MTH65 resources
- There is no need to purchase textbook or online access code.
Materials here are free!
- Go through each lesson's lecture notes and video lectures. Do homework
online to practice. If you made a mistake in a homework question, you can
try the same problem with different numbers, until you master the concepts.
- Log in at https://webwork.pcc.edu/webwork2/mthalc65-yao-f15/ to use the online homework system. You need a username and password. Email Carl Yao at
xiaolong.yao@pcc.edu to create
one.
Open all
Close all
Company A made 2.1 million dollars this fiscal year, and on average it's making 0.4 million more dollars every year.
Your company made 1.7 million dollars this fiscal year, and on average it's making 0.62 million more dollars every year.
Your boss asks you to figure out, how many years later, your company will catch up with Company A in sales?
System equation is here to rescue you. Study hard!
You might need to go back to MTH60's Unit 3 to review basic exponent rules.
Have you seen these:
The distance between Planet A and Planet B is approximately 2.5*10^23 miles.
Such a cell weighs 2*10^(-12) kilograms.
These numbers are written in scientific notation, which is easier than writing numbers like 250000000000000000000000.
To learn scientific notation, we need to learn how to use negative exponents, which requires a thorough understanding of many exponent rules.
We use polynomials to model many real-life data, such as modeling the distance travelled by a free-falling object.
We will also learn how to factor a polynomial, which is the basis for later math contents.
What is factoring?
12 = 2*2*3
x^2+7x+12=(x+3)(x+4)
We use sqrt() to represent the square root symbol.
Since 4^2=16, sqrt(16)=4.
Square and square root are inverse operations, and they cancel out each other:
sqrt(4^2)=4, and (sqrt(4))^2=4.
Earlier we learned how to solve linear equations like 2x-6=0.
In real life, more complicated equations need to be solved. Whenever a free-falling object is being studies, quadratic equations will be involved. In this unit, we will learn how to solve equations involving x^2.
A quadratic function looks like f(x)=2x^2+3x+4. It's graph is called a parabola. Tons of real-life applications are based on quadratic functions: the arc of bridges, the shape of headlight interior, a free falling object, etc.
If you forgot about function notation, please go to MTH60 content and review Introduction to Functions unit, and then come back to this unit. Basically, instead of using "y", we will use f(x) or h(t).
Unit 1: System Equations