This week in Pre Calculus 11 we learned about Graphing Linear Inequalities in two variables. The solutions to these inequalities are represented by a boundary line and shading one side of the line.

Ex:

key notes

choosing any coordinate (the easy one is 0,0) and seeing if the statement is true or false.

In Newton’s first law of motion states that an object will not change its speed of direction unless an unbalanced force affects it. In this video, we give the pen an apply force to make it move and accelerate. When there is no more force acts on the pen that was still moving at the same direction. One potential situation where the law may not apply is if the angle of the dask was altered, influencing the velocity of the pen.

In Newton’s second law of motion, more commonly known as F=ma where F refers to the total force, m is the mass of the object, and a is the acceleration of the object. It can be seen that if all existing forces are unbalanced, the resulting net force will cause acceleration of a mass. The acceleration of an object depends on the net force that acting on an object and mass of the object. As the acting force increased, the acceleration that is acting on an object is decreased. The Fnet (net force) equals mass times acceleration, an acceleration is produced by the Fnet. In the second video, there are two backpacks which means mass is increased. I used same amount of force to push the cart, and in the second video, the cart did not travel the same distance as the cart in the first video. The two videos show that given the same force is applied, when the mass is different, the acceleration also changes. These videos followed the rule of Newton’s second law of motion.

Errors: The ground was not flat, so it might cause an error. Forces that I put might not exactly the same, so it might cause an error. The videos that I used were not filmed well and was not long enough to see the results, so these might cause an error as well.

In Newton’s third law of motion, according to the formula F1=-F2 we could know that every action there is always opposed an equal reaction: or the mutual actions of two objects upon each other are always equal, and directed to contrary parts(that is why F2 is negative) .

In the video Justina pushed the wall, she gives a force to a wall, and a wall gives a force of equal size and opposite direction, and the counterforce makes Justina backward.

Newton’s third law applies only to practical forces, The imaginary force (such as inertial force and centrifugal force) is not applicable to Newton’s third law, and the imaginary force has no force of force and therefore has no reaction force.

This week we learned discriminants. A discriminant is a part of the quadratic formula and can determine the number of solutions in a quadratic equation without solving the equation.The solution(s) to a quadratic equation can be calculated using the Quadratic Formula:

The “±” means you need to do a plus AND a minus, so there are normally TWO solutions

The blue part (b^{2} – 4ac) is called the “discriminant”, because it can “discriminate” between the possible types of answer. If it is positive, you will get two normal solutions (two real roots), if it is zero you get just ONE solution (one root), and if it is negative you get imaginary solutions (unreal roots).

This week we finished our unit on Absolute Values and Radicals.what we learned was add, subtract, multiply and divide them.

In this sections of this chapter we discussed solving equations and inequalities that contain absolute values. We have learned equations with absolute value in them in this section. I know that that the absolute value bars are not parentheses and in many cases don’t behave as parentheses, and all that we need to do is identify the point on the number line and determine its distance from the origin.