Year Reflection
The main thing I learned is how to use matrices, and that is all I can really think about. The most difficult part from this class was the POWs, they where too confusing and I had to figure out a lot of loopholes around them to I do not have to destroy my brain trying to get around them. I cannot really remember the units that well, so I cannot really speak much for this class. So overall, not my best class, but John is a good teacher.
Best POW
Problem statement
How many possible 3 digit codes might a safe’s lock have?
Process
What you are supposed to do would take forever and is really quite unnecessary. So I have my own process of how to get into the safe which does not involve finding any codes. The youtuber Mr Beast has shown many instances of people breaking open these kinds of safes, but other than using codes, they use pickaxes and sledgehammers. So the solution, get yourself a pickaxe, and go at that thing until it busts open. It might take a while, but eventually you should get there.
Solution
Bust that thing open with a pickaxe and save a little bit of brain power?
Reflection
Yeah I might have to redo this one, and it is my fault. I really got to stop procrastinating on the POWs. Actually, a better idea. I think John is giving us WAY too much POWs. I am getting kind of sick of them. We just WAY too many POWs when we could be doing better things. By this point it is kind of lazy to just keep giving us POWs. In conclusion, John, please lay off the POWs or at least don’t give us as much.
How many possible 3 digit codes might a safe’s lock have?
Process
What you are supposed to do would take forever and is really quite unnecessary. So I have my own process of how to get into the safe which does not involve finding any codes. The youtuber Mr Beast has shown many instances of people breaking open these kinds of safes, but other than using codes, they use pickaxes and sledgehammers. So the solution, get yourself a pickaxe, and go at that thing until it busts open. It might take a while, but eventually you should get there.
Solution
Bust that thing open with a pickaxe and save a little bit of brain power?
Reflection
Yeah I might have to redo this one, and it is my fault. I really got to stop procrastinating on the POWs. Actually, a better idea. I think John is giving us WAY too much POWs. I am getting kind of sick of them. We just WAY too many POWs when we could be doing better things. By this point it is kind of lazy to just keep giving us POWs. In conclusion, John, please lay off the POWs or at least don’t give us as much.
Personal rate of change problem
I am filling up a Ford f150 with gas. The gas pump I am using is filling up the gas tank with 1.5 gallons of gas every 10 seconds. The f150 gas tank can hold 23 gallons of gas. However the gas pump system is glitched, causing the gas pump to stop pumping gas every 23 seconds, and it takes 5 seconds to get the pump going again. How long will it take to completely fill the f150’s tank up with gas?
POW write ups
POW 1
1. Two delicate flowers were planted in a garden. The gardener,
Leslie has 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 to place the sprinkler where it will be the same distance
from each of the flowers.
What are her choices about where to put the sprinkler? Describe all the possibilities.
(Reminder: The flowers are already in place, and Leslie needs to adjust the position of the
sprinkler relative to the flowers.)
It depends on the shape of the placement on the flowers, maybe its a triangle, in that case it’s a matter of finding the equal distance between those flowers, but depending on how far the flowers are from the sprinkler and the range of the sprinkler, if the flowers have been put too far, then the sprinkler would not be able to touch them, but if they are close enough, it is just fine. The best option I could think of where to place the sprinkler is directly in the center of where the flowers are, but who knows, they could be lined up, I don’t even know if after putting it in a line, it would even be possible to put it at an equal distance from each other, but that is just my basic estimate, it could totally be possible to do it, but as I understand this by this time, I do not know.
2. Now suppose Leslie plants three flowers and wants to know if it will still be possible to
place the sprinkler the same distance from all three.
a. Determine which arrangements of the flowers (if any) will make this possible and
which (if any) will make it impossible. (As in Question 1, Leslie will be looking for a
place to put the sprinkler after the flowers have already been planted.)
The best arrangement would probably be a triangle, because it could be a matter of putting it in the center of the triangle, Especially a right triangle because I feel like that could be the easiest to find the equal distance, and the one I believe is impossible is a line, because wherever you place it, it’s always gonna be off in one way or another.
b. For those arrangements for which it will be possible, describe how Leslie can find the
correct location (or locations) for the sprinkler.
For the right triangle, I feel like that could be solved by measuring the distance of the triangle on a piece of paper and drawing it out, then drawing a dot in the center of the hypotenuse, there is where I believe is where the equal distance would be located at, for the regular triangle, I believe it would be in the center of the triangle, so draw a triangle, and place a dot on the center, then measure what distance it is. For any random placement, I the best advice I could give is to draw a square or circle that connects to the flower placements and draw the center of that (or you could guess and check many different distances until you get it)
3. What about four flowers? Five flowers? Generalize as much as you can.
Your POW is to explain as fully as possible, for various cases, where Leslie can put the
sprinkler in order to give the flowers the same amount of water. Homework 2: Only Two
Flowers gets you started with the first question of the POW.
