*(The following is a power point I did on differential calculus and how we can use it in everyday life)*

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*(The following is a power point I did on differential calculus and how we can use it in everyday life)*

Script

https://www.desmos.com/calculator/kloagffuxc

Paste the link in to the search by address bar to open it in Desmos

This picture took 58 lines of equations to create. To figure out which equations to use I looked at each one available then imagined them with domain and range constraints that would get the shape I needed. It was really challenging to get the glasses right but after a wile I was able to write 22 lines of equations with domain and range constraints that pulled of the desired look. Some strategies I used were making one side first and then changing some of the plus and minus signs to switch it to the other side. Once I got it to the other side of the y-axis to change the domain and range constraints I reversed the pluses and minuses and then reversed the inequality signs. This assignment helped me understand how different parts of equations help move the shapes around for example the equation (y+a)^2+(x+b)^2= r^2 makes a circle with a radius of r with a center point of (-b,-a). So if I typed in (y+1)^2+(x+1)^2= 25 the circle would have a radius of 5 with a center point at (-1,-1).

*(The following are 10 questions from the exponents PLO that I have to explain.)*

1. Represent repeated multiplication with exponents.

2. Describe how powers represent repeated multiplication.

3. Demonstrate the difference between the exponent, and the base by building models of a given power.

4. Demonstrate the difference between two given powers in which the exponent and the base are interchanged by using repeated multiplication.

5. Evaluate powers with integral bases and whole number exponents.

6. Explain the role of parenthesis by evaluating a given set of powers.

7. Explain the exponent laws for multiplying and dividing powers with the same base.

8. explain the law for powers with an exponent of 0.

9. I can apply the laws of exponents.

10. I use the order of operations on expressions with powers.

1, 3, 5, 7, prime

2 factors together

11, 13, 17 prime

Only 1 multiplied itself

Used to find the GCF

hard to find the primes in need

17, 19, 23

All the primes are mine to find

This work is a prime example

**Problem Statement **

This problem is to make expressions for the numbers 1-25 using only the numbers 1-2-3-4 with the following rules:

- Your expression has to use each number once and cannot use each number more than once.
- You can only use the following operations: Division, Multiplication, Addition, Subtraction, Square root, Brackets and Factorial.
- You can use exponents 1-2-3-4 but it counts as one of your numbers. For example, one squared would count as using one and two.
- You can put 2 of your numbers together to make a 2 digit number. For example, 12 would count as using one and two, but you couldn’t make 10 this way seeing as how you don’t have 0.

**Expressions and Process **

To solve this problem and get what I got above, I started out trying different expressions in numerical order. When I got a number I wasn’t looking for at the time I moved it to a number I did need. A few tricks that I found worked really well were: saving the one on prime numbers to use it for addition or subtraction, throwing away the one by using it for multiplication and throwing away numbers by putting them as an exponent on one because one times itself is always one. When I got stuck I moved to a different number I needed, but if I was really stuck I traded an expression I had for one Ethan had.

**Evaluation **

Overall this was a fun challenge and I learned how to use different operations in combination with others to get passed restrictions like you have to use 1-2-3-4 once each. I found this slightly challenging and might want to try something a little more difficult. This problem reminds me of a game we played in 6th grade with my math teacher where we were given ordered numbers and had to find what operations to put between them. We played this game in teams and the challenge was to get it before the other team.