Month: November 2017
Week 13 in Precalculus
this week in Precalc we learned how to solve linear absolute value equations algebraically. the first step in doing this is split the equation into two different equation. One of the equations being the same as the original but without the absolute brackets. The other equation is too the same without absolute brackets, but has a negative sign in front. For example:
from there you solve the linear equations the same way you solve any other linear equation.
Once you’ve figured out X you must verify it to check for extraneous roots. To do this you can just plug the X value back into the equation. If the right side balances out with the left than it is not extraneous, but if it doesn’t than the root is in fact extraneous. Another thing you can do that will save you time is take the absolute value and create a restriction. From there you compare it with your Answer. If the statement is true then you do not have an extraneous route.
To determine what inequality to use think about what equation you’re using. For the original one you want to know what numbers you can use from the zero which will result in a positive. Same thing for the peicewise equation. You want the equation to result in a positive as well and sometimes you will need a negative
“Dead Poets Society” Reflection and Connection
The meanjng of this movie is heavily based around “carte diem”, meaning to seize the day. Mr. Keating teaches the boys a valuable lesson about how short life is and in that little bit of time you have to make it worth it. He taught them that you do not have to conform to your teachers and parents; you are your own individual that can make your own choices and take your own paths, even if it’s the “less travelled one”. This move connects to Macbeth soliloquy tomorrow, as they both connect to the meaning of life. Keatings meanjng is much more hopeful and motivational, rather than, Macbeth who has a more dreary look on life. He believes that life is pointless. It too may be short but the time spent alive has no impact and is meaningless. He doesn’t believe that there is any point to “seizing” the day.
I think this movie was really good. It had a very important message that could still be connected today. Many people try to conform into society and that still leads people to take their lives, much like Niel. The movie was very engaging and I never once looked away. I would definitely watch this again and would for sure take the meaning of this movie with me.
Week 12 in Precalculus
this week in Precalc I learned how to graph linear inequalities that contain 2 variables. Solutions to a liberal equation with 2 variables is represented by a boundary line and shading in one side.
A solid line for an inequality:
A broken line for an inequality:
to graph it you take the line and convert it to y=mx+b form. Things to look for in this form is the: Y-intercept so you have a point to start from, the X coefficient so you know the rise over run, and the inequality sign to figure out if the boundary line will be solid or broken.
Once you’ve graphed the equation, choose a test point. You can choose any point and plug it into the x and y spot. If the equation is proven true after solving, than you shade that section. If not the equation is false and you shade the other section. The two test points I’ll use is (0,0) and (-5,5)
Week 11 in Precalculus
This week in Precalc 11 we learned how to solve a quadratic inequality with one variable using a sign Chart.
The steps when using a sign chart is to:
1. Factor expression
2. Determine zeros
3. Use a sign chart for each factor
for example, take this equation and make it equal to zero the factor.
Once you have factored determine the zeros (-3/2 and 4) and place them on two number line. Each number line will represent a different factor. One will be (2x+3) and one will be (x-4).
For each factor do a test point in all 3 sections. Pick a point less than -3/4, between -3/4 and 4, and greater than 4. Plug these test points in to the factor and determine whether the outcome is negative or positive.
Add up the positives and negative of the two number lines to determine what the equation will finally equal.
Since the equation is asking for the equation to be less than zero we want x to be negative.
Persuasive Essay Corrections
Two things to improve on:
1. Writing clear thesis statements that effectively prove my point
2. My grammar
Two things I did well:
1. Having a unique writing style/ voice
2. The hook and conclusion
Week 10 in Precalc 11
This week in precalculus 11 I worked on remembering how to find the common difference of an arithmetic pattern and the common ration of a geometric pattern.
A common difference is what the Arithmetic pattern goes up or down by. An arithmetic sequence goes up by the same amount each time.
You can subtract two consecutive terms and can find the common difference.
For example:
For geometric sequence each term is multiplied by a constant known as the common ration. The common ration can be found by dividing a term by the previous term. For example:
Generally:
i also worked on figuring out if an equation diverges or converges.
If an equation diverges it means there is no sum. It is either greater than one or less than negative one= r>1 & r<-1
if an equation converges it has a sum. The solution falls between 0 and 1 and -1 and 0.
0<r<1
-1<r<0
if an equation converges it will be a fraction.
Week 9 in Precalc 11
This week in precalculus we learned how to solve modelling problems involving money; also known as revenue.
An example of this problem is: “a company cancel a phone for $500. At this price they can sell 60 phones. Every $50 increase, the number of phones sold will drop by 4. What price will result in the maximum revenue.
Some of the key information here would be maximum, telling us that the parabola would be negative meaning opening downward.
The equation for revenue is : a Price x the number sold. So our equation would be:
the x in the equation represents the price increase. The way the equation is set up right now is called factor form. In this form we can extract the roots, or, the x intercepts.
Since we have the roots we can also get the line of symmetry. To do this you add the zeros together and than divide by two. You do this because the line of symmetry is found in the middle of the x intercepts.
Since the line of symmetry is also equal the the x value of the vertex, we can take this value and substitute it into the x value of the equation.
So the maximum revenue venue would be an increase of $2.50 which will result in $31,250.