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Chapter 2 Section 4: Formulas In this section, we will… Use formulas to solve word problems Solve a formula for a given variable 2.4 Formulas We will use the following formulas from business: simple interest formula interest = principal rate time OR i prt Don’t forget to change your percent to a decimal before profit = revenue - cost OR p r c using it in a formula! retail price = cost + markup OR r cm We will use the following formulas from science: distance = rate time OR d rt 5( F 32) C Where C and F are the temperature in degrees 9 Celsius and Fahrenheit respectively. 2.4 Use Formulas to Solve Word Problems Example: Find the markup on a CD Example: After expenses of $55.15 player whose wholesale cost is $219 were paid, a Rotary Club donated and whose retail price is $395. $875.85 in proceeds from a pancake breakfast to a local health clinic. How much did the breakfast gross? 2.4 Use Formulas to Solve Word Problems Example: Cryobiologists freeze living matter to preserve it for future use. They can work with temperatures as low as 270 C. Change this to degrees Fahrenheit. 2.4 Use Formulas to Solve Word Problems Example: Three years after opening an account that paid 6.45% annually, a depositor withdrew the $3,483 in interest earned. How much money was left in the account? 2.4 Use Formulas to Solve Word Problems Example: Rose Parade floats travel down the 5.5 mile-long parade route at a rate of 2.5 miles per hour. How long will it take a float to complete the parade if there are no delays? 2.4 Use Formulas to Solve Word Problems Geometry Formulas to Know Rectangle Rectangular Box Perimeter = sum of all sides Volume l w h in 3 units or in units Perimeter 2l 2w in 2 Area = l w units 2.4 Use Formulas to Solve Word Problems Geometry Formulas to Know Triangle Parallelogram in units Perimeter = sum of all sides Perimeter = sum of all sides Area = 1 2 bh Area bh in 2 units For these formulas: The height meets the base-side at a 90-degree angle 2.4 Use Formulas to Solve Word Problems Geometry Formulas to Know Trapezoid Circle in units Perimeter = sum of all sides Circumference d a+b Area = h Area r 2 2 3.14159... 227 *To minimize rounding- errors we will use the button on our TI 2.4 Use Formulas to Solve Word Problems Geometry Formulas to Know base Pyramid Cone Volume hB 1 * Volume 1 r 2 h 3 * 3 B is the area of the base 2.4 Use Formulas to Solve Word Problems Geometry Formulas to Know Sphere Cylinder Volume 4 r 3 3 Volume r 2 h 2.4 Use Formulas to Solve Word Problems Example: For each of the following scenarios, indicate which geometric concept (perimeter, circumference, area or volume) should be used and which unit of measurement (units, units 2 , units 3 ) would be appropriate. • The amount of storage in a freezer • The distance around the outside of a building lot • The amount of land making up the Sahara Desert • How far a bike tire rolls in one revolution 2.4 Use Formulas to Solve Word Problems Example: A horse trots in a perfect Example: Find the perimeter and circle around its trainer at the end of area of the truss below: a 28 foot-long rope. How far does the horse travel as it circles the 6 ft trainer once? (Round your answer to the nearest tenth.) 16 ft perimeter: area: 2.4 Use Formulas to Solve Word Problems Example: Find the amount of space Example: Find the exact area of the in the hamster tube below. Round square road sign below: your answer to the nearest tenth. 12 in 3 in 2.4 Use Formulas to Solve Word Problems Example: Find the volume of a spherical-shaped pumpkin that has a diameter of 9 inches. Round your answer to the nearest hundredth. 2.4 Use Formulas to Solve Word Problems Solving Linear Equations in One Variable: 1. If the equation contains fractions, multiply both sides by the magic number (LCM of the denominators) to clear fractions 2. Use the Distributive Property to remove the parentheses “undoing” the operations: Isolate the variable by (then combine the like-terms on each side of the equation) 3. Use the Addition and Subtraction Properties to get all of the { variables on one side of the equation together (and all of the numbers on the other side of the equation) 4. Use the Multiplication and Division Properties to make the coefficient of the variable equal to 1 Remember that solving an equation means that we isolate the variable we are solving for! 2.4 Solve a Formula for a Given Variable Example: Solve each formula for the given variable. d rt for t I prt for r 2.4 Solve a Formula for a Given Variable Example: Solve each formula for the given variable. P 2l 2w for l K 1 mv 2 for m 2 2.4 Solve a Formula for a Given Variable Example: Solve each formula for the given variable. 5 y 25 x for y 6 y 12 5x for y We will need to have this skill for chapters 3 and 7. 2.4 Solve a Formula for a Given Variable Independent Practice You learn math by doing math. The best way to learn math is to practice, practice, practice. The assigned homework examples provide you with an opportunity to practice. Be sure to complete every assigned problem (or more if you need additional practice). Check your answers to the odd-numbered problems in the back of the text to see whether you have correctly solved each problem; rework all problems that are incorrect. Read pp.149-157 Homework: pp.157-162 #1, 2, 3, 5, 8, 11, 15-23 odds, 27, 31, 33, 37-51 odds, 65, 67, 69, 73, 75, 79, 83, 85, 91, 95(hint: it’s a half-sphere), 103, 105 2.4 Formulas