Problem Statement: Kevin needs to decide on the number of platforms he wants built, the height of the first platform, and the difference in height between platforms, in order for Camilla to build and decorate the structures. In this P.O.W we had to create two formulas that will solve all his problems instantly.
Process: I started by finding the components of each equation in order to find the variables needed in my equation. I used slope intercept form to show the increase in platforms as you move over. I then used Desmos to figure out the order they needed to be in. I just plugged in different random numbers until I got what I thought was right.
Solution: My two formulas found for this P.O.W. were h=p-id and h=l+d. In the first formula id determines the increased distance between the pillars, p represents the peak (height) of the tallest platform. For the second problem l is the length of the total amount of materials needed and d is the distance.
Formula 1: (h (d) = p - id = (h = p - id)): Height of tallest platform
Distance
Height
Peak
Increase in distance from platform to platform
Formula 2: (h = l + d): Length of total colorful material needed
Distance
Height
Length
Reflection: I tried my best on this P.O.W. but I don’t think I got the correct formulas. I believe if I spent more time plugging numbers into Desmos I would maybe be able to get my formulas correct. I think I could have done it better with more explanation/help understanding what it was asking. It was pretty confusing but a couple friends helped me get on the right track. I also think I over complicated it for no reason and realized it was somewhat easier than I thought.
P.O.W. #3
Problem Statement: The task of this POW was to find a pattern/ general rule that will determine the chair to sit in, in order to become the “winner” at King Arthur's table. King Arthur chooses his winner by seating the knights at a round table, and going around the table numbering off one two telling ones there in and twos there out. King Arthur continues doing this with the remaining ones telling them out or in the last person sitting at the table is King Arthur's table winner.
Process: I started by making columns for a lot of different numbers of knights after showing the winning knights for numbers 1 through 19 I found a pattern but it was very difficult to define with a formula/ equation. I continued my list to 31 in order to better define the pattern I found. I noticed that the winning knight was always an odd consecutive number, (1 - 1, 3 - 1, 3 ,5, 7, -1, 3, 7, 5, 9) I also found that the pattern was at the start of each power of 2, number of knights. (2 to the 1st power=2) (2 2nd power=4) so on and so forth. When the number of knights is a power of two the pattern begins at 2, 4, 8, 16, 32. The difference between the number of knights and winning seats were consistent.
At the start of the pattern 8 knights (8-1=7) The difference is always one less than the number of knights at the table The next number of knights 9 knights (9-6=3)
Solution: After I found multiple patterns within this problem I looked at it all together and finally found a formula to determine the winning seat at King Aurthur's regardless of how many knights are at the table. If you subtract from the number of knights the largest power of 2 less than it, multiply the answer by 2, and then add 1, you will figure out the winning seat number. Ex. If there are 13 knights at the round table, and 8 is the largest power of 2 that is less than 13, you would do the following
13 – 8 = 5
5 x 2 = 10
10 + 1 = 11
The winning seat is 11 if there were 13 knights around the table.\
Steps To Find Winning Seat:
Find the greatest power of 2 (less than # of knights)