This is a space for 803's math class. Your first assignment on this website is to post a comment about how your Christmas was, by 5pm, Friday, December 26th.
Make sure you include your name so you get credit!
Tuesday, December 23, 2008
Merry Christmas!
There are several parts to this problem. Your assignment is to post a comment that shows all your work. If you find it difficult to type out your solution, you can also hand-write it out, scan it, and e-mail it to me at jas.tsui@gmail.com .
If you get stuck, you can post your partial work as a comment. Check back, and I will occasionally post hints!
You can post your solution any time you like, but it is due Sunday, January 4 by 5pm. At 5pm, all comments will be posted and no further homework will be accepted.
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The problem:
Santa is in trouble! He has a dozen houses to visit, and if he wants to get to them all on Christmas Eve he needs to do it in the right order. However, he has lost his directions! Help Santa find the correct order in which he needs to visit each house so he can make it in time.
There are 12 houses total. Santa only needs to fly over each house to make the delivery. It's a common misconception that Santa actually goes down the chimney: he actually just flies overhead and drops them down. What actually takes up the most time is changing direction. His reindeer fly at nearly light-speed in straight lines, but they have poor handling at such high speeds. In order to turn, they need to slow down to regular speed, turn, and then speed up again. So, since Santa needs to use the least amount of time as possible, he wants to turn as few times as he can.
Here are the basic requirements:
1) Santa can only travel in straight lines.
2) Santa wants to have as few lines as possible.
3) Santa needs to start and end at the North Pole (the origin).
Part 1)
Let the letter t be the number of turns he has to make. It takes Santa's reindeer 10 minutes to make each turn.
Write an expression for the amount of time it takes Santa to make all his deliveries.
Part 2)
Find Santa's path!
Find the co-ordinate location (x, y) for each of the 12 houses. Then, tell which order Santa travels to each house. Give your answer as a list. How many different lines does Santa need?
Part 3)
For each line that you drew, find the equation of this line in slope-intercept form.
y = mx + b
m is the slope, and b is the y-intercept.
Part 4)
Santa has one hour to make all his deliveries in this part of the world. (He goes to bed early. He's old, you know.) Write an inequality relating your expression from part (1) to this time limit.
Part 5)
Solve the inequality. Then, check your answer with the number of turns you found in part (3). Does Santa make it in time?
If you get stuck, you can post your partial work as a comment. Check back, and I will occasionally post hints!
You can post your solution any time you like, but it is due Sunday, January 4 by 5pm. At 5pm, all comments will be posted and no further homework will be accepted.
-----------------------------------------------
The problem:
Santa is in trouble! He has a dozen houses to visit, and if he wants to get to them all on Christmas Eve he needs to do it in the right order. However, he has lost his directions! Help Santa find the correct order in which he needs to visit each house so he can make it in time.
There are 12 houses total. Santa only needs to fly over each house to make the delivery. It's a common misconception that Santa actually goes down the chimney: he actually just flies overhead and drops them down. What actually takes up the most time is changing direction. His reindeer fly at nearly light-speed in straight lines, but they have poor handling at such high speeds. In order to turn, they need to slow down to regular speed, turn, and then speed up again. So, since Santa needs to use the least amount of time as possible, he wants to turn as few times as he can.
Here are the basic requirements:
1) Santa can only travel in straight lines.
2) Santa wants to have as few lines as possible.
3) Santa needs to start and end at the North Pole (the origin).
Part 1)
Let the letter t be the number of turns he has to make. It takes Santa's reindeer 10 minutes to make each turn.
Write an expression for the amount of time it takes Santa to make all his deliveries.
Part 2)
Find Santa's path!
Find the co-ordinate location (x, y) for each of the 12 houses. Then, tell which order Santa travels to each house. Give your answer as a list. How many different lines does Santa need?
Part 3)
For each line that you drew, find the equation of this line in slope-intercept form.
y = mx + b
m is the slope, and b is the y-intercept.
Part 4)
Santa has one hour to make all his deliveries in this part of the world. (He goes to bed early. He's old, you know.) Write an inequality relating your expression from part (1) to this time limit.
Part 5)
Solve the inequality. Then, check your answer with the number of turns you found in part (3). Does Santa make it in time?
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