HW 2.2 Worksheet: Please take out your completed Section 2.2 homework worksheet now and pass it to the end of your table nearest the center of the room so the TA can pick them up. (Late papers won’t be accepted.) A new worksheet will be handed out now for HW. 2.3 due tomorrow.Reminder:Any questions on Section 2.2 ?Explore the online Gradebook function:PowerPoint PresentationSlide 6Section 2.3FormulaSlide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Example 4: Solve for vExample from today’s homework:2.3 HW NOTE: Dealing with negatives in the denominator:Word problem from today’s homework:Slide 22Slide 23HW 2.2 Worksheet:Please take out your completed Section 2.2 homework worksheet now and pass it to the end of your table nearest the center of the room so the TA can pick them up. (Late papers won’t be accepted.)A new worksheet will be handed out now for HW. 2.3 due tomorrow.Reminder:The next homework assignment on section 2.3 is due at the start of next class period.Make sure you turn in the worksheet showing all your work for problems #11-22 of this assignment. If you don’t turn this in, or if you don’t completely show your work on any problem/s, your online score will be reduced for those problems. The good news: No more worksheets for a week or so...Any questions on Section 2.2 ?Explore the online Gradebook function:1. Click the “Gradebook” menu button2. Select “Homework” in Assignments heading at top•Go to desired HW section, select “Review”•You can actually work or rework problems after the deadline has passed (e.g., to study for quiz, like the one that’s coming up in a few days) but it won’t change your grade.Now pleaseCLOSE YOUR LAPTOPSand turn off and put away your cell phones.Sample Problems Page Link(Dr. Bruce Johnston)Section 2.3Formulas & Problem SolvingFormulaA formula is an equation that states a known relationship among multiple quantities (has more than one variable in it).Examples of FormulasA = lw (Area of a rectangle = length · width)I = PRT (Simple Interest = Principal · Rate · Time)P = a + b + c (Perimeter of a triangle = side a + side b + side c)d = rt (distance = rate · time)V = lwh (Volume of a rectangular solid = length · width · height)C = 2r (Circumference of a circle = 2 ·  · radius)NOTE: You DO NOT have to memorize these formulas. You DO have to know how to use them.Example:A flower bed is in the shape of a triangle with one side twice the length of the shortest side, and the third side is 30 feet more than the length of the shortest side. Find the dimensions if the perimeter is 102 feet.Understand and Translate:Read and reread the problem. If we let x = the length of the shortest side, then 2x = the length of the second side, and x + 30 = the length of the third side.Perimeter = sum of all the sides = x + 2 x + x + 30So x + 2 x + x + 30 = 102 x 2xx + 30Relevant formula:P = a + b + c (Perimeter of a triangle = side a + side b + side c)Example (cont.)Solve102 = x + 2x + x + 30 102 = 4x + 30 (simplify right side)102 – 30 = 4x + 30 – 30 (subtract 30 from both sides)72 = 4x (simplify both sides)44472 x(divide both sides by 4)18 = x (simplify both sides)Example (cont.)InterpretCheck: If the shortest side of the triangle is 18 feet, then the second side is 2(18) = 36 feet, and the third side is 18 + 30 = 48 feet. This gives a perimeter of P = 18 + 36 + 48 = 102 feet, the correct perimeter.State: The three sides of the triangle have a length of 18 feet, 36 feet, and 48 feet.It is often necessary to rewrite a formula so that it is solved for one of the variables. This is accomplished by isolating the designated variable on one side of the equal sign.Steps for Solving Formulas:1) Multiply to clear fractions.2) Use distributive property to remove grouping symbols (parentheses and brackets).3) Combine like terms to simply each side.4) Get all terms containing specified variable on the same side, other terms on opposite side.5) Isolate the specified variable (using the distributive property in reverse).6) Divide both sides by the quantity that’s now in front of the variable you’re solving for. (Many times this will be an expression in parentheses, but not always.)mnrT mrmnrmrT(divide both sides by mr)nmrT(simplify right side)Example 2: Solve the formula for TPRTPA PRTPPPA (Subtract P from both sides)PRTPA (Simplify right side)PRPRTPRPA(Divide both sides by PR)TPRPA(Simplify right side)Example 3: Solve the formula for PPRTPA )1( RTPA (Isolate P by factoring out P from both terms on the right side)(1 )1 1A P RTRT RT+=+ +(Divide both sides by (1 + RT)PRTA1(Simplify the right side)Example 4: Solve for vT = 3vs – 4ws + 5vw Get rid of terms on right that don’t have a v, i.e. add 4ws to both sides:T + 4ws = 3vs + 5vwIsolate the v on the right by factoring it out of both terms: T + 4ws = v(3s + 5w)Divide both sides by the part in parentheses:T + 4ws = v(3s + 5w)(3s + 5w) (3s + 5w)Simplify by canceling the common part on the right:T + 4ws = v DONE!3s + 5wExample from today’s homework:Answer: T – 5C or T - 5 . BC BC B2.3 HW NOTE: Dealing with negatives in the denominator:EXAMPLE: Solve 6x – 7y = 15 for y1. Subtract 6x from both sides: -7y = 15 – 6x2. Divide both sides by -7: y = 15 – 6x -73. This is the answer, but not in simplified form. We must multiply the top and bottom by -1 to make the denominator positive:4. y = -1(15 – 6x) = -15 + 6x = 6x - 15 -1(-7) 7 7Word problem from today’s homework:Answer: 2940.22Remember to show work on worksheet for problems #11-22. (Show steps similar to those shown as it’s worked on the whiteboard in class.)Reminder:This homework assignment on section 2.3 is due at the start of next class period.Make sure you turn in the worksheet showing all your work. If you don’t complete this and turn it in, your online score will be reduced.You may now OPEN your LAPTOPSand begin working on the homework