# Newtons Laws

Newtons Law #1

Newton’s first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. This is represented in how the bottle on the roof moves with the car until the car stops, this in turn, changes the bottle’s state but continues to move it forward.

#### Newtons Law #1 Example

Uploaded by Rafael H. Sevilla III on 2018-06-18.

Newtons Law #2

The second law explains how the velocity of an object changes when it is subjected to an external force. The law defines a force to be equal to change in momentum (mass over velocity) per change in time. This is represented in how we push the car to move it forward, subjecting an external force to change the velocity.

#### Newtons Law #2 Example

Uploaded by Rafael H. Sevilla III on 2018-06-18.

Newtons Law #3

The third law states that for every action (force) in nature there is an equal and opposite reaction. More explained if object A exerts a force on object B, object B will exert the same force back to object A. This is represented in the video by how the wheels of the car when accelerated push against the ground, force is put into the earth and at the same time is pushed back into the car; however, because of the difference in size between earth and the car, earth becomes unaffected by the force while the car is sent forward leading to acceleration.

#### Newtons Law #3 Example

Uploaded by Rafael H. Sevilla III on 2018-06-18.

# Week 18- 5 Things I Learned in Pre Calculus 11

1. Factoring: Knowing how to factor was the most important thing to know in this course. Coming from Pre Calculus 10, I didn’t really remember how to properly factor. I can say now that it is engrained in my brain after using it in almost every unit this semester. Especially as the equations were only going to become increasingly harder, we constantly reviewed and went over factoring.

Example: $x^2+2-8$ = (x+4)(x-2)

2. Sine Law: Learning the Sine Law made things much easier for me. The Sine Law is a formula/law that basically allows you to find any angle/side in the triangle as long as you know a matching side+angle, and the opposite side/angle to the one you are trying to find. Making sine law a very useful tool when it comes to trigonometry. Angle A/B/C and side a/b/c are opposite to each other.

3. Completing the square: Due to the course of PreCalc 11 having lots of graphing and quadratics, you are going to need to know how to solve in the semi-frequent situation of when you cannot factor the equation. In this case you complete the square. Completing the square is when you take the middle term in the quadratic (also known as the “b” term), divide it by 2 and then square it. Then you take the original last team (or “c” term) and move it outside of the original quadratic, and solve to find the zeros of the equation.

4.

# Week 17

This week we learnt about the Sine Law. The Sine Law is basically a formula that you can use to find a missing side/angle if you know a matching angle+side and the opposing angle/side to which you are trying to find.

The formula:

Using the formula itself is pretty simple, you input the known information. Then remove the one of the a/b/c you do not have enough information to use, and solve for what you are looking for.

# Week 16

1. Since the denominators are all equivalent, the first step is to combine and simplify the numerators by combining all like terms.
2. You can then simplify further by eliminating x-3
3. This will leave you with 1/x+3

# Week 15-Addition and Subtraction of Rational Expressions

Simplify: 1/3a+2a/5a

The first step to adding these together is to find the common denominator of 3 and 5. This will be 15. You will have to multiply 1 and 3 by 5 and 2a and 5a by 3. This will result in 5/15a + 6a+15a=11/15a

# Week 14- Absolute Value

Solving equations algebraically

9= -1(-2x+6)

9=2x-6

15=2x

x=7.5

# Week 15- Adding Rational Expressions

Simplify 5/a+3/a

=8/a

1. Find common denominator (multiply denominator to do so)
2. add or subtract across like normal.

Simplify 4/a-2/3

12-2a/3a

# Week 13- Finding Asymptotes

An asymptote is a line that identifies the boundaries of a curve. As of pre caluclus 11, the y asymptote (horizontal)=0. The x asymptote (vertical) is a little bit more complicated. Looking at the y axis, identify where the point of line is at -1 and 1. In between these points is where the x asymptote will be.

# Week 12- Absolute Values

Today we reviewed some key points on absolute values:

-The values are ALWAYS positive.

-When graphing, the linear or quadratic equation will never enter the negative area (y.) As shown below, the line reaches 0 on the y axis and reflects up.

# week 11- Reading a Graph

This week, we learned how to read a linear equation.

y=2x-1

In this equation, the form is y=mx+b. The b in this situation is -1. This represents the y intercept. The mx in this situation is 2x. This represents the slope. The slope is 2/1 (2 right, 1 up.)