Quite simple, if you want to do 4, make it a square and find the center, 5, make it a pentagon and find the center, and for 2, just make a line, that point you can place the sprinkler right in between the flowers.
POW 2
Problem Statement: If I drew a line through the center of a 63x90 rectangle, how many individual squares would touch the line.
First I figured out how many Tiles i need. I first tried to make a 63 by 90 square in Dall E 2 but to no avail, so I plugged a 63 to 90 square into desmos with spectacular success. I also found a way to put a diagonal line through the rectangle to split it in half. Then I zoomed out so each square represents 5 tiles, and then I counted them all in 5s. In groups of 5, I counted 25 squares going up the diagonal line so I multiplied it by 5 and discovered that out of all the tiles, 125 of the tiles had to be more expensive than the rest of the tiles.
Work:
1. Two delicate flowers were planted in a garden. The gardener,
Leslie has 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 to place the sprinkler where it will be the same distance
from each of the flowers.
What are her choices about where to put the sprinkler? Describe all the possibilities.
(Reminder: The flowers are already in place, and Leslie needs to adjust the position of the
sprinkler relative to the flowers.)
It depends on the shape of the placement on the flowers, maybe its a triangle, in that case it’s a matter of finding the equal distance between those flowers, but depending on how far the flowers are from the sprinkler and the range of the sprinkler, if the flowers have been put too far, then the sprinkler would not be able to touch them, but if they are close enough, it is just fine. The best option I could think of where to place the sprinkler is directly in the center of where the flowers are, but who knows, they could be lined up, I don’t even know if after putting it in a line, it would even be possible to put it at an equal distance from each other, but that is just my basic estimate, it could totally be possible to do it, but as I understand this by this time, I do not know.
2. Now suppose Leslie plants three flowers and wants to know if it will still be possible to
place the sprinkler the same distance from all three.
a. Determine which arrangements of the flowers (if any) will make this possible and
which (if any) will make it impossible. (As in Question 1, Leslie will be looking for a
place to put the sprinkler after the flowers have already been planted.)
The best arrangement would probably be a triangle, because it could be a matter of putting it in the center of the triangle, Especially a right triangle because I feel like that could be the easiest to find the equal distance, and the one I believe is impossible is a line, because wherever you place it, it’s always gonna be off in one way or another.
b. For those arrangements for which it will be possible, describe how Leslie can find the
correct location (or locations) for the sprinkler.
For the right triangle, I feel like that could be solved by measuring the distance of the triangle on a piece of paper and drawing it out, then drawing a dot in the center of the hypotenuse, there is where I believe is where the equal distance would be located at, for the regular triangle, I believe it would be in the center of the triangle, so draw a triangle, and place a dot on the center, then measure what distance it is. For any random placement, I the best advice I could give is to draw a square or circle that connects to the flower placements and draw the center of that (or you could guess and check many different distances until you get it)
3. What about four flowers? Five flowers? Generalize as much as you can.
Your POW is to explain as fully as possible, for various cases, where Leslie can put the
sprinkler in order to give the flowers the same amount of water. Homework 2: Only Two
Flowers gets you started with the first question of the POW.
Quite simple, if you want to do 4, make it a square and find the center, 5, make it a pentagon and find the center, and for 2, just make a line, that point you can place the sprinkler right in between the flowers.
POW 2
Problem Statement: If I drew a line through the center of a 63x90 rectangle, how many individual squares would touch the line.
First I figured out how many Tiles i need. I first tried to make a 63 by 90 square in Dall E 2 but to no avail, so I plugged a 63 to 90 square into desmos with spectacular success. I also found a way to put a diagonal line through the rectangle to split it in half. Then I zoomed out so each square represents 5 tiles, and then I counted them all in 5s. In groups of 5, I counted 25 squares going up the diagonal line so I multiplied it by 5 and discovered that out of all the tiles, 125 of the tiles had to be more expensive than the rest of the tiles.
Work:
Solution:
According to my calculations, there are 125 squares that touch the line.
Evaluation:
I am starting to get better at POWs. In the past, I could barely get myself to work on them and understand them. I would not say that it is as good as the last POW of freshmen year, where I completely ruined that one using facts and logic. Although this one was pretty good. Overall, I like the progress I am making.