Unit Problem
Jebby Holt
Unit problem write up
Problem statement
How many long after planting the trees until the orchard finally becomes a hideout
Process
My first step towards solving the problem is converting the initial circumference to the initial area. I do this by using the Circumference formula C=23.14r. I started off by dividing 2pi on both sides and then I inserted the circumference of the tree that I already had which was 2.5, This left me with the equation 2.5/2 pi=R, which gave me the radius 0.398,after this I need to turn it in to Area , so I used the area formula (A=3.14r^)and started off by inserting my radius A=3.14 0.398^, which gave me A=3.140.158. I then just solved it and got 0.49 as the initial area. My next step was finding the final radius. I started off by taking the last line of sight which was 25 ½ and I made it into a right angle triangle where the adjacent was 25 and the opp was 0.5. From here I had to find the angle of the right triangle. Which I did by using the function tan=0.5/25 to which I got the angle 1.15 I then used the sin function to find the final radius. sin 1.15=fr to which I got 0.02. I then had to take 0.02 and turn it into inches. I did this by multiplying 0.02 10 12 and got 2.4 which is the Final Radius. I then needed my final area which I did by using the Area formula A=3.14(final area)^ I did this by inserting the final area 2.4, A=3.14(2.4)^. This gave me a final area of 18.0. I then had to find the answer to the amount of years it takes till it's a complete hideout. I started by putting my initial area plus the rate of change times x(years) and all of this added up had to equal my final area which is 18. 0.495+1.5x=18
Work
Solution
This was my final problem for finding x amount of years 0.495+1.5x=18 after solving I found out that x=11.67 is about how many years it takes
Evaluation
I feel like I did pretty good on this Write up but I think I could have done better If I put more effort while working on it in class. As far as the overall problem I think it was good because it pushed me outside of my comfort zone and I attempted something that I am not very good at. I also relized from this POW that I am more capable at math than it feels like at times. One thing that I took away/enjoyed from this unit is just putting numbers in to equations
Unit problem write up
Problem statement
How many long after planting the trees until the orchard finally becomes a hideout
Process
My first step towards solving the problem is converting the initial circumference to the initial area. I do this by using the Circumference formula C=23.14r. I started off by dividing 2pi on both sides and then I inserted the circumference of the tree that I already had which was 2.5, This left me with the equation 2.5/2 pi=R, which gave me the radius 0.398,after this I need to turn it in to Area , so I used the area formula (A=3.14r^)and started off by inserting my radius A=3.14 0.398^, which gave me A=3.140.158. I then just solved it and got 0.49 as the initial area. My next step was finding the final radius. I started off by taking the last line of sight which was 25 ½ and I made it into a right angle triangle where the adjacent was 25 and the opp was 0.5. From here I had to find the angle of the right triangle. Which I did by using the function tan=0.5/25 to which I got the angle 1.15 I then used the sin function to find the final radius. sin 1.15=fr to which I got 0.02. I then had to take 0.02 and turn it into inches. I did this by multiplying 0.02 10 12 and got 2.4 which is the Final Radius. I then needed my final area which I did by using the Area formula A=3.14(final area)^ I did this by inserting the final area 2.4, A=3.14(2.4)^. This gave me a final area of 18.0. I then had to find the answer to the amount of years it takes till it's a complete hideout. I started by putting my initial area plus the rate of change times x(years) and all of this added up had to equal my final area which is 18. 0.495+1.5x=18
Work
Solution
This was my final problem for finding x amount of years 0.495+1.5x=18 after solving I found out that x=11.67 is about how many years it takes
Evaluation
I feel like I did pretty good on this Write up but I think I could have done better If I put more effort while working on it in class. As far as the overall problem I think it was good because it pushed me outside of my comfort zone and I attempted something that I am not very good at. I also relized from this POW that I am more capable at math than it feels like at times. One thing that I took away/enjoyed from this unit is just putting numbers in to equations
POW 3
Problem Statement
There is a safe that has a keypad with the numbers 0,1,2,3,4,5,6,7,8,9 if you input the correct three digits in any combination the safe will unlock. How many different unlock codes are there?
Process/Work:
The first step that I took to solve this POW is to choose three digits that unlock the safe. The digits that I chose are 678. After choosing the numbers I then put it into the N and R formula to figure out how many different combinations there are. N is the total amount of numbers in the set, and R is the specific 3 numbers(678) that I am choosing from. Then since I knew it was a combination I put it into NCR=n!/r!(n-r) which is the formula you use when order doesn't matter.I then multiplied 10 all the way to 1, I then did the same with 3. After this I multiplied 3⨉2⨉1=6, and 10⨉9⨉8=720 after this all that was left was to divide 720(N) and 6(R) and after dividing these I got 120 different combinations. After this I decided to use the number combination of 111 to see whether or not there is still the same number of combinations as 678 which was 120. This made my N=10 and R=1 this was a lot easier seeing how anything times 1 is that number so this one only has 10 different combinations. This shows me that every three digit combo has a different number of combinations.
Solution
My final answer was 120 combinations
Evaluation
I feel like I understood this POW a lot more than all of the other POWS we have done this semester. One thing I learned while doing this POW is how to use the Ncr formula instead of just putting it in Desmos and getting the answer.
There is a safe that has a keypad with the numbers 0,1,2,3,4,5,6,7,8,9 if you input the correct three digits in any combination the safe will unlock. How many different unlock codes are there?
Process/Work:
The first step that I took to solve this POW is to choose three digits that unlock the safe. The digits that I chose are 678. After choosing the numbers I then put it into the N and R formula to figure out how many different combinations there are. N is the total amount of numbers in the set, and R is the specific 3 numbers(678) that I am choosing from. Then since I knew it was a combination I put it into NCR=n!/r!(n-r) which is the formula you use when order doesn't matter.I then multiplied 10 all the way to 1, I then did the same with 3. After this I multiplied 3⨉2⨉1=6, and 10⨉9⨉8=720 after this all that was left was to divide 720(N) and 6(R) and after dividing these I got 120 different combinations. After this I decided to use the number combination of 111 to see whether or not there is still the same number of combinations as 678 which was 120. This made my N=10 and R=1 this was a lot easier seeing how anything times 1 is that number so this one only has 10 different combinations. This shows me that every three digit combo has a different number of combinations.
Solution
My final answer was 120 combinations
Evaluation
I feel like I understood this POW a lot more than all of the other POWS we have done this semester. One thing I learned while doing this POW is how to use the Ncr formula instead of just putting it in Desmos and getting the answer.
Pre-calc reflection
Throughout this school year in math we had many units in which we learned how to solve systems of linear equations, add, multiply, and subtract matrices, permutations and combinations, and graphing inequalities. The most challenging thing for me this year in Pre-calc was mainly just my understanding of the math, but I got through this by asking for help when it was needed but also just by accepting the challenge of math and putting forth my best effort in order to learn and solve the problems. Pretty much every unit this year was fun and challenging but one unit in particular that I enjoyed was the matrices unit which was not only because its something I have never done but it was also the unit that I understood best throughout this year