Which isn't cool. So, I've already tried to do this problem and I obviously did something...wrong. I'm going to just type out the problem and hopefully, someone will be able to help me with what I have.
EQUALLY WET
1. Two delicate flowers were planted in a garden. The gardener, Leslie, hs a sprinkler that sprays water around in a circle. The closer a flower is to the sprinkler, the more water it gets. to be sure that her flowers each get the same amount of water, Leslie needs t o place the sprinkler where it wil lbe the same distance from each of the flowers. What are her choices about where to put the sprinkler? Describe all possibilities. The flowers are already in place and Leslie needs to adjust the position of the sprinkler relative to the flowers.
2. Now suppose Leslie plants three flowers and wants to know if it will still be possible to place the sprinkelr the same distance from all three.
3. What about four flowers? Five flowers? Generalize as much as you can.
We're suppoused to put this problem into "mathematical terms" instead of using flowers and other nonsense. So that means that there is perpendicular bisectors and line segments and all that stuff. *sigh* FOr the first question, I said that the sprinkler should be placed at the midpoint between the two flowers. THe easiest way is to use the two flowers to make a square, rhombus, or other rectangular shape- the two points being crucial. Then, by seperating the shape into two sections the midpoint can be reached by using the midpoint formula, as long as you have coordinates for the points. Otherwise, it is natural to easily assume the midpoint with a simple and accurate sketch.
ALSO: I've determined that [for three points and you want another point to be equidistant from the three points] you place the final point where all three of the perpendicular bisectors meet or cross, for it will always be equidistant from all te other points. Apparently, all my other work is rubbish, so if anyone can give me a helping hand... that would be terrific.
Thanks!
EQUALLY WET
1. Two delicate flowers were planted in a garden. The gardener, Leslie, hs a sprinkler that sprays water around in a circle. The closer a flower is to the sprinkler, the more water it gets. to be sure that her flowers each get the same amount of water, Leslie needs t o place the sprinkler where it wil lbe the same distance from each of the flowers. What are her choices about where to put the sprinkler? Describe all possibilities. The flowers are already in place and Leslie needs to adjust the position of the sprinkler relative to the flowers.
2. Now suppose Leslie plants three flowers and wants to know if it will still be possible to place the sprinkelr the same distance from all three.
3. What about four flowers? Five flowers? Generalize as much as you can.
We're suppoused to put this problem into "mathematical terms" instead of using flowers and other nonsense. So that means that there is perpendicular bisectors and line segments and all that stuff. *sigh* FOr the first question, I said that the sprinkler should be placed at the midpoint between the two flowers. THe easiest way is to use the two flowers to make a square, rhombus, or other rectangular shape- the two points being crucial. Then, by seperating the shape into two sections the midpoint can be reached by using the midpoint formula, as long as you have coordinates for the points. Otherwise, it is natural to easily assume the midpoint with a simple and accurate sketch.
ALSO: I've determined that [for three points and you want another point to be equidistant from the three points] you place the final point where all three of the perpendicular bisectors meet or cross, for it will always be equidistant from all te other points. Apparently, all my other work is rubbish, so if anyone can give me a helping hand... that would be terrific.
Thanks!
