Intro W12

•       Intro W12

  •  Objectives

      Suppose a stone falls from the edge of a cliff. The number of feet the stone has dropped after tt$t$ seconds can be found by multiplying 16 times the square of tt$t$. But to calculate the number of seconds it would take the stone to hit the land below, we need to use a square root. In this chapter, we will introduce and apply the properties of square roots, and extend these concepts to higher order roots and rational exponents. 
  • The sections for this week are:
    • 8.9 Use Direct and Inverse Variation
    • 9.1 Simplify and Use Square Roots
    • 9.2 Simplify Square Roots
    • 9.3 Add and Subtract Square Roots

   

   Intro and Learning Objectives (click on all tabs to see all sections)

  • • 8.9
    • 9.1
    • 9.2
    • 9.3

     Learning Outcomes

    In this section, you will:

    • Solve direct variation problems
    • Solve inverse variation problems

     Intro

    When two quantities are related by a proportion, we say they are proportional to each other. Another way to express this relation is to talk about the variation of the two quantities. We will discuss direct variation and inverse variation in this section.

     Learning Outcomes

    In this section, you will:

    • Simplify expressions with square roots
    • Estimate square roots
    • Approximate square roots
    • Simplify variable expressions with square roots

     Intro

    Sometimes we will need to look at the relationship between numbers and their squares in reverse. Because 225 is the square of 15, we can also say that 15 is a square root of 225. A number whose square is m is called a square root of m.

     Learning Outcomes

    In this section, you will:

    • Use the Product Property to simplify square roots
    • Use the Quotient Property to simplify square roots

     Intro

    In the last section, we estimated the square root of a number between two consecutive whole numbers. We can say that √50$\sqrt{50}$ is between 7 and 8. This is fairly easy to do when the numbers are small enough.

    But what if we want to estimate √500$\sqrt{500}$? If we simplify the square root first, we’ll be able to estimate it easily. There are other reasons, too, to simplify square roots as you’ll see later in this chapter.

    A square root is considered simplified if its radicand contains no perfect square factors.

     Learning Outcomes

    In this section, you will:

    • Add and subtract like square roots
    • Add and subtract square roots that need simplification

     Intro

    We know that we must follow the order of operations to simplify expressions with square roots. The radical is a grouping symbol, so we work inside the radical first. We simplify $\sqrt{2+7}$ in this way:

    Add inside the radical. \(\sqrt{9}\)     Simplify.3$\begin{array}{cccc}\text{Simplify.}\hfill & & & 3\hfill \end{array}$

    So if we have to add $\sqrt{2}+\sqrt{7}$ we must not combine them into one radical.

    \(\sqrt{2}+\sqrt{7}\ne\sqrt{2+7}\)

    Trying to add square roots with different radicands is like trying to add unlike terms.

    Adding square roots with the same radicand is just like adding like terms. We call square roots with the same radicand like square roots to remind us they work the same as like terms.

     Readings

    1. Text: Read the sections from Openstax book Links to an external site. (Links to an external site.)
    2. Videos: Watch all the videos from "Resources W12"

     Assignments

    • Take Notes Week 12         Due Friday night.
      

    Directions

    •  Each section is accompanied by a Handout. Each Handout contains a few definitions, a few "How To" explanations, examples, and "Try It" exercises. Using the structure of the handout you have to write your own notes. Your notes must contain:

    • • Your name
      • The name of the section
      • Definitions and "How To" from the provided handout (this is optional, however, it will be a good idea to have the complete notes)
      • Everywhere there is a "Read Ex nr..." you have to read the example from the ebook and write in your notes : "I read the Ex nr..." . The link for the section in the ebook is provided at the bottom of the page.
      • You have to solve ALL "Try It" exercises.

    After you complete your notes you have to submit them. See Take Notes Methods. 

     

    • Video quizzes Week 12          Due Saturday night 11:59pm.

    Directions

    • To learn the material for this sections, take notes while watching each video and then demonstrate what you learned by doing the exercise below it.

     

    • Homework Week  12              Due Sunday night 11:59pm.
    •  

    Directions

    • There are 4 Practice Homework this week. This are online Homework but you do not have to leave Canvas. Just click on each link, answer the questions, and came back for the next section. There is no partial credit, each question is either 100% good or not. However you have unlimited attempts for each question. A 5% per day penalty applies for Late work if you'll do it until Tuesday night. After that the Homework will be open only for practice.

     

    • Exam 5

      Exam 5 will assess your knowledge of Chapter 8. Be sure you have completed the Reading/Video Assignments as well as the Homework Assignments for these sections before you attempt the exam.

      The Homework assignments in particular will prepare you to do well on the exam, not only because they will help you master the material, but also because you will be familiar with entering answers in a way that can be read by the software. Be sure to use the same entry methods you used on the homework for notation, graphing, and equation-writing on this quiz.

      Resources

      Things You May Use for this exam: hand-written notes, calculator, scratch paper, writing implement, eraser.

      Things you may NOT use for this quiz: other people, anything else on your phone, anything else on your computer, anything not mentioned in the list of Things You May Use. I recommend that you put your phone away (or in airplane mode if you’re using it as a calculator) so it doesn’t distract you.

      If you have questions on the exam, please send me an Inbox message right away.

      Exam Settings

      • The 48-hour exam window opens Friday morning and closes Saturday night night. I recommend that you not wait until the last hour to take the test as servers can get busy then. 
      • You will have one attempt on this exam. 
      • The time limit is 120 minutes, which must be completed before the deadline on Sunday at midnight.

  The due dates for assignments are Friday, Saturday, and Sunday.

  However, you can submit them until Tuesday night next week.

  A 5% per day penalty applies for late work if you'll do it until Tuesday night.